natrona county school district #1 · 2015. 10. 2. · these numbers are composed of ten ones and...

Natrona County School District #1

Mission Statement The Natrona County School District empowers every learner to grow, excel and be

successful contributors to the local and global community.

K-12 Mathematics Curriculum

Natrona County School District Mathematics Education Curriculum

of 146, Revised by Committee June 2015

Table of Contents

Acknowledgements........................................................................................................................ 3

Introduction ...................................................................................................................................... 4

Grade Level Pacing Guides Kindergarten ...................................................................................................................... 6 1st Grade ............................................................................................................................ 18 2nd Grade ........................................................................................................................... 26 3rd Grade ............................................................................................................................ 33 4th Grade ............................................................................................................................ 43 5th Grade ............................................................................................................................ 51 Course 1 – 6th Grade .................................................................................................... 59 Course 2 – 7th Grade .................................................................................................... 67 Accelerated Math – 7th Grade .................................................................................. 74 Course 3 – 8th Grade .................................................................................................... 84 Algebra I ............................................................................................................................ 90 Geometry........................................................................................................................... 97 Algebra II........................................................................................................................ 105

NCSD Math Vocabulary

K – 8 Critical Vocabulary ........................................................................................ 113 Kindergarten ................................................................................................................ 117 First Grade ..................................................................................................................... 122 Second Grade ............................................................................................................... 125 Third Grade ................................................................................................................... 127 Fourth Grade ................................................................................................................ 129 Fifth Grade ..................................................................................................................... 131

NCSD Common Math Assessment Information

K – 5 .................................................................................................................................. 134 6 – 8 .................................................................................................................................. 135 High School ................................................................................................................... 136

CCSS-M Resources and Visuals

Overview of Domains ............................................................................................... 138 Standards of Mathematical Practice ................................................................. 139 Instructional Shifts .................................................................................................... 143

Long Range Plan ........................................................................................................................ 144 NCSD Standards-Based Terminology .............................................................................. 145

Natrona County School District Mathematics Education Curriculum

of 146, Revised by Committee June 2015

Acknowledgements Thank you to the members of the Math Curriculum Committee for their hard work on this curriculum:

Kindergarten Brandy Bentz DeLaine Britt Liz Harris

Carrie Patterson 1st Grade

Laurie Kilts Angela Ourth 2nd Grade

Kathy Christensen Noelle Clark 3rd Grade Jennifer Bonnett Buddy Johnson

Ashley Ujvary 4th Grade Kristin Fauss

Stan Hahn Amy Radden

5th Grade

Karen Bayert Cynthia Brachtenbach

Tonya Munari

Course 1 (6th Grade) Cheryl Anderson Emily Quintana

Sarah Willis Course 2 (7th Grade) Accelerated Math (7th Grade)

Teresa Bunker Jann Keller

James Russell David Sunday Course 3 (8th Grade)

Angela Cavalier Kerin Dillon

Jeanine Pickering Bud Sorenson High School

Jessica Bratton Rebecca Byer

Timothy Fauss Ashlie Howell Marla Switzer

Roger Switzer Debra White

Natrona County School District Mathematics Curriculum

Back to Table of Contents of 146, Revised by committee June 2015

Introduction Mathematics is the language that defines the blueprint of the universe. Mathematics is woven into all parts of our lives, and is more than a list of skills to be mastered. The essence of mathematics is the ability to employ critical thinking and reasoning to solve problems. To be successful in mathematics, one must see mathematics as sensible, useful, and worthwhile. The development and maturation of students’ conceptual understanding and application of the processes and procedures of mathematics is the driving force behind the 2011 Wyoming Mathematics Content and Performance Standards.

2011 WYOMING MATHEMATICS CONTENT AND PERFORMANCE STANDARDS DOCUMENT

The purpose of this document is to provide teachers with a horizontally and vertically articulated progression of the math standards. The intent is to ensure a guaranteed and viable curriculum for students as they progress through their educational journey in Natrona County School District. This document will provide guidance to teachers as they plan their instruction. Critical and supporting vocabulary has been identified to provide further guidance. 2011 WYOMING MATHEMATICS CONTENT AND PERFORMANCE STANDARDS RATIONALE:

The Common Core State Standards for Mathematics is a state-led effort to establish a single set of clear educational standards that states can share and voluntarily adopt. Including the Common Core State Standards into the 2011 Wyoming Mathematics Content and Performance Standards prepares Wyoming students to be competitive on the national and world stage. These standards are a set of specific, rigorous expectations that build students’ conceptual understanding, mathematical language, and application of processes and procedures coherently from one grade to the next so all students will be prepared for post-secondary experiences. The use of technology is expected throughout all levels of the standards. The focus areas for each grade level and conceptual category establish a depth of knowledge as opposed to a breadth of knowledge across multiple standards in each grade level or content area. The Standards for Mathematical Practices describe the essential ways of thinking and habits of mind that are the hallmark of a mathematically literate and informed citizen. The Common Core State Standards for mathematics stress both conceptual understanding and procedural skills to ensure students learn and can apply the critical information needed to succeed at each level. This creates a vertical articulation where the mathematics learned in elementary school provides the foundation for the study of statistics, probability, ratio and proportion, geometry, and algebra in middle school. This is, in turn, the bedrock upon which the knowledge needed for success in colleges and careers can be developed in the high school.



Algorithmic knowledge is no longer sufficient when preparing our students to become globally competitive. The knowledge of good practitioners goes beyond algorithmic learning and allows them to picture the problem and the many roads that may lead to absolution. They realize that mathematics is applicable outside of the classroom and are confident in their ability to apply mathematical concepts to all aspects of life. The symbiotic nature of the Standards of Mathematical Practice allows students to deepen their understandings of mathematical concepts and cultivates their autonomy as mathematically literate and informed citizens. Employing mathematics as a means of synthesizing complex concepts and making informed decisions is paramount to success in all post-secondary endeavors.

MATH CURRICULUM COMMITTEE PROCESS The alignment of math curriculum and shift towards a standards based approach in math education began in NCSD during the 2013-2014 school year with the adoption of a new primary resource. During professional development that school year teachers could choose to work in teams to create district pacing guides for each grade level and address district-wide concerns regarding a guaranteed and viable curriculum in math, common assessments, and the appropriate use of instructional resources. This committee work has continued as teacher teams have worked to revise the pacing guides, discuss critical vocabulary, and work on common assessments. In March 2015 the math curriculum committee surveyed teachers to gather input and were charged with making final revisions to the district pacing guides, identifying critical vocabulary, and revising district common assessments. Committee members were sensitive to the concerns of teachers and worked diligently to make appropriate changes to meet the needs of the entire district. As this work moves forward, teacher committees will continue to engage in the alignment of standards and assessment in math.



Kindergarten Math Pacing Guide The Pacing Guide has been aligned to Wyoming State Standards with consideration to the Critical Areas of Focus defined by Common Core State Standards for Math.

First Quarter Second Quarter Third Quarter Fourth Quarter

K.CC Know number names

and the count sequence.

K.CC Know number names

and the count sequence.

K.CC.1 Count to 75 by ones

and to100 by tens.

K.CC.1 Count to 100 by

ones.

K.CC.1 Count to 20 by ones. K.CC.1 Count to 50 by ones. K.CC.2 Count forward

beginning from a given

number within the known

sequence (instead of having

to begin at 1). Within the

range of 0-75.

K.CC.2 Count forward





range of 0-100.






range of 0-20.

K.CC.1 Count to100 by tens. K.CC.3 Write numbers from 0

to 15.

K.CC.3 Write numbers from 0

to 20.


to 5.






range 0-50.

K.CC.3 Represent a number

of objects with a written

numeral 0-15 (with 0

representing a count of no

objects).





objects).





numeral 0-5 (with 0


objects).


to 10.

K.CC.4a Count to tell the

number of objects:

Understand the relationship

between numbers and

quantities; connect

counting to cardinality.

When counting objects, say

the number names in the

standard order, pairing

each object with one and

only one number name and

each number name with

one and only one object.

K.CC.5 Count to answer

“how many?” questions

about as many as 20 things

arranged in a circle, or as

many as 10 things in a

scattered configuration.

K.CC.6 Compare numbers:

Identify whether the number

of objects in one group is

greater than, less than, or

equal to the number of

objects in another group,

e.g., by using matching and

counting strategies (groups

up to ten objects).





objects).

K.CC.4b Understand that the

last number name said tells

the number of objects

counted. The number of

objects is the same

regardless of their

arrangement or the order in

which they were counted.

K.OA.2 Solve addition and

subtraction word problems

and add and subtract within

10, e.g., by using objects or

drawings to represent the

problem.

K.G Identify and describe

shapes (squares, circles,

triangles, rectangles,

hexagons)

K.CC.7 Compare two

numbers between 1 and 10

presented as written

numerals.

K.CC.4c Understand that

each successive number

name refers to a quantity

that is one larger.

K.OA.5 Fluently subtract

within 5.



K.G.1 Describe objects in the

environment using names of

shapes.

K.OA.1 Represent addition

with objects, fingers, mental

images, drawings, sounds

(e.g., claps), acting out

situations, verbal

explanations, expressions, or

equations. (Drawings need

not show details, but should

show the mathematics in

the problem. This applies

wherever drawings are

mentioned in the

Standards).

K.CC.5 Count to answer

“how many?” questions

about as many as 20 things

arranged in a line, a

rectangular array.

K.NBT.1 Compose and

decompose numbers from

11 to 19 into ten ones and

some further ones, e.g., by

using objects or drawings,

and record each

composition or

decomposition by a

drawing or equation (e.g.,

18 = 10 + 8); understand that

these numbers are

composed of ten ones and

one, two, three, four, five, six,

seven, eight, or nine ones.

K.G.2 Correctly name two-

dimensional shapes

regardless of their

orientations or overall size.

K.OA.3 Decompose

numbers less than or equal

to 10 into pairs in more than

one way, e.g., by using

objects or drawings, and

record each decomposition

by a drawing or equation

(e.g., 5 = 2 + 3 and 5 = 4 + 1).

K.CC.5 Given a number from

1–20, count out that many

objects.

K.G.1 Identify and describe

shapes (cubes, cones,

cylinders, and spheres).

Describe objects in the

environment using names of

shapes.

K.G.4 Analyze and compare

two- and three- dimensional

shapes, in different sizes and

orientations using informal

language to describe their

similarities, differences, parts

(e.g., number of sides and

vertices/”corners”) and

other attributes (e.g. having

sides of equal length).

K.OA.4 For any number from

1 to 9, find the number that

makes 10 when added to

the given number, e.g., by

using objects or drawings,

and record the answer with

a drawing or equation.

K.OA.1 Represent addition

and subtraction with

objects, fingers, mental

images, drawings, sounds

(e.g., claps), acting out

situations, verbal

explanations, expressions, or

equations. (Drawings need

not show details, but should

show the mathematics in

the problem. This applies

wherever drawings are

K.G.2 Correctly name three-

dimensional shapes

regardless of their

orientations or overall size.



mentioned in the

Standards).

K.G.5 Model shapes in the

world by building shapes

from components (e.g.,

sticks and clay balls) and

drawing shapes.

K.MD.2 Directly compare

two objects with a

measurable attribute in

common, to see which

object has “more of”/“less

of” the attribute, and

describe the difference. For

example, directly compare

the heights of two children

and describe one child as

taller/shorter.

K.OA.2 Solve addition word

problems and add within 10,

e.g., by using objects or

drawings to represent the

problem.

K.G.3 Identify shapes as two-

dimensional (lying in a

plane, “flat”) or three-

dimensional (“solid”).

K.MD.3 Classify objects and

count the number of objects

in each category. Classify

objects into given

categories; count the

numbers of objects in each

category and sort the

categories by count. Limit

category counts to be less

than or equal to 10.

K.OA.5 Fluently add within 5. K.G.4 Analyze, compare,

create, and compose

shapes: Analyze and

compare three-dimensional

shapes, in different sizes and

orientations, using informal

language to describe their

similarities, differences, parts

(e.g., number of

vertices/“corners”) and

other attributes (e.g., having

sides of equal length).

K.G.1 Describe the relative

positions of objects using

terms such as above, below,

beside, in front of, behind,

and next to.

K.MD.1 Describe measurable

attributes of objects, such as

length or weight.



K.G.6 Compose simple

shapes to form larger

shapes. For example, “Can

you join these two triangles

with full sides touching to

make a rectangle?

11 14 13 12

Pacing Guide Section 1: Counting & Cardinality, Geometry First Quarter

Standards: K.CC Know number names and the count sequence. K.CC.1 Count to 100 by ones and by tens. K.CC.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1). K.CC.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a

count of no objects). K.CC.6 Identify whether the number of objects in one group is greater than, less than, or equal to the number of objects

in another group, e.g., by using matching and counting strategies (groups up to ten objects). K.G Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres). K.G.1 Describe objects in the environment using names of shapes, and describe the relative positions of these objects

using terms such as above, below, beside, in front of, behind, and next to. K.G.2 Correctly name shapes regardless of their orientations or overall size.

Clarification: K.CC. Identify Numbers K.CC.1 Verbally count to 20 by ones. K.CC.2 Within the range of 0-20 K.CC.3 Write numbers within the range 0-5. Represent a number of objects with written numeral within the range 0-5. Reversals are accepted, but not place value reversals like 16/61. K.G Identify 2-dimensional shapes K.G.1 Naming 2-dimensional shapes only; exclude relative positions K.G.2 2-dimensional shapes



K.G.4 Analyze and compare two- and three- dimensional shapes, in different sizes and orientations using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/”corners”) and other attributes (e.g. having sides of equal length).

K.G.5 Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.

K.G.4 2-dimensional shapes (Students must describe # of corners/vertices and sides without being prompted. (If they have not differentiated between the square and rectangle you may ask “how are they are different?”). K.G.5 2-dimensional shapes

Vocabulary: Critical number, count, zero, one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen, twenty, less (than/least), greater (than/more), fewer, equal, square, circle, triangle, rectangle, hexagon, sides, corners, vertices, curved, 2-dimensional

Resource: MyMath Chapter 1 Lesson 2, 4-9 Chapter 2 Lesson 8 Chapter 11 Lesson 1-4, 8, 9

Supporting flat, alike, attributes, different, group, large, model, objects, order, same, sequence, shape, small, straight, digits, make, rhombus, trapezoid

Instructional Days: 30 days Flex Days: 5 days (field trips, reteach/enrich, Discover days)

Pacing Guide Section 2: Counting & Cardinality, Geometry, Operations & Algebraic Thinking, Measurement & Data Second Quarter

Standards: K.CC Know number names and the count sequence. K.CC.1 Count to 100 by ones and by tens. K.CC.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1).

Clarification: K.CC. Identify Numbers K.CC.1 Verbally count to 50 by ones. Verbally count to 100 by tens. K.CC.2 Within the range of 0-50



K.CC.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a

count of no objects). K.CC.7 Compare two numbers between 1 and 10 presented as written numerals. K.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out

situations, verbal explanations, expressions, or equations. (Drawings need not show details, but should show the mathematics in the problem. This applies wherever drawings are mentioned in the Standards).

K.OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings,

and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1). K.OA.4 For any number from 1 to 9, find the number that makes 10 when added to the given number, e.g., by using

objects or drawings, and record the answer with a drawing or equation. K.MD.2 Directly compare two objects with a measurable attribute in common, to see which object has “more of”/“less of”

the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.

K.MD.3 Classify objects into given categories; count the numbers of objects in each category and sort the categories by

count. Limit category counts to be less than or equal to 10. K.G.1 Describe objects in the environment using names of shapes, and describe the relative positions of objects using

terms such as above, below, beside, in front of, behind, and next to.

K.CC.3 Write numbers within the range 0-10. Represent a number of objects with written numeral within the range 0-10. Reversals are accepted, but not place value reversals like 16/61.

K.CC.7 Use the vocabulary greater than, less than, or equal to/same- not symbols. K.OA.1 Addition only in the range of 0-10 K.OA.3 (2+3 and 3+2 are considered different) K.MD.2 (Must use vocabulary longer/shorter) K.G.1 Orally describe the relative position of objects. (Acceptable vocabulary: above, on top, over, below, under, beneath, on the



K.G.6 Compose simple shapes to form larger shapes. For example, “Can you join these two triangles with full sides

touching to make a rectangle?

bottom, next to, beside, to the left, to the right, in front of, behind, in back)

Vocabulary: Critical number, count, zero, one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen, twenty, greater (than/more), less (than/least), equal to, addition (add/plus/combine), number sentence, length, longer, shorter, sort, triangle, square, rectangle, hexagon, 2-dimensional, sides, vertices, fewer

Resource: MyMath Chapter 2 Lesson 3, 6, 7 Chapter 3 Lesson 8, 10 Chapter 4 Lesson 1-9 Chapter 5 Lesson 1-7 Chapter 8 Lesson 1-4, 6 Chapter 9 Lesson 1-5 Chapter 10 Lesson 1-4 Chapter 11 Lesson 7

Support color, group, order, above, on top, over, below, under, beneath, on the bottom, next to, beside, to the left, to the right, in front of, behind, in back, alike, attributes, compose, decompose, different, large, measure, objects, order, same, sequence, shape, small, digits, equations, make, rhombus, symbol, trapezoid, compare


Pacing Guide Section 3: Counting & Cardinality, Operations & Algebraic Thinking, Measurement & Data Third Quarter

Standards: K.CC.1 Count to 100 by ones and by tens. K.CC.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1). K.CC.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a

count of no objects).

Clarification: K.CC.1 Verbally count to 75 by ones.

K.CC.3 Write numbers within the



K.CC.4 Understand the relationship between numbers and quantities; connect counting to cardinality.

a. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number name with one and only one object.

b. Understand that the last number name said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted.

c. Understand that each successive number name refers to a quantity that is one larger. K.CC.5 Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a

circle, or as many as 10 things in a scattered configuration; given a number from 1 – 20, count out that many objects.

K.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings, sounds (e.g., claps), acting out

situations, verbal explanations, expressions, or equations. (Drawings need not show details, but should show the mathematics in the problem. This applies wherever drawings are mentioned in the Standards).

K.OA.2 Solve addition and subtraction word problems and add within 10, e.g., by using objects or drawings to represent

the problem. K.OA.5 Fluently add and subtract within 5.

range 0-15. Represent a number of objects with written numeral within the range 0-15. Reversals are accepted, but not place value reversals like 16/61. If the objects are miscounted but they write the correct numeral for what they counted, the answer is correct. K.CC.4a In the range of 1-20. K.CC.4b In the range of 1-20. K.CC.4c In the range of 1-20. K.CC.5 Students must independently count correctly without prompting. K.OA.1 In the range of 0-10. If students verbally explain how they solved the problems that is correct.

K.OA.2 Addition word problems only. K.OA.5 (Addition only) Must answer with automaticity (Cannot count by 1’s, count on, or build with fingers).



K.MD.1 Describe measurable attributes of objects, such as length or weight.

K.MD.1 Students should suggest a measurement of length, height, width, or weight.

Vocabulary: Critical number, count, zero, one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen, twenty, addition (add, plus, combine), height, tall(er), short(er), length, long(er), width, wide(r), narrow(er), weight, lighter, heavy, heavier, equal to, more, number sentence, subtraction (take away/minus)

Resource: MyMath Chapter 1 Lesson 1, 3, 10, 11 Chapter 2 Lesson 1, 2, 4, 5, 9 Chapter 3 Lesson 1-3 Chapter 6 Lesson 1-6 Chapter 8 Lesson 5

Support equation, facts, group, measure, objects, order, digits, equations, make, symbol


Pacing Guide Section 4: Counting & Cardinality, Geometry, Operations & Algebraic Thinking, Fourth Quarter Number & Operation in Base Ten

Standards: K.CC.1 Count to 100 by ones and by tens. K.CC.2 Count forward beginning from a given number within the known sequence (instead of having to begin at 1). K.CC.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a

count of no objects).

Clarification: K.CC.1 Verbally count to 100 by ones. K.CC.3 Write numbers within the range 0-20. Represent a number of objects with written numeral within the range 0-20. Reversals are accepted, but not place value reversals like 16/61.



K.CC.5 Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1 – 20, count out that many objects. K.OA.2 Solve addition and subtraction word problems and add within 10, e.g., by using objects or drawings to represent

the problem. K.OA.5 Fluently add and subtract within 5. K.NBT.1 Compose and decompose numbers from 11 to 19 into ten ones and some further ones, e.g., by using objects

or drawings, and record each composition or decomposition by a drawing or equation (e.g., 18 = 10 + 8); understand that these numbers are composed of ten ones and one, two, three, four, five, six, seven, eight, or nine ones.

K.G.1 Describe objects in the environment using names of shapes, and describe the relative positions of objects using

terms such as above, below, beside, in front of, behind, and next to. K.G.2 Correctly name shapes regardless of their orientations or overall size. K.G.3 Identify shapes as two-dimensional (lying in a plane, “flat”) or three- dimensional (“solid”). K.G.4 Analyze and compare two- and three- dimensional shapes, in different sizes and orientations using informal

language to describe their similarities, differences, parts (e.g., number of sides and vertices/”corners”) and other attributes (e.g. having sides of equal length).

K.CC.5 Students must independently count correctly without prompting. K.OA.5 (Subtraction only) Must answer with automaticity (Cannot count by 1’s, count down, or build with fingers). K.NBT.1 Compose (put together) and decompose (take apart). If the student writes 10+8 or 8+10 the equation is still correct. K.G.1 3-dimensional objects K.G.2 3-dimensional shapes K.G.3 2-D and 3-D shape cards K.G.4 3-dimensional shapes

Vocabulary: Critical number, count, zero, one, two, three, four, five, six, seven, eight, nine, ten, eleven, twelve, thirteen, fourteen, fifteen, sixteen, seventeen, eighteen, nineteen, twenty, addition (add, plus,

Resource: MyMath Chapter 3 Lesson 4-7, 9 Chapter 6 Lesson 7 Chapter 7 Lesson 1-5 Chapter 12 Lesson 1-5



combine), subtraction (minus/take away), cone, sphere, cylinder, cube, 3-dimensional, 2-dimensional, edges, faces, corners, vertices, curved, equal, more, number sentence, sides

Support flat, alike, attribute, compose, create, decompose, different, facts, group, objects, order, roll, same, sequence, shape, solid, stack, straight, digits, equations, make, symbol, slide, solve




1st Grade Math Pacing Guide

The Pacing Guide has been aligned to Wyoming State Standards with consideration to the Critical Areas of Focus defined by Common Core State Standards for Math.

43 Days

Quarter 1

Pacing Guide Section 1

● Addition and Subtraction Concepts Measurement

Clarification Based on pre and post testing, make decisions to skip lessons and / or add materials.

Standards

1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of

adding to, taking from, putting together, taking apart, and comparing, with unknowns in all

positions, e.g., by using objects, drawings, and equations with a symbol for the unknown

number to represent the problem. (See Glossary in the CCSSM document)

NCSD clarification -

1.OA.1 Within 10; with solving for unknowns

1.OA.3 Apply properties of operations as strategies to add and subtract. (Students need not use

formal terms for these properties.) Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is

also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two

numbers can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of

addition.)

NCSD clarification -

1.OA.3 Commutative Property

1.OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

1.OA.7 Understand the meaning of the equal sign, and determine equations involving addition and

subtraction are true or false. For example, which of the following equations are true and

which are false? 6=6, 7=8-1, 5+2=2+5, 4+1=5+2

1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals

and represent a number of objects with a written numeral.

1.NBT.2 Understand that the two digits of a two-digit number represent amounts of tens and ones.

Understand the following as special cases:

a. 10 can be thought of as a bundle of ten ones — called a “ten.”

b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five,

six, seven, eight, or nine ones.

1.MD.1 Order three objects by length; compare the lengths of two objects indirectly by using a

third object.

1.MD.2 Express the length of an object as a whole number of length units, by laying multiple

copies of a shorter object (the length unit) end to end; understand that the length

measurement of an object is the number of same-size length units that span it with no gaps

or overlaps. Limit to contexts where the object being measured is spanned by a whole

number of length units with no gaps or overlaps.

Vocabulary

Critical Vocabulary

bundle, compose, decompose, difference, digit, equations, even, length, odd, ones, place



value, sum, tens, unknown

Supporting Vocabulary

longer, longest, addition (add, plus, combine), subtraction (take away, minus)

Resource

My Math Chapter 1 Addition Concepts (17 days) ● Lesson 1 - Addition Stories

● Lesson 2 - Model Addition

● Lesson 3 - Addition Number Sentences

● Lesson 4 - Add 0

● Lesson 5 - Vertical Addition

● Lesson 6 - Problem-Solving Strategy: Write a Number Sentence

● Lesson 7 - Ways to Make 4 and 5

● Lesson 8 - Ways to make 6 and 7

● Lesson 9 - Ways to Make 8



● Lesson 12 - Find Missing Parts of 10

● Lesson 13 - True and False Statements

My Math Chapter 2 Subtraction Concepts (18 days) ● Lesson 1 - Subtraction Stories

● Lesson 2 - Model Subtraction

● Lesson 3 - Subtraction Number Sentences

● Lesson 4 - Subtract 0 and All

● Lesson 5 - Vertical Subtraction

● Lesson 6 - Problem Solving Strategy: Draw a Diagram

● Lesson 7 - Compare Groups

● Lesson 8 - Subtract from 4 and 5

● Lesson 9 - Subtraction from 6 and 7

● Lesson 10 - Subtract from 8



● Lesson 13 - Relate Addition and Subtraction

● Lesson 14 - True and False Statements

My Math Chapter 5 Place Value (4 days) ● Lesson 1 - Numbers 11 to 19

● Lesson 2 - Tens

My Math Chapter 8 Measurement and Time (4 days) ● Lesson 1 - Compare Lengths

● Lesson 2 - Compare and Order Lengths

● Lesson 3 - Nonstandard Units of Length

● Lesson 4 - Problem-Solving Strategy: Guess, Check, and Revise



46 Days

Quarter 2


● Addition and Subtraction Strategies

● Geometry


Standards





NCSD clarification

1.OA.1 - Within 20; with solving for unknowns.

1.OA.6 Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.

Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14);

decomposing a number leading to a ten (e.g., 13 – 4 = 13 – 3 – 1 = 10 – 1 = 9); using the

relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12

– 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating

the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

NCSD clarification

1.OA.6 - Addition within 10.

1.OA.7 Understand the meaning of the equal sign, and determine I equations involving addition

and subtraction are true or false. For example, which of the following equations are true

and which are false? 6=6, 7=8-1, 5+2=2+5, 4+1=5+2

1.NBT.1 Count to 120, starting at any number less than 120. In this range, read and write numerals

and represent a number of objects with a written numeral.



c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five,

six, seven, eight, or nine tens (and 0 ones).

1.NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording

the results of comparisons with the symbols >, =, and <.

NCSD clarification

1.NBT.3 - Compare 2 one-digit numbers.

1.G.1 Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus

non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to

possess defining attributes.

1.G.2 Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles,

and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right

circular cones, and right circular cylinders) to create a composite shape, and compose new

shapes from the composite shape. (Students do not need to learn formal names such as

“right rectangular prism.”)

NCSD clarification

1.G.2 - Both 2-dimensional and 3-dimensional shapes.



1.G.3 Partition circles and rectangles into two and four equal shares, describe the shares using the

words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of.

Describe the whole as two of, or four of the shares. Understand for these examples that

decomposing into more equal shares creates smaller shares.

Vocabulary

Critical Vocabulary

2 dimensional, 3 dimensional, circle, compose, decompose, difference, equal to, equations,

fourths, greater than, half circle, halves, less than, quarter circle, quarters, rectangle,

rectangular prism, sides, sum, symbol, trapezoid, triangular prism, vertex


Resource

My Math Chapter 3 Addition Strategies to 20 (12 days) ● Lesson 1 - Count on 1, 2, o r3

● Lesson 2 - Count On Using Pennies

● Lesson 3 - Use a Number Line to Add

● Lesson 4 - Use Doubles to Add

● Lesson 5 - Use Near Doubles to Add

● Lesson 6 - Problem-Solving Strategy: Act It Out

● Lesson 7 - Make 10 to Add

● Lesson 8 - Add in Any Order

● Lesson 9 - Add Three Numbers

My Math Chapter 4 Subtraction Strategies to 20 (11 days) ● Lesson 1 - Count Back 1, 2, or 3

● Lesson 2 - Use a Number Line to Subtract

● Lesson 3 - Use Doubles to Subtract


● Lesson 5 - Make 10 to Subtract

● Lesson 6 - Use Related Facts to Add and Subtract

● Lesson 7 - Fact Families

● Lesson 8 - Missing Addends

My Math Chapter 9 Two-Dimensional Shapes and Equal Shares (10 days) ● Lesson 1 - omit

● Lesson 2 - omit

● Lesson 3 - omit

● Lesson 4 - Compare Shapes

● Lesson 5 - Composite Shapes

● Lesson 6 - More Composite Shapes

● Lesson 7 - Problem-Solving Strategy: Use Logical Reasoning

● Lesson 8 - Equal Parts

● Lesson 9 - Halves

● Lesson 10 - Quarters and Fourths

My Math Chapter 10 Geometry (7 days) ● Lesson 1 - Cubes and Prisms

● Lesson 2 - Cones and Cylinders

● Lesson 3 - Problem Solving: Look for a Pattern

● Lesson 4 - Combine 3-D Shapes



42 Days

Quarter 3


● Place Value

● Two-Digit Addition and Subtraction

● Time


Standards

1.OA.2 Solve word problems that call for addition of three whole numbers whose sum is less than

or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the

unknown number to represent the problem.

