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for our FUTURE

Third Grade Math Pacing Guide

2014-2015

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4) Print the worksheets you need

Investigations Common Core additional lessons There are additional lessons and additional teaching notes to better

satisfy all common core state standards. These lessons, teaching

notes, and worksheets are in the book our district purchased last

year titled Investigations and the Common Core State Standards.

Smarter Balanced Sample Summative Items for Teachers http://www.ode.state.or.us/search/page/?id=3747

Balanced Math – The pacing guide represents the minimum set of

skills needed for students to meet the assessment required to receive a

diploma. Therefore, it is important to stay as close to the timing in the

pacing guide as possible. If you get to the end of a unit’s allotted time

and your students have not mastered all of the skills yet, those skills

become a part of the Review section of your lesson and the Conceptual

Lesson section moves with the pacing guide. This enables your

students to reach mastery without slowing the pace of instruction.

Balanced Math Instruction Distribution

Example:

60 minute lesson

15 minutes Review Review 5 minutes Mental Math 25-30% 40 minutes Conceptual

Conceptual Lesson

Lesson

65-70%

Mental Math

5-7%

Acquiring and Maintaining Skills – Throughout the year,

students need to review their addition and subtraction skills to maintain

fluency with their facts. Students are acquiring their multiplication

skills and need to be working on this throughout the year.

Kim Sutton

Use the Kim Sutton 10-block for addition and subtraction as appropriate

for your students.

Use the Kim Sutton 10-block pg. 22-40 starting at the beginning of the

year to build multiplication skills.

Each building has a 10-block binder.

Number Corner

Computational Fluency

Aug. through Jan. reviews addition and subtraction facts.

February through June has multiplication and division activities.

Grade 3 Math 2013-2014 Created: July 2013

3rd

Grade Key Concepts and Corresponding Activities

Key Concept Activity Multiplication and Division

Students need to relate multiplication to addition seeing one

meaning of multiplication as repeated addition.

Students need to understand that multiplication is finding an

unknown product using equal groups, arrays, a number line and area

models.

Students need to relate multiplication to division knowing that

division problems are finding an unknown factor.

Factor Pairs and Missing Factor Game

Introduced in Unit 5 Investigation 3.4 (pg. 98)

Continued in Unit 5: 3.6, 4.4, 4.5, 4.6

Fractions

Students work with unit fractions to build other fractions and

increase their understanding that a fraction is a part of a whole that

has been divided into equal groups.

Students combine fractions using visual models.

The Fraction Cookie Game*

Introduced in Unit 7 Investigation 2.2 (pg. 69-71)

Continued in Unit 7: 2.3, 2.4 (extension for advanced student on pg. 86)

*Similar to Kim Sutton’s “Build to One Whole”, and “Strive for Five” in Fractions: a part of the whole book.

Linear and Area Measurement

Students identify area as a measurement of space (covering) and

differentiate this from perimeter with is a measurement of length

(around). They break rectangular areas into rows and columns and

relate multiplication to area.

Real estate game

Kim Sutton Activity+

Introduce in Unit 4 Investigation 2

Continue to use throughout Unit 4

+Directions on Page 23

Bold lessons indicate a discussion or new level of rigor introduced

The above concepts are the key ideas for third grade that students will build on for the years to come. The students need to be familiar with the three

activities so, next year, the fourth grade teachers can use these activities before they start instruction that builds on these concepts. This will allow

fourth grade teachers to hear from the students what they remember from third grade. It will also remind the students what they learned so they can

connect the new learning to what they already know.


Unit 1: Addition, Subtraction, and the Number System

“Trading Stickers, Combining Coins”

nd thTime: 3.5 weeks September 2 to September 24

Standards to Mastery

None for this unit Standards for which this unit builds foundational skills

3.NBT.2

3.OA.8

Mathematical Practice Standards to Emphasize

Big Ideas

Addition means putting together.

Subtraction means taking away (removal), finding a missing part

(missing addend), and/or the difference between (comparing).

The position of a digit in a number determines its value (place value).

Essential Questions

How do you know when to add or subtract in a problem?

How does the location of a digit affect its value?

