Valley ElementaryCommon Core Mathematics

Grades 3-5 Vertical Alignment

January, 2015 Draft

Statement of Purpose:In order to provide the most inspiring, effective, and high quality math education for Valley Elementary students, the Valley teachers are committed to providing a coherent mathematical learning experience for the students across all the grades.

This document is designed to map how students will experience each core math concept and how we will intentionally connect the learning experiences from one grade level to the next.

It includes the key models, strategies and procedures that Valley teachers agree to provide for students at each grade level. (do we want to add tools?)

It also details the guaranteed learning experiences and tasks for each concept at each grade level that the teachers have identified as essential for students to develop deep understanding.

It includes the agreed upon math classroom routines that will shape the student math experience.

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And finally, it details the math vocabulary that will be highlighted for each concept, including English and Spanish.

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Core Elements of Mathematics at Valley Elementary

Environment Math Lessons Instruction

Safe culture for risk takingCollaborationDivergent thinking honoredExploratorySelf-discoveryFun and engagingStudent-centeredStudents persevereIncludes parents, students, and teachers

Number TalksRich TasksInvestigations and ExplorationsRich math discourseBalanced practice

Talk movesModelsValue and highlight different strategiesElicit and record student thinkingStudent-centered

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Numbers and Operations, Base Ten (Whole Number Addition and Subtraction) Grades 3-5

Grade Level

CC Content StandardsMath Models,

Strategies, and/or Procedures

Important Learning Experiences

Routines Vocabulary

3rd CCSS.Math.Content.3.NBT.A.2Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

3rd grade focuses heavily on multiplication and division, therefore this is a continuation standard, not a major focus at 3rd grade.

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

Decomposing numbers to add and subtract (breaking apart)

Traditional algorithm for addition

Open number line for subtractionTraditional algorithm for subtraction

Investigations:1,000 BookField Trip to the Zoo

Games:Close to 100Close to 1,000Race to 1,000PIGChanging PlacesBroken CalculatorSum and DifferenceLargest Difference

Number Talks: addition and subtraction – Chapter 6 Number Talks

DigitInverse operationsAddendSum

difference

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5th Addition and Subtraction for fifth grade focus on rational numbers (fractions and decimals). Students should still practice whole number addition and subtraction in Number Talks and spiral review . . .but they are not a major focus.

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Operations and Algebraic Thinking (Whole Number Multiplication) Grades 3-5

Grade Level

CC Content StandardsMath Models,

Strategies, and/or Procedures

Important Learning Experiences

Routines Vocabulary

3rd 3.OA.3Multiplication and division within 100

Grouping (circles and stars)

Rectangular array

Solve word problems

Multiple step problem solvingAssociative property

Circles and StarsThings That Come In Groups

Amanda Bean investigationHow Long? How Many?

Multiplication stories

100 Hungry Ants

Number Talks (3 x / week)

Daily fact practice (flashcards, multip. Tic Tac Toe)

Spiral review

ProductFactorArrayEqual groups

4th 4.OA.1Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7 as a statement that 35 is 5 times as many as 7 and 7 times as many as 5.

4.OA.2Multiply or divide to solve word problems involving multiplicative comparisons using drawings.

4OA.3Solve multistep word problems with all 4 operations.

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

Math Model: Rectangular

Area Model Arrays Standard

Algorithm Partial

Products

Strategy: Decompose

(Break Apart) Repeated

addition Partial

products

Investigations: Candy Box One Hundred Hungry

Ants How long? How

many? Array

Cards(multiplication pairs, Count and Compare, Small Array/Big Array

Braking Rectangles Apart Investigation

Games: Target 300 Pathways

Number Talks

Silent Multiplication

Content Specific Vocabulary: Factor Product Variable Groups of Multiple Prime Composite Square

number

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Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1–100 is a multiple of a given one-digit number. Determine whether a given whole number in the range 1–100 is prime or composite.

Times 10 Finding Factors Tic-Tac-Toe Factor Capture Circle and stars How Long? How

Many?

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Grade Level CC Content Standard

Math Models, Strategies, and/or

Procedures

Important Learning Experiences Routines Vocabulary

5th CCSS.Math.Content.5.NBT.B.5Fluently multiply multi-digit whole numbers using the standard algorithm.

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Operations and Algebraic Thinking & Numbers & Operations, Base Ten Whole Number Division, Grades 3-5

Grade Level CC Content Standards

Math Models, Strategies, and/or

Procedures

Important Learning Experiences Routines Vocabulary

3rd 3.OA.A.2Interpret 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.