NCSD clarification

1.OA.2 - Within 10.

1.OA.3 Apply properties of operations as strategies to add and subtract. (Students need not use

formal terms for these properties.) Examples: If 8 + 3 = 11 is known, then 3 + 8 = 11 is

also known. (Commutative property of addition.) To add 2 + 6 + 4, the second two numbers

can be added to make a ten, so 2 + 6 + 4 = 2 + 10 = 12. (Associative property of addition.)

NCSD clarification

1.OA.3 - Associative Property.







NCSD clarification

1.OA.6 - Addition and subtraction within 20.

1.OA.8 Determine the unknown whole number in an addition or subtraction equation relating to

three whole numbers. For example, determine the unknown number that makes the

equation true in each of the equations 8 + ? = 11, 5 = � – 3, 6 + 6 = �.

NCSD clarification

1.OA.8 - Combinations to 10.



c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five,

six, seven, eight, or nine tens (and 0 ones).

1.NBT.3 Compare two two-digit numbers based on meanings of the tens and ones digits, recording

the results of comparisons with the symbols >, =, and <.

NCSD clarification

1.NBT.3 - Compare 2 two-digit numbers.

1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a

two-digit number and a multiple of 10, using concrete models or drawings and strategies

based on place value, properties of operations, and/or the relationship between addition and

subtraction; relate the strategy to a written method and explain the reasoning used.



Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and

sometimes it is necessary to compose a ten.

1.NBT.5 Give a two-digit number, mentally find 10 more or 10 less than the number, without having

to count; explain the reasoning used.

1.NBT.6 Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90

(positive or zero differences), using concrete models or drawings and strategies based on

place value, properties of operations, and/or the relationship between addition and


Vocabulary

Critical Vocabulary

compose, decompose, difference, equations, sum


false, true

Resource

My Math Chapter 5 Place Value (21 days) ● Lesson 1 - addressed in Quarter 1

● Lesson 2 - addressed in Quarter 1

● Lesson 3 - Count by Tens Using Dimes

● Lesson 4 - Ten and Some More

● Lesson 5 - Tens and Ones

● Lesson 6 - Problem-Solving Strategy: Make a Table

● Lesson 7 - Numbers to 100

● Lesson 8 - Ten More, Ten Less

● Lesson 9 - Count by Fives Using Nickels

● Lesson 10 - Use Models to Compare Numbers

● Lesson 11 - Use Symbols to Compare Numbers

● Lesson 12 - Numbers to 120

● Lesson 13 - Count to 120

● Lesson 14 - Read and Write Numbers to 120

My Math Chapter 6 Two-Digit Addition (21 days) ● Lesson 1 - Add Tens

● Lesson 2 - Count On Tens and Ones

● Lesson 3 - Add Tens and Ones

● Lesson 4 - Problem-Solving Strategy: Guess, Check, and Revise

● Lesson 5 - Add Tens and Ones with Regrouping

● Lesson 6 - Subtract Tens

● Lesson 7 - Count Back by 10s

● Lesson 8 - Relate Addition and Subtraction of Tens



45 Days

Quarter 4


● Data

● Geometry


Standards





NCSD clarification

1.OA.1 - Within 20. Solving questions for the unknown.

1.OA.2 Solve word problems that call for addition of three whole numbers whose sum is less than

or equal to 20, e.g., by using objects, drawings, and equations with a symbol for the

unknown number to represent the problem.

NCSD clarification

1.OA.2 - Within 20.

1.OA.4 Understand subtraction as an unknown-addend problem. For example, subtract 10 – 8 by

finding the number that makes 10 when added to 8.

1.OA.5 Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).







NCSD clarification

1.OA.6 - Addition and subtraction within 20.

1.OA.8 Determine the unknown whole number in an addition or subtraction equation relating to


equation true in each of the equations 8 + ? = 11, 5 = � – 3, 6 + 6 = �.

NCSD clarification

1.OA.8 - Combinations to 20.

1.NBT.4 Add within 100, including adding a two-digit number and a one-digit number, and adding a

two-digit number and a multiple of 10, using concrete models or drawings and strategies

based on place value, properties of operations, and/or the relationship between addition and


Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and

sometimes it is necessary to compose a ten.

1.MD.3 Tell and write time in hours and half-hours using analog and digital clocks.

1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions

about the total number of data points, how many in each category, and how many more or



less are in one category than in another.

NCSD clarification

1.MD.4 - Graphing can be embedded within learning cycles throughout the year.

Vocabulary

Critical Vocabulary

analog, compose, decompose, difference, digital, equations, fact family, half hour, hour,

sum


Resource

My Math Chapter 7 Organize and Use Graphs (12 days) ● Lesson 1 - Tally Charts


● Lesson 3 - Make Picture Graphs

● Lesson 4 - Read Picture Graphs

● Lesson 5 - Make Bar Graphs

● Lesson 6 - Read Bar Graphs

My Math Chapter 8 Measurement and Time (10 days) ● Lesson 5 - Time to the Hour: Analog

● Lesson 6 - Time to the Hour: Digital

● Lesson 7 - Time to the Half Hour: Analog

● Lesson 8 - Time to the Half Hour: Digital

● Lesson 9 - Time to the Hour and Half Hour



2nd Grade Math Pacing Guide The Pacing Guide has been aligned to Wyoming State Standards with consideration to the Critical Areas of Focus defined by Common Core State Standards for Math.

43 Days Pacing Guide Section 1

● Addition and Subtraction Concepts

● Number Patterns

● Place Value to 1,000


Standards

2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems

involving situations of adding to, taking from, putting together, taking apart, and

comparing, with unknowns in all positions, e.g., by using drawings and equations with a

symbol for the unknown number to represent the problem. (See Glossary in the CCSSM

document)

NCSD clarification

2.OA.1 - Within 20.

2.OA.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from

memory all sums of two one-digit numbers.

2.OA.3 Determine whether a group of objects (up to 20) has an odd or even number of members,

e.g., by pairing objects or counting them by 2s; write an equation to express an even

number as a sum of two equal addends.

2.OA.4 Use addition to find the total number of objects arranged in rectangular arrays with up to 5

rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

2.NBT.1 Understand that the three digits of a three-digit number represent amounts of hundreds,

tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as

special cases:

a. 100 can be thought of as a bundle of ten tens — called a “hundred.”

b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three,

four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

2.NBT.2 Count within 1000; skip-count by 5s, 10s, and 100s.

2.NBT.3 Read and write numbers to 1000 using base-ten numerals, number names, and expanded

form.

2.NBT.4 Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits,

using >, =, and < symbols to record the results of comparisons.

2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of

operations, and/or the relationship between addition and subtraction.

NCSD clarification

2.NBT.5 - Within 20.

2.NBT.9 Explain why addition and subtraction strategies work, using place value and the properties

of operations.



2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced

points corresponding to the numbers 0, 1, 2,..., and represent whole-number sums and

differences within 100 on a number line diagram.

Vocabulary

Critical Vocabulary

addend, base ten numerals, expanded form, fact family, hundreds, number line, number

name, place value


columns, digits, equations, equivalent, expression, ones, sum, symbol, tens, unknown, whole

numbers, rows

Resource

My Math Chapter 1 Applying Addition and Subtraction Concepts (18 days) ● Lesson 1 - Addition Properties

● Lesson 2 - Count on to Add

● Lesson 3 - Doubles and Near Doubles

● Lesson 4 - Make a 10

● Lesson 5 - Add Three Numbers


● Lesson 7 - Count Back to Subtract

● Lesson 8 - Subtract All and Subtract Zero

● Lesson 9 - Use Doubles to Subtract

● Lesson10 - Relate Addition and Subtraction

● Lesson 11 - Missing Addends

● Lesson 12 - Fact Families

● Lesson 13 - Two-Step Word Problems

My Math Chapter 2 Number Patterns (12 days) ● Lesson 1 - Skip Count on a Hundred Chart

● Lesson 2 - Skip Count by 2s, 5s, and 10s

● Lesson 3 - Problem Solving Strategy: Find a Pattern

● Lesson 4 - Repeated Addition

● Lesson 5 - Repeated Addition with Arrays

● Lesson 6 - Even and Odd Numbers

● Lesson 7 - Sums of Equal Numbers

My Math Chapter 5 Place Value to 1,000 (13 days) ● Lesson 1 - Hundreds

● Lesson 2 - Hundreds, Tens, and Ones

● Lesson 3 - Place Value to 1,000

● Lesson 4 - Problem Solving Strategy: Use Logical Reasoning

● Lesson 5 - Read and Write Numbers to 1,000

● Lesson 6 - Count by 5s, 10s, and 100s

● Lesson 7 - Compare Numbers to 1,000




● Two-Digit Addition and Subtraction

● Measurement

● Time

● Money


Standards





document)



2.NBT.6 Add up to four two-digit numbers using strategies based on place value and properties of

operations.

2.MD.6 Represent whole numbers as lengths from 0 on a number line diagram with equally spaced

points corresponding to the numbers 0, 1, 2,..., and represent whole-number sums and

differences within 100 on a number line diagram.

2.MD.7 Tell and write time from analog and digital clocks to the nearest five minutes, using a.m.

and p.m.

2.MD.8 Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $

and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents

do you have?

Vocabulary

Critical Vocabulary

analog, compose, decompose, digital, fact family, number line


a.m., dime, dollar bill, equations, equivalent, expression, hour, hour hand, minute hand,

minutes, nickel, p.m., penny, quarter, quarter past, sum, symbol, unknown, whole numbers

Resource

My Math Chapter 3 Add Two-Digit Numbers (11 days) ● Integrate 2.MD.6 Adding and Subtracting on a number line*needs to be supplemented

● Lesson 1 - Take Apart Tens to Add

● Lesson 2 - Regroup Ones as Tens

● Lesson 3 - Add a Two-Digit Number

● Lesson 4 - Add Two-Digit Numbers

● Lesson 5 - Rewrite Two-Digit Addition

● Lesson 6 - Add Three or Four Two-Digit Numbers

● Lesson 7 - Problem Solving Strategy: Make a Model

My Math Chapter 4 Subtract Two-Digit Numbers (13 days) ● Lesson 1 - Two-Digit Fact Families

● Lesson 2 - Take Apart Tens to Subtract

● Lesson 3 - Regroup a Ten as Ones

● Lesson 4 - Subtract From a Two-Digit Number



● Lesson 5 - Subtract Two-Digit Numbers

● Lesson 6 - Rewrite Two-Digit Subtraction

● Lesson 7 - Check Subtraction


● Lesson 9 - Two-Step Word Problems

My Math Chapter 8 Money (10 days) ● Lesson 1 - Pennies, Nickels, and Dimes

● Lesson 2 - Quarters

● Lesson 3 - Count Coins

● Lesson 4 - Problem-Solving Strategy: Act it Out

● Lesson 5 - Dollars

My Math Chapter 10 Time (12 days) ● Lesson 1 - Time to the Hour

● Lesson 2 - Time to the Half Hour

● Lesson 3 - Problem Solving Strategy: Find a Pattern

● Lesson 4 - Time to the Quarter Hour

● Lesson 5 - Time to Five Minute Intervals

● Lesson 6 - A.M. and P.M.


● Add Three-Digit Numbers

● Data Analysis

● Geometry


Standards

2.MD.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up

to four categories. Solve simple put together, take-apart, and compare problems (See

Glossary) using information presented in a bar graph.



2.NBT.7 Add and subtract within 1000, using concrete models or drawings and strategies based on


subtraction; relate the strategy to a written method. Understand that in adding or subtracting

three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and

ones; and sometimes it is necessary to compose or decompose tens or hundreds.

2.NBT.8 Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a

given number 100-900.

2.G.1 Recognize and draw shapes having specified attributes, such as a given number of angles or

a given number of equal faces. (Sizes are compared directly or visually, not compared by

measuring.) Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

2.G.2 Partition a rectangle into rows and columns of same-size squares and count to find the total

number of them.

2.G.3 Partition circles and rectangles into two, three, or four equal shares, describe the shares

using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves,



three thirds, four fourths. Recognize that equal shares of identical wholes need not have the

same shape.





document)

Vocabulary

Critical Vocabulary

fact family, pentagon, picture graph, quadrilateral


angle, data, data table, edges, equal shares, equations, equivalent, expression, faces, fourths,

fraction, halves, horizontal, key, line plot, partition, quarters, rectangular prism, scale, sum,

survey, symbol, tally mark, thirds, unknown, vertical, whole numbers

Resource

My Math Chapter 6 Add Three-Digit Numbers (12 days) ● Lesson 1 - Make a Hundred to Add

● Lesson 2 - Add Hundreds

● Lesson 3 - Mentally Add 10 or 100

● Lesson 4 - Regroup Ones to Add

● Lesson 5 - Regroup Tens to Add

● Lesson 6 - Add Three-Digit Numbers

● Lesson 7 - Rewrite Three-Digit Addition

● Lesson 8 - Problem-Solving Strategy: Guess, Check and Revise

My Math Chapter 9 Data Analysis (12 days) ● Lesson 1 - Take a Survey

● Lesson 2 - Make Picture Graphs

● Lesson 3 - Analyze Picture Graphs

● Lesson 4 - Make Bar Graphs

● Lesson 5 - Analyze Bar Graphs


● Lesson 7 - Make Line Plots

● Lesson 8 - Analyze Line Plots

My Math Chapter 12 Geometric Shapes and Equal Shares (14 days) ● Lesson 1 - Two-Dimensional Shapes

● Lesson 2 - Sides and Angles

● Lesson 3 - Problem-Solving Strategy: Draw a Diagram

● Lesson 4 - Three-Dimensional Shapes

● Lesson 5 - Faces, Edges, and Solids

● Lesson 6 - Relate Shapes and Solids

● Lesson 7 - Halves, Thirds, and Fourths

● Lesson 8 - Area




● Subtract Three-Digit Numbers

● Measurement - Customary and Metric Lengths


Standards




symbol for the unknown number to represent the problem. (See Glossary)

2.MD.1 Measure the length of an object by selecting and using appropriate tools such as rulers,

yardsticks, meter sticks, and measuring tapes.

2.MD.2 Measure the length of an object twice, using length units of different lengths for the two

measurements; describe how the two measurements relate to the size of the unit chosen.

2.MD.3 Estimate lengths using units of inches, feet, centimeters, and meters.

2.MD.4 Measure to determine how much longer one object is than another, expressing the length

difference in terms of a standard length unit.

2.MD.5 Use addition and subtraction within 100 to solve word problems involving lengths that are

given in the same units, e.g., by using drawings (such as drawings of rulers) and equations

with a symbol for the unknown number to represent the problem.

2.MD.9 Generate measurement data by measuring lengths of several objects to the nearest whole

unit, or by making repeated measurements of the same object. Show the measurements by

making a line plot, where the horizontal scale is marked off in whole-number units.

2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties

of operations, and/or the relationship between addition and subtraction.

2.NBT.7 Add and subtract within 1000, using concrete models or drawings and strategies based on


subtraction; relate the strategy to a written method. Understand that in adding or

subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and

tens, ones and ones; and sometimes it is necessary to compose or decompose tens or

hundreds.

2.NBT.8 Mentally add 10 or 100 to a given number 100-900, and mentally subtract 10 or 100 from a

given number 100-900.

Vocabulary

Critical Vocabulary

centimeter, customary system, fact family, feet/foot, inch, meter, metric system, yard


equations, equivalent, expression, length, measuring tape, meter stick, ruler, symbol, unit,

unknown, yard stick

Resource

My Math Chapter 7 Subtract Three-Digit Numbers (16 days) ● Lesson 1 - Take Apart Hundreds to Subtract

● Lesson 2 - Subtract Hundreds

● Lesson 3 - Mentally Subtract 10 or 100



● Lesson 4 - Regroup Tens

● Lesson 5 - Regroup Hundreds

● Lesson 6 - Subtract Three-Digit Numbers

● Lesson 7 - Rewrite Three- Digit Subtraction


● Lesson 9 - Subtract Across Zeros

My Math Chapter 11 Customary and Metric Lengths (19 days) ● Lesson 1 - Inches

● Lesson 2 - Feet and Yards

● Lesson 3 - Select and Use Customary Tools

● Lesson 4 - Compare Customary Lengths

● Lesson 5 - Relate Inches, Feet, and Yards

● Lesson 6 - Problem-Solving Strategy: Using Logical Reasoning

● Lesson 7 - Centimeters and Meters

● Lesson 8 - Select and Use Metric Tools

● Lesson 9 - Compare Metric Lengths

● Lesson 10 - Relate Centimeters and Meters

● Lesson 11 - omit

● Lesson 12- Measurement Data



3rd Grade Math Pacing Guide The Pacing Guide has been aligned to Wyoming State Standards with consideration to the Critical Areas of Focus defined by Common Core State Standards for Math and the Wyoming PAWS Blueprint.

38-43

Days*


● Place Value, Addition and Subtraction Concepts, Geometry, Perimeter

* Five days leeway for first week routines and NWEA testing.


Standards

3.NBT.1 Use place value understanding to round whole numbers to the nearest 10 or 100.

3.NBT.2 Fluently add and subtract within 1000 using strategies and algorithms based on place value,

properties of operations, and/or the relationship between addition and subtraction.

3.OA.8 Solve two-step word problems using the four operations. Represent these problems using

equations with a letter standing for the unknown quantity. Assess the reasonableness of

answers using mental computation and estimation strategies including rounding. *

*This standard is limited to problems posed with whole numbers and having whole

number answers; students should know how to perform operations in the

conventional order when there are no parentheses to specify a particular order

(Order of Operations).

NCSD Clarification 3.OA.8 - Addition and subtraction only

3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table),

and explain them using properties of operations. For example, observe that 4 times a

number is always even, and explain why 4 times a number can be decomposed into two

equal addends.

NCSD Clarification

3.OA.9 - Addition only

3.G.1 Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may

share attributes (e.g., having four sides), and that the shared attributes can define a larger

category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples

of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these

subcategories.

3.MD.8 Solve real world and mathematical problems involving perimeters of polygons, including

finding the perimeter given the side lengths, finding an unknown side length, and

exhibiting rectangles with the same perimeter and different areas or with the same area and

different perimeters.

Vocabulary

Critical Vocabulary

angle(s), parallel, parallelogram, perimeter, place value, polygon, unit, whole numbers


fact family, quadrilateral, sum, difference



Resource

My Math Chapter 1 Place Value (9 days) ● Lesson 1 - Place Value Through Thousands

● Lesson 2 - Compare Numbers

● Lesson 3 - Order Numbers

● Lesson 4 - Round to the Nearest Ten

● Lesson 5 - Round to the Nearest Hundred

● Lesson 6 - Problem-Solving Investigation: Use the Four-Step Plan

My Math Chapter 2 Addition (12 days) ● Lesson 1 - Addition Properties

● Lesson 2 - Patterns in the Addition Table

● Lesson 3 - Addition Patterns

● Lesson 4 - Add Mentally

● Lesson 5 - Estimate Sums

● Lesson 6 - Hands On: Use Models to Add

● Lesson 7 - Add Three-Digit Numbers

● Lesson 8 - Add Four-Digit Numbers

● Lesson 9 - Problem-Solving Investigation: Reasonable Answers

My Math Chapter 14 Geometry (5 days) ● Use manipulatives

● Lesson 1 - Hands On: Angles

● Lesson 2 - Polygons

● Lesson 4 - Quadrilaterals

● Lesson 5 - Shared Attributes of Quadrilaterals

My Math Chapter 13 Perimeter and Area (3 days) ● Use additional resources to practice with 2- and 3- digit side lengths

● Lesson 1 - Hands On: Find Perimeter

● Lesson 2 - Perimeter

My Math Chapter 3 Subtraction (9 days) ● Lesson 1 - Subtract Mentally

● Lesson 2 - Estimate Differences

● Lesson 3 - Problem-Solving Investigation: Estimate or Exact Answer

● Lesson 4 - Hands On: Subtraction with Regrouping

● Lesson 5 - Subtract Three-Digit Numbers

● Lesson 6 - Subtract Four-Digit Numbers



● Multiplication and Division Concepts

● Patterns

● Connecting Area to Multiplication


Students should be aware of the different types of operation symbols

(𝑖. 𝑒. ,×,∙,∗,÷, 𝑎𝑏⁄ , 𝑎𝑛𝑑 𝑙𝑜𝑛𝑔 𝑑𝑖𝑣𝑖𝑠𝑜𝑛 𝑠𝑡𝑟𝑢𝑐𝑡𝑢𝑟𝑒)

Standards

3.OA.1 Interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5

groups of 7 objects each. For example, describe a context in which a total number of

objects can be expressed as 5 × 7.

3.OA.2 Interpret whole-number quotients of whole numbers, e.g., interpret 56 ÷ 8 as the number of



objects in each share when 56 objects are partitioned equally into 8 shares, or as a number

of shares when 56 objects are partitioned into equal shares of 8 objects each. For example,

describe a context in which a number of shares or a number of groups can be expressed as

56 ÷ 8.

3.OA.4 Determine the unknown whole number in a multiplication or division equation relating


equation true in each of the equations 8 × ? = 48, 5 = � ÷ 3, 6 × 6 = ?.

NCSD Clarification

3.OA.4 - Fact fluency for 0-5, 10

3.OA.5 Apply properties of operations as strategies to multiply and divide. (Students need not use

formal terms for these properties.) Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is

also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 =

15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of

multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2)

= (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

NCSD Clarification

3.OA.5 - Commutative Property of Multiplication only

3.OA.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding

the number that makes 32 when multiplied by 8.

NCSD Clarification


3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between

multiplication and division (e.g., knowing that 8 x 5 = 40, one knows 40 ÷ 5 = 8) or

properties of operations. By the end of Grade 3, know from memory all products of two

one-digit numbers.

NCSD Clarification




answers using mental computation and estimation strategies including rounding.*

*This standard is limited to problems posed with whole numbers and having whole

number answers; students should know how to perform operations in the

conventional order when there are no parentheses to specify a particular order

(Order of Operations).

NCSD Clarification

3.OA.8 - Multiplication and division only

3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10–90 (e.g., 9 × 80, 5 ×

60) using strategies based on place value and properties of operations.

3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area

measurement.

a. A square with side length 1 unit, called “a unit square,” is said to have “one square

unit” of area, and can be used to measure area.



b. A plane figure which can be covered without gaps or overlaps by n unit squares is

said to have an area of n square units.

3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and

improvised units).

3.MD.7 Relate area to the operations of multiplication and addition.

a. Find the area of a rectangle with whole-number side lengths by tiling it, and show

that the area is the same as would be found by multiplying the side lengths.

b. Multiply side lengths to find areas of rectangles with whole number side lengths in

the context of solving real world and mathematical problems, and represent whole-

number products as rectangular areas in mathematical reasoning.

Vocabulary

Critical Vocabulary

division, equal part, factor, label, multiplication, partitioned, product, quotient, unit,

variable, whole numbers


area, array, difference, fact family, interpret, multiple, sum

Resource

My Math Chapter 4 Understand Multiplication (9 days) ● Lesson 1 - Hands On: Model Multiplication

● Lesson 2 - Multiplication as Repeated Addition

● Lesson 3 - Hands On: Multiply with Arrays

● Lesson 4 - Arrays and Multiplication

● Lesson 5 - Problem-Solving Investigation: Make a Table

● Lesson 6 - Use Multiplication to Find Combinations

My Math Chapter 5 Understand Division (9 days) ● Lesson 1 - Hands On: Model Division

● Lesson 2 - Division as Equal Sharing

● Lesson 3 - Relate Division and Subtraction

● Lesson 4 - Hands On: Relate Division and Multiplication

● Lesson 5 - Inverse Operations

● Lesson 6 - Problem-Solving Investigations: Use Models

My Math Chapter 6 Multiplication and Division Problems (12 days) ● Lesson 1 - Patterns in the Multiplication Table

● Lesson 2 - Multiply by 2

● Lesson 3 - Divide by 2



● Lesson 6 - Problem-Solving Investigation: Look for a Pattern


● Lesson 8 - Multiples of 10


My Math Chapter 7 Multiplication and Division (11 days) ● Lesson 1 - Multiply by 3


● Lesson 3 - Hands On: Double a Known Fact



● Lesson 6 - Problem-Solving Investigation: Extra or Missing Information

● Lesson 7 - Multiply by 0 and 1

● Lesson 8 - Divide with 0 and 1



My Math Chapter 13 Perimeter and Area (no additional days) ● Area as an array model

● Embed area lessons within multiplication lessons by connecting the array model to area of a rectangle.

● Lesson 5 - Hands On: Tile Rectangle to Find Area

● Lesson 6 - Areas of Rectangles

40 Days* 3 days

leeway for

PAWS


● Fractions

● Measurement Related to Fractions

● Geometry Related to Fractions

● Data Analysis

● Multiplication and Division Concepts


Standards

3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving

equal groups, arrays, and measurement quantities, e.g., by using drawings and equations

with a symbol for the unknown number to represent the problem. (See Glossary)




NCSD Clarification

3.OA.4 - Fact Fluency for 6, 7, 8, 9



NCSD Clarification

3.OA.6 - Fact fluency for 6, 7, 8, 9

3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between

multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or

properties of operations. By the end of Grade 3, know from memory all products of two

one-digit numbers.

NCSD Clarification

3.OA.7 - Fact fluency for 6, 7, 8, 9

3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table),

and explain them using properties of operations. For example, observe that 4 times a

number is always even, and explain why 4 times a number can be decomposed into two

equal addends.


a. Find the area of a rectangle with whole number side lengths by tiling it, and show





c. Use tiling to show in a concrete case that the area of a rectangle with whole-number



side lengths a and b + c is the sum of a × b and a × c. Use area models to represent

the distributive property in mathematical reasoning.

d. Recognize area as additive. Find areas of rectilinear figures by decomposing them

into non-overlapping rectangles and adding the areas of the non-overlapping parts,

applying this technique to solve real world problems.

3.NF.1 Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into

b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

3.NF.2 Understand a fraction as a number on the number line; represent fractions on a number line

diagram.

a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to

1 as the whole and partitioning it into b equal parts. Recognize that each part has

size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the

number line.

b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b

from 0. Recognize that the resulting interval has size a/b and that its endpoint

locates the number a/b on the number line.

3.NF.3 Explain equivalence of fractions in special cases, and compare fractions by reasoning about

their size.

a. Understand two fractions as equivalent (equal) if they are the same size, or the same

point on a number line.

b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3).

Explain why the fractions are equivalent, e.g., by using a visual fraction model.

c. Express whole numbers as fractions, and recognize fractions that are equivalent to

whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6;

locate 4/4 and 1 at the same point of a number line diagram.

d. Compare two fractions with the same numerator or the same denominator by

reasoning about their size. Recognize that comparisons are valid only when the two

fractions refer to the same whole. Record the results of comparisons with the

symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction

model.

3.G.2 Partition shapes into parts with equal areas. Express the area of each part as a unit fraction

of the whole. For example, partition a shape into 4 parts with equal area, and describe the

area of each part as 1/4 of the area of the shape.

Vocabulary

Critical Vocabulary

denominator, division, equal part, factor, fraction, multiplication, numerator, partitioned,

polygon, product, quotient, unit, variable, whole numbers


array, equivalent, fact family, multiple

Supporting

Strategy number line

Resource

My Math Chapter 8 Apply Multiplication and Division (9 days) ● Lesson 1 - Multiply by 6




● Lesson 3 - Divide by 6 and 7




My Math Chapter 12 Represent and Interpret Data (12 days) ● Lesson 1 - Collect and Record Data

● Lesson 2 - Draw Scaled Picture Graphs

● Lesson 3 - Draw Scaled Bar Graphs

● Lesson 4 - Relate Bar Graphs to Scaled Picture Graphs

● Lesson 5 - Draw and Analyze Line Plots

● Lesson 6 - Hands On: Measure to Halves and Fourths of a Inch

● Lesson 7 - Collect and Display Measurement Data

My Math Chapter 10 Fractions (11 days) ○ Use manipulatives

● Lesson 1 - Unit Fractions

● Lesson 2 - Part of a Whole

● Lesson 3 - Part of a Set

● Lesson 4 - Problem -Solving Investigation: Draw a Diagram

● Lesson 5 - Hands on: Fractions on a Number Line

● Lesson 6 - Equivalent Fractions

● Lesson 7 - Fractions as One Whole

● Lesson 8 - Compare Fractions

My Math Chapter 14 Geometry (3 days) ● Lesson 3 - Hands on: Triangles

● Lesson 7 - Partition Shapes

My Math Chapter 13 Perimeter and Area (5 days) ○ May need additional resources

● Lesson 3 - Hands On: Understand Area

● Lesson 4 - Measure Area

● Lesson 8 - Area of Composite Figures

● Lesson 9 - Area and Perimeter

44 Days 4 days

leeway for

NWEA and

final week.