Concepts Skills

10 ones is equal to 1 group of 10 Create/find groups of 10

10 groups of ten is equal to 1 group of 100 Subtract using the number line

A digit in the ones place represents that many ones Subtract by adding on

A digit in the tens place represents that many groups of ten Add by place value

A digit in the hundreds place represents that many groups of one Add by breaking one addend into parts

hundred Find sums to 100

Add like values, like groups Identify strategies (near doubles, close to 10, etc) to build fluency with

One-to-one correspondence addition facts (using single digits)

Subtraction is equivalent to an addition problem with a missing addend Add coins to $1.00

There are multiple expressions that give the same sum Relate coin (pictures) to value

Order does not matter when adding Subtract from 100

A number can be broken into smaller parts (decomposing) for example: Solve multiple addend problems

26 = 10 + 10 + 6

26 = 20 + 6


Resources Standards Expectation by

end of Unit

Vocabulary

Bold are student words

Investigations:

Unit 1 Trading Stickers,

Combining Coins

Session 2.1 can be skipped or

used as intervention

Kim Sutton: Drills to Thrill

Before and After 32-41

Place Value with Pizzaz

Rounding Mountain 27

Place Value Pocket 16-29

Snap Follow Up 50-53

Place Value Clues 112-244

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.

Addition and

subtraction to 200

Sum

Addend

Add

Difference

Subtrahend

Minuend

Subtract

Estimate

Round

Digit

Commutative Property of

Addition

Associative Property of

Addition

Identity Property of Addition

Place Value

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

Addition and

subtraction only

Operations). Fact Families

Order of Operations

Expanded Form

Standard Form

Word Form

Pattern

Expression

Equation

Equal

Evaluate

Variable

Altogether

Combine

Total

Inverse

Increase

Decrease

Numeral


Unit 2: Measurement and Data “Surveys and Line Plots” th thTime: 3.5 weeks September 25 to October 17


3.MD.3

3.MD.4

Standards for which this unit builds foundational skills

None for this unit


Big Ideas

Graphs represent data and can be used to compare data.

Different types of graphs highlight different aspects of a data set.

Essential Questions

What kind of information can be shared in a graph?

Which type of graph would best represent a specific data set?

Concepts

Different data arrangements allow different questions

Graphs can have different scales/keys

Graphs can be used to compare data

The numbers on a line plot represent labels and the X’s are the data A symbol on a pictograph can represent a group of items

A ruler measures length

Skills

Classify data into categories

Pose questions from data

Answer questions posed from data

Create/revise survey questions

Create a pictograph, bar graph, and line graph

Interpret/describe data from a graph

Read and understand the scale/key

Use data to compare while using purposeful phrases

Use a key on a pictograph to interpret the symbols

Use a ruler to measure to the nearest ¼ inch



end of Unit

Vocabulary

Investigations:

Unit 2 Surveys and Line Plots

add 2.3A lesson pg. CC5-CC9*

2.3 – 2.7 (optional) can be used

as enrichment activity

Additional Resources are

Necessary for more

opportunities to draw bar graphs

and to measure data to the inch,

half inch, and quarter inch.

Number Corner:

Data Collector

December – read and

interpreting graphs

February – interpreting and

comparing charts and graphs

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.

Mastery Bar Graph

Line Plot

Pictograph/Picture Graph

Key/Legend

Scale

Data

Whole number

Half/Halves

Fourths

Horizontal

Vertical

Customary system

Inch

Foot (Feet)

Yard

Mile

Vocabulary note for teachers:

Standard units of measure

include units within both

customary and metric

systems, non-standard unit

examples include books,

paperclips, etc.

To minimize confusion in

later years and in science, the

Standard System (SI) are the

unit accepted internationally

and used in formulas such as

physics F=ma these units are

metric.

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.

Mastery

*Additional lessons are in the Investigations and the Common Core State Standards supplement referenced on pg. 2



“Collections and Travel Stories”

thTime: 4.5 weeks October 20 to November 21

st


3.NBT.1 Standards for which this unit builds foundational skills

3.NBT.2

3.OA.8

3.OA.9

3.MD.1


Big Ideas

Estimation is a way to show the reasonableness of an answer.

Addition means putting together. Subtraction means taking away

(removal), finding a missing part (missing addend), and/or the

difference between (comparing).

