West Contra Costa Unified School District Grade 5 Mathematics Curriculum Guide On-line: CP=Content Presentation, L=Lesson, GMR=General Mathematics Resources, IMT = Illustrative Mathematics Task Page 1 of 16 WCCUSD 09/07/17 Grade Level/Course Title: Grade 5 Trimester 1 Academic Year: 2017-2018 Grade Level Mathematics Focus - In Grade 5, instructional time should focus on three critical areas: (1) Developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in 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 developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations. (3) Developing understanding of volume. Essential Question: How can students develop understanding of base-ten numerals? Time Frame Standard Standard Description Content Resources (Aug- Sep) Chapter 1 - Number Sense and Place Value (Approx. 12 days) 5.NBT.1 Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents to its left. Place value for whole numbers and decimals Expanded form General “Chapter ___” refers to My Math Syntax [GMR] Bar Models Throughout the Grades [CP] 3 Reads for Word Problems (When you click on a [CP] here for a Content Presentation, you will be taken to the list of all CPs. Find the title of the CP you want and click on it. Also, loading through Firefox might be faster.) Number Sense and Place Value (12 days) Chapter 1 – Place Value (9 Lessons) 1-1: Place Value Through Millions The Power of Ten: Building a Magnitude Model [L] 1-2: Compare & Order Whole Numbers Thru Millions 1-3: Hands On: Model Fractions and Decimals Equivalent Decimals and Fractions [L] 1-4: Represent Decimals 1-5: Hands On: Understand Place Value Addition/Subtraction Strategies K-7 5.NBT.3 Read, write, and compare decimals to thousandths. a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3x100 + 4x10 + 7x1 + 3x(1/10) + 9x(1/100) + 2x(1/1000) b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record results of comparisons.
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West Contra Costa Unified School District
Grade 5 Mathematics Curriculum Guide
On-line: CP=Content Presentation, L=Lesson, GMR=General Mathematics Resources, IMT = Illustrative Mathematics Task Page 1 of 16 WCCUSD 09/07/17
Grade Level/Course Title: Grade 5 Trimester 1 Academic Year: 2017-2018
Grade Level Mathematics Focus - In Grade 5, instructional time should focus on three critical areas:
(1) Developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in 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 developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations.
(3) Developing understanding of volume.
Essential Question: How can students develop understanding of base-ten numerals?
Time Frame Standard Standard Description Content Resources
(Aug- Sep)
Chapter 1 -
Number Sense
and
Place Value
(Approx.
12 days)
5.NBT.1
Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents to its left.
Place value for whole numbers and decimals
Expanded form
General
“Chapter ___” refers to My Math Syntax [GMR] Bar Models Throughout the Grades [CP] 3 Reads for Word Problems (When you click on a [CP] here for a Content Presentation, you will be taken to the list of all CPs. Find the title of the CP you want and click on it. Also, loading through Firefox might be faster.)
Number Sense and Place Value (12 days)
Chapter 1 – Place Value (9 Lessons)
1-1: Place Value Through Millions The Power of Ten: Building a Magnitude Model [L]
1-2: Compare & Order Whole Numbers Thru Millions 1-3: Hands On: Model Fractions and Decimals Equivalent Decimals and Fractions [L]
1-4: Represent Decimals 1-5: Hands On: Understand Place Value Addition/Subtraction Strategies K-7
5.NBT.3 Read, write, and compare decimals to thousandths. a. Read and write decimals to thousandths using
base-ten numerals, number names, and expanded form, e.g., 347.392 = 3x100 + 4x10 + 7x1 + 3x(1/10) + 9x(1/100) + 2x(1/1000)
b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record results of comparisons.
West Contra Costa Unified School District
Grade 5 Mathematics Curriculum Guide
On-line: CP=Content Presentation, L=Lesson, GMR=General Mathematics Resources, IMT = Illustrative Mathematics Task Page 2 of 16 WCCUSD 09/07/17
Grade Level/Course Title: Grade 5 Trimester 1 Academic Year: 2017-2018
Grade Level Mathematics Focus - In Grade 5, instructional time should focus on three critical areas:
(1) Developing fluency with addition and subtraction of fractions, and developing understanding of the multiplication of fractions and of division of fractions in 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 developing understanding of operations with decimals to hundredths, and developing fluency with whole number and decimal operations.