Pacing Guide Section 4:

● Multiplication and Division Word Problems

● Measuring Time and Capacity

● Properties of Multiplication

● Strategies for Two-Digit Multiplication


Standards

3.OA.3 Use multiplication and division within 100 to solve word problems in situations involving

equal groups, arrays, and measurement quantities, e.g., by using drawings and equations

with a symbol for the unknown number to represent the problem. (See Glossary)




NCSD Clarification

3.OA.4 - Fact Fluency for 11, 12



3.OA.5 Apply properties of operations as strategies to multiply and divide. (Students need not use

formal terms for these properties.) Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is

also known. (Commutative property of multiplication.) 3 × 5 × 2 can be found by 3 × 5 =

15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of

multiplication.) Knowing that 8 × 5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2)

= (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)

NCSD Clarification

3.OA.5 - Associative and Distributive Properties of Multiplication



NCSD Clarification

3.OA.6 - Fact fluency and strategies for 11, 12

3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship

between multiplication and division (e.g., knowing that 8 × 5 = 40, one knows 40 ÷ 5 =

8) or properties of operations. By the end of Grade 3, know from memory all products

of two one-digit numbers.

NCSD Clarification

3.OA.7 - Fact fluency and strategies for 11, 12



answers using mental computation and estimation strategies including rounding. (This

standard is limited to problems posed with whole numbers and having whole number

answers; students should know how to perform operations in the conventional order when

there are no parentheses to specify a particular order (Order of Operations).)

NCSD Clarification

3.OA.8 - All four operations

3.MD.1 Tell and write time to the nearest minute and measure time intervals in minutes. Solve word

problems involving addition and subtraction of time intervals in minutes, e.g., by

representing the problem on a number line diagram.

3.MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams

(g), kilograms (kg), and liters (l). (Excludes compound units such as cm3 and finding the

geometric volume of a container.) Add, subtract, multiply, or divide to solve one-step word

problems involving masses or volumes that are given in the same units, e.g., by using

drawings (such as a beaker with a measurement scale) to represent the problem. [Excludes

multiplicative comparison problems (problems involving notions of “times as much”; see

Glossary, Table 2])

3.MD.3 Draw a scaled picture graph and a scaled bar graph to represent a data set with several

categories. Solve one- and two-step “how many more” and “how many less” problems

using information presented in scaled bar graphs. For example, draw a bar graph in which

each square in the bar graph might represent 5 pets.

3.MD.4 Generate measurement data by measuring lengths using rulers marked with halves and

fourths of an inch. Show the data by making a line plot, where the horizontal scale is



marked off in appropriate units— whole numbers, halves, or quarters.

3.MD.5 Recognize area as an attribute of plane figures and understand concepts of area

measurement.

a. A square with side length 1 unit, called “a unit square,” is said to have “one square

unit” of area, and can be used to measure area.

b. A plane figure which can be covered without gaps or overlaps by n unit squares is

said to have an area of n square units.

3.MD.6 Measure areas by counting unit squares (square cm, square m, square in, square ft, and

improvised units).


a. Find the area of a rectangle with whole-number side lengths by tiling it, and show





c. Use tiling to show in a concrete case that the area of a rectangle with whole-number

side lengths a and b + c is the sum of a × b and a × c. Use area models to represent

the distributive property in mathematical reasoning.

d. Recognize area as additive. Find areas of rectilinear figures by decomposing them

into non-overlapping rectangles and adding the areas of the non-overlapping parts,

applying this technique to solve real world problems.

Vocabulary

Critical Vocabulary

division, factor, label, liquid volume, multiplication, product, quotient, scale, unit, variable,

whole numbers


area, array, fact family, feet, inches, multiple

Resource

My Math Chapter 11 Measurement (11 days) ● Lesson 1 - Hands On: Estimate and Measure Capacity

● Lesson 2 - Solve Capacity Problems

● Lesson 3 - Hands On: Estimate and Measure Mass

● Lesson 4 - Solve Mass Problems

● Lesson 5 - Tell Time to the Minute

● Lesson 6 - Time Intervals

● Lesson 7 - Problem-Solving Investigation: Work Backward

My Math Chapter 8 Apply Multiplication and Division (4 days) ● Lesson 7 - Problem-Solving Investigation: Make an Organized List

● Lesson 8 - Multiply by 11 and 12


My Math Chapter 9 Properties and Equations (12 days) ● Lesson 1 - Hands On: Take Apart to Multiply

● Lesson 2 - The Distributive Property

● Lesson 3 - Hands On: Multiply Three Factors

● Lesson 4 - The Associative Property

● Lesson 5 - Write Expressions

● Lesson 6 - Evaluate Expressions



● Lesson 7 - Write Equations

● Lesson 8 - Solve Two-Step Word Problems

● Lesson 9 - Problem-Solving Investigation: Use Logical Reasoning

My Math Chapter 13 Perimeter and Area (3 days) ● Lesson 7 - Hands On: Area and the Distributive Property

● Lesson 10 - Problem-Solving Investigation: Draw a Diagram

My Math Chapter 14 Geometry (2 days) ○ Need to find more similar practice problems

○ Apply and Transfer Skills to Real Life Application, need additional resources.

● Lesson 6 - Problem-Solving Investigation: Guess, Check, and Revise



4th Grade Math Pacing Guide The Pacing Guide has been aligned to Wyoming State Standards with consideration to the Critical Areas of Focus defined by Common Core State Standards for Math and the Wyoming PAWS Blueprint.


● Place Value

● Addition and Subtraction

● Multiplication Concepts


Standards

4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what

it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by

applying concepts of place value and division.

4.NBT.2 Read and write multi-digit whole numbers using base-ten numerals, number names, and

expanded form. Compare two multi-digit numbers based on meanings of the digits in each

place, using >, =, and < symbols to record the results of comparisons.

4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place.

4.NBT.4 Fluently add and subtract multi-digit whole numbers using the standard algorithm.

4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply

two two-digit numbers, using strategies based on place value and the properties of

operations. Illustrate and explain the calculation by using equations, rectangular arrays,

and/or area models.

4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit

divisors, using strategies based on place value, the properties of operations, and/or the

relationship between multiplication and division. Illustrate and explain the calculation by

using equations, rectangular arrays, and/or area models.

4.OA.1 Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement

that 35 is 5 times as many as 7 and 7 times as many as 5. Represent verbal statements of

multiplicative comparisons as multiplication equations.

4.OA.2 Multiply or divide to solve word problems involving multiplicative comparison, e.g., by

using drawings and equations with a symbol for the unknown number to represent the

problem, distinguishing multiplicative comparison from additive comparison.

4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number

answers using the four operations, including problems in which remainders must be

interpreted. Represent these problems using equations with a letter standing for the

unknown quantity. Assess the reasonableness of answers using mental computation and

estimation strategies including rounding.

4.OA.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole

number is a multiple of each of its factors. Determine whether a given whole number in the

range 1–100 is a multiple of a given one-digit number. Determine whether a given whole

number in the range 1–100 is prime or composite.



4.OA.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of

the pattern that were not explicit in the rule itself. For example, given the rule “Add 3”

and the starting number 1, generate terms in the resulting sequence and observe that the

terms appear to alternate between odd and even numbers. Explain informally why the

numbers will continue to alternate in this way.

4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and

parallel lines. Identify these in two-dimensional figures.

NCSD Clarification

4.G.1 – Assessed on NCSD Benchmark 4 but needs to be addressed prior to PAWS

Vocabulary

Critical Vocabulary

algorithm, factors, inequalities, multiples, multiplicative inverse, quotient


area model, array, expanded form, expression, operation, place value, product

Resource

My Math Chapter 1 Place Value (7 days) ● Lesson 1 - Place Value

● Lesson 2 - Read and Write Multi-Digit Numbers

● Lesson 3 - Compare Numbers

● Lesson 4 - Order Numbers

● Lesson 5 - Use Place Value to Round

My Math Chapter 2 Add and Subtract Whole Numbers (9 days) ● Lesson 2 - Addition and Subtraction Patterns

● Lesson 3 - Add and Subtract Mentally

● Lesson 4 - Estimate Sums and Differences

● Lesson 5 - Add Whole Numbers

● Lesson 6 - Subtract Whole Numbers


● Lesson 9 - Solve Multi-Step Word Problems

My Math Chapter 3 Understand Multiplication and Division (10 days) ● Lesson 1 - Relate Multiplication and Division

● Lesson 3 - Multiplication as Comparison

● Lesson 4 - Compare to Solve Problems

● Lesson 5 - Multiplication Properties and Division Rules

● Lesson 6 - The Associative Property of Multiplication

● Lesson 7 - Factors and Multiples

○ Include more lessons covering Factors and Multiples

● Lesson 8 - Problem-Solving Investigation: Reasonable Answers


● Multiplication and Division

● Area and Perimeter


Standards

4.NBT.1 Recognize that in a multi-digit whole number, a digit in one place represents ten times what

it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying



concepts of place value and division.

4.NBT.3 Use place value understanding to round multi-digit whole numbers to any place.

4.NBT.5 Multiply a whole number of up to four digits by a one-digit whole number, and multiply

two two-digit numbers, using strategies based on place value and the properties of

operations. Illustrate and explain the calculation by using equations, rectangular arrays,

and/or area models.

4.NBT.6 Find whole-number quotients and remainders with up to four-digit dividends and one-digit

divisors, using strategies based on place value, the properties of operations, and/or the



4.OA.3 Solve multistep word problems posed with whole numbers and having whole-number

answers using the four operations, including problems in which remainders must be

interpreted. Represent these problems using equations with a letter standing for the

unknown quantity. Assess the reasonableness of answers using mental computation and

estimation strategies including rounding.

4.OA.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number

is a multiple of each of its factors. Determine whether a given whole number in the range

1–100 is a multiple of a given one-digit number. Determine whether a given whole number

in the range 1–100 is prime or composite.

4.MD.3 Apply the area and perimeter formulas for rectangles in real world and mathematical

problems. For example, find the width of a rectangular room given the area of the flooring

and the length, by viewing the area formula as a multiplication equation with an unknown

factor.

4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or

perpendicular lines, or the presence or absence of angles of a specified size. Recognize

right triangles as a category, and identify right triangles.

NCSD Clarification


Vocabulary

Critical Vocabulary

dividend, divisor, factors, inequalities, meter, multiples, remainder, yard


area, composite, formula, perimeter, prime

Resource

My Math Chapter 4 Multiply with One-Digit Numbers (11 days) ● Lesson 1 - Multiples of 10, 100, and 1000

● Lesson 2 - Round to Estimate Products

● Lesson 3 - omit

● Lesson 4 - Hands On: Use Models to Multiply

● Lesson 5 - Multiply by a Two-Digit Number

○ Focus on partial products, area model, or distributive property (not standard algorithm)

● Lesson 6 - omit


● Lesson 8 - Multiply with Regrouping



● Lesson 9 - Multiply by a Multi-Digit Number

● Lesson 10 - Problem Solve: Estimate or Exact Answer

● Lesson 11 - Multiply Across Zeros

My Math Chapter 5 Multiply with Two-Digit Numbers (7 days) ○ Focus on partial products, area model, or distributive property (not standard algorithm)

● Lesson 1 - Multiply by Tens

● Lesson 2 - Estimate Products

● Lesson 3 - Hands On: Use the Distributive Property to Multiply

● Lesson 4 - Multiply by a two-Digit Number


My Math Chapter 6 Divide by One-Digit Numbers (9 days) ○ Focus on partial products, area model, or distributive property (not standard algorithm)

● Lesson 1 - Divide Multiples of 10, 100, and 1,000

● Lesson 5 - Divide with Remainders

● Lesson 6 - Interpret Remainders

● Lesson 8 - Hands On: Distributive Property and Partial Quotients

● Lesson 9 - Divide Greater Numbers

● Lesson 10 - Quotients with Zeros


My Math Chapter 13 Perimeter and Area (7 days) ● Lesson 1 - Measure Perimeter

● Lesson 2 - Problem-Solving Investigations: Solve a Simpler Problem

● Lesson 3 - Hands On: Model Area

● Lesson 4 - Measure Area

● Lesson 5 - Relate Area and Perimeter


● Fractions/Decimals


Standards

4.OA.4 Find all factor pairs for a whole number in the range 1–100. Recognize that a whole number

is a multiple of each of its factors. Determine whether a given whole number in the range

1–100 is a multiple of a given one-digit number. Determine whether a given whole number

in the range 1–100 is prime or composite.

4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction

models, with attention to how the number and size of the parts differ even though the two

fractions themselves are the same size. Use this principle to recognize and generate

equivalent fractions.

4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by

creating common denominators or numerators, or by comparing to a benchmark fraction

such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the

same whole. Record the results of comparisons with symbols >, =, or <, and justify the

conclusions, e.g., by using a visual fraction model.

4.NF.3 Understand a fraction a/b with a > 1 as a sum of fractions 1 / b.

a. Understand addition and subtraction of fractions as joining and separating parts

referring to the same whole.

b. Decompose a fraction into a sum of fractions with the same denominator in more



than one way, recording each decomposition by an equation. Justify

decompositions, e.g., by using a visual fraction model. Examples: 3/8 = 1/8 + 1/8

+ 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.

c. Add and subtract mixed numbers with like denominators, e.g., by replacing each

mixed number with an equivalent fraction, and/or by using properties of operations

and the relationship between addition and subtraction.

d. Solve word problems involving addition and subtraction of fractions referring to the

same whole and having like denominators, e.g., by using visual fraction models and

equations to represent the problem.

4.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction by a

whole number.

a. Understand a fraction a/b as a multiple of 1/b. For example, use a visual fraction

model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the

equation 5/4 = 5 × (1/4).

b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to

multiply a fraction by a whole number. For example, use a visual fraction model to

express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n ×

(a/b) = (n × a)/b.)

c. Solve word problems involving multiplication of a fraction by a whole number, e.g.,

by using visual fraction models and equations to represent the problem. For

example, if each person at a party will eat 3/8 of a pound of roast beef, and there

will be 5 people at the party, how many pounds of roast beef will be needed?

Between what two whole numbers does your answer lie?

4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and

use this technique to add two fractions with respective denominators 10 and 100. (Students

who can generate equivalent fractions can develop strategies for adding fractions with

unlike denominators in general. But addition and subtraction with unlike denominators in

general is not a requirement at this grade.) For example, express 3/10 as 30/100, and add

3/10 + 4/100 = 34/100.

4.NF.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62

as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that

comparisons are valid only when the two decimals refer to the same whole. Record the

results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by

using a visual model.

4.G.3

Recognize a line of symmetry for a two-dimensional figure as a line across the figure such

that the figure can be folded along the line into matching parts. Identify line-symmetric

figures and draw lines of symmetry.

NCSD Clarification


Vocabulary

Critical Vocabulary

common denominator, decimal, decimal point, equivalent fraction, factors, multiples,

numerator




denominator, hundredths, improper fractions, mixed numbers

Resource

My Math Chapter 8 Fractions (11 days) ● Lesson 1 - Factors and Multiples

● Lesson 2 - Prime and Composite Numbers

● Lesson 3 - Hands On: Model Equivalent Fractions

● Lesson 4 - Equivalent Fractions

● Lesson 5 - Simplest Form

○ Use models

● Lesson 6 - Compare and Order Fractions

● Lesson 7 - Use Benchmark Fractions to Compare and Order

● Lesson 9 - Mixed Numbers

● Lesson 10 - Mixed Numbers and Improper Fractions

My Math Chapter 9 Operations with Fractions (10 days) ● Lesson 1 - Hands On: Use Models to Add Like Fractions

● Lesson 2 - Add Like Fractions

● Lesson 3 - Hands On: Use Models to Subtract Like Fractions

● Lesson 4 - Subtract Like Fractions

● Lesson 6 - Add Mixed Numbers

● Lesson 7 - Subtract Mixed Numbers

● Lesson 8 - Hands On: Model Fractions and Multiplication

● Lesson 9 - Multiply Fractions by Whole Numbers

My Math Chapter 10 Fractions and Decimals (10 days) ● Lesson 1 - Hands On: Place Value Through Tenths and Hundredths

● Lesson 2 - Tenths

● Lesson 3 - Hundredths

● Lesson 4 - Hands On: Model Decimals and Fractions

● Lesson 5 - Decimals and Fractions

● Lesson 6 - Use Place Value and Models to Add

● Lesson 7 - Compare and Order Decimals

● Lesson 8 - Problem-Solving Investigation: Extra or Missing Information

Mini Lessons on 4.G.3 (3 days) ● Standard 4.G.3 will not be on the benchmark, but it needs to be addressed prior to PAWS.


● Measurement

● Geometry

● Patterns and Sequences


Standards

4.OA.5 Generate a number or shape pattern that follows a given rule. Identify apparent features of

the pattern that were not explicit in the rule itself. For example, given the rule “Add 3” and

the starting number 1, generate terms in the resulting sequence and observe that the terms

appear to alternate between odd and even numbers. Explain informally why the numbers

will continue to alternate in this way.

4.MD.1 Know relative sizes of measurement units within one system of units including km, m, cm;

kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express



measurements in a larger unit in terms of a smaller unit. Record measurement equivalents

in a two column table. For example, know that 1 ft is 12 times as long as 1 in. Express the

length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the

number pairs (1, 12), (2, 24), (3, 36), …

4.MD.2 Use the four operations to solve word problems involving distances, intervals of time,

liquid volumes, masses of objects, and money, including problems involving simple

fractions or decimals, and problems that require expressing measurements given in a larger

unit in terms of a smaller unit. Represent measurement quantities using diagrams such as

number line diagrams that feature a measurement scale.

4.MD.4 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).

Solve problems involving addition and subtraction of fractions by using information

presented in line plots. For example, from a line plot find and interpret the difference in

length between the longest and shortest specimens in an insect collection.

4.MD.5 Recognize angles as geometric shapes that are formed wherever two rays share a common

endpoint, and understand concepts of angle measurement:

a. An angle is measured with reference to a circle with its center at the common

endpoint of the rays, by considering the fraction of the circular arc between the

points where the two rays intersect the circle. An angle that turns through 1/360 of a

circle is called a “one-degree angle,” and can be used to measure angles.

b. An angle that turns through n one-degree angles is said to have an angle measure of

n degrees.

4.MD.6 Measure angles in whole-number degrees using a protractor. Sketch angles of specified

measure.

4.MD.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping

parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve

addition and subtraction problems to find unknown angles on a diagram in real world and

mathematical problems, e.g., by using an equation with a symbol for the unknown angle

measure.

4.G.1 Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and

parallel lines. Identify these in two-dimensional figures.

4.G.2 Classify two-dimensional figures based on the presence or absence of parallel or

perpendicular lines, or the presence or absence of angles of a specified size. Recognize right

triangles as a category, and identify right triangles.

4.G.3 Recognize a line of symmetry for a two-dimensional figure as a line across the figure such

that the figure can be folded along the line into matching parts. Identify line-symmetric

figures and draw lines of symmetry.

Vocabulary

Critical Vocabulary

acute angle, angle, endpoint (vertex), line of symmetry, meter, obtuse angle, right angle,

yard


capacity, centimeter, cup, customary system, degree, gallon, gram, hour, intersecting lines,

interval (time), kilogram, line, line plot, line segment, liter, metric system, milliliter,



minute, ounce, parallel lines, pattern, perpendicular lines, pint, point, pound, protractor,

quart, ray

Resource

My Math Chapter 11 Customary Measurement (12 days) ● Lesson 1 - Customary Units of Length

● Lesson 2 - Convert Customary Units of Length

● Lesson 3 - Customary Units of Capacity

● Lesson 4 - Convert Customary Units of Capacity

● Lesson 5 - Customary Units of Weight

● Lesson 6 - Convert Customary Units of Weight

● Lesson 7 - Convert Units of Time

● Lesson 8 - Display Measurement Data in a Line Plot

● Lesson 9 - Solve Measurement Problems (More lessons over line plot are needed.)


My Math Chapter 12 Metric Measurement (7 days) ● Lesson 1 - Metric Units of Length

● Lesson 2 - Metric Units of Capacity

● Lesson 3 - Metric Units of Mass

● Lesson 5 - Convert Metric Units

● Lesson 6 - Solve Measurement Problems

My Math Chapter 14 Geometry (13 days) ● Lesson 1 - Draw Points, Lines, and Rays

● Lesson 2 - Draw Parallel and Perpendicular Lines

● Lesson 3 - Hands On: Model Angles

● Lesson 4 - Classify Angles

● Lesson 5 - Measure Angles

● Lesson 6 - Draw Angles

● Lesson 7 - Solve Problems with Angles

● Lesson 8 - Triangles

● Lesson 9 - Quadrilaterals

● Lesson 10 - Draw Lines of Symmetry

● Lesson 11 - Problem-Solving Investigation: Make a Model

My Math Chapter 7 Patterns and Sequences (11 days) ● Lesson 1 - Non-numeric Patterns

● Lesson 2 - Numeric Patterns

● Lesson 3 - Sequences


● Lesson 5 - Addition and Subtraction Rules

● Lesson 6 - Multiplication and Division Rules

● Lesson 7 - Order of Operations

● Lesson 8 - Hands On: Equations with Two Operations

● Lesson 9 - Equations with Multiple Operations



5th Grade Math Pacing Guide The Pacing Guide has been aligned to Wyoming State Standards with consideration to the Critical Areas of Focus defined by Common Core State Standards for Math and the Wyoming PAWS Blueprint.


● Place Value

● Multiplication and Division


Standards

Understand the place value system.

5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as

it represents in the place to its right and 1/10 of what it represents in the place to its left.

5.NBT.2 Explain patterns in the number of zeros of the product when multiplying a number by

powers of 10, and explain patterns in the placement of the decimal point when a decimal is

multiplied or divided by a power of 10. Use whole-number exponents to denote powers of

10.

5.NBT.3 Read, write, and compare decimals to thousandths.

a. Read and write decimals to thousandths using base-ten numerals, number names,

and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 ×

(1/100) + 2 × (1/1000).

b. Compare two decimals to thousandths based on meanings of the digits in each

place, using >, =, and < symbols to record the results of comparisons.

5.NBT.5 Fluently multiply multi-digit whole numbers using the standard algorithm.

5.NBT.6 Find whole-number quotients of whole numbers with up to four-digit dividends and two-

digit divisors, using strategies based on place value, the properties of operations, and/or the



Vocabulary

Critical Vocabulary

braces, brackets, composite, cubed, dividend, divisor, expression, factors, hundredths,

parentheses, prime factorization, product, quotient, rule, squared, standard form, tenths,

thousandths


algorithm, base, decimal point (and), expanded form, inequalities, number line, remainder

Resource

My Math Chapter 1 Place Value (9 days) ● Lesson 1 - Place Value Through Millions

● Lesson 2 - Compare and Order Whole Number Through Millions

● Lesson 3 - Hands On: Model Fractions and Decimals

● Lesson 4 - Represent Decimals

● Lesson 5 - Hands On: Understand Place Value

● Lesson 6 - Place Value Through Thousandths

● Lesson 7 - Compare Decimals



● Lesson 8 - Order Whole Numbers and Decimals

● Lesson 9 - Problem-Solving Investigation: Use the Four-Step Plan

My Math Chapter 2 Multiply Whole Numbers (10 days) ● Lesson 1 - Prime Factorization

● Lesson 2 - Hands On: Prime Factorization Patterns

● Lesson 3 - Powers and Exponents

● Lesson 4 - Multiplication Patterns

● Lesson 5 - Problem-Solving Investigation: Make a Table

● Lesson 6 - Hands On: Use Partial Products and the Distributive Property



● Lesson 9 - Multiply by One-Digit Numbers

● Lesson 10 - Multiply by Two-Digit Numbers

My Math Chapter 3 Divide by a One-Digit Divisor (13 days) ● Lesson 1 - Relate Division to Multiplication

● Lesson 2 - Hands On: Division Models

● Lesson 3 - Two-Digit Dividends

● Lesson 4 - Division Patterns

● Lesson 5 - Estimate Quotients

● Lesson 6 - Hands On: Division Models with Greater Numbers

● Lesson 7 - Hands On: Distributive Property and Partial Quotients

● Lesson 8 - Divide Three- and Four-Digit Dividends

● Lesson 9 - Place the First Digit

● Lesson 10 - Quotients with Zeros

● Lesson 11 - Hands On: Use Models to Interpret the Remainder

● Lesson 12 - Interpret the Remainder

● Lesson 13 - Problem-Solving Investigation: Determine Extra or Missing Information

My Math Chapter 4 Divide by a Two-Digit Divisor (6 days) ● Lesson 1 - Estimate Quotients

● Lesson 2 - Hands On: Divide Using Base-Ten Blocks

● Lesson 3 - Divide by a Two-Digit Divisor

● Lesson 4 - Adjust Quotients

● Lesson 5 - Divide Greater Numbers

● Lesson 6 - Problem-Solving Investigation: Solve a Simpler Problem


● Algebraic Thinking, Introduction to Fractions and Decimals


Standards

5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions

with these symbols.

5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical

expressions without evaluating them. For example, express the calculation “add 8 and 7,

then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as

large as 18932 + 921, without having to calculate the indicated sum or product.

5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships

between corresponding terms. Form ordered pairs consisting of corresponding terms from

the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the



rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting

number 0, generate terms in the resulting sequences, and observe that the terms in one

sequence are twice the corresponding terms in the other sequence. Explain informally why

this is so.

5.NBT.4 Use place value understanding to round decimals to any place.

5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or

drawings and strategies based on place value, properties of operations, and/or the

relationship between addition and subtraction; relate the strategy to a written method and

explain the reasoning used.

NCSD clarification

5.NBT.7 - Add and subtract decimals will be assessed.

5.NF.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve

word problems involving division of whole numbers leading to answers in the form of

fractions or mixed numbers, e.g., by using visual fraction models or equations to represent

the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4

multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each

person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by

weight, how many pounds of rice should each person get? Between what two whole

numbers does your answer lie?

5.NF.5 Interpret multiplication as scaling (resizing), by:

a. Comparing the size of a product to the size of one factor on the basis of the size of

the other factor, without performing the indicated multiplication.

NCSD clarification

5.NF.5 – Only 5.NF.5a addressed in this section of the pacing guide

Vocabulary

Critical Vocabulary

braces, brackets, dividend, divisor, expression, factors, greatest common factor (GCF),

hundredths, least common denominator, least common multiple, mixed numbers,

parentheses, quotient, rule, scaling, simplest form, standard form, tenths, thousandths

Supporting

Vocabulary algorithm, decimal point (and), denominator, expanded form, inequalities, multiples,

number line, numerator

Resources

My Math Chapter 7 Expressions and Patterns (6 days)

● Lesson 1 - Hands On: Numerical Expressions

● Lesson 2 - Order of Operations

● Lesson 3 - Write Numerical Expressions

● Lesson 4 - Problem-Solving Investigation: Work Backwards

● Lesson 5 - Hands On: Generate Patterns

● Lesson 6 - Patterns

My Math Chapter 5 Add and Subtract Decimals (10 days)

● Lesson 1 - Round Decimals


● Lesson 3 - Problem-Solving Investigation: Estimate or Exact Answer

● Lesson 4 - Hands On: Add Decimals Using Base-Ten Blocks

● Lesson 5 - Hands On: Add Decimals Using Models



● Lesson 6 - Add Decimals

● Lesson 7 - Addition Properties

● Lesson 8 - Hands On: Subtract Decimals Using Base-Ten Blocks

● Lesson 9 - Hands On: Subtract Decimals Using Models

● Lesson 10 - Subtract Decimals

My Math Chapter 6 Multiply and Divide Decimals (14 days)

● Lesson 1 - Estimate Products of Whole Numbers and Decimals

● Lesson 2 - Hands On: Use Models to Multiply

● Lesson 3 - Multiply Decimals by Whole Numbers

● Lesson 4 - Hands On: Use Models to Multiply Decimals

● Lesson 5 - Multiply Decimals

● Lesson 6 - Multiply Decimals by Powers of Ten


● Lesson 8 - Multiplication Properties


● Lesson 10 - Hands On: Divide by Decimals

● Lesson 11 - Divide Decimals by Whole Numbers

● Lesson 12 - Hands On: Use Models to Divide Decimals

● Lesson 13 - Divide Decimals

● Lesson 14 - Divide Decimals by Powers of Ten

My Math Chapter 8 Fractions and Decimals (8 days)

● Lesson 1 - Fractions and Division

● Lesson 2 - Greatest Common Factor

● Lesson 3 - Simplest Form


● Lesson 5 - Least Common Multiple

● Lesson 6 - Compare Fractions

● Lesson 7 - Hands On: Use Models to Write Fractions as Decimals

● Lesson 8 - Write Fractions as Decimals

34 Days Pacing Guide Section 3 All fraction computation in this section (+ - * /)

● Fraction Operations

● Volume


Standards

5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by

replacing given fractions with equivalent fractions in such a way as to produce an

equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 =

8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same

whole, including cases of unlike denominators, e.g., by using visual fraction models or

equations to represent the problem. Use benchmark fractions and number sense of fractions

to estimate mentally and assess the reasonableness of answers. For example, recognize an

incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

5.NF.3 Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve

word problems involving division of whole numbers leading to answers in the form of

fractions or mixed numbers, e.g., by using visual fraction models or equations to represent

the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4



multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4 people each

person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by

weight, how many pounds of rice should each person get? Between what two whole

numbers does your answer lie?

