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MOUNT VERNON CITY SCHOOL DISTRICT

CCLS MathematicsGrade 5

Curriculum Guide

THIS HANDBOOK IS FOR THE IMPLEMENTATION OF THE GRADE 5MATHEMATICS CURRICULUM IN MOUNT VERNON.

2015-2016

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Mount Vernon City School District

Board of Education

Elias Steven GootzeitPresident

Serigne GningueVice President

Board TrusteesBrenda Crump

Charmaine FearonRosemarie M. Jarosz

Omar McDowellDarcy Miller

Adriane SaundersFrances Wynn

Superintendent of SchoolsDr. Kenneth Hamilton

Assistant Superintendent of BusinessKen Silver

Assistant Superintendent of Human ResourcesDenise Gagne-Kurpiewski

Assistant Superintendent for Innovation, Accountability and GrantsGertrude Karabas

Administrator of Mathematics and Science (K-12)Satish Jagnandan, Ed.D.

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TABLE OF CONTENTS

I. COVER …..……………………………………....... 1

II. MVCSD BOARD OF EDUCATION …..……………………………………....... 2

III. TABLE OF CONTENTS …..……………………………………....... 3

IV. IMPORTANT DATES …..……………………………………....... 4

V. VISION STATEMENT …..……………………………………....... 5

VI. PHILOSOPHY OF MATHEMATICS CURRICULUM ……………. 6

VII. NYS GRADE 5 COMMON CORE LEARNING STANDARDS ……………..7

VIII. MVCSD GRADE 5 MATHEMATICS PACING GUIDE …………....13

IX. WORD WALL …………... 32

X. SETUP OF A MATHEMATICS CLASSROOM …………... 33

XI. ELEMENTARY GRADING POLICY …………... 34

XII. SAMPLE NOTEBOOK RUBRIC …………... 35

XIII. CLASSROOM AESTHETICS …………... 36

XIV. SYSTEMATIC DESIGN OF A MATHEMATICS LESSON …………... 37

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IMPORTANT DATES 2015-16

REPORT CARD – 10 WEEK PERIOD

MARKINGPERIOD

MARKINGPERIODBEGINS

INTERIMPROGRESSREPORTS

MARKINGPERIOD

ENDS

DURATION REPORT CARDDISTRIBUTION

MP 1 September 8,2015

October 9,2015

November 13,2015

10 weeks Week ofNov. 23, 2015

MP 2 November 16,2015

December 18,2015

January 29,2016

10 weeks Week ofFebruary 8, 2016

MP 3 February 1,2016

March 11,2016

April 15,2016

9 weeks Week ofApril 25, 2016

MP 4 April 18,2016

May 20,2016

June 23,2016

10 weeks Last Day of SchoolJune 23, 2016

The Parent Notification Policy states “Parent(s) / guardian(s) or adult students are

to be notified, in writing, at any time during a grading period when it is apparent -

that the student may fail or is performing unsatisfactorily in any course or grade

level. Parent(s) / guardian(s) are also to be notified, in writing, at any time during

the grading period when it becomes evident that the student's conduct or effort

grades are unsatisfactory.”

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VISION STATEMENT

True success comes from co-accountability and co-responsibility. In a coherentinstructional system, everyone is responsible for student learning and studentachievement. The question we need to constantly ask ourselves is, "How are ourstudents doing?"

The starting point for an accountability system is a set of standards andbenchmarks for student achievement. Standards work best when they are welldefined and clearly communicated to students, teachers, administrators, andparents. The focus of a standards-based education system is to provide commongoals and a shared vision of what it means to be educated. The purposes of aperiodic assessment system are to diagnose student learning needs, guideinstruction and align professional development at all levels of the system.

The primary purpose of this Instructional Guide is to provide teachers andadministrators with a tool for determining what to teach and assess. Morespecifically, the Instructional Guide provides a "road map" and timeline forteaching and assessing the Common Core Learning Standards.

I ask for your support in ensuring that this tool is utilized so students are able tobenefit from a standards-based system where curriculum, instruction, andassessment are aligned. In this system, curriculum, instruction, and assessment aretightly interwoven to support student learning and ensure ALL students have equalaccess to a rigorous curriculum.

We must all accept responsibility for closing the achievement gap and improvingstudent achievement for all of our students.

Dr. Satish Jagnandan

Administrator for Mathematics and Science (K-12)

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PHILOSOPHY OF MATHEMATICS CURRICULUM

The Mount Vernon City School District recognizes that the understanding of mathematics is

necessary for students to compete in today’s technological society. A developmentally

appropriate mathematics curriculum will incorporate a strong conceptual knowledge of

mathematics through the use of concrete experiences. To assist students in the understanding and

application of mathematical concepts, the mathematics curriculum will provide learning

experiences which promote communication, reasoning, and problem solving skills. Students will

be better able to develop an understanding for the power of mathematics in our world today.

Students will only become successful in mathematics if they see mathematics as a whole, not as

isolated skills and facts. As we develop mathematics curriculum based upon the standards,

attention must be given to both content and process strands. Likewise, as teachers develop their

instructional plans and their assessment techniques, they also must give attention to the

integration of process and content. To do otherwise would produce students who have temporary

knowledge and who are unable to apply mathematics in realistic settings. Curriculum,

instruction, and assessment are intricately related and must be designed with this in mind. All

three domains must address conceptual understanding, procedural fluency, and problem solving.

If this is accomplished, school districts will produce students who will

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.

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New York State P-12 Common Core Learning Standards forMathematics

Mathematics - Grade 5: Introduction

In Grade 5, instructional time should focus on three critical areas: (1) developing fluency with addition andsubtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractionsin limited cases (unit fractions divided by whole numbers and whole numbers divided by unit fractions); (2)extending division to 2-digit divisors, integrating decimal fractions into the place value system and developingunderstanding of operations with decimals to hundredths, and developing fluency with whole number and decimaloperations; and (3) developing understanding of volume.