(3) Developing understanding of volume.
Essential Question: How can students develop understanding of base-ten numerals?
Time Frame Standard Standard Description Content Resources
(Aug- Sep)
Chapter 1 -
Number Sense
and
Place Value
(continued)
1-6: Place Value Through Thousandths Are These Equivalent to 9.52? [IMT]
1-7: Compare Decimals Comparing Decimals on the Number Line [IMT]
1-8: Order Whole Numbers and Decimals 1-9: Problem-Solving: Use the 4-Step Plan SBAC Sample Questions Claim 1C: Place Value
West Contra Costa Unified School District
Grade 5 Mathematics Curriculum Guide
On-line: CP=Content Presentation, L=Lesson, GMR=General Mathematics Resources, IMT = Illustrative Mathematics Task Page 3 of 16 WCCUSD 09/07/17
[
Grade Level/Course Title: Grade 5 Trimester 1 Academic Year: 2017-2018
Essential Question: How can students develop understanding of why whole number multiplication procedures work based on the meaning of base-ten numerals and properties of operations?
Time Frame Standard Standard Description Content Resources
(Sep)
Chapter 2 -
Multiply Whole
Numbers
(Approx.
12 days)
5.OA.2.1 Express a whole number in the range 2-50 as a product of its prime factors
Prime factoring
Multiply and divide by powers of 10
Multiply using Partial Products
Distributive Property
Estimating products
Multiply using Area Model
Multiply using standard algorithm
Multiply Whole Numbers (12 days)
Parent Guide (English): Multiplying Numbers – Multiple Methods Parent Guide (Spanish): Multiplicando Números Common Multi. & Div. Situations (CCSS Resource) Multiplication/Division Strategies K-7 Chapter 2 – Multiply Whole Numbers (10 Lessons)
2-1: Prime Factorization Prime Factorization [CP]
Sieve of Eratosthenes [CP]
Hundreds Chart [GMR]
2-2: Hands On: Prime Factorization Patterns 2-3: Powers and Exponents 2-4: Multiplication Patterns 2-5: Problem-Solving: Make a Table 2-6: Hands on: Use Partial Products and the
Distributive Property Multiplying Whole Numbers – Generic Rectangle [L]
2-7: The Distributive Property Distributive Property [CP]
2-8: Estimate Products Area Models Through the Grades [CP]
2-9: Multiply by One-Digit Numbers 2-10 Multiply by Two-Digit Numbers Problem Solving with Multiplication and Division [L]
Elmer’s Multiplication Error [IMT]
5.NBT.2 Explain patterns in the number of zeroes of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
5.NBT.5
Fluently multiply multi-digit whole numbers using the standard algorithm.
West Contra Costa Unified School District
Grade 5 Mathematics Curriculum Guide
On-line: CP=Content Presentation, L=Lesson, GMR=General Mathematics Resources, IMT = Illustrative Mathematics Task Page 4 of 16 WCCUSD 09/07/17
Grade Level/Course Title: Grade 5 Trimester 1 Academic Year: 2017-2018
Essential Question: How can students develop understanding of why whole number division procedures work based on the meaning of base-ten numerals and properties of operations?
Time Frame Standard Standard Description Content Resources
(Sep-Oct)
Chapters 3 & 4
Divide
Whole
Numbers
(Approx.