5.NF.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole

number by a fraction.

a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts;

equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a

visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this

equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares

of the appropriate unit fraction side lengths, and show that the area is the same as

would be found by multiplying the side lengths. Multiply fractional side lengths to

find areas of rectangles, and represent fraction products as rectangular areas.

5.NF.5 Interpret multiplication as scaling (resizing), by:

a. Comparing the size of a product to the size of one factor on the basis of the size of

the other factor, without performing the indicated multiplication.

b. Explaining why multiplying a given number by a fraction greater than 1 results in a

product greater than the given number (recognizing multiplication by whole

numbers greater than 1 as a familiar case); explaining why multiplying a given

number by a fraction less than 1 results in a product smaller than the given number;

and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of

multiplying a/b by 1.

5.NF.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by

using visual fraction models or equations to represent the problem.

5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole

numbers and whole numbers by unit fractions. (Students able to multiply fractions in

general can develop strategies to divide fractions in general, by reasoning about the

relationship between multiplication and division. But division of a fraction by a fraction is

not a requirement at this grade.)

a. Interpret division of a unit fraction by a non-zero whole number, and compute such

quotients. For example, create a story context for (1/3) ÷ 4, and use a visual

fraction model to show the quotient. Use the relationship between multiplication and

division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3.

b. Interpret division of a whole number by a unit fraction, and compute such quotients.

For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to

show the quotient. Use the relationship between multiplication and division to

explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

c. Solve real world problems involving division of unit fractions by non-zero whole

numbers and division of whole numbers by unit fractions, e.g., by using visual

fraction models and equations to represent the problem. For example, how much

chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How

many 1/3-cup servings are in 2 cups of raisins?

5.MD.1 Convert among different-sized standard measurement units within a given measurement



system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real

world problems.

5.MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume

measurement.

a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit”

of volume, and can be used to measure volume.

b. A solid figure which can be packed without gaps or overlaps using n unit cubes is

said to have a volume of n cubic units.

5.MD.4 Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised

units.

5.MD.5 Relate volume to the operations of multiplication and addition and solve real world and

mathematical problems involving volume.

a. Find the volume of a right rectangular prism with whole-number side lengths by

packing it with unit cubes, and show that the volume is the same as would be found

by multiplying the edge lengths, equivalently by multiplying the height by the area

of the base. Represent threefold whole-number products as volumes, e.g., to

represent the associative property of multiplication.

b. Apply the formulas V=l×w×h and V=b×h for rectangular prisms to find volumes of

right rectangular prisms with whole number edge lengths in the context of solving

real world and mathematical problems.

c. Recognize volume as additive. Find volumes of solid figures composed of two non-

overlapping right rectangular prisms by adding the volumes of the non- overlapping

parts, applying this technique to solve real world problems.

Vocabulary

Critical

Vocabulary cubed, expression, improper fractions, mixed numbers, rule, simplest form, volume

Supporting

Vocabulary composite figure, cubic, denominator, height, measure, number line, numerator

Resources

My Math Chapter 9 Add and Subtract Fractions (13 days) ● Lesson 1 - Round Fractions

● Lesson 2 - Add Like Fractions

● Lesson 3 - Subtract Like Fractions

● Lesson 4 - Hands On: Use Models to Add Unlike Fractions

● Lesson 5 - Add Unlike Fractions

● Lesson 6 - Hands On: Use Models to Subtract Unlike Fractions

● Lesson 7 - Subtract Unlike Fractions

● Lesson 8 - Problem-Solving Investigation: Determine Reasonable Answers


● Lesson 10 - Hands On: Use Models to Add Mixed Numbers

● Lesson 11 - Add Mixed Numbers

● Lesson 12 - Subtract Mixed Numbers

● Lesson 13 - Subtract with Renaming

My Math Chapter 10 Multiply and Divide Fractions (12 days) ● Lesson 1 - Hands On: Part of a Number

● Lesson 2 - Estimate Products of Fractions



● Lesson 3 - Hands On: Model Fraction Multiplication

● Lesson 4 - Multiply Whole Numbers and Fractions

● Lesson 5 - Hands On: Use Models to Multiply Fractions

● Lesson 6 - Multiply Fractions

● Lesson 7 - Multiply Mixed Numbers

● Lesson 8 - Hands On: Multiplication as Scaling

● Lesson 9 - Hands On: Division with Unit Fractions

● Lesson 10 - Divide Whole Numbers by Unit Fractions

● Lesson 11 - Divide Unit Fractions by Whole Numbers

● Lesson 12 - Problem-Solving Investigation: Draw a Diagram

My Math Chapter 12 Geometry (5 days) ● Lesson 8 - Hands On: Use Models to Find Volume

● Lesson 9 - Volume of Prisms

● Lesson 10 - Hands On: Build Composite Figures

● Lesson 11 - Volume of Composite Figures

● Lesson 12 - Problem-Solving Investigation: Make a Model


● Measurement

● Data

● Geometry


Standards

5.MD.1 Convert among different-sized standard measurement units within a given measurement

system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real

world problems.

5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8).

Use operations on fractions for this grade to solve problems involving information

presented in line plots. For example, given different measurements of liquid in identical

beakers, find the amount of liquid each beaker would contain if the total amount in all the

beakers were redistributed equally.

5.G.1 Use a pair of perpendicular number lines, called axes, to define a coordinate system, with

the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a

given point in the plane located by using an ordered pair of numbers, called its coordinates.

Understand that the first number indicates how far to travel from the origin in the direction

of one axis, and the second number indicates how far to travel in the direction of the second

axis, with the convention that the names of the two axes and the coordinates correspond

(e.g., x-axis and x-coordinate, y-axis and y-coordinate).

5.G.2 Represent real world and mathematical problems by graphing points in the first quadrant of

the coordinate plane, and interpret coordinate values of points in the context of the

situation.

5.G.3 Understand that attributes belonging to a category of two-dimensional figures also belong

to all subcategories of that category. For example, all rectangles have four right angles and

squares are rectangles, so all squares have four right angles.

5.G.4 Classify two-dimensional figures in a hierarchy based on properties.



Vocabulary

Critical

Vocabulary capacity, convert, coordinate plane, customary system, metric system, ordered pairs, plane,

quadrant, rule, scalene triangle, scaling, solid figure, vertex, volume, x-axis, x-coordinate, y-

axis, y-coordinate

Supporting

Vocabulary acute angle, area, axis, composite figure, cube, cubic, edges, equilateral triangle, faces,

height, intersecting lines, isosceles triangle, kilo, line plot, measure, measurement unit,

milli, obtuse angle, obtuse triangle, parallel, parallelogram, perimeter, polygon,

quadrilateral, rhombus, right angle, trapezoid

Resource

My Math Chapter 7 Expressions and Patterns (2 days) ● Lesson 8 - Ordered Pair

● Lesson 9 - Graph Patterns

My Math Chapter 11 Measurement (10 days) ● Lesson 1 - Hands On: Measure with a Ruler

● Lesson 2 - Convert Customary Units of Length

● Lesson 3 - Problem-Solving Investigation: Use Logical Reasoning

● Lesson 4 - Hands On: Estimate and Measure Weight

● Lesson 5 - Convert Customary Units of Weight

● Lesson 6 - Hands On: Estimate and Measure Capacity

● Lesson 7 - Convert Customary Units of Capacity

● Lesson 8 - Display Measurement Data on a Line Plot

● Lesson 9 - Hands On: Metric Rulers

● Lesson 10 - Convert Metric Units of Length

My Math chapter 12 Geometry (7 days) ● Lesson 1 - Polygons

● Lesson 2 - Hands On: Sides and Angles of Triangles

● Lesson 3 - Classify Triangles

● Lesson 4 - Hands On: Sides and Angles of Quadrilaterals

● Lesson 5 - Classify Quadrilaterals

● Lesson 6 - Hands On: Build Three-Dimensional Figures

● Lesson 7 - Three-Dimensional Figures



Course 1 Math (6th Grade) Pacing Guide The Pacing Guide has been aligned to Wyoming State Standards with consideration to the Critical Areas of Focus defined by Common Core State Standards for Math and the Wyoming PAWS Blueprint.

40 Days Pacing Guide Section 1: The Number System

● Compute with Multi-Digit Numbers

● Multiply and Divide Fractions

Standards

6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division

of fractions by fractions, e.g., by using visual fraction models and equations to represent

the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction

model to show the quotient; use the relationship between multiplication and division to

explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.)

How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally?

How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip

of land with length 3/4 mi and area 1/2 square mi?

6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.

6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard

algorithm for each operation.

6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the

least common multiple of two whole numbers less than or equal to 12. Use the distributive

property to express a sum of two whole numbers 1–100 with a common factor as a

multiple of a sum of two whole numbers with no common factor. For example, express 36

+ 8 as 4 (9 + 2).

6.NS.5 Understand that positive and negative numbers are used together to describe quantities

having opposite directions or values (e.g., temperature above/ below zero, elevation

above/below sea level, credits/debits, positive/negative electric charge); use positive and

negative numbers to represent quantities in real-world contexts, explaining the meaning of

0 in each situation.

6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams

and coordinate axes familiar from previous grades to represent points on the line and in the

plane with negative number coordinates.

a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0

on the number line; recognize that the opposite of the opposite of a number is the

number itself, e.g., –(–3) = 3, and that 0 is its own opposite.

b. Understand signs of numbers in ordered pairs as indicating locations in quadrants

of the coordinate plane; recognize that when two ordered pairs differ only by signs,

the locations of the points are related by reflections across one or both axes.

c. Find and position integers and other rational numbers on a horizontal or vertical

number line diagram; find and position pairs of integers and other rational numbers

on a coordinate plane.

6.NS.7 Understand ordering and absolute value of rational numbers.



a. Interpret statements of inequality as statements about the relative position of two

numbers on a number line diagram. For example, interpret –3 > –7 as a statement

that –3 is located to the right of –7 on a number line oriented from left to right.

b. Write, interpret, and explain statements of order for rational numbers in real-world

contexts. For example, write –3 oC > –7 oC to express the fact that –3 oC is

warmer than –7 oC.

c. Understand the absolute value of a rational number as its distance from 0 on the

number line; interpret absolute value as magnitude for a positive or negative

quantity in a real-world situation. For example, for an account balance of –30

dollars, write |–30| = 30 to describe the size of the debt in dollars.

d. Distinguish comparisons of absolute value from statements about order. For

example, recognize that an account balance less than –30 dollars represents a debt

greater than 30 dollars.

6.NS.8 Solve real-world and mathematical problems by graphing points in all four quadrants of

the coordinate plane. Include use of coordinates and absolute value to find distances

between points with the same first coordinate or the same second coordinate.

Vocabulary

Critical Vocabulary

bar notation, exponents


difference, estimate, factor, multiple, product, quotient, rational number, simplest form,

sum

Resource

Glencoe Math Course 1 Chapter 3 Compute with Multi-Digit Numbers (20 days) ● Lesson 1 - Add and Subtract Decimals


● Lesson 3 - Multiply Decimals by Whole Numbers

● Lesson 4 - Multiply Decimals by Decimals

● Lesson 5 - Divide Multi-Digit Numbers


● Lesson 7 - Divide Decimals by Whole Numbers

● Lesson 8 - Divide Decimals by Decimals

Glencoe Math Course 1 Chapter 4 Multiply and Divide Fraction (20 days) ● Lesson 1 - Estimate Products of Fractions

● Lesson 2 - Multiply Fractions and Whole Numbers


● Lesson 4 - Multiply Mixed Numbers

● Lesson 5 - Convert Measurement Units

● Lesson 6 - Divide Whole Numbers by Fractions

● Lesson 7 - Divide Fractions

● Lesson 8 - Divide Mixed Numbers




● Ratios and Proportional Relationships

● Fractions, Decimals and Percent

Standards

6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship

between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A

received, candidate C received nearly three votes.”

6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use

rate language in the context of a ratio relationship. For example, “This recipe has a

ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of

sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.”

6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by

reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams,

or equations.

a. Make tables of equivalent ratios relating quantities with whole number

measurements, find missing values in the tables, and plot the pairs of values on the

coordinate plane. Use tables to compare ratios.

b. Solve unit rate problems including those involving unit pricing and constant speed. For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns

could be mowed in 35 hours? At what rate were lawns being mowed.

c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100

times the quantity); solve problems involving finding the whole, given a part and

the percent.

d. Use ratio reasoning to convert measurement units; manipulate and transform units

appropriately when multiplying or dividing quantities.

6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division

of fractions by fractions, e.g., by using visual fraction models and equations to represent

the problem. For example, create a story context for (2/3) ÷ (3/4) and use a visual fraction

model to show the quotient; use the relationship between multiplication and division to

explain that (2/3) ÷ (3/4) = 8/9 because 3/4 of 8/9 is 2/3. (In general, (a/b) ÷ (c/d) = ad/bc.)

How much chocolate will each person get if 3 people share 1/2 lb of chocolate equally?

How many 3/4-cup servings are in 2/3 of a cup of yogurt? How wide is a rectangular strip

of land with length 3/4 mi and area 1/2 square mi?

6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the

least common multiple of two whole numbers less than or equal to 12. Use the distributive

property to express a sum of two whole numbers 1–100 with a common factor as a

multiple of a sum of two whole numbers with no common factor. For example, express 36

+ 8 as 4 (9 + 2).

Vocabulary

Critical Vocabulary

equivalent ratios, percent, ratio, scaling




estimate, factor, multiple, ordered pair, proportion, unit rate

Resource

Glencoe Math Course 1 Chapter 1 Ratios and Rates (18 days) ● Lesson 1 - Factors and Multiples

● Lesson 2 - Ratios

● Lesson 3 - Rates

● Lesson 4 - Ratio Tables

● Lesson 5 - Graph Ratio Tables

● Lesson 6 - Equivalent Ratios

● Lesson 7 - Ratio and Rate Problems

Glencoe Math Course 1 Chapter 2 Fractions, Decimals, and Percents (22 days) ● Lesson 1 - Decimals and Fractions

● Lesson 2 - Percent and Fractions

● Lesson 3 - Percents and Decimals

● Lesson 4 - Omit

● Lesson 5 - Compare and Order Fractions, Decimals and Percents

● Lesson 6 - Estimate with Percent

● Lesson 7 - Percent of a Number

● Lesson 8 - Solve Percent Problems


● Expressions and Equations

● Functions and Inequalities

● Integers and the Coordinate Plane

Standards

6.NS.5 Understand that positive and negative numbers are used together to describe quantities

having opposite directions or values (e.g., temperature above/ below zero, elevation

above/below sea level, credits/debits, positive/negative electric charge); use positive and

negative numbers to represent quantities in real-world contexts, explaining the meaning of

0 in each situation.

6.NS.6 Understand a rational number as a point on the number line. Extend number line diagrams

and coordinate axes familiar from previous grades to represent points on the line and in the

plane with negative number coordinates.

a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0

on the number line; recognize that the opposite of the opposite of a number is the

number itself, e.g., –(–3) = 3, and that 0 is its own opposite.

b. Understand signs of numbers in ordered pairs as indicating locations in quadrants

of the coordinate plane; recognize that when two ordered pairs differ only by signs,

the locations of the points are related by reflections across one or both axes.

c. Find and position integers and other rational numbers on a horizontal or vertical

number line diagram; find and position pairs of integers and other rational numbers

on a coordinate plane.

6.NS.7 Understand ordering and absolute value of rational numbers.



6.EE.1 Write and evaluate numerical expressions involving whole-number exponents.

6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.

a. Write expressions that record operations with numbers and with letters standing for

numbers. For example, express the calculation “Subtract y from 5” as 5 – y.

b. Identify parts of an expression using mathematical terms (sum, term, product,

factor, quotient, coefficient); view one or more parts of an expression as a single

entity. For example, describe the expression 2 (8 + 7) as a product of two factors;

view (8 + 7) as both a single entity and a sum of two terms.

c. Evaluate expressions at specific values of their variables. Include expressions that

arise from formulas used in real-world problems. Perform arithmetic operations,

including those involving whole number exponents, in the conventional order when

there are no parentheses to specify a particular order (Order of Operations). For

example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area

of a cube with sides of length s = 1/2.

6.EE.3 Apply the properties of operations to generate equivalent expressions. For example, apply

the distributive property to the expression 3 (2 + x) to produce the equivalent expression 6

+ 3x; apply the distributive property to the expression 24x + 18y to produce the

equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce

the equivalent expression 3y.

6.EE.4 Identify when two expressions are equivalent (i.e., when the two expressions name the

same number regardless of which value is substituted into them). For example, the

expressions y + y + y and 3y are equivalent because they name the same number

regardless of which number y stands for.

6.EE.5 Understand solving an equation or inequality as a process of answering a question: which

values from a specified set, if any, make the equation or inequality true? Use substitution

to determine whether a given number in a specified set makes an equation or inequality

true.

6.EE.6 Use variables to represent numbers and write expressions when solving a real-world or

mathematical problem; understand that a variable can represent an unknown number, or,

depending on the purpose at hand, any number in a specified set.

6.EE.7 Solve real-world and mathematical problems by writing and solving equations of the form

x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.

6.EE.8 Write an inequality of the form x > c or x < c to represent a constraint or condition in a

real-world or mathematical problem. Recognize that inequalities of the form x > c or x < c

have infinitely many solutions; represent solutions of such inequalities on number line

diagrams.

6.EE.9 Use variables to represent two quantities in a real-world problem that change in

relationship to one another; write an equation to express one quantity, thought of as the

dependent variable, in terms of the other quantity, thought of as the independent variable.

Analyze the relationship between the dependent and independent variables using graphs

and tables, and relate these to the equation. For example, in a problem involving motion at

constant speed, list and graph ordered pairs of distances and times, and write the

equation d = 65t to represent the relationship between distance and time.



Vocabulary

Critical Vocabulary

algebraic expressions, coefficient, dependent variable, distributive property, independent

variable, quadrant, term


absolute value, coordinate plane, equation, evaluate, factor, function, inequality, integers,

ordered pair, simplify

Resource

Glencoe Math Course 1 Chapter 6 Expressions (15 days) ● Lesson 1 - Powers and Exponents

● Lesson 2 - Numerical Expressions

● Lesson 3 - Algebra: Variables and Expressions

● Lesson 4 - Algebra: Write Expressions

● Lesson 5 - Algebra:Properties

● Lesson 6 - Distributed Property

● Lesson 7 - Equivalent Expressions

Glencoe Math Course 1 Chapter 7 Equations (12 days) ● Lesson 1 - Equations

● Lesson 2 - Solve and Write Addition Equations

● Lesson 3 - Solve and Write Subtraction Equations

● Lesson 4 - Solve and Write Multiplication Equations

● Lesson 5 - Solve and Write Division Equations

Glencoe Math Course 1 Chapter 8 Functions and Inequalities (15 days) ● Lesson 1 - Function Tables

● Lesson 2 - Function Rules

● Lesson 3 - Functions and Equations

● Lesson 4 - Multiple Representations of Functions

● Lesson 5 - Inequalities

● Lesson 6 - Write and Graph Inequalities

● Lesson 7 - Solve One-Step Inequalities

Glencoe Math Course 1 Chapter 5 Integers and the Coordinate Plane (6 days) ● Lesson 1 - Integers and Graphing

● Lesson 2 - Absolute Value

● Lesson 3 - Compare and Order Integers

● Lesson 4 - omit

● Lesson 5 - omit

● Lesson 6 - Coordinate Plane

● Lesson 7 - Graph on the Coordinate Plane


● Statistics and Probability

● Area, Volume, and Surface Area

Standards

6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by

composing into rectangles or decomposing into triangles and other shapes; apply these

techniques in the context of solving real-world and mathematical problems.

6.G.2 Find the volume of a right rectangular prism with fractional edge lengths by packing it



with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is

the same as would be found by multiplying the edge lengths of the prism. Apply the

formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional

edge lengths in the context of solving real-world and mathematical problems.

6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates

to find the length of a side joining points with the same first coordinate or the same second

coordinate. Apply these techniques in the context of solving real-world and mathematical

problems.

6.G.4 Represent three-dimensional figures using nets made up of rectangles and triangles, and

use the nets to find the surface area of these figures. Apply these techniques in the context

of solving real-world and mathematical problems.

6.SP.1 Recognize a statistical question as one that anticipates variability in the data related to the

question and accounts for it in the answers

6.SP.2 Understand that a set of data collected to answer a statistical question has a distribution

which can be described by its center, spread, and overall shape

6.SP.3 Recognize that a measure of center for a numerical data set summarizes all of its values

with a single number, while a measure of variation describes how its values vary with a

single number.

6.SP.4 Display numerical data in plots on a number line, including dot plots, histograms, and box

plots.

6.SP.5 Summarize numerical data sets in relation to their context, such as by:

a. Reporting the number of observations.

b. Describing the nature of the attribute under investigation, including how it was

measured and its units of measurement.

c. Giving quantitative measures of center (median and/or mean) and variability

(interquartile range and/or mean absolute deviation), as well as describing any

overall pattern and any striking deviations from the overall pattern with reference

to the context in which the data were gathered.

d. Relating the choice of measures of center and variability to the shape of the data

distribution and the context in which the data were gathered.

Vocabulary

Critical

Vocabulary

composite figure, interquartile range, mean/average, mean absolute deviation, measures of

center, median, mode, outliers, quartiles, range, surface area, vertices/vertex, volume

Supporting

Vocabulary

trapezoid, dimensions, rectangular prism, square pyramid, slant height, square units, cubic

units, distribution, symmetric

Resource

Glencoe Math Course 1 Chapter 9 Area (11 days) ● Lesson 1 - Area of Parallelograms

● Lesson 2 - Area of Triangles

● Lesson 3 - Area of Trapezoids

● Lesson 4 - Changes in Dimension

● Lesson 5 - Polygons on the Coordinate Plane




Glencoe Math Course 1 Chapter 10 Volume and Surface Area (12 days) ● Lesson 1 - Volume of Rectangular Prisms

● Lesson 2 - Volume of Triangular Prisms

● Lesson 3 - Surface Area of Rectangular Prisms

● Inquiry Lab - Nets of Triangular Prisms

● Lesson 4 - Surface Area of Triangular Prisms

● Inquiry Lab - Nets of Pyramids

● Lesson 5 -Surface Area of Pyramids

Glencoe Math Course 1 Chapter 11 Statistical Measure (11 days) ● Lesson 1 - Mean

● Lesson 2 - Median and Mode

● Lesson 3 - Measures of Variation

● Lesson 4 - Mean absolute Deviation

● Lesson 5 - Appropriate Measures

Glencoe Math Course Chapter 12 Statistical Displays (11 days) ● Lesson 1 - Line Plots

● Lesson 2 - Histograms

● Lesson 3 - Box Plots

● Lesson 4 - Shape and Data Distributions

● Lesson 5 - Interpret Line Graphs

● Lesson 6 - Select an Appropriate Display





● The Number System

Standards

7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract

rational numbers; represent addition and subtraction on a horizontal or vertical number line

diagram.

a. Describe situations in which opposite quantities combine to make 0. For example,

a hydrogen atom has 0 charge because its two constituents are oppositely charged.

b. Understand p + q as the number located a distance |q| from p, in the positive or

negative direction depending on whether q is positive or negative. Show that a

number and its opposite have a sum of 0 (are additive inverses). Interpret sums of

rational numbers by describing real-world contexts.

c. Understand subtraction of rational numbers as adding the additive inverse, p – q =

p + (–q). Show that the distance between two rational numbers on the number line

is the absolute value of their difference, and apply this principle in real-world

contexts.

d. Apply properties of operations as strategies to add and subtract rational numbers.

7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions

to multiply and divide rational numbers.

a. Understand that multiplication is extended from fractions to rational numbers by

requiring that operations continue to satisfy the properties of operations,

particularly the distributive property, leading to products such as (–1)(–1) = 1 and

the rules for multiplying signed numbers. Interpret products of rational numbers by

describing real-world contexts.

b. Understand that integers can be divided, provided that the divisor is not zero, and

every quotient of integers (with non-zero divisor) is a rational number. If p and q

are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers

by describing real world contexts.

c. Apply properties of operations as strategies to multiply and divide rational

numbers.

d. Convert a rational number to a decimal using long division; know that the decimal

form of a rational number terminates in 0s or eventually repeats.

7.NS.3 Solve real-world and mathematical problems involving the four operations with rational

numbers. (Computations with rational numbers extend the rules for manipulating fractions

to complex fractions.

Vocabulary

Critical

Vocabulary

additive inverse, integer, opposites, rational number, repeating decimal, terminating

decimal



Supporting

Vocabulary

bar notation

Resource

Glencoe Math Course 2 Chapter 3 Integers (14 days) ● Lesson 1 - Integers and Absolute Value

● Lesson 2 - Add Integers

● Lesson 3 - Subtract Integers

● Lesson 4 - Multiply Integers

● Lesson 5 - Divide Integers

Glencoe Math Course 2 Chapter 4 Rational Numbers (17 days) ● Lesson 1 - Terminating and REpeating Decimals

● Lesson 2 - Compare and Order Rational Numbers

● Lesson 3 - Add and Subtract Like Fractions

● Lesson 4 - Add and Subtract Unlike Fractions

● Lesson 5 - Add and Subtract Mixed Numbers


● Lesson 7 - Convert Between Systems

● Lesson 8 - Divide Fractions


● Expressions and Equations

Standards

7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear

expressions with rational coefficients.

7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed

light on the problem and how the quantities in it are related. For example, a + 0.05a =

1.05a means that “increase by 5%” is the same as “multiply by 1.05.”

7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative

rational numbers in any form (whole numbers, fractions, and decimals), using tools

strategically. Apply properties of operations to calculate with numbers in any form;

convert between forms as appropriate; and assess the reasonableness of answers using

mental computation and estimation strategies. For example: If a woman making $25 an

hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50,

for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center

of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from

each edge; this estimate can be used as a check on the exact computation.

7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and

construct simple equations and inequalities to solve problems by reasoning about the

quantities.

a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r,

where p, q, and r are specific rational numbers. Solve equations of these forms

fluently. Compare an algebraic solution to an arithmetic solution, identifying the

sequence of the operations used in each approach. For example, the perimeter of a

rectangle is 54 cm. Its length is 6 cm. What is its width?

b. Solve word problems leading to inequalities of the form px + q > r or px + q < r,



where p, q, and r are specific rational numbers. Graph the solution set of the

inequality and interpret it in the context of the problem. For example: As a

salesperson, you are paid $50 per week plus $3 per sale. This week you want your

pay to be at least $100. Write an inequality for the number of sales you need to

make, and describe the solutions.

Vocabulary

Critical

Vocabulary

constant, equivalent expressions, like terms

Supporting

Vocabulary

additive identity, algebraic expressions, associative property, coefficient, commutative

property, dependent variable, distributive property, independent variable, factored form,

factoring, linear expression, monomial, simplest form (factoring), solution set

Resource

Glencoe Math Course 2 Chapter 5 Expressions (17 days) ● Lesson 1 - Algebraic Expressions

● Lesson 2 - Sequences

● Lesson 3 - Properties of Operations


● Lesson 5 - Simplify Algebraic Expressions

● Lesson 6 - Add Linear Expressions

● Lesson 7 - Subtract Linear Expressions

● Lesson 8 - Factor Linear Expressions

Glencoe Math Course 2 Chapter 6 Equations and Inequalities (20 days) ● Lesson 1 - Solve One-Step Addition and Subtraction Equations

● Lesson 2 - Solve Multiplication and Division Equations

● Lesson 3 - Solve Equations with Rational Coefficients

● Lesson 4 - Solve Two-Step Equations

● Lesson 5 - More Two-Step Equations

● Lesson 6 - Solve Inequalities by Addition or Subtraction

● Lesson 7 - Solve Inequalities by Multiplication or Division

● Lesson 8 - Solve Two-Step Inequalities


● Ratios and Proportional Relationships

Standards

7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas

and other quantities measured in like or different units. For example, if a person walks 1/2

mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per

hour, equivalently 2 miles per hour.