1. Students apply their understanding of fractions and fraction models to represent the addition and subtraction offractions with unlike denominators as equivalent calculations with like denominators. They develop fluency incalculating sums and differences of fractions, and make reasonable estimates of them. Students also use the meaningof fractions, of multiplication and division, and the relationship between multiplication and division to understandand explain why the procedures for multiplying and dividing fractions make sense. (Note: this is limited to the caseof dividing unit fractions by whole numbers and whole numbers by unit fractions.)

2. Students develop understanding of why division procedures work based on the meaning of base-ten numerals andproperties of operations. They finalize fluency with multi-digit addition, subtraction, multiplication, and division.They apply their understandings of models for decimals, decimal notation, and properties of operations to add andsubtract decimals to hundredths. They develop fluency in these computations, and make reasonable estimates oftheir results. Students use the relationship between decimals and fractions, as well as the relationship between finitedecimals and whole numbers (i.e., a finite decimal multiplied by an appropriate power of 10 is a whole number), tounderstand and explain why the procedures for multiplying and dividing finite decimals make sense. They computeproducts and quotients of decimals to hundredths efficiently and accurately.

3. Students recognize volume as an attribute of three-dimensional space. They understand that volume can bemeasured by finding the total number of same-size units of volume required to fill the space without gaps oroverlaps. They understand that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume. Theyselect appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume.They decompose three-dimensional shapes and find volumes of right rectangular prisms by viewing them asdecomposed into layers of arrays of cubes. They measure necessary attributes of shapes in order to determinevolumes to solve real world and mathematical problems.

Mathematical Practices

1. Make sense of problems and persevere in solvingthem.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoningof 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.

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Grade 5 Overview

Operations and Algebraic Thinking• Write and interpret numerical expressions.• Analyze patterns and relationships.

Number and Operations in Base Ten• Understand the place value system.• Perform operations with multi-digit wholenumbers and with decimals to hundredths.

Number and Operations—Fractions• Use equivalent fractions as a strategy to addand subtract fractions.• Apply and extend previous understandingsof multiplication and division to multiply anddivide fractions.

Measurement and Data• Convert like measurement units within a givenmeasurement system.• Represent and interpret data.• Geometric measurement: understand conceptsof volume and relate volume to multiplicationand to addition.

Geometry• Graph points on the coordinate plane to solvereal-world and mathematical problems.• Classify two-dimensional figures into categoriesbased on their properties.

Operations & Algebraic Thinking 5.OA

Write and interpret numerical expressions.1. Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.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 theindicated sum or product.

Analyze patterns and relationships.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 pairson a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in onesequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

Number & Operations in Base Ten 5.NBT

Understand the place value system.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.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. Usewhole-number exponents to denote powers of 10.

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

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Perform operations with multi-digit whole numbers and with decimals to hundredths.5. Fluently multiply multi-digit whole numbers using the standard algorithm.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 relationship between multiplication anddivision. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

7. Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategiesbased on place value, properties of operations, and/or the relationship between addition and subtraction; relatethe strategy to a written method and explain the reasoning used.

Number & Operations—Fractions 5.NF

Use equivalent fractions as a strategy to add and subtract fractions.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 likedenominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

2. Solve word problems involving addition and subtraction of fractions referring to the same whole, includingcases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Usebenchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness ofanswers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.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., byusing visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result ofdividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, and that when 3 wholes are shared equally among 4people 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?

4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by afraction.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, andcreate 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 unitfraction 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 rectangularareas.

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); explainingwhy multiplying a given number by a fraction less than 1 results in a product smaller than the givennumber; and relating the principle of fraction equivalence a/b = (n × a)/(n × b) to the effect of multiplyinga/b by 1.

6. Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visualfraction models or equations to represent the problem.

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7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and wholenumbers by unit fractions.1

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 therelationship 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 astory context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationshipbetween 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 ofwhole numbers by unit fractions, e.g., by using visual fraction models and equations to represent theproblem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolateequally? How many 1/3-cup servings are in 2 cups of raisins?

_________________1 Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about therelationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.

Measurement & Data 5.MD

Convert like measurement units within a given measurement system.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.

Represent and interpret data.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, givendifferent measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if thetotal amount in all the beakers were redistributed equally.

Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.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 beused 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 ofn cubic units.

4. Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.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 bymultiplying 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 rectangularprisms 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 rightrectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solvereal world problems.

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Geometry 5.G

Graph points on the coordinate plane to solve real-world and mathematical problems.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 anordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel fromthe origin in the direction of one axis, and the second number indicates how far to travel in the direction of thesecond axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis andx-coordinate, y-axis and y-coordinate).

2. Represent real world and mathematical problems by graphing points in the first quadrant of the coordinateplane, and interpret coordinate values of points in the context of the situation.

Classify two-dimensional figures into categories based on their properties.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 havefour right angles.

4. Classify two-dimensional figures in a hierarchy based on properties.

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Grade 5 Cluster Emphases for Instruction

Cluster Emphases for Instruction on the 2014 Grade 5 Common Core Mathematics TestCluster Emphasis Recommended Instructional

TimeApproximate Number of Test

PointsMajor 65–75% 70–80%

Supporting 15–25% 10–20%Additional 5–15% 5–10%

CCLS Standard ContentEmphasis

Operations and Algebraic Thinking5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions

with these symbolsAdditional

5.OA.2 Write simple expressions that record calculations with numbers, and interpret numericalexpressions without evaluating them.

Additional

5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationshipsbetween corresponding terms. Form ordered pairs consisting of corresponding termsfrom the two patterns, and graph the ordered pairs on a coordinate plane.

AdditionalPost

Number and Operations in Base Ten5.NBT.1 Recognize that in a multi-digit whole 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 toits left

Major

5.NBT.2 Explain patterns in the number of zeroes of the product when multiplying a number bypowers of 10, and explain patterns in the placement of the decimal point when a decimalis multiplied or divided by a power of 10. Use whole-number exponents to denotepowers of 10.