20 days)
5.NBT.6
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Divide using Base Ten blocks
Divide using standard algorithm
Estimate quotients
Divide using Partial Quotients
Distributive Property
Divide using Area Model
Divide Whole Numbers (20 days)
Parent Guide (English): Dividing Numbers- Multiple Methods Parent Guide (Spanish): Dividiendo Números Division – Multiple Representations [CP]
Chapter 3 – Divide by a 1-Digit Divisor (13 Lessons)
3-1: Relate Division to Multiplication Division Algorithms [L]
3-2: Hands On: Division Models 3-3: Two-Digit Dividends 3-4: Division Patterns 3-5: Estimate Quotients 3-6: Hands On: Division Models w/ Greater
Numbers 3-7: Hands On: Distributive Property and Partial
Quotients 3-8: Divide Three- and Four-Digit Dividends 3-9: Place the First Digit 3-10: Quotients with Zeroes 3-11: Hands On: Use Models to Interpret Remainders 3-12: Interpret Remainder 3-13: Problem-Solving: Extra or Missing Information
West Contra Costa Unified School District
Grade 5 Mathematics Curriculum Guide
On-line: CP=Content Presentation, L=Lesson, GMR=General Mathematics Resources, IMT = Illustrative Mathematics Task Page 5 of 16 WCCUSD 09/07/17
Grade Level/Course Title: Grade 5 Trimester 1 Academic Year: 2017-2018
Essential Question: How can students develop understanding of why whole number division procedures work based on the meaning of base-ten numerals and properties of operations?
Time Frame Standard Standard Description Content Resources
(Sep-Oct)
Chapters 3 & 4
Divide
Whole
Numbers
(continued)
Chapter 4 – Divide by a 2-Digit Divisor (6 Lessons)
4-1: Estimate Quotients 4-2: Hands On: Divide Using Base-Ten Blocks 4.3: Divide by a Two-Digit Divisor 4.4: Adjust Quotient 4.5: Divide Greater Numbers 4.6: Problem-Solving: Solve a Simpler Problem Problem Solving with Multiplication and Division [L]
BENCHMARK 1 (Chapters 1 through 4)
West Contra Costa Unified School District
Grade 5 Mathematics Curriculum Guide
On-line: CP=Content Presentation, L=Lesson, GMR=General Mathematics Resources, IMT = Illustrative Mathematics Task Page 6 of 16 WCCUSD 09/07/17
Grade Level/Course Title: Grade 5 Trimester 1 Academic Year: 2017-2018
Essential Question: How can students develop understanding of why decimal addition and subtraction procedures work based on the meaning of base-ten numerals and properties of operations?
Time Frame Standard Standard Description Content Resources (Suggested Number of Days)
(Nov)
Chapter 5 –
Add & Subtract
Decimals
(incl.
Rounding)
(Approx.
12 days)
5.NBT.4
Use place value to round decimals to any place.
Decompose numbers
Estimating
Rounding w/ open number line
Adding and subtracting decimals using Base Ten blocks
Associative Property of Addition
Commutative Property of Addition
Add & Subtract Decimals (incl. Rounding) (12 days)
Common Addition & Subtraction Situations (CCSS Resource) Adding & Subtracting Whole Numbers – Multiple Methods [CP] Number Line Worksheets [GMR] Decimal Operations [CP]
Chapter 5 – Add and Subtract Decimals (10 Lessons, includes Rounding)
5-1: Round Decimals
Rounding and Estimating [L]
Rounding Tenths and Hundredths [IMT]
5-2: Estimate Sums & Differences
5-3: Problem-Solving: Estimate of Exact Answer
5-4: Hands On: Add Decimals Using Base-Ten Blocks
5-5: Hands On: Add Decimals Using Models
Adding Whole Numbers and Decimals [L]
5-6: Add Decimals
5-7: Addition Properties
5-8: Hands On: Subtract Decimals Using Base-Ten Blocks
5-9: Hands On: Subtract Decimals Using Models
5-10: Subtract Decimals
5.NBT.7 Add, subtract, multiply, & divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain reasoning used.
West Contra Costa Unified School District
Grade 5 Mathematics Curriculum Guide
On-line: CP=Content Presentation, L=Lesson, GMR=General Mathematics Resources, IMT = Illustrative Mathematics Task Page 7 of 16 WCCUSD 09/07/17
Grade Level/Course Title: Grade 5 Trimester 2 Academic Year: 2017-2018
Essential Question: How can students develop understanding of why decimal multiplication and division procedures work based on the meaning of base-ten numerals and properties of operations?
Time Frame Standard Standard Description Content Resources (Suggested Number of Days)
(Nov-Dec)
Chapter 6 –
Multiply
and Divide
Decimals
(Approx.