Working with elapsed time is regrouping minutes at 60 instead of 100.

Essential Questions

How do I know if my answer is reasonable?

How do I know when to add and when to subtract in a problem?

How is elapsed time related to addition and subtraction?

Concepts Skills

Ten groups of 100 is equal to 1 group of 1000 Read, write and sequence numbers to 1000

There are different uses for estimates and exact answers Use place value to determine what two multiples of 10 or 100 an

A digit in the ones place represents that many ones number is between

A digit in the tens place represents that many groups of ten Use landmark numbers to locate other numbers on a number line,

A digit in the hundreds place represents that many groups of one hundreds grid, and thousands chart

hundred Estimate the sums of 2 and 3 digit numbers

Subtraction is equivalent to an addition problem with a missing addend Find pairs of numbers that add to 100

Estimation tells about how large an answer will be Tell how many tens are in a 3-digit number

There are 60 minutes in 1 hour Find the difference between two 3-digit numbers using subtraction on a

The meaning of the numbers and the hands on an analog clock number line and/or a 1000 chart.

Rounding is a way to estimate Round to the nearest 10 or 100



end of Unit

Vocabulary

Investigations:

Unit 3 Collections and Travel

Stories

add 1.7A lesson pg CC14-CC18

definitely include ten-minute

math from Investigations 3 + 4

to hit time standard 3.MD.1

Kim Sutton: Dynamic Dice

Let’s Standardize pg. 126-129

Number Corner:

Calendar Grid

January–Analog+Dig.Clocks

Clocks, Coins + Bills:

October- An Hour or Bust

November–What Time is it Now?

What Time Would it be?

3.NBT.1. Use place value understanding to round whole numbers

to the nearest 10 or 100.

Mastery Sum

Addend

Add

Difference

Subtrahend

Minuend

Subtract

Estimate

Round

Digit

Commutative

Associative

Identity Property

Place Value

Fact Families

Order of Operations

Expanded Form

Standard Form

Word Form

Pattern

Expression

Evaluate

Equation

Solve

Equal

a.m. / p.m.

second/minute/hour

Elapsed Time

Intervals

Quarter Hour

Half Hour

Algorithm

Teacher note:

Expressions are evaluated and

equations are solved.

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.

Add to 1000 and

subtract from 300.

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.

Addition only

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. (Note: 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).

Add to 1000 and

subtract from 300.

Use estimation to

justify the

reasonableness of

the answer.

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.

To the nearest 5

minutes.


Unit 4: 2-D Geometry and Measurement

“Perimeter, Angles, and Area”

thTime: 5 weeks December 1

st to January 16

Standards to Mastery Standards for which this unit builds foundational skills

3.MD.5 3.G.1 3.MD.7

3.MD.6

3.MD.8


Big Ideas

Attributes (number of vertices, perimeter, area, etc) are used to describe

objects.

Perimeter is a linear measurement and is useful when surrounding an

object (framing a picture) while area measurements are useful when

covering an object (painting a wall).

Essential Questions

How can objects be described?

How are area and perimeter different and when is each more useful?

Concepts

Different aspects of a shape can be measured (length, width, perimeter,

area, etc)

Perimeter is the measure around the outside edges of a 2-dimensional

figure

Perimeter is a measurement of length (inches, meters, etc)

Different shapes can have the same perimeter

Area is a measurement of space (square inches, square meters, etc)

Area is additive

Triangles have three sides, three vertices, and three angles

Quadrilaterals have four sides, four vertices, and four angles

The attributes of a shape determine its name

Skills

Measure accurately with standard and metric units

Estimate measurements

Find the perimeter of a figure by measuring the side lengths

Find an unknown side length of a figure when given the other side

lengths and the perimeter.

Draw and label a straight line that represent the perimeter of a figure

Identify congruent figures

Measure area by tiling leaving no gaps or overlaps

Identify different shapes with the same area

Estimate the area and perimeter of irregular figures

Create rectangles with the same area and different perimeters

Create rectangles with the same perimeter and different areas

Identify right angles

Classify angles as less than, greater than, or equal to a right angle

Choose appropriate units to measure



end of Unit

Vocabulary

Investigations:

Unit 4 Perimeter, Angles, and Area

add 2.5A lesson pg. CC23-CC27

When doing Practicing Place

Value 10-minute math, also have

students write the number in

expanded form and round to the

nearest 10 and 100

Kim Sutton:

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.