7.RP.2 Recognize and represent proportional relationships between quantities.

a. Decide whether two quantities are in a proportional relationship, e.g., by testing for

equivalent ratios in a table or graphing on a coordinate plane and observing

whether the graph is a straight line through the origin.

b. Identify the constant of proportionality (unit rate) in tables, graphs, equations,

diagrams, and verbal descriptions of proportional relationships.

c. Represent proportional relationships by equations. For example, if total cost t is



proportional to the number n of items purchased at a constant price p, the

relationship between the total cost and the number of items can be expressed as t =

pn.

d. Explain what a point (x, y) on the graph of a proportional relationship means in

terms of the situation, with special attention to the points (0, 0) and (1, r) where r is

the unit rate.

7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples:

simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent

increase and decrease, percent error.

Vocabulary

Critical

Vocabulary

commission, complex fraction, cross products, discount, gratuity/tip, markdown/markup,

percent change, percent decrease/increase, percent equation, percent error, percent

proportion, principle, proportion, proportional, rate, repeating decimal, sales tax, selling

price, simple interest, terminating decimal, unit rate

Supporting

Vocabulary

constant of variation, constant of proportionality, constant rate of change, direct variation,

non-proportional, slope, equivalent ratios, origin, ratio

Resource

Glencoe Math Course 2 Chapter 1 Ratios and Proportional Reasoning (16 days) ● Lesson 1 - Rates

● Lesson 2 - Complex Fractions and Unit Rates

● Lesson 3 - Convert Unit Rates

● Lesson 4 - Proportional and Nonproportional Relationships

● Lesson 5 - Graph Proportional Relationships

● Lesson 6 - Solve Proportional Relationships

● Lesson 7 - Constant Rate of Change

● Lesson 8 - Slope

● Lesson 9 - Direct Variation

Glencoe Math Course 2 Chapter 2 Percents (18 days) ● Lesson 1 - Percent of a Number

● Lesson 2 - Percent and Estimation

● Lesson 3 - The Percent Proportion

● Lesson 4 - The Percent Equation

● Lesson 5 - Percent of Change

● Lesson 6 - Sales Tax, Tips, and Markups

● Lesson 7 - Discount

● Lesson 8 - Financial Literacy: Compound Interest




● Geometry

● Statistics

● Probability

Standards

7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual

lengths and areas from a scale drawing and reproducing a scale drawing at a different

scale.

7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with

given conditions. Focus on constructing triangles from three measures of angles or sides,

noticing when the conditions determine a unique triangle, more than one triangle, or no

triangle.

7.G.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as

in plane sections of right rectangular prisms and right rectangular pyramids.

7.G.4 Know the formulas for the area and circumference of a circle and use them to solve

problems; give an informal derivation of the relationship between the circumference and

area of a circle.

7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-

step problem to write and solve simple equations for an unknown angle in a figure.

7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of

two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes,

and right prisms.

7.SP.1 Understand that statistics can be used to gain information about a population by examining

a sample of the population; generalizations about a population from a sample are valid

only if the sample is representative of that population. Understand that random sampling

tends to produce representative samples and support valid inferences.

7.SP.2 Use data from a random sample to draw inferences about a population with an unknown

characteristic of interest. Generate multiple samples (or simulated samples) of the same

size to gauge the variation in estimates or predictions. For example, estimate the mean

word length in a book by randomly sampling words from the book; predict the winner of a

school election based on randomly sampled survey data. Gauge how far off the estimate or

prediction might be.

7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with

similar variabilities, measuring the difference between the centers by expressing it as a

multiple of a measure of variability. For example, the mean height of players on the

basketball team is 10 cm greater than the mean height of players on the soccer team,

about twice the variability (mean absolute deviation) on either team; on a dot plot, the

separation between the two distributions of heights is noticeable.

7.SP.4 Use measures of center and measures of variability for numerical data from random

samples to draw informal comparative inferences about two populations. For example,

decide whether the words in a chapter of a seventh-grade science book are generally

longer than the words in a chapter of a fourth-grade science book.



7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that

expresses the likelihood of the event occurring. Larger numbers indicate greater

likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2

indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a

likely event.

7.SP.6 Approximate the probability of a chance event by collecting data on the chance process

that produces it and observing its long-run relative frequency, and predict the approximate

relative frequency given the probability. For example, when rolling a number cube 600

times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly

200 times.

7.SP.7 Develop a probability model and use it to find probabilities of events. Compare

probabilities from a model to observed frequencies; if the agreement is not good, explain

possible sources of the discrepancy.

a. Develop a uniform probability model by assigning equal probability to all

outcomes, and use the model to determine probabilities of events. For example, if

a student is selected at random from a class, find the probability that Jane will be

selected and the probability that a girl will be selected.

b. Develop a probability model (which may not be uniform) by observing frequencies

in data generated from a chance process. For example, find the approximate

probability that a spinning penny will land heads up or that a tossed paper cup will

land open-end down. Do the outcomes for the spinning penny appear to be equally

likely based on the observed frequencies?

7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and

simulation.

a. Understand that, just as with simple events, the probability of a compound event is

the fraction of outcomes in the sample space for which the compound event occurs.

b. Represent sample spaces for compound events using methods such as organized

lists, tables and tree diagrams. For an event described in everyday language (e.g.,

“rolling double sixes”), identify the outcomes in the sample space which compose

the event.

c. Design and use a simulation to generate frequencies for compound events. . For

example, use random digits as a simulation tool to approximate the answer to the

question: If 40% of donors have type A blood, what is the probability that it will

take at least 4 donors to find one with type A blood?

Vocabulary

Critical

Vocabulary

adjacent angles, circumference, complementary angles, cross section, diameter, double

box plot, double dot plot, lateral face, lateral surface, pi, radius, semi-circle, slant height,

supplementary angles, vertical angles

Supporting

Vocabulary

absolute value, biased sample, compound event, convenience sample, dependent events,

experimental probability, fundamental counting principle, independent event, inferences,

invalid, likelihood, measures of variability, outcome, permutation, probability, random,

relative frequency, sample, sample space, simple event, simple random sample,

simulation, statistics, systematic random sample, theoretical probability, tree diagram,

unbiased sample, valid, voluntary response sample, measures of center, coplaner, straight



angles, acute triangle, equilateral triangle, isosceles triangle, obtuse triangles, scalene

triangle

Resource

Glencoe Math Course 2 Chapter 7 Geometric Figures (15 days) ● Lesson 1 - Classify Angles

● Lesson 2 - Complementary and Supplementary Angles


● Lesson 4 - Scale Drawings

● Lesson 5 - Draw Three Dimensional Figures

● Lesson 6 - Cross Sections

Glencoe Math Course 2 Chapter 8 Measure Figures (21 days) ● Lesson 1 - Circumference

● Lesson 2 - Area of Circles



● Lesson 5 - Volume of Pyramids

● Lesson 6 - Surface Area of Prisms

● Lesson 7 - Surface Area of Pyramids

● Lesson 8 - Volume and Surface Area of Composite Figures

Glencoe Math Course 2 Chapter 9 Probability (15 days) ● Lesson 1 - Probability of Simple Events

● Lesson 2 - Theoretical and Experimental Probability

● Lesson 3 - Probability of Compound Events

● Lesson 4 - Simulations

● Lesson 5 - Fundamental Counting Principle

● Lesson 6 - Permutations

● Lesson 7 - Independent and Dependent Events

Glencoe Math Course 2 Chapter 10 Statistics (15 days) ● Lesson 1 - Make Predictions

● Lesson 2 - Unbiased and Biased Samples

● Lesson 3 - Misleading Graphs and Statistics

● Lesson 4 - Compare Populations

● Lesson 5 - Select an Appropriate Display



Accelerated Math (7th Grade) Pacing Guide The Pacing Guide has been aligned to Wyoming State Standards with consideration to the Critical Areas of Focus defined by Common Core State Standards for Math and the Wyoming PAWS Blueprint.


● The Number System, Expressions, Equations

Standards

7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract

rational numbers; represent addition and subtraction on a horizontal or vertical number line

diagram.

a. Describe situations in which opposite quantities combine to make 0. For example,

a hydrogen atom has 0 charge because its two constituents are oppositely charged.

b. Understand p + q as the number located a distance |q| from p, in the positive or

negative direction depending on whether q is positive or negative. Show that a

number and its opposite have a sum of 0 (are additive inverses). Interpret sums of

rational numbers by describing real-world contexts.

c. Understand subtraction of rational numbers as adding the additive inverse, p – q =

p + (–q). Show that the distance between two rational numbers on the number line

is the absolute value of their difference, and apply this principle in real-world

contexts.

d. Apply properties of operations as strategies to add and subtract rational numbers.

7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions

to multiply and divide rational numbers.

a. Understand that multiplication is extended from fractions to rational numbers by

requiring that operations continue to satisfy the properties of operations,

particularly the distributive property, leading to products such as (–1)(–1) = 1 and

the rules for multiplying signed numbers. Interpret products of rational numbers by

describing real-world contexts.

b. Understand that integers can be divided, provided that the divisor is not zero, and

every quotient of integers (with non-zero divisor) is a rational number. If p and q

are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers

by describing real world contexts.

c. Apply properties of operations as strategies to multiply and divide rational

numbers.

d. Convert a rational number to a decimal using long division; know that the decimal

form of a rational number terminates in 0s or eventually repeats.

7.NS.3 Solve real-world and mathematical problems involving the four operations with rational

numbers. (Computations with rational numbers extend the rules for manipulating fractions

to complex fractions.

8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that

every number has a decimal expansion; for rational numbers show that the decimal

expansion repeats eventually, and convert a decimal expansion, which repeats eventually

into a rational number.



8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational

numbers, locate them approximately on a number line diagram, and estimate the value of

expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that

√2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get

better approximations

8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical

expressions. For example, 32 × 3–5 = 3–3 = 1/33 = 1/27.

8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x2 =

p and x3 = p, where p is a positive rational number. Evaluate square roots of small

perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to

estimate very large or very small quantities, and to express how many times as much one

is than the other. For example, estimate the population of the United States as 3 × 108 and

the population of the world as 7 × 109, and determine that the world population is more

than 20 times larger.

8.EE.4 Perform operations with numbers expressed in scientific notation, including problems

where both decimal and scientific notation are used. Use scientific notation and choose

units of appropriate size for measurements of very large or very small quantities (e.g., use

millimeters per year for seafloor spreading). Interpret scientific notation that has been

generated by technology.

Vocabulary

Critical

Vocabulary

additive inverse, constant, equivalent expressions, integer, like terms, opposites, rational

number, repeating decimal, terminating decimal

Supporting

Vocabulary

additive identity, algebraic expressions, associative property, bar notation, coefficient,

commutative property, dependent variable, distributive property, independent variable,

factored form, factoring, linear expression, monomial, simplest form (factoring), solution

set

Resource

Glencoe Math 7th Accelerated Chapter 1 The Language of Algebra (12 days) ● Lesson 1 - A Plan for Problem Solving

● Lesson 2 - Words and Expressions

● Lesson 3 - Variables and Expressions

● Lesson 4 - Properties of Numbers

● Lesson 5 - Problem-Solving Strategies

● Lesson 6 - Ordered Pairs and Relations

● Lesson 7 - Words, Equations, Tables and Graphs

Glencoe Math 7th Accelerated Chapter 2 Operations with Integers (13 days) ● Lesson 1 - Integers and Absolute Value

● Lesson 2 - Adding Integers

● Lesson 3 - Subtracting Integers

● Lesson 4 - Multiplying Integers

● Lesson 5 - Dividing Integers

● Lesson 6 - Graphing in Four Quadrants



Glencoe Math 7th Accelerated Chapter 3 Operations with Rational Numbers (11 days) ● Lesson 1 - Fractions and Decimals

● Lesson 2 - Rational Numbers

● Lesson 3 - Multiplying Rational Numbers

● Lesson 4 - Dividing Rational Numbers

● Lesson 5 - Adding and Subtracting Like Fractions

● Lesson 6 - Adding and Subtracting Unlike Fractions

Glencoe Math 7th Accelerated Chapter 4 Powers and Roots (12 days) ● Lesson 1 - Powers and Exponents

● Lesson 2 - Negative Exponents

● Lesson 3 - Multiplying and Dividing Monomials

● Lesson 4 - Scientific Notation

● Lesson 5 - Compute with Scientific Notation

● Lesson 6 - Square Roots and Cube Roots

● Lesson 7 - The Real Number System


● Ratios & Proportions

Standards

7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas

and other quantities measured in like or different units. For example, if a person walks 1/2

mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per

hour, equivalently 2 miles per hour.

7.RP.2 Recognize and represent proportional relationships between quantities.

a. Decide whether two quantities are in a proportional relationship, e.g., by testing for

equivalent ratios in a table or graphing on a coordinate plane and observing

whether the graph is a straight line through the origin.

b. Identify the constant of proportionality (unit rate) in tables, graphs, equations,

diagrams, and verbal descriptions of proportional relationships.

c. Represent proportional relationships by equations. For example, if total cost t is

proportional to the number n of items purchased at a constant price p, the

relationship between the total cost and the number of items can be expressed as t =

pn.

d. Explain what a point (x, y) on the graph of a proportional relationship means in

terms of the situation, with special attention to the points (0, 0) and (1, r) where r is

the unit rate.

7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples:

simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent

increase and decrease, percent error.

8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph.

Compare two different proportional relationships represented in different ways. For

example, compare a distance-time graph to a distance-time equation to determine which of

two moving objects has greater speed.

Vocabulary

Critical commission, complex fraction, cross products, discount, gratuity/tip, markdown/markup,



Vocabulary percent change, percent decrease/increase, percent equation, percent error, percent

proportion, principle, proportion, proportional, rate, repeating decimal, sales tax, selling

price, simple interest, terminating decimal, unit rate

Supporting

Vocabulary

constant of variation, constant of proportionality, constant rate of change, direct variation,

non-proportional, slope, equivalent ratios, origin, ratio

Resource

Glencoe Math 7th Accelerated Chapter 5 Ratios, Proportions, and Similar Figures (15 days) ● Lesson 1 - Ratios

● Lesson 2 - Unit Rates

● Lesson 3 - Complex Fractions and Unit Rates

● Lesson 4 - Converting Rates

● Lesson 5 - Proportional and NonProportional Relationships

● Lesson 6 - Graphing Proportional Relationships

● Lesson 7 - Solving Proportions

● Lesson 8 - Scale Drawings and Models

● Lesson 9 - Similar Figures

● Lesson 10 - Indirect Measurement

Glencoe Math 7th Accelerated Chapter 6 Percents (12 days) ● Lesson 1 - Using the Percent Proportion

● Lesson 2 - Find Percent of a Number Mentally

● Lesson 3 - Using the Percent Equation

● Lesson 4 - Percent of Change

● Lesson 5 - Discount and Markup

● Lesson 6 - Simple and Compound Interest


● Expressions

● Equations

● Linear Functions

Standards

7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear

expressions with rational coefficients.

7.EE.2 Understand that rewriting an expression in different forms in a problem context can shed

light on the problem and how the quantities in it are related. For example, a + 0.05a =

1.05a means that “increase by 5%” is the same as “multiply by 1.05.”

7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative

rational numbers in any form (whole numbers, fractions, and decimals), using tools

strategically. Apply properties of operations to calculate with numbers in any form;

convert between forms as appropriate; and assess the reasonableness of answers using

mental computation and estimation strategies. For example: If a woman making $25 an

hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50,

for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center

of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from

each edge; this estimate can be used as a check on the exact computation.

7.EE.4 Use variables to represent quantities in a real-world or mathematical problem, and



construct simple equations and inequalities to solve problems by reasoning about the

quantities.

a. Solve word problems leading to equations of the form px + q = r and p(x + q) = r,

where p, q, and r are specific rational numbers. Solve equations of these forms

fluently. Compare an algebraic solution to an arithmetic solution, identifying the

sequence of the operations used in each approach. For example, the perimeter of a

rectangle is 54 cm. Its length is 6 cm. What is its width?

b. Solve word problems leading to inequalities of the form px + q > r or px + q < r,

where p, q, and r are specific rational numbers. Graph the solution set of the

inequality and interpret it in the context of the problem. For example: As a

salesperson, you are paid $50 per week plus $3 per sale. This week you want your

pay to be at least $100. Write an inequality for the number of sales you need to

make, and describe the solutions.

8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct

points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line

through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

8.EE.7 Solve linear equations in one variable.

a. Give examples of linear equations in one variable with one solution, infinitely

many solutions, or no solutions. Show which of these possibilities is the case by

successively transforming the given equation into simpler forms, until an

equivalent equation of the form x = a, a = a, or a = b results (where a and b are

different numbers).

b. Solve linear equations with rational number coefficients, including equations

whose solutions require expanding expressions using the distributive property and

collecting like terms.8.EE.8 Analyze and solve pairs of simultaneous linear

equations.

8.EE.8 Analyze and solve pairs of simultaneous linear equations.

a. Understand that solutions to a system of two linear equations in two variables

correspond to points of intersection of their graphs, because points of intersection

satisfy both equations simultaneously.

b. Solve systems of two linear equations in two variables algebraically, and estimate

solutions by graphing the equations. Solve simple cases by inspection. For

example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot

simultaneously be 5 and 6.

c. Solve real-world and mathematical problems leading to two linear equations in two

variables. For example, given coordinates for two pairs of points, determine

whether the line through the first pair of points intersects the line through the

second pair.

8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The

graph of a function is the set of ordered pairs consisting of an input and the corresponding

output.

8.F.2 Compare properties of two functions each represented in a different way (algebraically,

graphically, numerically in tables, or by verbal descriptions). For example, given a linear

function represented by a table of values and a linear function represented by an algebraic



expression, determine which function has the greater rate of change.

8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight

line; give examples of functions that are not linear. For example, the function A = s2

giving the area of a square as a function of its side length is not linear because its graph

contains the points (1,1), (2,4) and (3,9), which are not on a straight line.

8.F.4 Construct a function to model a linear relationship between two quantities. Determine the

rate of change and initial value of the function from a description of a relationship or from

two (x, y) values, including reading these from a table or from a graph. Interpret the rate of

change and initial value of a linear function in terms of the situation it models, and in

terms of its graph or a table of values.

8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a

graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a

graph that exhibits the qualitative features of a function that has been described verbally.

Vocabulary

Critical

Vocabulary

constant, equivalent expressions, like terms

Supporting

Vocabulary

additive identity, algebraic expressions, associative property, coefficient, commutative

property, dependent variable, distributive property, independent variable, factored form,

factoring, linear expression, monomial, simplest form (factoring), solution set

Resource

Glencoe Math 7th Accelerated Chapter 7 Algebraic Expressions (10 days) ● Lesson 1 - The Distributive Property

● Lesson 2 - Simplifying Algebraic Expressions

● Lesson 3 - Adding Linear Expressions

● Lesson 4 - Subtracting Linear Expressions

● Lesson 5 - Factoring Linear Expressions

Glencoe Math 7th Accelerated Chapter 8 Equations and Inequalities (14 days) ● Lesson 1 - Solving Equations with Rational Coefficients

● Lesson 2 - Solving Two-Step Equations

● Lesson 3 - Writing Equations

● Lesson 4 - More Two-Step Equations

● Lesson 5 - Solving Equations with Variables on Each Side

● Lesson 6 - Inequalities

● Lesson 7 - Solving Inequalities

● Lesson 8 - Solving Multi-Step Equations and Inequalities

Glencoe Math 7th Accelerated Chapter 9 Linear Functions (12 days) ● Lesson 1 - Functions

● Lesson 2 - Representing Linear Functions

● Lesson 3 - Constant Rate of Change and Slope

● Lesson 4 - Direct Variation

● Lesson 5 - Slope-Intercept Form

● Lesson 6 - Solve Systems of Equations by Graphing

● Lesson 7 - Solve Systems of Equations Algebraically




● Geometry

● Pythagorean Theorem

● Statistics & Probability

Standards

7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual

lengths and areas from a scale drawing and reproducing a scale drawing at a different

scale.

7.G.2 Draw (freehand, with ruler and protractor, and with technology) geometric shapes with

given conditions. Focus on constructing triangles from three measures of angles or sides,

noticing when the conditions determine a unique triangle, more than one triangle, or no

triangle.

7.G.3 Describe the two-dimensional figures that result from slicing three-dimensional figures, as

in plane sections of right rectangular prisms and right rectangular pyramids.

7.G.4 Know the formulas for the area and circumference of a circle and use them to solve

problems; give an informal derivation of the relationship between the circumference and

area of a circle.

7.G.5 Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-

step problem to write and solve simple equations for an unknown angle in a figure.

7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of

two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes,

and right prisms.

7.SP.1 Understand that statistics can be used to gain information about a population by examining

a sample of the population; generalizations about a population from a sample are valid

only if the sample is representative of that population. Understand that random sampling

tends to produce representative samples and support valid inferences.

7.SP.2 Use data from a random sample to draw inferences about a population with an unknown

characteristic of interest. Generate multiple samples (or simulated samples) of the same

size to gauge the variation in estimates or predictions. For example, estimate the mean

word length in a book by randomly sampling words from the book; predict the winner of a

school election based on randomly sampled survey data. Gauge how far off the estimate or

prediction might be.

7.SP.3 Informally assess the degree of visual overlap of two numerical data distributions with

similar variabilities, measuring the difference between the centers by expressing it as a

multiple of a measure of variability. For example, the mean height of players on the

basketball team is 10 cm greater than the mean height of players on the soccer team,

about twice the variability (mean absolute deviation) on either team; on a dot plot, the

separation between the two distributions of heights is noticeable.

7.SP.4 Use measures of center and measures of variability for numerical data from random

samples to draw informal comparative inferences about two populations. For example,

decide whether the words in a chapter of a seventh-grade science book are generally

longer than the words in a chapter of a fourth-grade science book.



7.SP.5 Understand that the probability of a chance event is a number between 0 and 1 that

expresses the likelihood of the event occurring. Larger numbers indicate greater

likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2

indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a

likely event.

7.SP.6 Approximate the probability of a chance event by collecting data on the chance process

that produces it and observing its long-run relative frequency, and predict the approximate

relative frequency given the probability. For example, when rolling a number cube 600

times, predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly

200 times.

7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and

simulation.

a. Understand that, just as with simple events, the probability of a compound event is

the fraction of outcomes in the sample space for which the compound event occurs.

b. Represent sample spaces for compound events using methods such as organized

lists, tables and tree diagrams. For an event described in everyday language (e.g.,

“rolling double sixes”), identify the outcomes in the sample space which compose

the event.

c. Design and use a simulation to generate frequencies for compound events. For

example, use random digits as a simulation tool to approximate the answer to the

question: If 40% of donors have type A blood, what is the probability that it will

take at least 4 donors to find one with type A blood?

8.G.1 Verify experimentally the properties of rotations, reflections, and translations:

a. Lines are taken to lines, and line segments to line segments of the same length.

b. Angles are taken to angles of the same measure.

c. Parallel lines are taken to parallel lines.

8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be

obtained from the first by a sequence of rotations, reflections, and translations; given two

congruent figures, describe a sequence that exhibits the congruence between them.

8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional

figures using coordinates.

8.G.4 Understand that a two-dimensional figure is similar to another if the second can be

obtained from the first by a sequence of rotations, reflections, translations, and dilations;

given two similar two-dimensional figures, describe a sequence that exhibits the similarity

between them.

8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of

triangles, about the angles created when parallel lines are cut by a transversal, and the

angle-angle criterion for similarity of triangles. For example, arrange three copies of the

same triangle so that the sum of the three angles appears to form a line, and give an

argument in terms of transversals why this is so.

8.G.6 Explain a proof of the Pythagorean Theorem and its converse.

NCSD Clarification – 8.G.6

The 7th Grade Accelerated McGraw-Hill resource does not address Pythagorean Theorem.



Utilize other resources to address these standards.

8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in

real-world and mathematical problems in two and three dimensions.




8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate

system.




8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve

real-world and mathematical problems.

Vocabulary

Critical

Vocabulary

adjacent angles, circumference, complementary angles, cross section, diameter, double

box plot, double dot plot, lateral face, lateral surface, pi, radius, semi-circle, slant height,

supplementary angles, vertical angles

Supporting

Vocabulary

absolute value, biased sample, compound event, convenience sample, dependent events,

experimental probability, fundamental counting principle, independent event, inferences,

invalid, likelihood, measures of variability, outcome, permutation, probability, random,

relative frequency, sample, sample space, simple event, simple random sample,

simulation, statistics, systematic random sample, theoretical probability, tree diagram,

unbiased sample, valid, voluntary response sample, measures of center, coplaner, straight

angles, acute triangle, equilateral triangle, isosceles triangle, obtuse triangles, scalene

triangle

Resource

Glencoe Math 7th Accelerated Chapter 10 Statistics and Probability (14 days) ● Lesson 1 - Measures of Center

● Lesson 2 - Measures of Variability

● Lesson 3 - Mean Absolute Deviation

● Lesson 4 - Compare Populations

● Lesson 5 - Using Sampling to Predict

● Lesson 6 - Probability of Simple Events

● Lesson 7 - Theoretical and Experimental Probability

● Lesson 8 - Probability of Compound Events

Glencoe Math 7th Accelerated Chapter 11 Congruence, Similarities, and Transformations (14 days) ● Lesson 1 - Angle and Line Relationships


● Lesson 3 - Polygons

● Lesson 4 - Translations and Reflections on the Coordinate Plane

● Lesson 5 - Rotations on the Coordinate Plane

● Lesson 6 - Congruence and Transformations

● Lesson 7 - Dilations on the Coordinate Plane

● Lesson 8 - Similarity and Transformations



Glencoe Math 7th Accelerated Chapter 12 Volume and Surface Area (16 days) ● Lesson 1 - Circles and Circumference

● Lesson 2 - Area of Circles


● Lesson 4 - Three-Dimensional Figures


● Lesson 6 - Volume of Cylinders

● Lesson 7 - Volume of Pyramids, Cones and Spheres

● Lesson 8 - Surface Area of Prisms

● Lesson 9 - Surface Area of Cylinders

● Lesson 10 - Surface Area of Pyramids and Cones

Pythagorean Theorem school resources




45 Days


● Real Numbers

● Equations in One Variable

Standards

8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that

every number has a decimal expansion; for rational numbers show that the decimal

expansion repeats eventually, and convert a decimal expansion, which repeats eventually

into a rational number.

8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational

numbers, locate them approximately on a number line diagram, and estimate the value of

expressions (e.g., π2). For example, by truncating the decimal expansion of √2, show that

√2 is between 1 and 2, then between 1.4 and 1.5, and explain how to continue on to get

better approximations.

8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical

expressions. For example, 32 × 3

–5 = 3

–3 = 1/3

3 = 1/27.


p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect

squares and cube roots of small perfect cubes. Know that √2 is irrational.

8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to

estimate very large or very small quantities, and to express how many times as much one

is than the other. For example, estimate the population of the United States as 3 × 108 and

the population of the world as 7 × 109, and determine that the world population is more

than 20 times larger.

8.EE.4 Perform operations with numbers expressed in scientific notation, including problems

where both decimal and scientific notation are used. Use scientific notation and choose

units of appropriate size for measurements of very large or very small quantities (e.g., use

millimeters per year for seafloor spreading). Interpret scientific notation that has been

generated by technology.

8.EE.7 Solve linear equations in one variable.

a. Give examples of linear equations in one variable with one solution, infinitely

many solutions, or no solutions. Show which of these possibilities is the case by

successively transforming the given equation into simpler forms, until an

equivalent equation of the form x = a, a = a, or a = b results (where a and b are

different numbers).

b. Solve linear equations with rational number coefficients, including equations

whose solutions require expanding expressions using the distributive property and

collecting like terms.



Vocabulary

Critical

Vocabulary

irrational, scientific notation, solve (an equation)

Supporting

Vocabulary

base, coefficient, cube root, exponent, identity, multiplicative inverse, monomial, null set,

perfect cube, perfect square, power, radical sign, rational number, real number, repeating

decimal, square root, terminating decimal

Resource

Glencoe Math Chapter 1 Real Numbers (25 days) ● Lesson 1 - Rational Numbers

● Lesson 2 - Powers and Exponents

● Lesson 3 - Multiply and Divide Monomials

● Lesson 4 - Powers of Monomials

● Lesson 5 - Negative Exponents

● Lesson 6 - Scientific Notation

● Lesson 7 - Compute with Scientific Notation

● Lesson 8 - Roots

● Lesson 9- Estimate Roots

● Lesson 10- Compare Real Numbers

Glencoe Math Chapter 2 Equations in One Variable (20 days) ● Lesson 1 - Solve Equations with Rational Coefficients

● Lesson 2 - Solve Two-Step Equations

● Lesson 3 - Write Two-Steps Equations

● Lesson 4 - Solve Equations with Variables on Each Side

● Lesson 5 - Solve Multi-Step Equations


● Equations in Two Variables

● Functions

Standards

8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph.

Compare two different proportional relationships represented in different ways. For

example, compare a distance-time graph to a distance-time equation to determine which of

two moving objects has greater speed.