Major

5.NBT.3 Read, write, and compare decimals to thousandths. Major5.NBT.4 Use place value understanding to round decimals to any place. Major

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

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/orthe relationship between multiplication and division. Illustrate and explain thecalculation by using equations, rectangular arrays, and/or area models.

Major

5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models ordrawings and strategies based on place value, properties of operations, and/or therelationship between addition and subtraction; relate the strategy to a written method andexplain the reasoning used.

Major

Number and Operations—Fractions4.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.Major

4.NF.6 Use decimal notation for fractions with denominators 10 or 100. Major

4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize thatcomparisons are only valid when the two decimals refer to the same whole. Record theresults of comparisons with the symbols >, =, or < and justify the conclusions

Major

5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) byreplacing given fractions with equivalent fractions in such a way as to produce anequivalent sum or difference of fractions with like denominators.

Major

5.NF.2 Solve word problems involving addition and subtraction of fractions referring to thesame whole, including cases of unlike denominators. Use benchmark fractions andnumber sense of fractions to estimate mentally and assess the reasonableness of answers

Major

5.NF.3 Interpret a fraction as division of the numerator by the denominator. Solve word Major

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problems involving division of whole numbers leading to answers in the form offractions or mixed numbers

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

Major

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 theother factor, without performing the indicated multiplicationb. Explaining why multiplying a given number by a fraction greater than 1 results in aproduct greater than the given number (recognizing multiplication by whole numbersgreater than 1 as a familiar case); explaining why multiplying a given number by afraction less than 1 results in a product smaller than the given number; and relating theprinciple of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.

Major

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.

Major

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

Major

Measurement and Data4.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, expressmeasurements in a larger unit in terms of a smaller unit. Record measurementequivalents in a two-column table.

Supporting

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 simplefractions or decimals, and problems that require expressing measurements given in alarger unit in terms of a smaller unit. Represent measurement quantities using diagramssuch as number line diagrams that feature a measurement scale.

Supporting

5.MD.1 Convert among different-sized standard measurement units within a given measurementsystem, and use these conversions in solving multi-step, real world problems.

Supporting

5.MD.2 Make a line plot to display a data set of measurements in fractions of a unit. Useoperations on fractions for this grade to solve problems involving information presentedin line plots.

Supporting

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

Major

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

Major

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

Major

Geometry5.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 agiven point in the plane located by using an ordered pair of numbers, called itscoordinates. Understand that the first number indicates how far to travel from the originin the direction of one axis, and the second number indicates how far to travel in thedirection of the second axis, with the convention that the names of the two axes and thecoordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

AdditionalPost

5.G.2 Represent real world and mathematical problems by graphing points in the first quadrantof the coordinate plane, and interpret coordinate values of points in the context of thesituation.

AdditionalPost

5.G.3 Understand that attributes belonging to a category of two-dimensional figures alsobelong to all subcategories of that category.

Additional

5.G.4 Classify two-dimensional figures in a hierarchy based on properties. Additional

= Standards recommended for greater emphasis

Post = Standards recommended for instruction in May-June

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MVCSD GRADE 5 MATHEMATICS PACING GUIDE

This guide using NYS Grade 5 Mathematics CCLS Modules was created to provide teachers with a time frame to complete theGrade 5 New York State Mathematics Curriculum.

Module Unit Title Standards Days Month i-Ready Lessons

1Place Value and Decimal

Fractions5.NBT.1, 5.NBT.2, 5.NBT.3a, 5.NBT.3b,

5.NBT.7, 5.MD.120 Sept. 8 – Oct. 8

Topic A – 1, 2; Topic B – 3;Topic C – 4; Topic D – 7; Topic

E – 8; Topic F – 9

2Multi-Digit Whole Number and

Decimal Fraction Operations5.OA.1, 5.OA.2, 5.NBT.5, 5.NBT.6, 5.NBT.7,

5.MD.130 Oct. 9 – Nov. 23

Topic A – 1, 2; Topic B – 5;Topic C – 8; Topic D – 21, 22;Topic E – 6; Topic F – 6; Topic

G – 9; Topic H – 9

3Addition and Subtraction of

Fractions5.NF.1, 5.NF.2 20 Nov. 24 – Dec. 23

Topic A – Grade 4 L13; TopicB – 10; Topic C – 10; Topic D –

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4Multiplication and Division of

Fractions and Decimal Fractions

5.OA.1, 5.OA.2, 5.NBT.7, 5.NF.3, 5.NF.4a,5.NF.5a, 5.NF.5b, 5.NF.6, 5.NF.7a, 5.NF.7b,

5.NF.7c, 5.MD.1, 5.MD.235 Jan. 4 – Feb. 29

Topic A – 23; Topic B – 12;Topic C – 13; Topic D – 16;Topic E – 13; Topic F – 15;

Topic G – 17, 18; Topic H – 19

5Addition and Multiplication with

Volume and Area5.NF.4b, 5.MD.3a, 5.MD.3b, 5.MD.4,

5.MD.5a, 5.MD.5b, 5.MD.5c, 5.G.3, 5.G.425 Mar. 1 – Apr. 12

Topic A – 24, 25; Topic B – 26,27; Topic C – 14; Topic D – 30,

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NYSED GRADE 5 MATHEMATICS TEST: WEDNESDAY, APRIL 13 – FRIDAY, APRIL 15, 2016

6Problem Solving with the

Coordinate Plane5.OA.2, 5.OA.3, 5.G.1, 5.G.2 46 Apr. 18 – Jun 22 Topic A – 28; Topic B – 20;

Topic C – 29; Topic D – 29

Red – End of Module Assessment PeriodGreen – Priority Standards account for approximately 70-80% of number of test points.

Note that the curriculum assumes that each school day includes 70-75 minutes of math: one hour on the day’s Session, and 10-15 minutes on Fluency activities.Designed to fit within the calendar of a typical school year, grade 5 includes a total of 149 lessons. This provides some leeway for going further with particularideas and/or accommodating local circumstances. Although pacing will vary somewhat in response to variations in school calendars, needs of students, yourschool's years of experience with the curriculum, and other local factors, following the suggested pacing and sequence will ensure that students benefit from theway mathematical ideas are introduced, developed, and revisited across the year.