Mastery Measure

Unit

Perimeter

Area

Square Unit

Attribute

Compose

Decompose

Overlapping

Non-

overlapping

Triangle

Square

Rectangle

Rhombus

(Rhombi)

Trapezoid

Parallelogram

Quadrilateral

Pentagon

Hexagon

Octagon

3.MD.6. Measure areas by counting unit squares (square cm,

square m, square in, square ft, and improvised units).

Mastery

3.MD.8. Solve real world and mathematical problems Mastery Dynamic Dice involving perimeters of polygons, including finding the Tiling Polygon

Rolling Polygons 116-117 perimeter given the side lengths, finding an unknown side Plane Figure Perimeter

length, and exhibiting rectangles with the same perimeter and Rectilinear- Sides

Number Corner:

Calendar Grid

November – 2D geometry

different areas or with the same area and different perimeters. Figure

Triangular

Rectangular

Customary

System

Inch

Foot (Feet)

Yard

Mile

Metric System

Centimeter

Meter

Kilometer

Vertex/Vertices

Angles

Acute

Obtuse

Right

Scalene

Isosceles

Equilateral

Equiangular

Parallel Lines

Perpendicular

Congruent

Compare

Line

Line Segment

Ray

2-Dimensional

Symmetry

Side Length

Dimensions

Closed Figure

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.

Mastery

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.

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.

Parts b and c will

be addressed in

later units.


Unit 5: Multiplication and Division “Equal Groups” th thTime: 6.5 weeks January 20 to March 6


3.OA.1 3.OA.5 3.OA.7

3.OA.2 3.OA.6 3.OA.8

3.OA.3 3.NBT.3 3.OA.9

3.OA.4 3.MD.7 3.MD.1


Big Ideas

Multiplication finds the total number of objects when there is an equal

number of objects in each group.

Multiplication is repeated addition.

Division breaks things into equal groups.

Multiplication and division are inverse operations. Division situations

can be written as unknown-factor problems.

Essential Questions

How can we represent situations with equal groups?

How is multiplication related to addition?

How can we represent situations where we are sharing equally?

How are multiplication and division related?

Concepts Skills

Situations where things come in equal groups can be represented with Skip count accurately

multiplication or division Find products using repeated addition/skip counting

Skip counting, repeated addition, arrays, and multiplication are all ways Use multiplication and division notation

of finding a product Identify multiples of 2, 3, 4, 5, 6, and 10 by skip counting

The number of groups and the number of objects in each group are the Use doubles and halves of known products to find related products

factors and the total number is the product Represent a multiplication problem using arrays, equal groups, and

Multiples of a given number share characteristics (e.g. all multiples of number lines

10 have a 0 in the ones place) Identify prime numbers and square numbers

Multiplication and division are inverse operation Manipulate problems using number flexibility to create a solvable

Division is breaking something into equal groups problem (e.g. think of 9 x 4 as 10 x 4 – 4)

Division can be thought of as a missing factor multiplication problem Multiply by multiples of 10



end of Unit

Vocabulary

Investigations:

Unit 5 Equal Groups



add 3.5B lesson pg CC42-CC46


Make sure to include

10-minute math from

Investigations 1, 3 and 4 to hit

time standard 3.MD.1


Necessary to teach products to

100

Number Corner (time acts.):


December–How Long Between?

Kim Sutton:

Dynamic Dice

Rolling Your Facts 60, 65-69

Number Line Workbook

My Multiples Book 87-93

Pattern Sticks 35-36

Drills to Thrill

Multiplication Strategies 116-141

Input/Output 150-152

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.

Mastery Multiply

Divide

Divisor

Dividend

Quotient

Number Patterns

Equal Groups

Factors

Multiples

Product

Array

Area Model

Measure

Intervals

Number Line

Interpret

Partition

Distributive Property

Parenthesis

Commutative Property

of Multiplication

Associative Property

of Multiplication

Zero Property of

Multiplication

Expression

Evaluate

Equation

Solve

Rounding

Repeated Addition

Repeated

Subtraction

Hundreds Grid

More Vocabulary on

next page

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.

