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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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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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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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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