Required Fluency: 5.NBT.5 Multi-digit multiplication.

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Module Unit Title Standards Days Month Workbook Lessons

1Place Value and Decimal

Fractions5.NBT.1, 5.NBT.2, 5.NBT.3a, 5.NBT.3b,

5.NBT.7, 5.MD.120 Sept. 8 – Oct. 8

Topic A – 1, 2; Topic B – 3; Topic C – 4;

Topic D – 7; Topic E – 8; Topic F – 9

In Module 1, students’ understanding of the patterns in the base ten system are extended from Grade 4’s work with place value of multi-digit whole numbers anddecimals to hundredths to the thousandths place. In Grade 5, students deepen their knowledge through a more generalized understanding of the relationshipsbetween and among adjacent places on the place value chart, e.g., 1 tenth times any digit on the place value chart moves it one place value to the right (5.NBT.1).Toward the module’s end students apply these new understandings as they reason about and perform decimal operations through the hundredths place.

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Standards Topics and Objectives Days

5.NBT.15.NBT.25.MD.1

A Multiplicative Patterns on the Place Value ChartLesson 1: Reason concretely and pictorially using place value understanding to relate adjacent baseten units from millions to thousandths.Lesson 2: Reason abstractly using place value understanding to relate adjacent base ten units frommillions to thousandths.Lesson 3: Use exponents to name place value units and explain patterns in the placement of thedecimal point.Lesson 4: Use exponents to denote powers of 10 with application to metric conversions.

4

5.NBT.3 B Decimal Fractions and Place Value PatternsLesson 5: Name decimal fractions in expanded, unit, and word forms by applying place valuereasoning.Lesson 6: Compare decimal fractions to the thousandths using like units and express comparisonswith >, <, = .

2

5.NBT.4 C Place Value and Rounding Decimal FractionsLesson 7–8: Round a given decimal to any place using place value understanding and the verticalnumber line.

2

Mid-Module Assessment: Topics A–C (assessment ½ day, return ½ day, remediation or furtherapplications 1 day)

2

5.NBT.25.NBT.35.NBT.7

D Adding and Subtracting DecimalsLesson 9: Add decimals using place value strategies and relate those strategies to a written method.Lesson 10: Subtract decimals using place value strategies and relate those strategies to a writtenmethod.

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E Multiplying DecimalsLesson 11: Multiply a decimal fraction by single-digit whole numbers, relate to a written methodthrough application of the area model and place value understanding, and explain the reasoningused.Lesson 12: Multiply a decimal fraction by single-digit whole numbers, including using estimation to

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confirm the placement of the decimal point.

5.NBT.35.NBT.7

F Dividing DecimalsLesson 13: Divide decimals by single-digit whole numbers involving easily identifiable multiplesusing place value understanding and relate to a written method.Lesson 14: Divide decimals with a remainder using place value understanding and relate to a writtenmethod.Lesson 15: Divide decimals using place value understanding including remainders in the smallestunit.Lesson 16: Solve word problems using decimal operations.

4

End-of-Module Assessment: Topics A–F (assessment ½ day, return ½ day, remediation or furtherapplications 1 day)

2

Total Number of Instructional Days 20

18


2Multi-Digit Whole Number and

Decimal Fraction Operations5.OA.1, 5.OA.2, 5.NBT.5,

5.NBT.6, 5.NBT.7, 5.MD.130 Oct. 9 – Nov. 23

Topic A – 1, 2; Topic B – 5; Topic C – 8; Topic D

– 21, 22; Topic E – 6; Topic F – 6; Topic G – 9;

Topic H – 9

In Module 1, students explored the relationships of adjacent units on the place value chart to generalize whole number algorithms to decimal fraction operations.

In Module 2, students apply the patterns of the base ten system to mental strategies and the multiplication and division algorithms. Module 2 begins by usingplace value patterns and the distributive and associative properties to multiply multi-digit numbers by multiples of 10 and leads to fluency withmulti-digit whole number multiplication. For multiplication, students must grapple with and fully understand the distributive property (one of thekey reasons for teaching the multi-digit algorithm). While the multi-digit multiplication algorithm is a straightforward generalization of the one-digit multiplication algorithm, the division algorithm with two-digit divisors requires far more care to teach because students have to also learnestimation strategies, error correction strategies, and the idea of successive approximation (all of which are central concepts in math, science, andengineering).

19


5.NBT.15.NBT.25.OA.1

A Mental Strategies for Multi-Digit Whole Number MultiplicationLesson 1: Multiply multi-digit whole numbers and multiples of 10 using place value patterns and the distributive andassociative properties.Lesson 2: Estimate multi-digit products by rounding factors to a basic fact and using place value patterns.

2

5.OA.15.OA.2

5.NBT.5

B The Standard Algorithm for Multi-Digit Whole Number MultiplicationLesson 3: Write and interpret numerical expressions and compare expressions using a visual model.Lesson 4: Convert numerical expressions into unit form as a mental strategy for multi-digit multiplication.Lesson 5: Connect visual models and the distributive property to partial products of the standard algorithm withoutrenaming.Lesson 6: Connect area diagrams and the distributive property to partial products of the standard algorithm withoutrenaming.Lesson 7: Connect area diagrams and the distributive property to partial products of the standard algorithm withrenaming.Lesson 8: Fluently multiply multi-digit whole numbers using the standard algorithm and using estimation to checkfor reasonableness of the product.Lesson 9: Fluently multiply multi-digit whole numbers using the standard algorithm to solve multi-step wordproblems.

7

5.NBT.75.OA.15.OA.2

5.NBT.1

C Decimal Multi-Digit MultiplicationLesson 10: Multiply decimal fractions with tenths by multi-digit whole numbers using place value understanding torecord partial products.Lesson 11: Multiply decimal fractions by multi-digit whole numbers through conversion to a whole number problemand reasoning about the placement of the decimal.Lesson 12: Reason about the product of a whole number and a decimal with hundredths using place valueunderstanding and estimation.