Mastery

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 Table 2.)

Mastery

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

division equation relating three whole numbers. For example, determine

the unknown number that makes the equation true in each of the

equations 8 × ? = 48, 5 = ÷ 3, 6 × 6 = ?.

Mastery

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.)

Mastery

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.

Mastery

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.

More standards for this unit on next page

Mastery


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.

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.

Mastery Tiling

Additive

Quantity

Decompose

Compose

Rectilinear

Rectangle

Second/Minute/Hour

Elapsed Time

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.

Students are

building conceptual

understanding and

number fluency.

Working toward

mastery by unit 8


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. (Note: 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).

Continue to build

skills working

towards mastery in

unit 8

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.

Identify patterns

with multiples on

100 grid

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.

To the nearest

minute


Unit 7: Fractions and Decimals “Finding Fair Shares” th thTime: 5.5 weeks March 9 to April 24


3.NF.1 3.G.2 None for this unit

3.NF.2 3.MD.1

3.NF.3


Big Ideas

Fractions represent part of a whole.

Fractions are composed of one (unit fraction) or more equal parts which

the whole is divided into. The numerator tells us how many parts we

have and the denominator tells us how many equal parts make one

whole.

Equivalent fractions of the same whole have the same area, and they are

located at the same place on the number line.

Essential Questions

How do we represent amounts that are less than one whole?

What does the numerator and denominator tell us about a fraction?

How do we know if two fractions are equivalent?

Concepts Skills

When breaking a whole into fractional pieces, each piece must be the Name equal parts of one whole with a fraction

same size Divide an area into equal parts

A unit fraction is one equal part of a whole Order unit fractions from largest to smallest

The denominator of a fraction tells how many equal pieces the whole is Create area models for fractions

divided into Create set models for fractions

Larger denominators mean the whole is divided into more pieces Represent fractions on a number line

making each piece smaller Compare fractions using number lines and area models

The numerator of a fraction tells how many equal pieces you have Use inequality notation (<, >) with fractions

If the numerator (number of pieces you have) is equal to the Write equivalent fractions

denominator (number of pieces the whole is broken into) then you have Find fractions that sum to one

one whole Combine fractions using models

Improper fractions represent more than one whole Create a situation to represent a given fraction (use pattern blocks to

Mixed numbers represent some number of wholes and some number of make a design that is half yellow)

fractional pieces

Pieces smaller than one whole can be represented with fractions

Fractions and mixed numbers lie between the whole numbers on the

number line



end of Unit

Vocabulary

Investigations:

Unit 7 Fractions and Decimals


add 1.4B lesson pg CC62-CC67


Value 10-minute math, also

have students write the

number in expanded form

and round to the nearest 10

and 100

Skip Investigation 3

Kim Sutton: Fractions: Part of the Whole

Critical Fraction Questions 8

Fraction Chats 126

Chocolate Fractions pg 44

Circle of Children pg 68

Pattern Block Fraction 90

Number Line Fractions 144

Comparing Fractions after pg 199

Number Corner:

Calendar Grid

April – Equivalent Fractions

May+June–Frac., Dec.+$

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.

Mastery Unit Fraction

Equivalent Fraction

Numerator

Denominator

Fraction

Equal Parts of:

-whole

-set

-point/distance

Halves

Fourths

Sixths

Eigths

Tenths

Number Line

Compare

Order

Greater Than >

Less Than <

Equal to =

Partition

Diagram

End Point

Point

Increase

Decrease

Mixed Number

Improper Fraction

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.

Mastery

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.

Mastery

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.

Mastery

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.

Mastery


Unit 6: Patterns, Functions, and Change

“Stories, Tables, and Graphs”

th thTime: 2 weeks April 27 to May 8

Standards to Mastery Standards for which this unit reinforces skills

3.OA.1 3.OA.8

3.OA.3 3.OA.9

3.OA.5


Big Ideas

Patterns or relationships can be represented using sequences, tables,

graphs, and described with words (and in later grades equations).

The constant rate of change is how many are added each unit (day) it

can also be multiplied by the number of units (days) and then added

to the start amount to find the total at any point in the pattern (on any

given day).