8.EE.8 Analyze and solve pairs of simultaneous linear equations.

a. Understand that solutions to a system of two linear equations in two variables

correspond to points of intersection of their graphs, because points of intersection

satisfy both equations simultaneously.

b. Solve systems of two linear equations in two variables algebraically, and estimate

solutions by graphing the equations. Solve simple cases by inspection. For

example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot

simultaneously be 5 and 6.

c. Solve real-world and mathematical problems leading to two linear equations in two



variables. For example, given coordinates for two pairs of points, determine

whether the line through the first pair of points intersects the line through the

second pair.

8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The

graph of a function is the set of ordered pairs consisting of an input and the corresponding

output.

8.F.2 Compare properties of two functions each represented in a different way (algebraically,

graphically, numerically in tables, or by verbal descriptions). For example, given a linear

function represented by a table of values and a linear function represented by an algebraic

expression, determine which function has the greater rate of change.

8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight

line; give examples of functions that are not linear. For example, the function A = s2 giving

the area of a square as a function of its side length is not linear because its graph contains

the points (1,1), (2,4) and (3,9), which are not on a straight line.

8.F.4 Construct a function to model a linear relationship between two quantities. Determine the

rate of change and initial value of the function from a description of a relationship or from

two (x, y) values, including reading these from a table or from a graph. Interpret the rate of

change and initial value of a linear function in terms of the situation it models, and in

terms of its graph or a table of values.

8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a

graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a

graph that exhibits the qualitative features of a function that has been described verbally.

Vocabulary

Critical

Vocabulary

constant of proportionality, constant rate of change, direct variation, linear equations,

linear functions, slope, slope-intercept form, substitution, x-intercept, y-intercept

Supporting

Vocabulary

constant of variation, linear relationship, point-slope form, rise, run, standard form,

systems of equations, continuous data, dependent variable, discrete data, domain, function,

function table, independent variable, non-linear function, quadratic function, qualitative

graph, range, relation

Resource

Glencoe Math Chapter 3 Equations in Two Variables (18 days) ● Lesson 1 - Constant Rate of Change

● Lesson 2 - Slope

● Lesson 3 - Equations in y=mx Form

● Lesson 4 - Slope-Intercept Form

● Lesson 5 - Graph a Line Using Intercepts

● Lesson 6 - Write Linear Equations

● Lesson 7 - Solve Systems of Equations by Graphing

● Lesson 8 - Solve Systems of Equations Algebraically

Glencoe Math Chapter 4 Functions (18 days) ● Lesson 1 - Represent Relationships

● Lesson 2 - Relations

● Lesson 3 - Functions

● Lesson 4 - Linear Functions

● Lesson 5 - Compare Properties of Functions



● Lesson 6 - Construct Functions

● Lesson 7 - Linear and Nonlinear Functions

● Lesson 8 - Quadratic Functions

● Lesson 9- Qualitative Graphs


● Triangles and the Pythagorean Theorem

● Transformations

Standards








8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional

figures using coordinates.






8.G.6 Explain a proof of the Pythagorean Theorem and its converse.

8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in

real-world and mathematical problems in two and three dimensions.

8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate

system.


p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect

squares and cube roots of small perfect cubes. Know that √2 is irrational.

Vocabulary

Critical

Vocabulary

alternate exterior angles, alternate interior angles, angle sum (interior of a figure),

corresponding angles, dilation, exterior angles, hypotenuse, image, leg (of a right

triangle), pre-image, Pythagorean Theorem, reflection, rotation, transformation,

translation, transversal

Supporting

Vocabulary

distance formula, equiangular, interior angle, parallel lines, perpendicular lines, regular

polygons, remote interior angles, angle of rotation, center of dilation, center of rotation,

congruent, line of reflection, rotational symmetry

Resource

Glencoe Math Chapter 5 Triangles and the Pythagorean Theorem (18 days) ● Lesson 1 - Lines



● Lesson 2 - omit

● Lesson 3 - Angles of Triangles

● Lesson 4 - Polygons and Angles

● Lesson 5 - The Pythagorean Theorem

● Lesson 6 - Use the Pythagorean Theorem

● Lesson 7 - Distance on the Coordinate Plane

Glencoe Math Chapter 6 Transformations (13 days) ● Lesson 1 - Translations

● Lesson 2 - Reflections

● Lesson 3 - Rotations

● Lesson 4 - Dilations


● Congruence and Similarity

● Volume

● Scatter Plots and Data Analysis

Standards








8.G.4 Understand that a two-dimensional figure is similar to another if the second can be

obtained from the first by a sequence of rotations, reflections, translations, and dilations;

given two similar two-dimensional figures, describe a sequence that exhibits the similarity

between them.









8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve

real-world and mathematical problems.

8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns

of association between two quantities. Describe patterns such as clustering, outliers,

positive or negative association, linear association, and nonlinear association.

8.SP.2 Know that straight lines are widely used to model relationships between two quantitative

variables. For scatter plots that suggest a linear association, informally fit a straight line,

and informally assess the model fit by judging the closeness of the data points to the line.



8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate

measurement data, interpreting the slope and intercept. For example, in a linear model for

a biology experiment, interpret a slope of 1.5 cm/hr as meaning that an additional hour of

sunlight each day is associated with an additional 1.5 cm in mature plant height.

8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by

displaying frequencies and relative frequencies in a two-way table. Construct and interpret

a two-way table summarizing data on two categorical variables collected from the same

subjects. Use relative frequencies calculated for rows or columns to describe possible

association between the two variables. For example, collect data from students in your

class on whether or not they have a curfew on school nights and whether or not they have

assigned chores at home. Is there evidence that those who have a curfew also tend to have

chores?

Vocabulary

Critical

Vocabulary

line of best fit, linear association, negative association, nonlinear association, positive

association, relative frequency, scatterplot, two-way table

Supporting

Vocabulary

corresponding parts, indirect measurement, scale factor, similar polygons, composite

solids, hemisphere, sphere, volume, bivariate data, distribution, 5-number summary, mean

absolute deviation, qualitative data, quantitative data, standard deviation, symmetric

Resource

Glencoe Math Chapter 7 Congruency and Similarities (17 days) ● Lesson 1 - Congruence of Transformations

● Lesson 2 - Congruence

● Lesson 3 - Similarity and Transformations

● Lesson 4 - Properties of Similar Polygons

● Lesson 5 - Similar Triangles and Indirect Measurement

● Lesson 6 - Slope and Similar Triangles

● Lesson 7 - Area and Perimeter of Similar Figures

Glencoe Math Chapter 8 Volume and Surface Area (17 days) ● Lesson 1 - Volume of Cylinders

● Lesson 2 - Volume of Cones

● Lesson 3 - Volume of Spheres

● Lesson 4 and Lesson 5 - omit

● Lesson 6 - Changes in Dimensions

Glencoe Math Chapter 9 Scatter Plots and Data Analysis (15 days) ● Lesson 1 - Scatter Plots

● Lesson 2 - Lines of Best Fit

● Lesson 3 - Two-Way Tables

● Lesson 4 - Descriptive Statistics

● Lesson 5 - Measures of Variation

● Lesson 6 - Analyze Data Distributions



Algebra I Pacing Guide

Algebra I 1ST

SEMESTER

CCSS Mathematical Content CCSS Mathematical Practice

Content and Educator Notes

Reason quantitatively and use units to solve problems. N.Q.1 - Use Clusters as a way to understand problems and to guide the solution of multi-step problems; choose and interpret Clusters consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. N.Q.2 - Define appropriate quantities for the purpose of descriptive modeling. N.Q.3 - Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. Interpret the structure of expressions. A.SSE.1 - Interpret expressions that represent a quantity in terms of its context. Limit to

linear expressions and to exponential expressions with integer exponents.

a. Interpret parts of an expression, such as terms, factors, and coefficients.

b. Interpret complicated expressions by viewing one or more of their parts as a single entity.

Create equations that describe numbers or relationships. A.CED.1 - Create equations and inequalities in one variable and use them to solve

problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A.CED.2 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. A.CED.3 - Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. A.CED.4 - Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R.

1. Make sense of

problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision. 7. Look for and make

use of structure. 8. Look for and express

regularity in repeated reasoning.

2.6, 2.7, 2.8 (N.Q.1) 2.6 extended lab (N.Q.2) 1.3 extended lab (N.Q.3) *Rounding throughout the year 1.1, 1.4 (A.SSE.1a) 1.2, 1.3 (A.SSE.1b) 1.5, 2.1-2.5, 3.2 (A.CED.1) 3.1, 3.4, 3.5, 3.6, 4.1-4.6 (A.CED.2) 4.2 (A.CED.3) 2.8, 4.1 (A.CED.4)

https://docs.google.com/document/d/1OGSqIeqAV169_mhrdm8nL8lw3v5Kdwql9vppBalGeP8/edit?authkey=CNLuhN4E&hl=en_US&authkey=CNLuhN4E

https://docs.google.com/document/d/1Cp1nv1wznjg74G3_Nyycq8dSPwwTIH8dSi97Jd0UHMw/edit?authkey=CIfIzYgI&hl=en_US&authkey=CIfIzYgI

https://docs.google.com/document/d/1KsF0QsEKFKiOXGuHinDnOsZ-95KCb6VRP4LlCdCz8qI/edit?authkey=CNu2jMoL&hl=en_US&authkey=CNu2jMoL

https://docs.google.com/document/d/1EgBQSZap3g4iybCEHN9bUVxr2WjsHiCCPD3-vvubEI4/edit?authkey=COC8qpkM&hl=en_US&authkey=COC8qpkM

https://docs.google.com/document/d/1Sfq73OJP9nQEdSEngYGAY5auuPbEuDoou9rK9-PNqIY/edit?authkey=CIOA39wP&hl=en_US&authkey=CIOA39wP

https://docs.google.com/document/d/1ewRsYvtH3jbTDHK9BrY7SPPY5A8L3wAvK2fE_L4JUHU/edit?usp=sharing

https://docs.google.com/document/d/1L2u61KdSYRXmkQ2CUC0Ilu9era5Svs-tPLHsfOkwbPQ/edit

https://docs.google.com/document/d/1G2dvLU9qP2sxcMVBs1WN_EBef0p5htAlkigHauKWHEI/edit

http://sdcounts.tie.wikispaces.net/file/view/SMP2.pdf









Understand solving equations as a process of reasoning and explain the reasoning. A.REI.1 - Explain each step in solving a simple equation as following from the equality of

numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method. Focus on and master linear equations and be able to extend and apply their reasoning to other types of equations in future courses. Solve equations and inequalities in one variable A.REI.3 - Solve linear equations and inequalities in one variable, including equations with

coefficients represented by letters. Extend earlier work with solving linear equations to solving linear inequalities in one variable and to solving literal equations that are linear in the variable being solved for. Include simple exponential equations that rely only on application of the laws of exponents, such as 5

x=125 or 2

x=1/16

Solve systems of equations A.REI.5 – Prove that, given a system of equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions. A.REI.6 – Solve systems of linear equations exactly and approximately (e.g. with graphs),

focusing on pairs of linear equations in two variables. Focus on justification of the methods used. Include cases where the two equations describe the same line (yielding infinitely many solutions) and cases where two equations describe parallel lines (yielding no solution); connect to to GPE.5 when it is taught in Geometry, which requires students to prove the slope criteria for parallel line. Represent and solve equations and inequalities graphically A.REI.10 - Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line). Focus on linear and exponential equations and be able to adapt and apply that learning to other types of equations in future courses. A.REI.11 - Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions. Focus on cases where f(x) and g(x) are linear or exponential. A.REI.12 - Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

1.5, 2.2-2.6 (A.REI.1) 1.5, 2.2-2.8 (A.REI.3) 6.4 (A.REI.5) 6.1-6.5 (A.REI.6) 1.6, 1.7, 3.1, 3.2, 3.4 (A.REI.10) 6.1(A.REI.11) 5.6, 6.6(A.REI.12)

https://docs.google.com/document/d/1hXEWWNTWWJ59finjqc0aA9uZDLMBPLMRsRw2SLCL738/edit?authkey=COOvstQE&hl=en_US&authkey=COOvstQE

https://docs.google.com/document/d/1jhFfQkXCfKhgx-KPFs8rshDSXRnoIGUu03NaGoLa4fs/edit?authkey=COGhq4kM&hl=en_US&authkey=COGhq4kM

https://docs.google.com/document/d/1TzJY457nN-sXPRxPAwtEOCzNF5KGS4R4ysIoSzKPies/edit?authkey=CIzxzJUK&hl=en_US&authkey=CIzxzJUK

https://docs.google.com/document/d/1k-EbTUTgo20dl-7lhRdr9zsxDCJGXZk63tj253J6Yk4/edit

https://docs.google.com/document/d/15aoWLGl0vrvz4lSWfwya1iwhayDNnpy3vr1f6SiYMCA/edit?authkey=COSx--AJ&hl=en_US&authkey=COSx--AJ



Understand the concept of a function and use functions notation F.IF.1 - Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x). F.IF.2 - Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context. F.IF.3 - Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1. Students should experience a variety of types of situations modeled by functions. Detailed analysis of any particular class of functions at this stage is not advised. Students should apply these concepts throughout their future mathematics courses. Draw examples from linear and exponential functions. Draw connection between F.IF.3 and F.BF.2 which required students to write arithmetic and geometric sequences. Emphasize arithmetic and geometric sequences as examples of linear and exponential functions. Interpret functions that arise in applications in terms of a context F.IF.4 - For a function that models a relationship between two quantities, interpret key

features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. Focus on linear and exponential functions. F.IF.6 - Calculate and interpret the average rate of change of a function (presented

symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Focus on linear functions and exponential functions whose domain is a subset of the integers. Analyze functions using different representations F.IF.7 - Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Focus on linear and exponential functions. Include comparisons of two functions presented algebraically. For example, compare the growth of two linear functions, or two exponential functions.

a. Graph linear and quadratic functions and show intercepts, maxima, and minima. F.IF.9 - Compare properties of two functions each represented in a different way

(algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.

1.6, 1.7 (F.IF.1) 1.7, 3.6, 4.3 (F.IF.2) 3.5 (F.IF.3) 1.8, 3.1, 4.1 (F.IF.4) 3.3 (F.IF.6) 3.1,3.2,3.4,4.1 (F.IF.7a) 1.7,3.6,4.3 (F.IF.9)

https://docs.google.com/document/d/1_3uJo9I5t0MTS52lSlqN08q2cykuRZct8BhQxm5tEUk/edit?authkey=CKGy7K8L&hl=en_US&authkey=CKGy7K8L

https://docs.google.com/document/d/17elUCIPLRvMqN5idR3q1c8BzugorjQInjklvSCwlyhc/edit?authkey=CPXTvOUH&hl=en_US&authkey=CPXTvOUH

https://docs.google.com/document/d/1WiCx5vrFZ8jETluq4KVRkiji5K2X-g4utKXpOlvGLn8/edit?authkey=CKWLmqAN&hl=en_US&authkey=CKWLmqAN

https://docs.google.com/document/d/1sYhL4sj2HiFnYZdAeHa8At6oQjf587Pf37Bbe1DFtTk/edit?authkey=CMOvl8wD&hl=en_US&authkey=CMOvl8wD

https://docs.google.com/document/d/1k7k7bUhZ-aJAADuS0AQD6oDF0HStXEZS3PH5u8y1-8w/edit?authkey=CI6Bu5YM&hl=en_US&authkey=CI6Bu5YM

https://docs.google.com/document/d/13duGO3Qhr4PKTg5vdwMt0f4eO51-2Qcvl8sRpy1LlYY/edit?authkey=CLrYzmw&hl=en_US&authkey=CLrYzmw

https://docs.google.com/document/d/1kr88d0KMqPovoyUV3riYDcW-F2ZFwcfzHh4JNJLvQDM/edit?authkey=CNjAkLEM&hl=en_US&authkey=CNjAkLEM



Build a function that models a relationship between two quantities F.BF.1 - Write a function that describes a relationship between two quantities. Limit to F.BF.1a, 1b, and 2 to linear and exponential functions.

a. Determine an explicit expression, a recursive process, or steps for calculation from a context.

b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

F.BF.2 – Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two form. F.BF.3 – Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graphs using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. F.BF.4 – Find the inverse functions.

a. Solve an equation of the form f(x)=c for a simple function f that has an inverse and write an expression for the inverse.

Construct and compare linear, quadratic, and exponential models and solve problems F.LE.1 - Distinguish between situations that can be modeled with linear functions and with

exponential functions. a. Prove that linear functions grow by equations grow by equal differences over equal intervals; and that exponential functions grow by equal factors over equal intervals.

b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

F.LE.2 - Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table). Draw on and consolidate previous work in grade 8 on finding equations for lines and linear functions. F.LE.3 - Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function. Limit to comparisons between linear and exponential models. Interpret expressions for functions in terms of the situation they model F.LE.5 - Interpret the parameters in a linear or exponential function in terms of a context.

1.7,3.1,3.4,3.6,4.1-4.6 (F.BF.1a) 4.2 (F.BF.1b) 3.5, 7.7, 7.8 (F.BF. 2) 9.3(F.BF.3) 4.7 (F.BF.4) 3.3, 3.5 (F.LE.1a) 3.5, 3.6 (F.LE.1b) 7.6, 7.7 (F.LE.1c) 3.5, 3.6, 4.2-4.6 (F.LE.2) 9.6 (F.LE.3) 3.4, 4.1, 4.5 (F.LE.5)

https://docs.google.com/document/d/1YZovUOExKlhTrco9Mil3RsOxtz4tbHRCIOYZxFwfKUk/edit?authkey=COqO4ckO&hl=en_US&authkey=COqO4ckO

https://docs.google.com/document/d/1YZovUOExKlhTrco9Mil3RsOxtz4tbHRCIOYZxFwfKUk/edit?authkey=COqO4ckO&hl=en_US&authkey=COqO4ckO

https://docs.google.com/document/d/1Ptnq8SCpQnWOmvKwAsO5IyqILrN_GawGEwYd3RIRzsc/edit?authkey=CKOZmNYC&hl=en_US&authkey=CKOZmNYC

https://docs.google.com/document/d/1N8euzAgo2-7hxJNHsoL7Jv_IxkSeyfZRveqTVJhtNPE/edit?authkey=CNmIivkB&hl=en_US&authkey=CNmIivkB

https://docs.google.com/document/d/1vQ63a-N2CFliVA7ZGZFwhjUrWiqB7GJXqOFMQtA9iyg/edit?authkey=CMjm2PwD&hl=en_US&authkey=CMjm2PwD

https://docs.google.com/document/d/11xFBmG1A0QVv_02wlFgOFa5rYDWKn0OYnlhL414I6oU/edit?authkey=CN-wi_0P&hl=en_US&authkey=CN-wi_0P



Summarize, represent, and interpret data on two categorical and quantitative variables S.ID.6 - Represent data on two quantitative variables on a scatter plot, and describe how

the variables are related. Focus on linear models, but may be used to preview quadratic functions in unit 5 of this course.

a. Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear and exponential models.

b. Informally assess the fit of a function by plotting and analyzing residuals.

c. Fit a linear function for a scatter plot that suggests a linear association. Students model the relationship between two numerical variables. In addition to fitting a line to data, students assess how well the model fits by analyzing residuals.

Interpret linear models S.ID.7 - Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data. S.ID.8 - Compute (using technology) and interpret the correlation coefficient of a linear fit. S.ID.9 – Distinguish between correlation and causation.

4.5, 4.6 (S.ID.6a, b, c) 4.1, 4.4, 4.5 (S.ID. 7) 4.6 (S.ID.8) 4.5 (S.ID.9)

Algebra I 2ND

SEMESTER


Content and Educator Notes

Extend the properties of exponents to rational exponents. N.RN.1 – Explain how the definition of the meaning of rational exponents follows from

extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define (5

1/3)3 = 5

(1/3)3 must equal

5. N.RN.2 – Rewrite expressions involving radicals and rational exponents using the

properties of exponents. N.RN.3 – Explain why the sum or product of two rational numbers is rational; that the sum

of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational

1. Make sense of

problems and persevere in solving them.



4. Model with

7.3 (N.RN.1) 7.3(N.RN.2) 10-2 (N.RN.3)

https://docs.google.com/document/d/1Rn-XKwm5tZQcSk7OQcqRpilqt3ScXyMu23TpMY1YOmU/edit?authkey=CLmqsYkB&hl=en_US&authkey=CLmqsYkB&pli=1

https://docs.google.com/document/d/1GIliRrIFg6V4-WZ4Z6jBwDeZ94SAwgTORh565WI1Kf8/edit?authkey=CL_i96kD&hl=en_US&authkey=CL_i96kD

https://docs.google.com/document/d/1W8CsKx5bepfw9cyNsNAwpt171CuQ6XzlHWq6uXHL_hU/edit?authkey=CIrRjeME&hl=en_US&authkey=CIrRjeME





Interpret the structure of expressions A.SSE.1 - Interpret expressions that represent a quantity in terms of its context. Focus on quadratic and exponential expressions.

a. Interpret parts of an expression, such as terms, factors, and coefficients. A.SSE.2 - Use the structure of an expression to identify ways to rewrite it. For example, see

x4 – y

4 as (x

2)2 – (y

2)2, thus recognizing it as a difference of squares that can be factored as

(x2 – y

2)(x

2 + y

2).

Write expressions in equivalent forms to solve problems A.SSE.3 - Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression. It is important to balance conceptual understanding and procedural fluency in work with equivalent expressions. For example, development of skill in factoring and completing the square goes hand-in-hand with understanding what different forms of a quadratic expression reveal.

a. Factor a quadratic expression to reveal the zeros of the function it defines.

b. Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

c. Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15

t can be rewritten as (1.15

1/12)12t

= 1.01212t

(approx..) to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

Perform arithmetic operations on polynomials A.APR.1 - Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Focus on polynomial expressions that simplify to forms that are linear or quadratic in a positive integer power of x. Create equations that describe numbers or relationships A.CED.1 - Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A.CED.2 - Create equations in two or more variables to represent relationships between

quantities; graph equations on coordinate axes with labels and scales. A.CED.3 - Represent constraints by equations or inequalities, and by systems of equations

and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Solve equations and inequalities in one variable

mathematics. 5. Use appropriate tools

strategically. 6. Attend to precision. 7. Look for and make

use of structure. 8. Look for and express


8.1, 9.1 (A.SSE.1) 7.1, 7.2, 8.6, 8.8 (A.SSE.2) 8.5, 8.6, 8.8 (A.SSE.3a) 9.3, 9.3(A.SSE.3b) 7.6extention (A.SSE.3c) 8.1-8.4 (A.APR.1) 5.1-5.5, 8.5, 8.6 (A.CED.1) 6.1-6.5, 8.6, 8.8, 9.1, 9.2, 9.5 (A.CED.2) 5.6, 6.1, 6.2 (A.CED.3)

https://docs.google.com/document/d/1EgBQSZap3g4iybCEHN9bUVxr2WjsHiCCPD3-vvubEI4/edit?authkey=COC8qpkM&hl=en_US&authkey=COC8qpkM

https://docs.google.com/document/d/1EKjrQYGS_vCJpyP2ODbkftapbg8JezD3Bsnn5u-cR-w/edit?authkey=CMLA8_AC&hl=en_US&authkey=CMLA8_AC

https://docs.google.com/document/d/10Bzo0IBGKCQvWRKiliXIO94Kew7_IBFKk_8BiqCMWEA/edit?authkey=CLDsrrMM&hl=en_US&authkey=CLDsrrMM

https://docs.google.com/document/d/1ioAep3c7TMlfDqqHf4WalIoMgBp8Z2ZtaQUsYlHO0S0/edit?authkey=CMKn7sgL&hl=en_US&authkey=CMKn7sgL

https://docs.google.com/document/d/1Sfq73OJP9nQEdSEngYGAY5auuPbEuDoou9rK9-PNqIY/edit?authkey=CIOA39wP&hl=en_US&authkey=CIOA39wP

https://docs.google.com/document/d/1pmbe5ZprsFqW1KQyu8NS6deoAMXx8Gislsn7nd3udEg/edit?authkey=CJGUso8C&hl=en_US&authkey=CJGUso8C


http://sdcounts.tie.wikispaces.net/file/view/SM6.pdf





Interpret functions that arise in applications in terms of a context F.IF.5 - Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. Analyze functions using different representations F.IF.8 - Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

a. Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

b. Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)

t, y =

(0.97)t, y = (1.01)

12t, y = (1.2)

t/10, and classify them as representing exponential

growth or decay A.REI.4 – Solve quadratic equations in one variable.

a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x-p)

2=q that has the same solutions. Derive the

quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for x

2=49), taking square roots,

completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex

solutions and write them as for real numbers a and b. Summarize, represent, and interpret data on a single count or measurement variable S.ID.1 - Represent data with plots on the real number line (dot plots, histograms, and box

plots). S.ID.2 - Use statistics appropriate to the shape of the data distribution to compare center

(median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. S.ID.3 - Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers). In grades 6-8 students describe center and spread in a data distribution. Here they choose a summary statistic appropriate to the characteristics of the data distribution, such as the shape of the distribution or the existence of extreme data points.

9.1, 9.2 (F.IF. 5) 9.2, 9.3 (F.IF.8a) 7.1, 7.2 (F.IF.8b) 9.4, 9.5, 10.2 (A.REI.4a) 8.6, 8.7, 8.8, 9.2, 9.4, 9.5 (A.REI.4b) 0.13, 12.3, 12.4 (S.ID.1) 12.2, 12.3, 12.4 (S.ID.2) 12.3-12.4 (S.ID.3)

https://docs.google.com/document/d/1KazmKUlL9WtK2HsB5S9kt5M2g1Z8ZCulWjEGEc1uBB0/edit?authkey=CMufhqwC&hl=en_US&authkey=CMufhqwC

https://docs.google.com/document/d/1fQcJ2WEJ0z4vkyrdSV2_tEmZhwZbgLp2W9ScAc4brbA/edit?authkey=CMHlpacL&hl=en_US&authkey=CMHlpacL

https://docs.google.com/document/d/1Ga0tAbsWUT6t31iLWMDfT0hs5lRGpcriArYlq6ua6Mw/edit?authkey=CNPb1bEO&hl=en_US&authkey=CNPb1bEO

https://docs.google.com/document/d/1HlK7S6ADPb6JCQIMt5a80-vbKSEPo9rtQF8TF6f1hyI/edit?authkey=CMOa96QI&hl=en_US&authkey=CMOa96QI

https://docs.google.com/document/d/19mCMdwzEOXGs8knm4la21v16mADN3O7t6UfkUh1Z4IA/edit?authkey=CNKu8vwI&hl=en_US&authkey=CNKu8vwI



Geometry Pacing Guide

Geometry 1st

Semester

Geometry Instructional Focus 1: Congruence, Proof, and Constructions Suggested Quarter/Time: 1st/30 days


Content and Educator Content

Experiment with transformations in the plane G.CO.1 - Know precise definitions of angle, circle, perpendicular line, parallel line, and line

segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G.CO.2 - Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). G.CO.3 - Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. G.CO.4 - Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G.CO.5 - Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. Understand congruence in terms of rigid motions. G.CO.6 - Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. G.CO.7 - Use the definition of congruence in terms of rigid motions to show that two

triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. G.CO.8 - Explain how the criteria for triangle congruence (ASA, SAS, and, SSS) follow from the definition of congruence in terms of rigid motions.

1. Make sense of problems

and persevere in solving them.





6. Attend to precision. 7. Look for and make use

of structure. 8. Look for and express


G.CO.1 (1.1-1.4, 3.1-3.2, 10.1) G.CO.2 (9.4) G.CO.3 (9.5) G.CO.4 (9.1-9.3) G.CO.5 (9.1-9.4) G.CO.6 (4.7) G.CO.7 (4.3, 4.7) G.CO.8 (4.4, 4.5)

https://docs.google.com/document/d/1ZO4nxNfc4tCrJlQfHGxLdswGNoGJNOsypI6kmFN-I0w/edit?usp=sharing

https://docs.google.com/document/d/1uoU2COj1JuAWkBoJETO02cobZ308iRZCXdABBj3iQao/edit?usp=sharing

https://docs.google.com/document/d/1rre1mAWA04uzKWn7KQ_ACd7UXNS2quC1eWpJwk_xIAQ/edit?usp=sharing

https://docs.google.com/document/d/1WNjPaLELrC_9XI629J_dnCaJnGV70WxhFO0jflOPRWE/edit?usp=sharing

https://docs.google.com/document/d/1X-og959-7zAcsXTtpT9Ap09tgenwcWvKGghTuvGWh_4/edit?usp=sharing

https://docs.google.com/document/d/1DJVm4KMOBpXuwLYSoTH3radKWvY_IPKuXiJZsZai1yM/edit?usp=sharing

https://docs.google.com/document/d/13hx3Kkixi-g5uxFjTXr1f0hWtfd8K81KN2_lH_ISdAk/edit?usp=sharing

https://docs.google.com/document/d/1pvEIE0epF75cfVNfOl6qnQwX2CQmXVuChALRgDGBTvY/edit?usp=sharing








Rigid motions are at the foundation of the definition of congruence. Students reason from the basic properties of rigid motions (that they preserve distance and angle), which are assumed without proof. Rigid motions and their assumed properties can be used to establish the usual triangle congruence criteria, which can then be used to prove other theorems. Prove Geometric Theorems G.CO.9 - Prove theorems about lines and angles. Theorems include: vertical angles are

congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints. G.CO.10 - Prove theorems about triangles. Theorems include: measures of interior

angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point. G.CO.11 - Prove theorems about parallelograms. Theorems include: opposite sides are

congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals. Encourage multiple ways of writing proofs, such as in narrative paragraphs, using flow diagrams, in two-column format, and using diagrams without words. Students should be encouraged to focus on the validity of the underlying reasoning while exploring a variety of formats for expressing that reasoning. Implementation of G.CO.10 may be extended to include concurrence of perpendicular bisectors and angle bisectors as preparation for G.C.3 in Unit 5. Make geometric constructions. G.CO.12 - Make formal geometric constructions with a variety of tools and methods

(compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line. G.CO.13 - Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle. Build on prior student experience with simple constructions. Emphasize the ability to formalize and explain how these constructions result in the desired objects. Some of these constructions are closely related to previous standards and can be introduced in conjunction with them.