3

5.NBT.55.NBT.75.MD.15.NBT.15.NBT.2

D Measurement Word Problems with Whole Number and Decimal MultiplicationLesson 13: Use whole number multiplication to express equivalent measurements.Lesson 14: Use decimal multiplication to express equivalent measurements.Lesson 15: Solve two-step word problems involving measurement and multi-digit multiplication.

3

Mid-Module Assessment: Topics A–D 1

20



E Mental Strategies for Multi-Digit Whole Number DivisionLesson 16: Use divide by 10 patterns for multi-digit whole number division.Lessons 17–18: Use basic facts to approximate quotients with two-digit divisors.

2

5.NBT.6 F Partial Quotients and Multi-Digit Whole Number DivisionLesson 19: Divide two- and three-digit dividends by multiples of 10 with single-digit quotients and makeconnections to a written method.Lesson 20: Divide two- and three-digit dividends with single-digit quotients and make connections to awritten method.Lesson 21: Divide two- and three-digit dividends by two-digit divisors with single-digit quotients and makeconnections to a written method.Lessons 22–23: Divide three- and four-digit dividends by two-digit divisors resulting in two- and three-digit quotients, reasoning about the decomposition of successive remainders in each place value.

5

5.NBT.25.NBT.7

G Partial Quotients and Multi-Digit Decimal DivisionLesson 24: Divide decimal dividends by multiples of 10, reasoning about the placement of the decimal pointand making connections to a written method.Lesson 25: Use basic facts to approximate decimal quotients with two-digit divisors, reasoning about theplacement of the decimal point.Lessons 26–27: Divide decimal dividends by two-digit divisors, estimating quotients, reasoning about theplacement of the decimal point, and making connections to a written method.

3

5.NBT.65.NBT.7

H Measurement Word Problems with Multi-Digit DivisionLessons 28–29: Solve division word problems involving multi-digit division with group size unknown andthe number of groups unknown.

2

End-of-Module Assessment: Topics A–H (assessment ½ day, return ½ day, remediation or furtherapplication 1 day)

2


21


3Addition and Subtraction of

Fractions5.NF.1, 5.NF.2 20 Nov. 24 – Dec. 23

Topic A – Grade 4 L13; Topic B – 10; Topic C –

10; Topic D – 11

In Module 3, students’ understanding of addition and subtraction of fractions extends from earlier work with fraction equivalence and decimals. This modulemarks a significant shift away from the elementary grades’ centrality of base ten units to the study and use of the full set of fractional units from Grade 5 forward,especially as applied to algebra.

22


4.NF.14.NF.3c4.NF.3d

A Equivalent FractionsLesson 1: Make equivalent fractions with the number line, the area model, and numbers.Lesson 2: Make equivalent fractions with sums of fractions with like denominators.

2

5.NF.15.NF.2

B Making Like Units PictoriallyLesson 3: Add fractions with unlike units using the strategy of creating equivalent fractions.Lesson 4: Add fractions with sums between 1 and 2.

Lesson 5: Subtract fractions with unlike units using the strategy of creating equivalent fractions.Lesson 6: Subtract fractions from numbers between 1 and 2.Lesson 7: Solve two-step word problems.

5

Mid-Module Assessment: Topics A–B (assessment ½ day, return ½ day, remediation or further applications 1 day) 2

5.NF.15.NF.2

C Making Like Units NumericallyLesson 8: Add fractions to and subtract fractions from whole numbers using equivalence and the number line asstrategies.Lesson 9: Add fractions making like units numerically.Lesson 10: Add fractions with sums greater than 2.Lesson 11: Subtract fractions making like units numerically.Lesson 12: Subtract fractions greater than or equal to one.

5

5.NF.15.NF.2

D Further ApplicationsLesson 13: Use fraction benchmark numbers to assess reasonableness of addition and subtraction equations.Lesson 14: Strategize to solve multi-term problems.Lesson 15: Solve multi-step word problems; assess reasonableness of solutions using benchmark numbers.Lesson 16: Explore part to whole relationships.

4

End-of-Module Assessment: Topics C–D (assessment ½ day, return ½ day, remediation or further applications 1 day) 2


23


4Multiplication and Division of

Fractions and Decimal Fractions

5.OA.1, 5.OA.2, 5.NBT.7, 5.NF.3, 5.NF.4a,5.NF.5a, 5.NF.5b, 5.NF.6, 5.NF.7a, 5.NF.7b,

5.NF.7c, 5.MD.1, 5.MD.235

Jan. 4 – Feb.

29

Topic A – 23; Topic B – 12;

Topic C – 13; Topic D – 16;

Topic E – 13; Topic F – 15;

Topic G – 17, 18; Topic H – 19

In Module 4, students learn to multiply fractions and decimal fractions and begin work with fraction division.

24


5.MD.2 A Line Plots of Fraction MeasurementsLesson 1: Measure and compare pencil lengths to the nearest 1/2, 1/4, and 1/8 of an inch, and analyze thedata through line plots.

1

5.NF.3 B Fractions as DivisionLessons 2–3: Interpret a fraction as division.Lesson 4: Use tape diagrams to model fractions as division.Lesson 5: Solve word problems involving the division of whole numbers with answers in the form offractions or whole numbers.

4

5.NF.4a C Multiplication of a Whole Number by a FractionLesson 6: Relate fractions as division to fraction of a set.Lesson 7: Multiply any whole number by a fraction using tape diagrams.Lesson 8: Relate fraction of a set to the repeated addition interpretation of fraction multiplication.Lesson 9: Find a fraction of a measurement, and solve word problems.

4

5.OA.15.OA.25.NF.4a5.NF.6

D Fraction Expressions and Word ProblemsLesson 10: Compare and evaluate expressions with parentheses.Lesson 11–12: Solve and create fraction word problems involving addition, subtraction, and multiplication.