Essential Questions

What are different ways to represent patterns or relationships?

Why is the constant rate of change helpful when working with patterns?

Concepts

Sequences that follow a pattern can be extended based on that pattern

The numbers in the same row of a table are related

Tables are good tools to compare different situations

Graphs are good tools to compare the rate of change in different

situations

In a linear relationship, the total number after a given time depends on

both the starting value and the rate of change (magic marbles)

Variables represent quantities that can change

Skills

Identify the unit of a repeating pattern

Extend a pattern

Skip count by the length of the unit in a pattern

Extend a number sequenced with a constant rate of change (2, 5, 8,. . .)

Identify numbers based on how they are related to the multiples of 3

Recognize and identify a constant rate of change

Use tables to record data

Interpret numbers in a table in terms of the situation that table represents

Generalize a situation where there is a constant rate of change by

writing a rule using variables

Use data from a table to graph a situation in the coordinate plane



end of Unit

Vocabulary

Investigations:

Unit 6 Stories, Tables, and

Graphs

Skip Investigation 1

Sessions 3.4-3.7 optional

(enrichment)


Value 10-minute math, also

have students write the

number in expanded form

and round to the nearest 10

and 100


Necessary to work with

arithmetic patterns in the

addition and multiplication

tables.


Even/Odd Mult. pat.148-149

Input.Output 150-152

Number Corner:

Number Grids

October – Counting Patterns

Data Collector

December – Reading and

Interpreting Graphs

February–Interpreting and

Comparing Charts and Graphs

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.

Mastery Sequence

Pattern

-repeating

-growing

-geometric

Horizontal Axis

x-axis

Vertical Axis

y-axis

Table

Row

Column

Properties of Multiplication

Arrays

Equal Groups

Quantity

Variable

Constant Rate of Change

Increase

Decrease

Rule

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 Table 2)

Mastery

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.)

Mastery


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).

Continue to build

skills working

towards mastery in

unit 8

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

Identify patterns in

addition and

multiplication table

Continue to practice fact fluency for 3.OA.7

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

one-digit numbers.


Unit 9: Volume and Mass “Solids and Boxes” th thTime: 1 week May 11 to May 15


3.MD.9 Standards for which this unit builds foundational skills

None for this unit


Big Ideas

The standard units for mass are kilograms and grams.

The standard unit for liquid volume is liters.

Essential Questions

What are the standard units for liquid volume and mass?

Concepts Skills

Liquid volume is the amount of space a liquid takes up Estimate the measure of a liquid volume

1,000 milliliters is 1 liter* Use milliliters and liters appropriately

1,000 gram is 1 kilograms* Estimate the measure of weight and mass

Use grams and kilograms appropriately

*Students do not need to convert units, the relationships are to help them Solve one step word problems involving masses or volumes where

determine the better unit to use (e.g. milliliters are better to describe the measurements are given in the same unit

volume of water in an eyedropper while liters are better to describe the

volume of water in a pool).

Students are not expected to know the difference between weight and

mass at this point in their career but a description for teacher benefit is

on pg. CC78 in the Math Notes in Investigations and the Common Core

State Standards.



end of Unit

Vocabulary

Investigations:

Unit 9 Solids and Boxes

Additional Sessions ONLY




Number Corner:

Calendar Grids

Aug+Sept – Measuring Tools

3.MD.2. Measure and estimate liquid volumes and masses of objects

using standard units of grams (g), kilograms (kg), and liters (l). 3

(Excludes compound units such as cm 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. (see Table 2).

Mastery Grams

Kilograms

Milliliters

Liters

Mass

Volume

Units

Continue to practice fact fluency for 3.OA.7

By the end of Grade 3, know from memory all products of two one-

digit numbers.



“How Many Hundreds? How Many Miles?"

th thTime: 3.5 weeks May 18 to June 11


3.NBT.2 3.OA.8

3.OA.7 3.OA.9

Standards for which this unit builds foundational skills


Big Ideas

When we change an expression to make it easier to simplify, we must

adjust the answer to maintain equality with the original problem.

The equal sign shows that the expressions on either side represent the

same quantity.

Essential Questions

How can we use what we know to solve harder problems?