G.CO.9 (2.7-2.8, 3.2, 3.5) G.CO.10 (4.2, 4.4, 4.5, 4.6, 4.8, 5.1, 5.2, 5.3, 5.5, 5.6) G.CO.11 (6.2, 6.4, 6.5) G.CO.12 (Throughout) G.CO.13 (Throughout)

https://docs.google.com/document/d/1w3372BSdMcDs3V6XVelQFbkLo5ES-uEtN0wzLOBCOVI/edit?usp=sharing

https://docs.google.com/document/d/1RNv7s63a9BpAOxXAkKiPCNx4EJWrq6Hr7cka5ZoQfbQ/edit?usp=sharing

https://docs.google.com/document/d/1aLg8PQYuysLW1_H2cZVLzpFs-dA4pc7PeeWjjCTw_FQ/edit?usp=sharing

https://docs.google.com/document/d/1545Ef_LXFbCxhipLSjnXMOa72Cy4LY5x8QlT9f2JTzQ/edit?usp=sharing

https://docs.google.com/document/d/1obCK3tmxH4pBTj2tIDUesUWauxBrXHHBeHXtayFKXbc/edit?usp=sharing



Geometry Instructional Focus 2: Similarity, Proof and Trigonometry

Suggested Quarter/Time: 1st

– 2nd

/45 days



Understand similarity in terms of similarity transformations G.SRT.1 - Verify experimentally the properties of dilations given by a center and a

scale factor. G.SRT.1a - A dilation takes a line not passing through the center of the dilation to a

parallel line, and leaves a line passing through the center unchanged. G.SRT.1b - The dilation of a line segment is longer or shorter in the ratio given by the

scale factor. G.SRT.2 - Given two figures, use the definition of similarity in terms of similarity

transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides. G.SRT.3 - Use the properties of similarity transformations to establish the AA criterion for

two triangles to be similar. Prove theorems involving similarity G.SRT.4 - Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity. G.SRT.5 - Use congruence and similarity criteria for triangles to solve problems and to

prove relationships in geometric figures. Define trigonometric ratios and solve problems involving right triangles G.SRT.6 - Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles. G.SRT.7 - Explain and use the relationship between the sine and cosine of complementary angles. G.SRT.8 - Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.







6. Attend to precision. 7. Look for and make use of

structure. 8. Look for and express


G.SRT.1 (9.6 a and b) G.SRT.2 (7.2, 7.6) G.SRT.3 (7.3) G.SRT.4 (7.3, 7.4, 7.5, 8.1) G.SRT.5 (4.3-4.5) (7-3, 7-4, 7-5, 7-6, 8-1) G.SRT.6 (8-3, 8-4) G.SRT.7 (8.4) G.SRT.8 (8.5)

https://docs.google.com/document/d/1rs-aOcjWxZ5qmMMC6F4k0TDDgQFyUqTwEGThMgGqsBs/edit?usp=sharing

https://docs.google.com/document/d/1S8u-YpJEXHCmSqW3a4t0EtUu7130-41oGo5OAKiga70/edit?usp=sharing

https://docs.google.com/document/d/1QifB010fA-tk_fHnWXisfPKOKsefJ6AXoaK2LMeqS6s/edit?usp=sharing

https://docs.google.com/document/d/1vZ7oN_wfygoF5o_EtRE6tq8yMMp7N7Y5vOhMqPHmIuQ/edit?usp=sharing

https://docs.google.com/document/d/19gLC5VvgnxFBePYIkFtE2Cp854km3V-Q4aPXijw3Ptg/edit?usp=sharing

https://docs.google.com/document/d/18SmpPGZ4jF2zJ9rsBWHF0U0wgCLovUm_FIt1EaHs0dk/edit?usp=sharing

https://docs.google.com/document/d/1riYA74_YTZv8P4WDhIVdKrIFcK6gyk1OU4tltkYjz88/edit?usp=sharing

https://docs.google.com/document/d/17a5Yh9VR3GzqM3y6kRSDrPbUthBUCXSUo_CEtgGSMgc/edit?usp=sharing








Apply geometric concepts in modeling situations G.MG.1 - Use geometric shapes, their measures, and their properties to describe objects

(e.g., modeling a tree trunk or a human torso as a cylinder).* G.MG.2 - Apply concepts of density based on area and volume in modeling situations

(e.g., persons per square mile, BTUs per cubic foot). G.MG.3 - Apply geometric methods to solve design problems (e.g., designing an object or

structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). Focus on situations well modeled by trigonometric ratios for acute angles. Apply trigonometry to general triangles G.SRT.9 - (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. G.SRT.10 - (+) Prove the Laws of Sines and Cosines and use them to solve problems. G.SRT.11- (+) Understand and apply the Law of Sines and the Law of Cosines to find

unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces). With respect to the general case of the Laws of sines and Cosines, the definitions of sine and cosine must be extended to obtuse angles.

G.MG.1 (Throughout) G.MG.2 (Ch 12) G.MG.3 (Throughout)

Geometry 2nd

Semester

Geometry Instructional Focus 3: Extending to Three Dimensions

Suggested Quarter/Time: 3rd

/20 days



Explain volume formulas and use them to solve problems. G.GMD.1 - Give an informal argument for the formulas for the circumference of a circle,

area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri’s principle, and informal limit arguments. G.GMD.3 - Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.




G.GMD.1 (11.3, 12.5, 12.6) G.GMD.3 (11.3, 12.5, 12.6)

https://docs.google.com/document/d/13BzMbD4KB0Dvh4n6odbMfMvmSnaecsjoTF6fzEP47LE/edit?usp=sharing

https://docs.google.com/document/d/1KERXL7MCBG52qO1K382fEQfh1cqYR8V_4CHY3D4Sr4E/edit?usp=sharing

https://docs.google.com/document/d/1dMrObDyixtzyHUMVRKD2M_aBe_oEeeh1CYTWxpOGfIA/edit?usp=sharing

https://docs.google.com/document/d/1hnYjUl3I2hA7RLhf-LBavvR10YIZGfBGQEdRQENPHmU/edit?usp=sharing

https://docs.google.com/document/d/1-UCudvPACSM-bg-4B4AHspyBZtdU1pI1XPLLAV69HVI/edit?usp=sharing

https://docs.google.com/document/d/1f9iz68tSUKyRALiwVRPU26PWm2N3ANchltFTcPaYvRA/edit?usp=sharing

https://docs.google.com/document/d/1hF_6OgenI_KKQ2X6o9h86NYhJ5_xBe6KUQin-ynQ-Jg/edit?usp=sharing

https://docs.google.com/document/d/1Qjt0kUK2uht03ZafD1GDbOLFXKEz3WkxbolLOnzEXkc/edit?usp=sharing



Informal arguments for area and volume formulas can make use of the way in which area and volume scale under similarity transformations: when one figure in the plane results from another by applying a similarity transformation with scale factor k, its area is k2 times the area of the first. Similarly, volumes of solid figures scale by k3 under a similarity transformation with scale factor k. Visualize the relation between two-dimensional and three-dimensional objects. G.GMD.4 - Identify the shapes of two-dimensional cross-sections of three-dimensional

objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. Apply geometric concepts in modeling situations. G.MG.1 - Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder). Focus on situations that require relating two- and three-dimensional objects, determining and using volume, and the trigonometry of general triangles.




6. Attend to precision. 7. Look for and make use of



G.GMD.4 (12.1) G.MG.1 (Throughout)

Geometry Instructional Focus 4: Connecting Algebra and Geometry through Coordinates

Suggested Quarter/Time: 3rd

/20 days



Use coordinates to prove simple geometric theorems algebraically G.GPE.4 - Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). G.GPE.5 - Prove the slope criteria for parallel and perpendicular lines and uses them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). G.GPE.6 - Find the point on a directed line segment between two given points that

partitions the segment in a given ratio. G.GPE.7 - Use coordinates to compute perimeters of polygons and areas of triangles





4. Model with mathematics. 5. Use appropriate tools

G.GPE.4 (6.2-6.4, 6.6) G.GPE.5 (3.3-3.4) G.GPE.6 (8.7, 10.8) G.GPE.7 (1.6, 11.1)

https://docs.google.com/document/d/1hdzTcV9kqaMCDzXw5RwJINgI97ET73TdzpLyPL2gOuo/edit?usp=sharing








https://docs.google.com/document/d/1X2O8Dsjl87G1BaKMjP8Hng_OaRMSK5do6Ck9FEANU1s/edit?usp=sharing

https://docs.google.com/document/d/1sXEnzBygI99GfAoabfBKVRJOTk78fEDZmRjFWyWxXyk/edit?usp=sharing

https://docs.google.com/document/d/1gmuPU2ZQsLH7WVoc9HeSoeYZnTsqPsQXf_Cdw1NcdvA/edit?usp=sharing

https://docs.google.com/document/d/1o5d-l6g8pbvy_D2c5KPC5xjDTCuE7DZ4wMuWfiDH7x8/edit?usp=sharing






and rectangles, e.g., using the distance formula.

This provides practice with the distance formula and its connection with the Pythagorean theorem. This unit has a close connection with the next unit. For example, a curriculum might merge G.GPE.1 and the Unit 5 treatment of G.GPE.4 with the standards in this unit. Reasoning with triangles in this unit is limited to right triangles; e.g., derive the equation for a line through two points using similar right triangles. Relate work on parallel lines in G.GPE.5 to work on A.REI.5 in High School Algebra I involving systems of equations having no solution or infinitely many solutions. Translate between the geometric description and the equation for a conic section. G.GPE.2 - Derive the equation of a parabola given a focus and directrix.

The directrix should be parallel to a coordinate axis.

strategically. 6. Attend to precision. 7. Look for and make use of



Geometry Instructional Focus 5: Circles With and Without Coordinates Suggested Quarter/Time: 4

th/25 days



Understand and apply theorems about circles G.C.1 - Prove that all circles are similar. G.C.2 - Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. G.C.3 - Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. G.C.4 - (+) Construct a tangent line from a point outside a given circle to the circle. Find arc lengths and areas of sectors of circles G.C.5 - Derive using similarity the fact that the length of the arc intercepted by an angle is

proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.







6. Attend to precision. 7. Look for and make use

G.C.1 (10.1) G.C.2 (10.2-10.4) G.C.3 (10.4, 10.5) G.C.4 (Plus) G.C.5 (10.2, 11.3)

https://docs.google.com/document/d/12_71GKE-IAbQqFVrcnqgABpmW4WGFklu6q_Tq04jEhE/edit?usp=sharing




https://docs.google.com/document/d/1eBLL9SvQIAeMJ77nK6AG_GJRw9aBVwGocpmsGwFO3_c/edit?usp=sharing

https://docs.google.com/document/d/1qAk7_qoh0P6fzgT8UcMNnnDLavsh9lWQy2XKhTz0GoA/edit?usp=sharing

https://docs.google.com/document/d/1cWBjtWoDkbSSLvk45Re1N-hLDeazaHHze1_BWXMXtWk/edit?usp=sharing

https://docs.google.com/document/d/1tNu1kqhgeDQS3AAfqDutNvLOFrWqxm9lWSZK-y3ccRo/edit?usp=sharing

https://docs.google.com/document/d/1A6MN4UEiabDTyW1p2iQtnm5t9cnsgyud404cX7KvRhI/edit?usp=sharing








Emphasize the similarity of all circles. Note that by similarity of sectors with the same central angle, arc lengths are proportional to the radius. Use this as a basis for introducing radian as a unit of measure. It is not intended that it be applied to the development of circular trigonometry in this course. Translate between the geometric description and the equation for a conic section G.GPE.1 - Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. Use coordinates to prove simple geometric theorems algebraically G.GPE.4 - Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0,2). Include simple proofs involving circles. Apply geometric concepts in modeling situations G.MG.1 - Use geometric shapes, their measures, and their properties to describe objects

(e.g., modeling a tree trunk or a human torso as acylinder). Focus on situations in which the analysis of circles is required.



G.GPE.1 (10.8) G.GPE.4 (6.2-6.4, 6.6) G.MG.1 (Throughout)

Geometry Instructional Focus 6: Applications of Probability

Suggested Quarter/Time: 4th

/20 days



Understand independence and conditional probability and use them to interpret data. S.CP.1 - Describe events as subsets of a sample space (the set of outcomes) using

characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). S.CP.2 - Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to




3. Construct viable

S.CP.1 (13.6) S.CP.2 (13.5)

https://docs.google.com/document/d/1c4SOFPKt4DmGYFgSN0ZG5CNAAPuCBroeXCxNSd5z-3A/edit?usp=sharing

https://docs.google.com/document/d/1X2O8Dsjl87G1BaKMjP8Hng_OaRMSK5do6Ck9FEANU1s/edit?usp=sharing


https://docs.google.com/document/d/1LbhPtHC3matKk_54EyOuVD-q7LzxmWWSoQJ1uxyHvvI/edit?usp=sharing

https://docs.google.com/document/d/17-IgsJ2x-nOXl93_N6J_Mm1qyKWzkOXTXL3Vf6KatP0/edit?usp=sharing




determine if they are independent. S.CP.3 - Understand the conditional probability of A given B as P(A and B)/P(B), and

interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. S.CP.4 - Construct and interpret two-way frequency tables of data when two categories are

associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. S.CP.5 - Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. Build on work with two-way tables from Algebra I Unit 3 (S.ID.5) to develop understanding of conditional probability and independence. Use the rules of probability to compute probabilities of compound events in a uniform probability model S.CP.6 - Find the conditional probability of A given B as the fraction of B’s outcomes that

also belong to A, and interpret the answer in terms of the model. S.CP.7 - Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the

answer in terms of the model. S.CP.8 - (+) Apply the general Multiplication Rule in a uniform probability model, P(A and

B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model. S.CP.9 - (+) Use permutations and combinations to compute probabilities of compound

events and solve problems. Use probability to evaluate outcomes of decisions S.MD.6 - (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random

number generator). S.MD.7- (+) Analyze decisions and strategies using probability concepts (e.g., product

testing, medical testing, pulling a hockey goalie at the end of a game). This unit sets the stage for work in Algebra II, where the ideas of statistical inference are introduced. Evaluating the risks associated with conclusions drawn from sample data (i.e. incomplete information) requires an understanding of probability concepts.

arguments and critique the reasoning of others.


strategically. 6. Attend to precision. 7. Look for and make use



S.CP.3 (13.5) S.CP.4 (13.5 Lab only) S.CP.5 (Throughout Ch 13) S.CP.6 (13.5 lab only) S.CP.7 (13.6)

https://docs.google.com/document/d/1MLaV-dAdj-0vnyjQVbbTMonpwltUsrD3XXMXSSe6HVU/edit?usp=sharing

https://docs.google.com/document/d/1BcNNCZuiEwcZ47sVHZazSjKGbnEzfK19OTUlQJS2x_I/edit?usp=sharing

https://docs.google.com/document/d/1qH0KaHKkJxspFVsSZvZYYqDoja1K4cANnIkAM-qhVls/edit?usp=sharing

https://docs.google.com/document/d/1ht6_PswOcHwfDzPo2xQWSBnNAkCOd1JrW3V3jKlXeD8/edit?usp=sharing

https://docs.google.com/document/d/1wSsF-9B3Hp-nQqGQEi0JF79xrzIX8-S0f8had3lvV7E/edit?usp=sharing

https://docs.google.com/document/d/1ti_NrcRZI1gShPlI7tDITu1SfU2__JrY-GHd7KAZc8w/edit?usp=sharing

https://docs.google.com/document/d/1ufrIL3WmcbI3XOz_Fq1MGGJGN0IoVIRKll5szcJjpug/edit?usp=sharing

https://docs.google.com/document/d/12RB5RPbrdB2merjsWoPc6FOuyAy0VWzMMkBPo4swtZ4/edit?usp=sharing

https://docs.google.com/document/d/1hUcWXasOuP3z0UsS-rXMxOXUlXRP2J0ecBAGjiPsGnM/edit?usp=sharing







Algebra II Pacing Guide

Algebra II 1ST

SEMESTER


Content and Educator

Notes

Perform arithmetic operations with complex numbers N.CN.1 - Know there is a complex number i such that i

2 = −1, and every complex number

has the form a + bi with a and b real. N.CN.2 - Use the relation i

2 = –1 and the commutative, associative, and distributive

properties to add, subtract, and multiply complex numbers. Use complex numbers in polynomial identities and equations N.CN.7 – Solve quadratic equations with real coefficients that have complex solutions. Interpret the structure of expressions A.SSE.1- Interpret expressions that represent a quantity in terms of its context. Extend to polynomial and rational expressions.


b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)

n as the product of P and a factor not depending

on P.

A.SSE.2 - Use the structure of an expression to identify ways to rewrite it. For example, see x

4 – y

4 as (x

2)2 – (y


(x2 – y

2)(x

2 + y

2).

Perform arithmetic operations on polynomials A.APR.1 - Understand that polynomials form a system analogous to the integers, namely,

they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Extend beyond the quadratic polynomials found in Algebra I. Understand the relationship between zeros and factors of polynomials. A.APR.2-Know and apply the Remainder Theorem: For a polynomial p(x) and a number a,









4.4 (N.CN.1) 4.4 (N.CN.2) 4.5, 4.6 (N.CN.7) 5.1, 5.2 (A.SSE.1a) 4.7(A.SSE.1b) 4.3, 5.1 (A.SSE.2)

5.1 (A.APR.1) 5.6 (A.APR.2)

https://docs.google.com/document/d/1jl4wVY7Mzpb7o12-uVA2LeO3Q3c_pLpPQmD2voco2C4/edit?usp=sharing

https://docs.google.com/document/d/1baVIPirHMiDa6FZFJ9rH-61E4txtvJ1LTvEdrgY7pZM/edit?usp=sharing

https://docs.google.com/document/d/16Oyxz1VxTXaLi4TCyOHQJ7nOuFlsP5F1pk31L6E4CIM/edit?usp=sharing

https://docs.google.com/a/k12.sd.us/document/d/1EgBQSZap3g4iybCEHN9bUVxr2WjsHiCCPD3-vvubEI4/edit?authkey=COC8qpkM&hl=en_US&authkey=COC8qpkM

https://docs.google.com/document/d/1EKjrQYGS_vCJpyP2ODbkftapbg8JezD3Bsnn5u-cR-w/edit

https://docs.google.com/document/d/1Zpmg9z7jj8YyXalAYnAJDvXzKzYUVfr0-fz8p2L1EiM/edit?usp=sharing

https://docs.google.com/document/d/1SHvdk3RfsWThu0px3kNWLtHTloQaPYl5g33v3hOv5cA/edit?usp=sharing











the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x). A.APR.3 - Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial. Use polynomial identities to solve problems A.APR.4 - Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x

2 + y

2)2 = (x

2 – y

2)2 + (2xy)

2 can be used to generate

Pythagorean triples. Rewrite rational expressions A.APR.6 - Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form

q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system. A.REI.11- Explain why the x-coordinates of the points where the graphs of the

equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

Include combinations of linear, polynomial, rational, radical, absolute value, and exponential functions. Create equations that describe numbers or relationships. A.CED.1 - Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A.CED.2 - Create equations in two or more variables to represent relationships between

quantities; graph equations on coordinate axes with labels and scales. A.CED.3 - Represent constraints by equations or inequalities, and by systems of equations

and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. A.CED.4 - Rearrange formulas to highlight a quantity of interest, using the same reasoning

as in solving equations. For example, rearrange Ohm’s law V = IR to highlight resistance R. For A.CED.1, use all available types of functions to create such equations, including root functions, but constrain to simple cases. While functions used in A.CED.2, 3, and 4 will often be linear, exponential, or quadratic the types of problems should draw from more complex situations than those addressed in Algebra I. For example, finding the equation of a line through a given point perpendicular to another line allows one to find the distance

4.3, 4.5, 4.6 (A.APR.3) 5.7 extension (A.APR.4) 5.2 (A.APR.6) In sections 4-2, 6-3 and 7-2 graphing technology lab- extend to include intersection with a line (A.REI.11) 4.7, 4.8, 7.1, 7.8 (A.CED.1) 4.1, 4.2, 4.7 (A.CED.2) 4.8, 7.8(A.CED.3) 4.7 (A.CED.4)

https://docs.google.com/document/d/1l9YMA94AfTD8eE5D1D2ERDmpYRJ_w7kUh-WpM9z7hpk/edit?usp=sharing

https://docs.google.com/document/d/1FhDCSkJDsOHDGSJgmm2V95F9peYnuqsGYa6pK37948s/edit?usp=sharing

https://docs.google.com/document/d/1Ziu3bt4DN6h60dukCFvEFmKSJOWQDBbecwr8mvbZwCE/edit?usp=sharing

https://docs.google.com/document/d/1S-M7rVkyHaLj1fBW_6rYHOV9cZuK-dlPlp8xxcCH11k/edit?usp=sharing


https://docs.google.com/document/d/1Sfq73OJP9nQEdSEngYGAY5auuPbEuDoou9rK9-PNqIY/edit



https://docs.google.com/document/d/1G2dvLU9qP2sxcMVBs1WN_EBef0p5htAlkigHauKWHEI/edit



from a point to a line. Note that the example given for A.CED.4 applies to earlier instances of this standard, not to the current course. Interpret functions that arise in applications in terms of a context. F.IF.4 - For a function that models a relationship between two quantities, interpret key

features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. F.IF.5 - Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function. F.IF.6 - Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph. Focus on linear functions and exponential functions whose domain is a subset of the integers. Emphasize the selection of a model function based on behavior of data and context. Analyze functions using different representations F.IF.7 - Graph functions expressed symbolically and show key features of the graph, by

hand in simple cases and using technology for more complicated cases. b. Graph square root, cube root, and piecewise-defined functions, including step functions

and absolute value functions.

c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

Relate F.IF.7c to the relationship between zeros of quadratic functions and their factored form. e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude. F.IF.8 - Write a function defined by an expression in different but equivalent forms to reveal

and explain different properties of the function. F.IF.9 - Compare properties of two functions each represented in a different way

(algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum. Focus on applications and how key features relate to characteristics of a situation, making selection of a particular type of function model appropriate.

4.1, 4.2, 5.4 (F.IF.4) 2.6, 4.1 (F.IF.5) 4.7 extension (F.IF.6) 4.1, 5.4 (F.IF.7) 4.7 (F.IF.8) 4.1 (F.IF.9)

https://docs.google.com/document/d/1sYhL4sj2HiFnYZdAeHa8At6oQjf587Pf37Bbe1DFtTk/edit?authkey=CMOvl8wD

https://docs.google.com/document/d/1KazmKUlL9WtK2HsB5S9kt5M2g1Z8ZCulWjEGEc1uBB0/edit?authkey=CMufhqwC

https://docs.google.com/document/d/1k7k7bUhZ-aJAADuS0AQD6oDF0HStXEZS3PH5u8y1-8w/edit?authkey=CI6Bu5YM

https://docs.google.com/document/d/13duGO3Qhr4PKTg5vdwMt0f4eO51-2Qcvl8sRpy1LlYY/edit?usp=sharing&authkey=CLrYzmw

https://docs.google.com/document/d/1fQcJ2WEJ0z4vkyrdSV2_tEmZhwZbgLp2W9ScAc4brbA/edit?authkey=CMHlpacL

https://docs.google.com/document/d/1kr88d0KMqPovoyUV3riYDcW-F2ZFwcfzHh4JNJLvQDM/edit?authkey=CNjAkLEM



Building new functions from existing functions F.BF.3 - Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

2.7, 4.7 (F.BF.3)

Algebra II 2ND

SEMESTER


Content and Educator

Notes

Create equations that describe numbers or relationships. A.CED.1 - Create equations and inequalities in one variable and use them to solve

problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions. A.CED.2 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales. A.CED.3 - Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods. Interpret functions that arise in applications in terms of a context. F.IF.4 - For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity. F.IF.5 - Relate the domain of a function to its graph and, where applicable, to the

quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.









4.7, 4.8, 7.1, 7.4, 7.5, 7.8 (A.CED.1) 4.1, 4.2, 4.7, 6.3, 7.1 (A.CED.2) 4.8, 7.8(A.CED.3) 4.1, 4.2, 5.4, 6.3 (F.IF.4) 2.6, 4.1, 6.3 (F.IF.5)

https://docs.google.com/document/d/1vu5LMTs-9qfuqtLnVQNCOYOBhzFZ8JmJhTmNt_Hii7g/edit?authkey=CNqXm40J

https://docs.google.com/document/d/1Sfq73OJP9nQEdSEngYGAY5auuPbEuDoou9rK9-PNqIY/edit



https://docs.google.com/document/d/1sYhL4sj2HiFnYZdAeHa8At6oQjf587Pf37Bbe1DFtTk/edit?authkey=CMOvl8wD

https://docs.google.com/document/d/1KazmKUlL9WtK2HsB5S9kt5M2g1Z8ZCulWjEGEc1uBB0/edit?authkey=CMufhqwC











Analyze functions using different representations F.IF.7 - Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

b. Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

c. Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

Relate F.IF.7c to the relationship between zeros of quadratic functions and their factored form.

e. Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

Interpret the structure of expressions A.SSE.1- Interpret expressions that represent a quantity in terms of its context. Extend to polynomial and rational expressions.


b. Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)

n as the product of P and a factor not depending

on P. A.SSE.2 - Use the structure of an expression to identify ways to rewrite it. For example, see x

4 – y

4 as (x

2)2 – (y


(x2 – y

2)(x

2 + y

2).

Write expressions in equivalent forms to solve problems A.SSE.4 - Derive the formula for the sum of a finite geometric series (when the common

ratio is not 1), and use the formula to solve problems. For example, calculate mortgage payments. Consider extending A.SSE.4 to infinite geometric series in curricular implementations of this course description. Represent and solve equations and inequalities graphically. Understand solving equations as a process of reasoning and explain the reasoning. A.REI.2 - Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise. Extend to simple rational and radical equations. A.REI.11- Explain why the x-coordinates of the points where the graphs of the

equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

4.1, 5.4, 6.3 (F.IF.7) 5.1, 5.2 (A.SSE.1a) 4.7, 6.5, 7.1 (A.SSE.1b) 4.3, 5.1, 6.5, 7.5 (A.SSE.2) 7.2, 10.3 (A.SSE.4) 6.7, 8.6 (A.REI.2) In sections 4-2, 6-3 and 7-2 graphing technology lab- extend to include intersection with a line (A.REI.11)

https://docs.google.com/document/d/13duGO3Qhr4PKTg5vdwMt0f4eO51-2Qcvl8sRpy1LlYY/edit?usp=sharing&authkey=CLrYzmw

https://docs.google.com/a/k12.sd.us/document/d/1EgBQSZap3g4iybCEHN9bUVxr2WjsHiCCPD3-vvubEI4/edit?authkey=COC8qpkM&hl=en_US&authkey=COC8qpkM

https://docs.google.com/document/d/1EKjrQYGS_vCJpyP2ODbkftapbg8JezD3Bsnn5u-cR-w/edit

https://docs.google.com/document/d/1Zb8GYhXPvmUxAaBllr_ZimbDJq9EPtC0FQqHePB48jA/edit?usp=sharing

https://docs.google.com/document/d/1zWGKmMn9EqNAIjciXughynQS0VIu9QQ1uswZdrqMi_c/edit?usp=sharing





Include combinations of linear, polynomial, rational, radical, absolute value, and exponential functions. Build a function that models a relationship between two quantities F.BF.1 - Write a function that describes a relationship between two quantities.

b. Combine standard function types using arithmetic operations. For example, build a function that models the temperature of a cooling body by adding a constant function to a decaying exponential, and relate these functions to the model.