3

Mid-Module Assessment: Topics A–D (assessment 1 day) 1

5.NBT.75.NF.4a5.NF.65.MD.15.NF.4b

E Multiplication of a Fraction by a FractionLesson 13: Multiply unit fractions by unit fractions.Lesson 14: Multiply unit fractions by non-unit fractions.Lesson 15: Multiply non-unit fractions by non-unit fractions.Lesson 16: Solve word problems using tape diagrams and fraction-by-fraction multiplication.Lessons 17–18: Relate decimal and fraction multiplication.Lesson 19: Convert measures involving whole numbers, and solve multi-step word problems.Lesson 20: Convert mixed unit measurements, and solve multi-step word problems.

8

25


5.NF.55.NF.6

F Multiplication with Fractions and Decimals as Scaling and Word ProblemsLesson 21: Explain the size of the product, and relate fraction and decimal equivalence to multiplying afraction by 1.Lessons 22–23: Compare the size of the product to the size of the factors.Lesson 24: Solve word problems using fraction and decimal multiplication.

4

5.OA.15.NBT.75.NF.7

G Division of Fractions and Decimal FractionsLesson 25: Divide a whole number by a unit fraction.Lesson 26: Divide a unit fraction by a whole number.Lesson 27: Solve problems involving fraction division.Lesson 28: Write equations and word problems corresponding to tape and number line diagrams.Lessons 29: Connect division by a unit fraction to division by 1 tenth and 1 hundredth.Lessons 30–31: Divide decimal dividends by non‐unit decimal divisors.

6

5.OA.15.OA.2

H Interpretation of Numerical ExpressionsLesson 32: Interpret and evaluate numerical expressions including the language of scaling and fractiondivision.Lesson 33: Create story contexts for numerical expressions and tape diagrams, and solve word problems.

2

End-of-Module Assessment: Topics A–H (assessment 1 day, remediation or further applications 1 day) 2


26

Module Unit Title Standards Days MonthWorkbook

Lessons

5Addition and Multiplication with

Volume and Area5.NF.4b, 5.MD.3a, 5.MD.3b, 5.MD.4,

5.MD.5a, 5.MD.5b, 5.MD.5c, 5.G.3, 5.G.425 Mar. 1 – Apr. 12

Topic A – 24, 25; Topic

B – 26, 27; Topic C –

14; Topic D – 30, 31

NYSED GRADE 5 MATHEMATICS TEST: WEDNESDAY, APRIL 13 – FRIDAY, APRIL 15, 2016

In this 25-day module, students work with two- and three-dimensional figures. Volume is introduced to students through concrete exploration of cubic units andculminates with the development of the volume formula for right rectangular prisms. The second half of the module turns to extending students’ understandingof two-dimensional figures. Students combine prior knowledge of area with newly acquired knowledge of fraction multiplication to determine the area ofrectangular figures with fractional side lengths. They then engage in hands-on construction of two-dimensional shapes, developing a foundation for classifyingthe shapes by reasoning about their attributes. This module fills a gap between Grade 4’s work with two-dimensional figures and Grade 6’s work with volumeand area.

27


5.MD.35.MD.4

A Concepts of VolumeLesson 1: Explore volume by building with and counting unit cubes.Lesson 2: Find the volume of a right rectangular prism by packing with cubic units and counting.Lesson 3: Compose and decompose right rectangular prisms using layers.

3

5.MD.35.MD.5

B Volume and the Operations of Multiplication and AdditionLesson 4: Use multiplication to calculate volume.Lesson 5: Use multiplication to connect volume as packing with volume as filling.Lesson 6: Find the total volume of solid figures composed of two non-overlapping rectangular prisms.Lesson 7: Solve word problems involving the volume of rectangular prisms with whole number edgelengths.Lessons 8–9: Apply concepts and formulas of volume to design a sculpture using rectangular prisms withingiven parameters.

6

Mid-Module Assessment: Topics A–B (assessment 1 day) 1

5.NF.4b5.NF.6

C Area of Rectangular Figures with Fractional Side LengthsLesson 10: Find the area of rectangles with whole-by-mixed and whole-by-fractional number side lengths bytiling, record by drawing, and relate to fraction multiplication.Lesson 11: Find the area of rectangles with mixed-by-mixed and fraction-by-fraction side lengths bytiling, record by drawing, and relate to fraction multiplication.Lesson 12: Measure to find the area of rectangles with fractional side lengths.Lessons 13: Multiply mixed number factors, and relate to the distributive property and the area model.Lessons 14–15: Solve real world problems involving area of figures with fractional side lengths usingvisual models and/or equations.

6

5.G.35.G.4

D Drawing, Analysis, and Classification of Two-Dimensional ShapesLesson 16: Draw trapezoids to clarify their attributes, and define trapezoids based on those attributes.Lesson 17: Draw parallelograms to clarify their attributes, and define parallelograms based on thoseattributes.Lesson 18: Draw rectangles and rhombuses to clarify their attributes, and define rectangles and rhombusesbased on those attributes.

6

28

Lesson 19: Draw kites and squares to clarify their attributes, and define kites and squares based on thoseattributes.Lesson 20: Classify two-dimensional figures in a hierarchy based on properties.Lesson 21: Draw and identify varied two-dimensional figures from given attributes.

End-of-Module Assessment: Topics A–D (assessment 1 day, remediation or further applications 2 days) 3


29


6Problem Solving with the Coordinate

Plane5.OA.2, 5.OA.3, 5.G.1, 5.G.2 46 Apr. 18 – Jun 22

Topic A – 28; Topic B – 20;

Topic C – 29; Topic D – 29

In this 40-day module, students develop a coordinate system for the first quadrant of the coordinate plane and use it to solve problems. Students use the familiarnumber line as an introduction to the idea of a coordinate and construct two perpendicular number lines to create a coordinate system on the plane. They see thatjust as points on the line can be located by their distance from 0, the plane’s coordinate system can be used to locate and plot points using two coordinates. Theythen use the coordinate system to explore relationships between points, ordered pairs, patterns, lines and, more abstractly, the rules that generate them. Thisstudy culminates in an exploration of the coordinate plane in real world applications.