What does the equal sign mean?

Concepts

When using a related subtraction problem to solve a more difficult

subtraction problem, if the minuend (# we are taking away) is larger (or

smaller) then difference will be smaller (or larger) by the same amount.

When using a related addition problem to solve a more difficult addition

problem, if an addend is larger (or smaller) the sum will be larger (or

smaller)

When adding and subtracting multiples of 10 (and 100) the ones (and

tens) digit does not change

The equal sign shows the expression on either side represent the same

quantity

Addition and subtraction are inverse operations

Subtraction can have one of three meanings; removal (taking away),

comparison (difference between), or missing part (unknown addend)

Skills

Estimate sums and differences of 3-digit numbers using number

flexibility, the number line, multiples of 10 and 100, etc

Subtract from multiples of 100

Compose and decompose numbers to add and subtract

Combine hundreds to numbers over 1000

Use number lines, hundreds grids, and thousands charts to subtract 3-

digit numbers

Use a known subtraction problem to solve a related problem (for

example 200-75=125, then 200-78=122 because we are taking 3 more

away so the difference is 3 smaller)

Add and subtract multiples of 10 and 100

Fluently multiply and divide within 100

Solve addition problems with more than 2 addends

Create equivalent addition expressions

Explain why 2 expressions are equivalent using context (story situation)

Change the numbers in an addition problem to create an equivalent but

simpler problem

Solve multi-step addition and subtraction problems

Subtract 3-digit numbers by adding on or counting back

Change one or more addends a landmark number and find the sum then

change the sum to compensate for the changes



end of Unit

Vocabulary

Investigations:

Unit 8 How Many Hundreds? How

Many Miles?

Make sure to include

10-minute math from

Investigations 1, 3 and 4 to hit

time standard 3.MD.1


Triangular Relationships pg.100-106

Equations Compared (+/) pg.162-163

Dynamic Dice

Cover the Quantity pg.18-23

First Sum Wins! pg.74-75

Rolling to 99 pg.122-123

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.

Mastery Sum

Addend

Add

Altogether

Combine

Increase

Total

Difference

Subtrahend

Minuend

Subtract

Decrease

Inverse

Estimate

Round

Digit

Numeral

Number Line

Hundreds Grid

Thousands Chart

Landmark

Benchmark

Commutative

Associative

Identity Property

Place Value

Fact Families

Multiples

Order of

Operations

Composing

Decomposing

Expanded Form

Standard Form

Word Form

Pattern

Expression

Evaluate

Equation

Solve

Equal

Algorithm

Teacher note:

Expressions are

evaluated and

equations are

solved.

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.

Mastery

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. (Note: 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).

Mastery

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.

Mastery


Real Estate Game

Materials

A crayon for each student (different color than their partner)

Game board or centimeter grid paper

Pencil for each student

A double die (or two regular dice) for each pair

Directions

1) First student rolls the double die and builds an array with dimensions equal to the numbers rolled anywhere on

the game board using their color crayon.

2) The student then labels the dimensions of their array and writes the multiplication equations inside their new

property using their pencil.

3) The second student now rolls the double die and builds an array using their color crayon with dimensions equal

to the numbers rolled. Their array can touch, but not overlap the array(s) already on the board.

4) This student then labels the dimension of their array and writes the multiplication equation inside their new

property using their pencil.

5) The first student rolls again and the process repeats alternating between students.

6) If a student rolls dimensions that build an array that will not fit on the board, they lose their turn.

7) When two turns in a row, both students, are unable to find space on the board for their array, the game is over.

8) Students add up the total area in their color crayon and the largest total area wins.

The game can be played for a specific amount of time instead of playing until the board is too full to continue.