Sharing equal groupsIntro to terms

Equal groupsIntro to notation

Solving word problems

Everybody Wins

The Doorbell Rang

Dividing Cookies

Division Stories

Practice facts Divide Quotients Equal groups Dividend Divisor

4th 4.NBT.6Find whole number quotients with remainders up to 4 digits /1 digit.

4.OA.2Multiply or divide to solve word problems involving multiplicative comparisons using drawings.

4OA.3Solve multistep word problems with all 4 operations.

Math Model: Rectangular Area

Model, Partial Quotient

Strategy: Decompose (Break Apart) & Divide using the distributive property.

Investigations: Everybody Wins, 100 Hungry Ants, Remainder of 1, Take Me Out to the Ballgame, The Zoo Field Trip, 17 Kings & 42 Elephants

Games: Leftovers with 25, Division Dash

Number Talks – silent division

Content Specific Vocabulary:Dividend, Divisor, Quotient, Remainder, Digit, Variable

Academic Vocabulary:

Interpret, analyze, unknown

5th CCSS.Math.Content.5.NBT.B.6Find whole-number quotients of whole numbers with up to four-digit dividends and two-

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digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

Numbers and Operations, Fractions, Grades 3-5

Grade Level

CC Content Standards Math Models, Strategies, and/or Procedures

Important Learning Experiences

Routines Vocabulary

3rd 3.NF.A.1Develop understanding of fractions

3.NF.A.2Fractions on number line

Fraction Kit

Andrea’s Fraction Number Line Lesson

Cover up GameUncover Game (version 1 and 2)

Number line

Play fraction games (menu)

Use number line in math talks

Whole Half Numerator Denominator EquivalentNumber line

4th Extend Understanding of Equivalence and Ordering4.NF.A1 Equivalent Fractions4NF.A2 Compare Fractions

Build Fractions from Unit Fractions (Use

Math Model: Fraction Strips Grid Paper Geoboards Number Line

Strategy:Drawing, folding, shading, coloring,

Investigations:

Identifying, Exploring and Comparing Fraction with: The Fraction Strips Kit, The Garden, Geoboards, What Part is Blue? and Tangrams portions.

Number Talks:

Comparisons of equivalent fractions as well as lesser or greater amounts

Content Specific Vocabulary:Fraction/partitionedNumeratorDenominatorEquivalentMultiplePortion

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visual models and properties of operations)4NFB3 A – D Add/Subtract fractions as

join/separate from same whole.

Decompose fractions into sum of fractions with like denominators.

Add and subtract mixed numbers with like denominators

Add/Subt. Word problems, like denominators (visual models)

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

marking visual representations of equally divided fractional parts in comparison with different size portions or other denominators.

Games: Cover Up Uncover One, Two Fill One, Two Wipeout Pick Two, Three Roll Five Make a Whole What’s Missing? Comparing Pairs

being represented.

Identifying what part is shaded, missing, represented and/or compared with a decimal or percentage.

/PercentageDecimal

Academic Vocabulary:Comparison/compareReasoning/explainFraction unit/equal sizeDecompose/ungrouping by tenths, hundredths, thousandths.Represent/demonstrate.

Grade Level

CC Content StandardMath Models,

Strategies, and/or Procedures

Important Learning Experiences

Routines Vocabulary

5th

5.NF.1 Adding and Subtracting numbers with unlike denominators by replacing with equivalent fractions.

5.NF.4 and 5.NF.7Apply and extend previous understanding of

Addition and Subtraction Using the

fraction strips Fraction clock

model

Multiplication and Division

Use area models to multiply fractions (fraction

Addition and Subtraction

Building the Fraction Tool Kit

Cover and Uncover

In between Fraction Tracks

Multiplication and DivisionComparison Chart (Compare multiplication

Number talks

Math Menus

Daily Math Review

Addition/Subtraction:

Multiplication/Division

Factor Product Multiples

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multiplication/division to multiply/divide a fraction.

Multiplication: Fraction by fraction; fraction by whole number; fraction by mixed number; mixed number by mixed number

Division: Whole number by unit fraction and unit fraction by whole number

strips, rectangular array)

What about number line?

What about division?

properties of whole numbers vs. fractions properties)

What about division?

Let’s add to this

Dividend Divisor Quotient x=”groups of” ¾ (of) 2/3

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Numbers and Operations, Fractions (Decimals) Grades 3-5

Grade Level

CC Content StandardsMath Models,

Strategies, and/or Procedures

Important Learning Experiences

Routines Vocabulary

3rd N/A

4th Understand decimal notation for fractions, and compare decimal fractions.

N.F.C.6Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as0.62 meters; locate 0.62 on a number line diagram.