30


5.G.1 A Coordinate SystemsLesson 1: Construct a coordinate system on a line.Lesson 2: Construct a coordinate system on a plane.Lessons 3–4: Name points using coordinate pairs, and use the coordinate pairs to plot points.Lessons 5–6: Investigate patterns in vertical and horizontal lines, and interpret points on the plane asdistances from the axes.

7

5.OA.25.OA.35.G.1

B Patterns in the Coordinate Plane and Graphing Number Patterns from RulesLesson 7: Plot points, use them to draw lines in the plane, and describe patterns within the coordinatepairs.Lesson 8: Generate a number pattern from a given rule, and plot the points.Lesson 9: Generate two number patterns from given rules, plot the points, and analyze the patterns.Lesson 10: Compare the lines and patterns generated by addition rules and multiplication rules.Lesson 11: Analyze number patterns created from mixed operations.Lesson 12: Create a rule to generate a number pattern, and plot the points.

7

Mid-Module Assessment: Topics A–B (assessment 1 day, return 1 day, remediation or furtherapplications 1 day)

3

5.G.15.G.2

C Drawing Figures in the Coordinate PlaneLesson 13: Construct parallel line segments on a rectangular grid.Lesson 14: Construct parallel line segments, and analyze relationships of the coordinate pairs.Lesson 15: Construct perpendicular line segments on a rectangular grid.Lesson 16: Construct perpendicular line segments, and analyze relationships of the coordinate pairs.Lesson 17: Draw symmetric figures using distance and angle measure from the line of symmetry.

6

5.OA.35.G.2

D Problem Solving in the Coordinate PlaneLesson 18: Draw symmetric figures on the coordinate plane.Lesson 19: Plot data on line graphs and analyze trends.Lesson 20: Use coordinate systems to solve real world problems.

4

31


End-of-Module Assessment: Topics A–D (assessment 1 day, return 1 day, remediation or furtherapplications 2 days)

4

5.NF.25.NF.35.NF.65.NF.7c5.MD.15.MD.55.G.2

E Multi-Step Word ProblemsLessons 21–25: Make sense of complex, multi-step problems and persevere in solving them. Shareand critique peer solutions.

5

F The Years in Review: A Reflection on A Story of UnitsLessons 26–27: Solidify writing and interpreting numerical expressions.Lesson 28: Solidify fluency with Grade 5 skills.Lessons 29─30: Solidify the vocabulary of geometry. Lesson 31: Explore the Fibonacci sequence.Lesson 32: Explore patterns in saving money.Lessons 33–34: Design and construct boxes to house materials for summer use.

10


WORD WALLS ARE DESIGNED …

to promote group learning support the teaching of important general principles about words and how they work Foster reading and writing in content area Provide reference support for children during their reading and writing Promote independence on the part of young students as they work with words Provide a visual map to help children remember connections between words

and the characteristics that will help them form categories Develop a growing core of words that become part of their vocabulary

Important Notice A Mathematics Word Wall must be present in every mathematics classroom.

Math Word Wall

Create a math wordwall

Place math words onyour current wordwall but highlightthem in some way.

33

SETUP OF THE MATHEMATICS CLASSROOM

I. Prerequisites for a Mathematics Classroom Teacher Schedule Class List Seating Chart Code of Conduct / Discipline Grade Level Common Core Learning Standards (CCLS) Updated Mathematics Student Work Mathematics Grading Policy Mathematics Diagrams, Charts, Posters, etc. Grade Level Number Line Grade Level Mathematics Word Wall Mathematics Portfolios Mathematics Center with Manipulatives (Grades K - 12)

II. Updated Student WorkA section of the classroom must display recent student work. This can be of anytype of assessment, graphic organizer, and writing activity. Teacher feedback mustbe included on student’s work.

III. Board Set-UpEvery day, teachers must display the Lesson # and Title, Objective(s), CommonCore Learning Standard(s), Opening Exercise and Homework. At the start ofthe class, students are to copy this information and immediately begin on theFluency Activity or Opening Exercise.

IV. Spiraling HomeworkHomework is used to reinforce daily learning objectives. The secondary purposeof homework is to reinforce objectives learned earlier in the year. Theassessments are cumulative, spiraling homework requires students to reviewcoursework throughout the year.

Student’s Name: School:

Teacher’s Name: Date:

Lesson # and Title:

Objective(s)

CCLS:

Opening Exercise:

34

ELEMENTARY MATHEMATICS GRADING POLICY

This course of study includes different components, each of which are assigned the followingpercentages to comprise a final grade. I want you--the student--to understand that your gradesare not something that I give you, but rather, a reflection of the work that you give to me.

COMPONENTS OF OVERALL GRADE

LEVEL 1 (0-54%), LEVEL 2 (55-74%), LEVEL 3 (75-89%) AND LEVEL 4 (90-100%)

1. End of Module Assessments → 35%

2. Mid Module Assessments → 15%

3. Homework → 20%

4. Notebook and/or Journal → 15%

5. Classwork / Class Participation → 15%

o Class participation will play a significant part in the determination of your grade.Class participation will include the following: attendance, punctuality to class,contributions to the instructional process, effort, contributions during small groupactivities and attentiveness in class.

PERFORMANCE LEVEL DESCRIPTORS

Level 4 Student demonstrates an in-depth understanding of concepts, skills and processestaught in this reporting period and exceeds the required performance

Level 3 Student consistently demonstrates an understanding of concepts, skills and processestaught in this reporting period

Level 2 Student is beginning to demonstrate an understanding of concepts, skills andprocesses taught during this reporting period

Level 1 Student does not yet demonstrate an understanding of concepts, skills and processestaught in this reporting period and needs consistent support

NE Not evaluated at this time

IMPORTANT NOTICE

As per MVCSD Board Resolution 06-71, the Parent Notification Policy states “Parent(s) /guardian(s) or adult students are to be notified, in writing, at any time during a grading periodwhen it is apparent - that the student may fail or is performing unsatisfactorily in any course orgrade level. Parent(s) / guardian(s) are also to be notified, in writing, at any time during thegrading period when it becomes evident that the student's conduct or effort grades areunsatisfactory.”