Additional Resources for 3rd

Grade by Unit

Unit 1 Unit 2 Unit 3 Unit 4



Equations Compared to 98-99

Dynamic Dice

Cover Up 88-89

Expanded Notation 90-93

Compare Quantities 94-97

Between 10s 104-105

Let’s Standardize! 126-129

Number Roads 132-135

Compare if you Dare 136-143

Computation Practice 144-155

Sorting Numbers 156-159

The Powerful Numbers 0-100

Arrow Math 24-33






Number Corner:

Data Collector

December – read and interpreting

graphs

February – interpreting and

comparing charts and graphs

Bridges Support Materials:

www.mathlearningcenter.com

Data Analysis E1 Graphing (3 activities)



Equations Compared to 98-99

Dynamic Dice

Cover Up 88-89

Expanded Notation 90-93

Compare Quantities 94-97

Between 10s 104-105

Let’s Standardize! 126-129

Number Roads 132-135

Compare if you Dare 136-143

Computation Practice 144-155

Sorting Numbers 156-159


Arrow Math 24-33






Number Corner:

Calendar Grid







March–What Time is it Now? What Time Would it be?

Kim Sutton:

Real Estate Game See Appendix B

Dynamic Dice

Rolling Polygons 116-117

Number Corner:

Calendar Grid

November – 2D geometry

Data Collector

March – Linear Measurement

Bridges Support Materials C1 Parallel, Perpendicular, and

Intersecting Lines (1 activity)

C2 Triangles and More (2 activities)

C4 Quadrilaterals (5 activites)

Discovery Education Streaming:

Discovery math: Geometry (grades 3-

5) 35 segments

Measurement – perimeter

Introduction – Sadman/Batman

Math Mansion; 3.1 All The way Round Rectangles + Perimeter


http://www.mathlearningcenter.com/

Unit 5

Kim Sutton:

Dynamic Dice

Picture This (Groups of) 110-111

Factor Fun 76-81

Lights Out 82-83

Rolling Your Facts 60, 65-69

Even/Odd Outcomes 56-67

Number Line Workbook

My Multiples Book 87-93

Pattern Sticks 35-36

How Many Groups 37-49

Skip Counting

3’s pg. 62-63

6’s pg. 68-69

9’s pg. 74-75

4’s pg. 64-65

8’s pg. 72-733

7’s pg. 70-71

Drills to Thrill

Groups of 212-227

Multiplication Strategies 116-141

Even/Odd Mult. Patterns 148-159

Input/Output 150-152

Triangular Relations 168-172

Powerful Numbers

Sorting Styles 96-103

Matrix Sorting 104-105

Factor Freak Out 106-107

Unit 5 continued

Number Corner:

Number Grid

November – Multiples of 3

Magnetic Board

May/June (1x2 digit mult)

Computational Fluency

February – mult. Workout wheel

March – What’s Missing Bingo April – 10 to Win

Support Materials

Spinning Around Mult. 13

What’s Missing Bingo 16 10 to Win 17

Make Zero 18

Number Corner (time acts.):

Calendar Grid







March–What Time is it Now? What

Time Would it be?

Bridges Support Materials:

www.mathlearningcenter.com

Numbers and Operations

Grade 2 A3 Division (1 activity)

Grade 3 A1 Equal Expressions

A2 Basic Mult. and Division

Unit 7

Kim Sutton: Dynamic Dice

Fraction Match Up 38-50

Make a Fraction 32-35

Fraction Brick Wall 36-37

Fractions:part of the whole

Entire Book!

Number Corner:

Calendar Grid

April – Equivalent Fractions

May+June–Frac., Dec.+$

Magnetic Board

December – Tile Fractions

January–Equivalent Fractions

Bridges Support Materials www.mathlearningcenter.com

Number and Operations

A5 Fractions (1 activity)

Unit 6


Even/Odd Mult. pat.148-149

Input.Output 150-152

Number Corner:

Number Grids

October – Counting Patterns

Data Collector

December – Reading and Interpreting

Graphs

February–Interpreting and Comparing

Charts and Graphs

Bridges Support Materials www.mathlearningcenter.com

Data Analysis

E1 Graphing (3 activity)

Discovery Education Videos

Graphing Unit 8


Equations Compared To pg.98-99

Triangular Relationships pg.100-106

Equations Compared (+/) pg.162-163

Dynamic Dice

The Difference Game pg.12-13

Sorting Equations pg.16-17

Cover the Quantity pg.18-23

Tic-Fact-Toe pg.72-73

First Sum Wins! pg.74-75

Rolling to 99 pg.122-123


Double Up pg.58-61

Unit 9

Number Corner:

Calendar Grids

Aug+Sept – Measuring Tools





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