N.F.C.7Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only whenthe two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify theconclusions, e.g., by using the number line or another visual model. CA

Base Ten Block Model(Month to Month p.271)

Decimal Bongo(Month to Month p.267)

Place Value Game(Month to Month p.278)

Greatest ___Wins(Month to Month p.278)

Put in order: The Sequel.(Month to Month p.275)

Fill one

Fill two

Hundredths grids

decimal cards

Base-ten blocks

linear measures for breaking up decimals

Number Talks4x times a weekCan you show me in a drawing 0.5?

Can you have 0.5 of a cookie?

Where would I find 0.5 on a number line?

How many hundredths make up a whole?

How many tenths make up a whole?

Jack says that 0.5 is greater than 1/2. Do you agree or disagree?What strategy

Place valuedecimal pointonestenshundredstenthshundredthsthousandthsequivalentless thangreater than

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could you use to support your reasoning?

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Grade Level CC Content Standards

Math Models, Strategies, and/or

Procedures

Important Learning Experiences Routines Vocabulary

5th 5.NBT.7 Add, subtract, multiply and divide decimals to hundredths.

Decimal Grids

Fraction to Decimal Chart

Fraction, decimal and percent equivalent

Decimal/Grid patterns

Money Model

Close to 1 In Between

Game

Everyday uses of….

Math Menus

Daily Math Review

Number Talk

Whole NumberDecimal pointTenthsHundredthsThousandthsRoundingEquivalentAligningIncreaseDecreasePower of 10

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Numbers and Operations, Measurement and Data Grades 3-5

Grade Level

CC Content StandardsMath Models,

Strategies, and/or Procedures

Important Learning Experiences

Routines Vocabulary

3rd Topics for 3rd Grade (not a “major cluster”)

Time Liquid volume Scaled picture and bar

graphs Area & Perimeter

4th Topics for 3rd Grade (not a “major cluster”)

Measurement Conversions

Area & Perimeter (SBAC favorites!)

Line plots to display data in fractional units (another SBAC favorite)

Angles: What are they? Relative sizes of angles. Angles are additive. Find unknown angles.

5th 5.MD.3-5 Recognizing, measuring and relating volume

**Note from Andrea – Nets are not part of the 5th grade standards. Please remove.**

Nets Prisms V= L x w x h

Geo-solid investigation

Nets

Number Talks

Daily Math Review

Math Menus

NetPrismsHeightLengthWidthBaseApexCubicEdgesFacesVertexComplex

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FiguresUnit cubes

Volume

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The Common Core Standards for MathematicsThe Major Work of Each Grade Level

(Borrowed from North Carolina, Engage New York, and Arizona Common Core Progressions Documents)

3rd Grade 4th Grade 5th GradeMajor

ClustersOperations and Algebraic Thinking Represent and solve problems

involving multiplication and division.

Understand properties of multiplication and the relationship between multiplication and division.

Multiply and divide within 100.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Number and Operations—Fractions Develop understanding of

fractions as numbers.

Measurement and Data Solve problems involving

measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Geometric measurement: understand concepts of area

Operations and Algebraic Thinking Use the four operations with

whole numbers to solve problems.

Number and Operations in Base Ten Generalize place value

understanding for multi-digit whole numbers.

Use place value understanding and properties of operations to perform multi-digit arithmetic.

Number and Operations—Fractions Extend understanding of

fraction equivalence and ordering.

Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

Understand decimal notation for fractions, and compare decimal fractions.

Number and Operations in Base Ten Understand the place

value system. Perform operations with

multi-digit whole numbers and with decimals to hundredths.

Number and Operations—Fractions Use equivalent fractions

as a strategy to add and subtract fractions.

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

Measurement and Data Geometric measurement:

understand concepts of volume and relate volume to multiplication and to addition.

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and relate area to multiplication and to addition.

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3rd Grade 4th Grade 5th GradeSupportin

g/Additional Clusters

Number and Operations in Base Ten Use place value

understanding and properties of operations to perform multi-digit arithmetic.

Measurement and Data Represent and interpret data. Geometric measurement:

recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

Geometry Reason with shapes and their

attributes.

Operations and Algebraic Thinking Gain familiarity with factors

and multiples. Generate and analyze patterns.

Measurement and Data Solve problems involving

measurement and conversion of measurements from a larger unit to a smaller unit.

Represent and interpret data. Geometric measurement:

understand concepts of angle and measure angles.

Geometry Draw and identify lines and

angles, and classify shapes by properties of their lines and angles.

Operations and Algebraic Thinking Write and interpret

numerical expressions. Analyze patterns and

relationships.

Measurement and Data Convert like

measurement units within a given measurement system.

Represent and interpret data.

Geometry Graph points on the

coordinate plane to solve real-world and mathematical problems.

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

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