35

SAMPLE NOTEBOOK SCORING RUBRIC

Student Name:______________________________________________

Teacher Name:___________________________________________

Criteria 4 3 2 1 Points

Completion ofRequired Sections

All requiredsections arecomplete.

One requiredsection ismissing.

Two or threerequired sections

are missing.

More than threerequired sections

are missing.

Missing SectionsNo sections of

the notebook aremissing.

One sections ofthe notebook is

missing.

Two sections of thenotebook are

missing.

Three or moresections of thenotebook are

missing.

Headers / Footers

No requiredheader(s) and/or

footer(s) aremissing within

notebook.

One or tworequired

header(s) and/orfooter(s) are

missing withinnotebook.

Three or fourrequired header(s)and/or footer(s) are


More than fourrequired header(s)and/or footer(s) are


Organization

All assignmentand/or notes arekept in a logical

or numericalsequence.

One or twoassignments

and/or notes arenot in a logical or

numericalsequence.

Three or Fourassignments and/ornotes are not in a

logical ornumericalsequence.

More than fourassignments and/ornotes are not in a

logical ornumericalsequence.

NeatnessOverall notebookis kept very neat.

Overall notebookis kept in asatisfactorycondition.

Overall notebook iskept in a below

satisfactorycondition.

Overall notebook isunkept and very

disorganized.

Total

Teacher’s Comments:

36

CLASSROOM AESTHETICS

“PRINT–RICH” ENVIRONMENT CONDUCIVE TO LEARNING

TEACHER NAME: _________________________________________________________

COURSE / PERIOD: _________________________________________________________

ROOM: _________________________________________________________

CHECKLISTYES NO

Teacher Schedule

Class List

Seating Chart

Code of Conduct / Discipline

Grade Level Mathematics CCLS

Mathematics Grading Policy

Mathematics Diagrams, Posters, Displays, etc.

Grade Level Number Line

Updated Student Work (Projects, Assessments, Writing, etc.)

Updated Student Portfolios

Updated Grade Level Mathematics Word-Wall

Mathematics Centers with Manipulatives

Organization of Materials

Cleanliness

Principal Signature: _________________________________________ Date: ____________

Asst. Pri. Signature: _________________________________________ Date: ____________

37

SYSTEMATIC DESIGN OF A MATHEMATICS LESSON

What are the components of an Elementary Mathematics Block?

ComponentFluency Practice Information processing theory supports the view that automaticity in math facts is

fundamental to success in many areas of higher mathematics. Without the ability to retrievefacts directly or automatically, students are likely to experience a high cognitive load as theyperform a range of complex tasks. The added processing demands resulting from inefficientmethods such as counting (vs. direct retrieval) often lead to declarative and procedural errors.Accurate and efficient retrieval of basic math facts is critical to a student’s success inmathematics.

Opening Exercise - Whole Group This can be considered the motivation or Do Now of the lesson It should set the stage for the day's lesson Introduction of a new concept, built on prior knowledge Open-ended problemsConceptual Development - Whole Group (Teacher Directed, Student Centered) Inform students of what they are going to do. Refer to Objectives. Refer to the Key Words

(Word Wall) Define the expectations for the work to be done Provide various demonstrations using modeling and multiple representations (i.e. model a

strategy and your thinking for problem solving, model how to use a ruler to measure items,model how to use inch graph paper to find the perimeter of a polygon,)

Relate to previous work Provide logical sequence and clear explanations Provide medial summaryApplication Problems - Cooperative Groups, Pairs, Individuals, (Student Interaction &Engagement, Teacher Facilitated) Students try out the skill or concept learned in the conceptual development Teachers circulate the room, conferences with the students and assesses student work (i.e.

teacher asks questions to raise the level of student thinking) Students construct knowledge around the key idea or content standard through the use of

problem solving strategies, manipulatives, accountable/quality talk, writing, modeling,technology applied learning

Student Debrief - Whole Group (Teacher Directed, Student Centered) Students discuss their work and explain their thinking Teacher asks questions to help students draw conclusions and make references Determine if objective(s) were achieved Students summarize what was learned Allow students to reflect, share (i.e. read from journal)Homework/Enrichment - Whole Group (Teacher Directed, Student Centered) Homework is a follow-up to the lesson which may involve skill practice, problem solving

and writing

38

Homework, projects or enrichment activities should be assigned on a daily basis. SPIRALLING OF HOMEWORK - Teacher will also assign problems / questions pertaining to

lessons taught in the past

Remember: Assessments are on-going based on students’ responses.Assessment: Independent Practice (It is on-going! Provide formal assessment whennecessary / appropriate) Always write, use and allow students to generate Effective Questions for optimal learning Based on assessment(s), Re-teach the skill, concept or content using alternative strategies

and approaches

Important Notice

All lessons must be numbered with corresponding homework. For example, lesson #1 will

corresponded to homework #1 and so on.

Writing assignments at the end of the lesson (closure) bring great benefits. Not only do they

enhance students' general writing ability, but they also increase both the understanding of

content while learning the specific vocabulary of the disciplines.

Spiraling Homework

o Homework is used to reinforce daily learning objectives. The secondary purpose of

homework is to reinforce objectives learned earlier in the year. The assessments are

cumulative, spiraling homework requires students to review coursework throughout the

year.

Manipulative must be incorporated in all lessons. With students actively involved in

manipulating materials, interest in mathematics will be aroused. Using manipulative

materials in teaching mathematics will help students learn:

a. to relate real world situations to mathematics symbolism.

b. to work together cooperatively in solving problems.

c. to discuss mathematical ideas and concepts.

d. to verbalize their mathematics thinking.

e. to make presentations in front of a large group.

f. that there are many different ways to solve problems.

g. that mathematics problems can be symbolized in many different ways.

h. that they can solve mathematics problems without just following teachers' directions.

ccls mathematics grade 5 curriculum guidemvcsd.sharpschool.net/userfiles/servers/server... · 5...

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