Develop models for more complex or sophisticated situations than in previous courses. Building new functions from existing functions F.BF.3 - Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them. F.BF.4 - Find inverse functions.

a. Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. For example, f(x) = 2 x

3 or f(x) = (x+1)/(x-1) for x ≠

1. Use transformations of functions to find models as students consider increasingly more complex situations. For F.BF.3, note the effect of multiple transformations on a single graph and the common effect of each transformation across function types. Extend F.BF.4a to simple rational, simple radical, and simple exponential functions; connect F.BF.4a to F.LE.4. Construct and compare linear, quadratic, and exponential models and solve problems F.LE.4 - For exponential models, express as a logarithm the solution to ab

ct = d where a, c,

and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. Consider extending this unit to include the relationship between properties of logarithms and properties of exponents, such as the connection between the properties of exponents and the basic logarithm property that log xy = log x +log y. Summarize, represent, and interpret data on a single count or measurement variable S.ID.4 - Use the mean and standard deviation of a data set to fit it to a normal distribution

and to estimate population percentages. Recognize that there are data sets for which such

6.1 without composition (F.BF.1) 2.7, 4.7 (F.BF.3) 6.2 without domain restrictions and no composition (F.BF.4) 7.2, 7.8 (F.LE.4) Seek additional resources (S.ID.4)

https://docs.google.com/document/d/1YZovUOExKlhTrco9Mil3RsOxtz4tbHRCIOYZxFwfKUk/edit?authkey=COqO4ckO

https://docs.google.com/document/d/1vu5LMTs-9qfuqtLnVQNCOYOBhzFZ8JmJhTmNt_Hii7g/edit?authkey=CNqXm40J

https://docs.google.com/document/d/1EpPyp6FgEg58u12SDx2eEkPIYXZHZoNfs5z9vAURuug/edit?usp=sharing

https://docs.google.com/document/d/112c59fKeb-wM1Q36W95U5A_ZmaJRD93SclMPdoXDThE/edit?usp=sharing

https://docs.google.com/document/d/1lsLBT_ICXrSS9dJXmjqMkoVFEZPMnkF-wa55wGxnfsI/edit?usp=sharing



a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve. While students may have heard of the normal distribution, it is unlikely that they will have prior experience using it to make specific estimates. Build on students’ understanding of data distributions to help them see how the normal distribution uses area to make estimates of frequencies (which can be expressed as probabilities). Emphasize that only some data are well described by a normal distribution. Understand and evaluate random processes underlying statistical experiments S.IC.1 - Understand statistics as a process for making inferences about population parameters based on a random sample from that population. S.IC.2 - Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation. For example, a model says a spinning coin falls heads up with probability 0.5. Would a result of 5 tails in a row cause you to question the model? For S.IC.2, include comparing theoretical and empirical results to evaluate the effectiveness of a treatment. Make inferences and justify conclusions from sample surveys, experiments, and observational studies S.IC.3 - Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each. S.IC.4 - Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling. S.IC.5 - Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant. S.IC.6 - Evaluate reports based on data. In earlier grades, students are introduced to different ways of collecting data and use graphical displays and summary statistics to make comparisons. These ideas are revisited with a focus on how the way in which data is collected determines the scope and nature of the conclusions that can be drawn from that data. The concept of statistical significance is developed informally through simulation as meaning a result that is unlikely to have occurred solely as a result of random selection in sampling or random assignment in an experiment. For S.IC.4 and 5, focus on the variability of results from experiments - that is, focus on statistics as a way of dealing with, not eliminating, inherent randomness. Extend the domain of trigonometric functions using the unit circle F.TF.1 - Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

Seek additional resources (S.IC.1) Seek additional resources (S.IC.2) Seek additional resources (S.IC.3) Seek additional resources (S.IC.4) Seek additional resources (S.IC.5) Seek additional resources (S.IC.6) 12.2 (F.TF.1)

https://docs.google.com/document/d/1jKdFgRY2O2rU8pRwx-X-tSYITUwp14UcmjbEmf0vsVA/edit?usp=sharing

https://docs.google.com/document/d/1G48ephsF0QOHipvT4nM-ltiMQuK-m0nwsfSv9Yyi0gg/edit?usp=sharing

https://docs.google.com/document/d/1lextR5fuDFfj6KmgINnJXzayD0_J8ZmX5jqjc95K-UY/edit?usp=sharing

https://docs.google.com/document/d/1w7OrOP1R8zLdGswmc7EOzRX3S_9Zo9lYwIVP-B6CIPQ/edit?usp=sharing

https://docs.google.com/document/d/1QNxLD_vU6bdM3SosxE2dsDECgWEfuKO0YLZLHx67Qrg/edit?usp=sharing

https://docs.google.com/document/d/1YFhGbIlhrFlpknXTYvR4Kby7BhiRSqMF9Qt6wUZqMsU/edit?usp=sharing

https://docs.google.com/document/d/12LHe24F7eijxNYOjY0Hi5FhsWemT9kR4VaR8r0waarg/edit?usp=sharing



F.TF.2 - Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle. Model periodic phenomena with trigonometric functions. F.TF.5 - Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline. Prove and apply trigonometric identities. F.TF.8 - Prove the Pythagorean identity sin

2(θ) + cos

2(θ) = 1 and use it to find sin (θ), cos

(θ), or tan (θ), given sin (θ), cos (θ), or tan (θ), and the quadrant of the angle. An Algebra II course with an additional focus on trigonometry could include the (+) standard F.TF.9: Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems. This could be limited to acute angles in Algebra II.

12.2 (F.TF.2) 12.7(F.TF.5) 12.2 (F.TF.8)

https://docs.google.com/document/d/1LZwQ79otrxwgrI1pbhMjShtAsGAG94EhYaj-rDPbFnQ/edit?usp=sharing

https://docs.google.com/document/d/1h46_thRXqaXEOVIO1FuqlGXmFWlvldm3Vkmn9_GuRKQ/edit?usp=sharing

https://docs.google.com/document/d/1UXLnweL7lwjj9MENLx9DF3-7wQzY66W2b24hI4smqQ8/edit?usp=sharing



NCSD Math Vocabulary

Research by Marzano indicates that the importance of direct vocabulary instruction cannot be overstated. Vocabulary provides essential background knowledge and is linked to academic achievement. NCSD Math Curriculum Committee members worked to create a vertically aligned vocabulary progression for which key terms were identified and labeled as critical or supporting. Critical vocabulary words are those words that all students are expected to master by the end of the grade and will appear on common assessments. Based on research about vocabulary acquisition, committee members attempted to limit the number of Tier 3 critical math vocabulary to fewer than 30 words. Supporting vocabulary words are those words students should be exposed to throughout the year. The purpose of this work is to focus instruction and provide guidance to teachers. Teachers will be asked to provide feedback in order to guide to revision of these lists. The following table includes the critical Tier 3 vocabulary words that students should master by the end of the school year.

NCSD Math Vocabulary K - 8

Kindergarten First Grade Second Grade Third Grade Fourth Grade Fifth Grade Sixth Grade Seventh Grade Eighth Grade

2-dimensional 2-

dimensional addend angle(s) acute angle braces

algebraic expressions

additive inverse alternate

exterior angles

3-dimensional 3-

dimensional analog denominator algorithm brackets bar notation adjacent angles

alternate interior angles

addition (add, plus, combine)

analog base ten

numerals division angle capacity coefficient circumference

angle sum (interior of a

figure)

circle bundle centimeter

(cm) equal part

common denominator

composite composite

figure commission

constant of proportionality

cone circle compose factor decimal convert dependent

variable complementary

angles constant rate of

change

corners compose customary

system fraction decimal point

coordinate plane

distributive property

complex fraction corresponding

angles

count decompose decompose label dividend cubed equivalent

ratios constant dilation

cube difference digital liquid volume divisor customary

system exponents cross products direct variation

curved digit expanded form multiplication endpoint (vertex)

dividend independent

variable cross section exterior angle





cylinder digital fact family numerator equivalent

fraction divisor

interquartile range

diameter hypotenuse

edges equal to feet/foot (ft) parallel factors expression mean / average

discount image

eight equations hundreds parallelogram inequalities factors mean

absolute deviation

double box plot irrational

eighteen even inch (in.) partitioned line of

symmetry

greatest common

factor (gcf)

measures of center

double dot plot leg (of a right

triangle)

eleven fact family meter perimeter meter (m) hundredths median equivalent

expressions line of best fit

equal (to) fourths metric system place value multiples improper fractions

mode gratuity / tip linear

association

faces greater

than number line polygon

multiplicative inverse

least common denominator

outliers integer linear equations

fewer half circle number name product numerator least common

multiple percent lateral face linear functions

fifteen half hour pentagon quotient obtuse angle metric system quadrant lateral surface negative

association

five halves picture graph scale quotient mixed

numbers quartiles like terms

nonlinear association

four hour place value unit remainder ordered pairs range markdown/

markup positive

association

fourteen length quadrilateral variable right angle parentheses ratio opposites pre-image

greater (than) (more)

less than yard (yd) whole

numbers yard (yd) plane scaling percent change

Pythagorean Theorem

heavy/heavier odd

prime factorization

surface area percent

decrease/increase reflection

height ones

product term (in a sequence)

percent equation relative

frequency





hexagon place value

quadrant vertices /

vertex percent error rotation

length quarter circle

quotient volume percent proportion scatterplot

less (than) (least) quarters

rule

pi scientific notation

lighter rectangle

scalene triangle

principle slope

long/longer rectangular

prism

scaling

proportion slope-intercept

form

narrow/narrower sides

simplest form

proportional solve

(an equation)

nine sum

solid figure

radius substitution

nineteen symbol

squared

rate transformation

number tens

standard form

rational number translation

number sentence trapezoid

tenths

repeating decimal transversal

one triangular

prism

thousandths

sales tax two-way table

rectangle unknown

vertex

selling price x-intercept

seven vertex

volume

semi circle y-intercept

seventeen

x-axis

simple interest short/shorter

x-coordinate

slant height

sides

y-axis

supplementary angles

six

y-coordinate

terminating decimal

sixteen

unit rate sort

vertical angles

sphere square





subtraction (take away, minus)

tall/taller ten thirteen three triangle twelve twenty two vertices weight wide/wider width

zero



Kindergarten Critical Math Vocabulary Please note: These words are critical to be mastered by the end of the year. This chart aligns the critical vocabulary to our NCSD Pacing Guides. Supporting words are listed at the bottom of each column.

Critical Vocabulary Benchmark 1 Benchmark 2 Benchmark 3 Benchmark 4

2-dimensional X X X

3-dimensional X

addition (add, plus, combine) X X X

circle X X

cone X

corners X X

count X X X X

cube X

curved X X

cylinder X

edges X

eight X X X X

eighteen X X X X

eleven X X X X

equal (to) X X X X

faces X

fewer X X



fifteen X X X X

five X X X X

four X X X X

fourteen X X X X

greater (than) (more) X X X X

heavier X

height X

hexagon X X X

length X X

less (than) (least) X X X

lighter X

long/longer X X

narrower X

nine X X X X

nineteen X X X X

number X X X X

number sentence X X X

one X X X X

rectangle X X X

seven X X X X



seventeen X X X X

short/shorter X X

sides X X X

six X X X X

sixteen X X X X

sort X

sphere X

square X X X

subtraction (take away, minus) X X

taller X

ten X X X X

thirteen X X X X

three X X X X

triangle X X X

twelve X X X X

twenty X X X X

two X X X X

vertices X X X

weight X

wider X



width X

zero X X X X

SUPPORTING

TIER 1 WORDS

flat color flat

SUPPORTING TIER 2 WORDS

alike

attribute

different group

large

model objects

order same

sequence

shape

small straight

above

alike

attribute

behind

below

beneath

beside

combine

compose

decompose

different group

in back of in front of large

measure

next to

objects on the bottom

on top

order over same

sequence

shape

small to the left to the right under

combine

facts

group

measure

objects

order

alike

attribute

combine

compose

create

decompose

different facts

group

model objects

order roll same

sequence

shape

solid

stack

straight



SUPPORTING TIER 3 WORDS

digits

make

rhombus

trapezoid

digits

equations

make

rhombus

symbol take apart trapezoid

digits

equations

make

symbol take apart

digits

equations

make

ones

symbol take apart tens

SUPPORTING CONCEPTS how many how many how many how many

SUPPORTING STRATEGIES

counting on

ten frame

counting on

ten frame

counting on

ten frame

counting on

ten frame



1st Grade Critical Math Vocabulary Please note: These words are critical to be mastered by the end of the year. This chart aligns the critical vocabulary to our NCSD Pacing Guides. Supporting words are listed at the bottom of each column.


2-dimensional X

3-dimensional X

analog X

bundle X

circle X

compose X X X X

decompose X X X X

difference X X X X

digit X

digital X

equal to X

equations X X X X

even X

fact family X

fourths

X

greater than

X

half circle

X



half hour X

halves

X

hour X

length X

less than

X

odd X

ones X

place value X

quarter circle

X

quarters

X

rectangle

X

rectangular prism

X

sides X

sum X X X X

symbol X

tens X

trapezoid

X

triangular prism

X

unknown X

vertex

X




addition (add, plus, combine) longer longest subtraction (take away, minus)

false

true



2nd Grade Critical Math Vocabulary Please note: These words are critical to be mastered by the end of the year. This chart aligns the critical vocabulary to our NCSD Pacing Guides. Supporting words are listed at the bottom of each column.


addend X

analog X

base ten numerals X

centimeter (cm) X

compose X

customary system X

decompose X

digital X

expanded form X

fact family X X X X

feet/foot X

hundreds X

inch (in) X

meter X

metric system X

number line X X

number name X



pentagon X

place value X

picture graph X

quadrilateral X

yard X


columns digits equations equivalent expressions ones rows sum symbol tens unknown whole numbers

a.m. dime dollar bill equations equivalent expression hour hour hand minute hand minutes nickel p.m. penny quarter quarter past sum symbol unknown whole numbers

angle data data table edges equal shares equations equivalent expression faces fourths fraction halves horizontal key line plot partition quarters rectangular prims scale sum survey symbol tally mark thirds unknown vertical whole numbers

equations equivalent expression length measuring tape meter stick ruler symbol unit unknown yard stick



3rd Grade Critical Math Vocabulary Please note: These words are critical to be mastered by the end of the year. This chart aligns the critical vocabulary to our NCSD Pacing Guides. Supporting words are listed at the bottom of each column.


angle(s) X

denominator X

division X X X

equal part X X

factor X X X

fraction X

label X X

liquid volume X

multiplication X X X

numerator X

parallel X

parallelogram X

partitioned X X

perimeter X

place value X

polygon X X

product X X X



quotient X X X

scale X

unit X X X X

variable X X X

whole numbers X X X X

SUPPORTING WORDS

fact family

quadrilateral sum difference

area

array difference

fact family

interpret multiple sum

array

equivalent fact family

multiple

area

array

fact family

feet inches

multiple

SUPPORTING STRATEGY

number line



4th Grade Critical Math Vocabulary Please note: These words are critical to be mastered by the end of the year. This chart aligns the critical vocabulary to our NCSD Pacing Guides. Supporting words are listed at the bottom of each column.


acute angle X

algorithm X

angle X

common denominator X

decimal X

decimal point X

dividend

X

divisor

X

endpoint (vertex)

X

equivalent fraction X

factors X X X

inequalities X X

line of symmetry X

meter (m) X X

multiples X X X

multiplicative inverse X

numerator X



obtuse angle X

quotient X

remainder X

right angle X

yard (yd) X X


area model array expanded form expression operation place value product

area composite formula perimeter prime

denominator hundredths improper fractions mixed numbers

capacity centimeter cup customary system degree gallon gram hour intersecting lines interval (time) kilogram line line plot line segment liter metric system milliliter minute ounce parallel lines pattern perpendicular lines pint point pound protractor quart ray



5th Grade Critical Math Vocabulary Please note: These words are critical to be mastered by the end of the year. This chart aligns the critical vocabulary to our NCSD Pacing Guides. Supporting words are listed at the bottom of each column.


braces X X

brackets X X

capacity

X

composite X

convert

X

coordinate plane

X

cubed X

X

customary system

X

dividend X X

divisor X X

expression X X X

factors X X

greatest common factor (GCF)

X

hundredths X X

improper fractions

X

least common denominator X

least common multiple X



metric system X

mixed numbers X X

ordered pairs X

parentheses X X

plane X

prime factorization X

product X

quadrant X

quotient X X

rule X X X X

scalene triangle X

scaling X X

simplest form X X

solid figure X

squared X

standard form X X

tenths X X

thousandths X X

vertex X

volume X X



x-axis X

x-coordinate X

y-axis X

y-coordinate X

Supporting Words (These words are introduced or reinforced)

algorithm

base

decimal point (and) expanded form

inequalities

number line

remainder

algorithm

decimal point (and) denominator expanded form

inequalities

multiples

number line

numerator

composite figure

cubic

denominator height measure

number line

numerator

acute angle

area

axis

composite figure

cube

cubic

edges

equilateral triangle

faces

height intersecting lines

isosceles triangle

kilo

line plot measure

measurement unit milli obtuse angle

obtuse triangle

parallel parallelogram

perimeter polygon

quadrilateral rhombus

right angle

trapezoid



NCSD Common Assessment Information

2015-2016 NCSD Math Benchmark Summary K-5

The purpose of these common benchmark assessments is to monitor progress towards mastery of standards.

IEP and 504 accommodations should be followed according to the student plan.

Benchmarks are to be administered to all students, regardless of IEP or 504, without review.

Grade Benchmark 1 Benchmark 2 Benchmark 3 Benchmark 4 Guidelines for all students

Kindergarten

Interviews

11 questions

14 questions

13 questions

13 questions

Kindergarten

Each benchmark is given one-on-one.

Grade 1

Read Aloud

Teacher

Discretion

16 questions

16 questions

14 questions

15 questions

Grade 1

Each benchmark can be read aloud in a whole

group setting or smaller learning

stations. Students will need scratch paper, pencil,

or whiteboard.

Grade 2

Independent

45-60 minutes

20 questions

22 questions

23 questions

19 questions

Grades 2 - 5

Second grades must read all benchmarks on their

own.

Teachers can read a vocabulary word but NOT

give the definition or an example.

Students will need scratch paper, pencil, or

whiteboard.

No calculators are allowed on any benchmark.

Each benchmark assessment is to be completed in

one 45-60 minute class session. This is done in

order to build fluency and use effective and

efficient strategies.

Grade 3

Independent

45-60 minutes

24 questions

24 questions

25 questions

22 questions

Grade 4

Independent

45-60 minutes

22 questions

23 questions

30 questions

26 questions

Grade 5

Independent

45-60 minutes

24 questions

23 questions

25 questions

18 questions



2015-2016 NCSD Math Benchmark Summary Course 1 – Course 3 (Grades 6-8)

The purpose of these common benchmark assessments is to monitor progress towards mastery of standards.

IEP and 504 accommodations should be followed according to the student plan.

Benchmarks are to be administered to all students, regardless of IEP or 504, without review.

Grade / Course Benchmark 1 Benchmark 2 Benchmark 3 Benchmark 4 Guidelines for all students

Grade 6-Course 1

Independent

Time: 40-60 minute

17 Questions

Calculator: no

20 Questions

Calculator: yes

22 Questions

Calculator: yes

18 Questions

Calculator: yes

Grade 6-8

-Teachers can read a vocabulary word but NOT give the definition or an example.

-Use of calculators is noted at the beginning of each benchmark.

-The benchmark assessment is designed to be completed in one 40-60 minute class period; the reason being is to build fluency and to use effective and efficient strategies.

Grade 7-Course 2

Independent

Time: 40-60 minute

18 Questions Calculator: no

18 Questions Calculator: yes



Grade 7

Accelerated

Independent

Time: 40-60 minute

18 Questions

Calculator: yes

18 Questions

Calculator: yes

22 Questions

Calculator: yes

18 Questions

Calculator: yes

Grade 8- Course 3

Independent

Time: 40-60 minute

21 Questions Calculator: no






2015-2016 NCSD Math Benchmark Summary High School

Benchmarks are to be administered to all students without review.

Course Benchmark 1 Benchmark 2 Guidelines for all students

Algebra 1

Independent

Time: 40-60 minute

34 Questions

Calculator: yes Testing window: Mid-point of course

34 Questions

Calculator: yes Testing window: End of Course

High School -IEP and 504 accommodations should be followed according to the student plan. ● Scientific or Graphing calculator allowed ● Graph paper allowed ● Scratch paper allowed Use of textbook and/or class notes NOT allowed -The benchmark assessment is designed to be completed in one 40-60 minute class period, the reason being is to build fluency and to use effective and efficient strategies. Geometry Provide formula sheet from back of Glencoe geometry book or provide a copy (see next page).

Geometry

Independent

Time: 40-60 minute

22 Questions


34 Questions


Algebra 2

Independent

Time: 40-60 minute

30 Questions


26 Questions




Goemetry Formula Sheet



Common Core State Standards for Mathematics Resources and Visuals



Standards of Mathematical Practice Math Practice Standard 1: Make sense of problems and persevere in solving them. Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals. They make conjectures about the form and meaning of the solution and plan a solution pathway rather than simply jumping into a solution attempt. They consider analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary. Older students might, depending on the context of the problem, transform algebraic expressions or change the viewing window on their graphing calculator to get the information they need. Mathematically proficient students can explain correspondences between equations, verbal descriptions, tables, and graphs or draw diagrams of important features and relationships, graph data, and search for regularity or trends. Younger students might rely on using concrete objects or pictures to help conceptualize and solve a problem. Mathematically proficient students check their answers to problems using a different method, and they continually ask themselves, "Does this make sense?" They can understand the approaches of others to solving complex problems and identify correspondences between different approaches. Math Practice Standard 2: Reason abstractly and quantitatively. Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects. Math Practice Standard 3: Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments. They make conjectures and build a logical progression of statements to explore the truth of their conjectures. They are able to analyze situations by breaking them into cases, and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others. They reason inductively about data, making plausible arguments that take into account the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments, distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects, drawings, diagrams, and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal until later grades. Later, students learn to determine



domains to which an argument applies. Students at all grades can listen or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments. Math Practice Standard 4: Model with mathematics. Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life, society, and the workplace. In early grades, this might be as simple as writing an addition equation to describe a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a problem in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know are comfortable making assumptions and approximations to simplify a complicated situation, realizing that these may need revision later. They are able to identify important quantities in a practical situation and map their relationships using such tools as diagrams, two-way tables, graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. Math Practice Standard 5: Use appropriate tools strategically. Mathematically proficient students consider the available tools when solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts. Math Practice Standard 6: Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.



Math Practice Standard 7: Look for and make use of structure. Mathematically proficient students look closely to discern a pattern or structure. Young students, for example, might notice that three and seven more is the same amount as seven and three more, or they may sort a collection of shapes according to how many sides the shapes have. Later, students will see 7 × 8 equals the well remembered 7 × 5 + 7 × 3, in preparation for learning about the distributive property. In the expression x2 + 9x + 14, older students can see the 14 as 2 × 7 and the 9 as 2 + 7. They recognize the significance of an existing line in a geometric figure and can use the strategy of drawing an auxiliary line for solving problems. They also can step back for an overview and shift perspective. They can see complicated things, such as some algebraic expressions, as single objects or as being composed of several objects. For example, they can see 5 - 3(x -y)2 as 5 minus a positive number times a square and use that to realize that its value cannot be more than 5 for any real numbers x and y. Math Practice Standard 8: Look for and express regularity in repeated reasoning. Mathematically proficient students notice if calculations are repeated, and look both for general methods and for shortcuts. Upper elementary students might notice when dividing 25 by 11 that they are repeating the same calculations over and over again, and conclude they have a repeating decimal. By paying attention to the calculation of slope as they repeatedly check whether points are on the line through (1, 2) with slope 3, middle school students might abstract the equation (y - 2)/(x - 1) = 3. Noticing the regularity in the way terms cancel when expanding (x - 1)(x + 1), (x - 1)(x2 + x + 1), and (x - 1)(x3 + x2 + x + 1) might lead them to the general formula for the sum of a geometric series. As they work to solve a problem, mathematically proficient students maintain oversight of the process, while attending to the details. They continually evaluate the reasonableness of their intermediate results.



=

=

=

Crosswalk of Common Core Instructional Shifts: Mathematics Both the 6 instructional shifts articulated by the NY State Department of Education and the 3 instructional shifts outlined by Student Achievement Partners help educators understand the major changes required by the Common Core in terms of curricular materials and classroom instruction in Mathematics.

1: Focus: Teachers use the power of the eraser and significantly narrow and deepen the scope of how time and energy is spent in the math classroom. They do so in order to focus deeply on only the concepts that are prioritized in the standards so that students reach strong foundational knowledge and deep conceptual understanding and are able to transfer mathematical skills and understanding across concepts and grades.

2: Coherence: Think across grades, and link to major topics within grades

1: Focus strongly where the Standards focus

3 Shifts: Student Achievement Partners www.achievethecore.org

6 Shifts: EngageNY www.engageny.org

2: Coherence: Principals and teachers carefully connect the learning within and across grades so that, for example, fractions or multiplication spiral across grade levels and students can build new understanding onto foundations built in previous years. Teachers can begin to count on deep conceptual understanding of core content and build on it. Each standard is not a new event, but an extension of previous learning.

3: Rigor: Require fluency, application, and deep understanding

6: Dual Intensity: Students are practicing and understanding. There is more than a balance between these two things in the classroom – both are occurring with intensity. Teachers create opportunities for students to participate in “drills” and make use of those skills through extended application of math concepts. The amount of time and energy spent practicing and understanding learning environments is driven by the specific mathematical concept and therefore, varies throughout the given school year.

4: Deep Understanding: Teachers teach more than “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives so that students are able to see math as more than a set of mnemonics or discrete procedures. Students demonstrate deep conceptual understanding of core math concepts by applying them to new situations as well as writing and speaking about their understanding.

5: Application: Students are expected to use math and choose the appropriate concept for application even when they are not prompted to do so. Teachers provide opportunities at all grade levels for students to apply math concepts in “real world” situations. Teachers in content areas outside of math, particularly science, ensure that students are using math – at all grade levels – to make meaning of and access content.

3: Fluency: Students are expected to have speed and accuracy with simple calculations; teachers structure class time and/or homework time for students to memorize, through repetition, core functions (found in the attached list of fluencies) such as multiplication tables so that they are more able to understand and manipulate more complex concepts.



Long-Range Plan

SUBJECTS 13/14 14/15 15/16 16/17 17/18 18/19 19/20 20/21 21/22 22/23

ELA C VC R/A VA C VC R/A VA

Health C VC R/A VA C VC R/A VA

PE C VC R/A VA C VC R/A

Social Studies C VC R/A VA C VC R/A

Fine & Performing Arts C VC R/A VA C VC R/A

Science C VC R/A VA C VC

Foreign Language C VC R/A VA C VC

Math C, A VC, VA VA C VC R/A VA C

Career & Vocational Education C VC R/A VA C

KEY

C=DEVELOPMENT OF CURRICULUM DOCUMENTS

VC=IMPLEMENTATION & VALIDATION OF NEW CURRICULUM

R=RESOURCE SELECTION

A=DEVELOPMENT OF ASSESSMENTS

VA=IMPLEMENTATION & VALIDATION OF ASSESSMENTS



NCSD Standards-Based Terminology

District Guaranteed & Viable Curriculum The District’s guaranteed & viable curriculum is identified as the learning curriculum that guarantees an equal

opportunity for the learning for all students. It also guaranteed adequate time for educators to teach content and for students to learn it. It guarantees that the curriculum being taught is the same curriculum that will be assessed. It is viable when adequate time is ensured to teach all determined essential content. The district’s curriculum is composed of identified learning components that are the essential learning that students must know or do in order to perform at the mastery level of the identified standards.

State & District Content Standards The state & district content standards are the minimum content expectations that students must meet as defined by the

state board of education. They provide a common understanding among educators as to what students should learn at particular grades. The standards are not the curriculum.

District Vertical Pacing Guide A district vertical Pacing Guide is the purposeful sequencing of a subject area’s route for teaching and learning

expectations across multiple developmental stages, ages or vertical grade levels. The progressions illustrate progress toward the mastery of content skills as students move throughout their K-12 learning experience. The exiting stage is defined as college and career readiness for the graduate.

District Grade Level Pacing Guide A district grade-level pacing guide is the district timeline for logical and progressive sequencing showing what a grade level content area should master over the course of an academic school year. Pacing guides include the timeline for interim benchmark assessments and summative grade level assessments for the district and/or the state.



NCSD Standards-Based Terminology

Classroom Curriculum Map A classroom curriculum map is the application of the District Grade Level Pacing Guide in an expanded format to guide

an educator in mapping out the essential outcomes of the grade level curriculum while differentiating to the needs of their students. It is designed to provide an overall picture of the what, the when and the length of relevant content outcomes to be mastered during a school year.

Classroom Unit A classroom unit targets the learning of outcomes and their components over a cycle/chunk of a few days to a few

weeks. It contains all three stages for a learning cycle/chunk: Desired results/learning Assessment/evidence Learning plan

Classroom Lesson Plan The classroom lesson plan is a detailed instructional lesson that is used to plan and guide the daily learning activities.

natrona county school district #1 · 2015. 10. 2. · these numbers are composed of ten ones and...

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