15 days)
5.NBT.2 Explain patterns in the number of zeroes of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.
Estimating products of whole numbers and decimals
Multiply decimals using Area Model
Multiply and divide by powers of 10
Associative Property of Multiplication
Commutative Property of Multiplication
Estimating quotients of whole numbers and decimals
Divide decimals using Base Ten blocks
Divide decimals using Partial Quotients
Multiply and Divide Decimals (15 days)
Decimal Operations [CP] Chapter 6 – Multiply and Divide Decimals (14 Lessons)
6-1: Estimate Products of Whole Numbers & Decimals
6-2: Hands On: Use Models to Multiply
6-3: Multiply Decimals by Whole Numbers
6-4: Hands On: Use Models to Multiply Decimals
6-5: Multiply Decimals
Multiplying Decimals [L]
6-6: Multiply Decimals by Powers of Ten
Kipton’s Scale (Multiply/divide by Powers of Ten) [IMT]
6-7: Problem-Solving: Look for a Pattern
6-8: Multiplication Properties
Marta’s Multiplication Error [IMT]
Value of Education (Add, Subtract, & Multiply Decimals [IMT]
6-9: Estimate Quotients
6-10: Hands On: Divide Decimals
6-11: Divide Decimals by Whole Numbers
6-12: Hands On: Use Models to Divide Decimals
What is 23 ÷ 5? [IMT]
6-13: Divide Decimals
Dividing Decimals [L]
6-14: Divide Decimals by Powers of Ten
Millions and Billions of People [IMT]
Tenths and Hundredths (explore relationship between adjacent place values) [IMT]
SBAC Sample Questions Claim 1D: Whole Number & Decimal Operations
5.NBT.7 Add, subtract, multiply, & divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain reasoning used.
West Contra Costa Unified School District
Grade 5 Mathematics Curriculum Guide
On-line: CP=Content Presentation, L=Lesson, GMR=General Mathematics Resources, IMT = Illustrative Mathematics Task Page 8 of 16 WCCUSD 09/07/17
Grade Level/Course Title: Grade 5 Trimester 2 Academic Year: 2017-2018
Essential Questions for this Unit: 1. How can students apply their understanding of arithmetic to formulate and evaluate expressions? 2. How can students generate terms in patterns, form ordered pairs, and graph them on a coordinate plane?
Time Frame Standard Standard Description Content Resources
(Jan)
Chapter 7 -
Expressions
and Patterns
(Approx.
9 days)
5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols.
Numerical expressions
Real-world application of expressions
Order of Operations
Find patterns and relationships and graph them
Graph on a coordinate plane in Quadrant I only
Expressions and Equations (9 days)
Progressions Document, Operations & Algebraic Thinking [GMR] Chapter 7 – Expressions and Patterns (9 Lessons)
7-1: Hands On: Numerical Expressions
Video Game Scores (Expressions) [IMT]
7-2: Order of Operations
(skip page 487 – The 5th grade standard is only the first step of the Order of Operations, which is grouping (parentheses, brackets and braces). Page 487 teaches the latter steps of the Order of Operations first, which confuses the order and is 6th grade standard 6.EE.2.c).
Bowling for Numbers (Grouping) [IMT]
7-3: Write Numerical Expressions
7-4: Problem-Solving: Work Backward
7-5: Hands On: Generate Patterns
Patterns: Foundations of Functions [L]
7-6: Patterns
Sidewalk Patterns (Discovering Rules and Relationships [IMT]
7-7: Hands On: Map Locations
5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7).Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921,without having to calculate the indicated sum or product.
5.OA.3 Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3” and the starting number 0, and given the rule “Add 6” and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.
Standards continued on next page.
West Contra Costa Unified School District
Grade 5 Mathematics Curriculum Guide
On-line: CP=Content Presentation, L=Lesson, GMR=General Mathematics Resources, IMT = Illustrative Mathematics Task Page 9 of 16 WCCUSD 09/07/17
Grade Level/Course Title: Grade 5 Trimester 2 Academic Year: 2017-2018
Essential Questions for this Unit: 1. How can students apply their understanding of arithmetic to formulate and evaluate expressions? 2. How can students generate terms in patterns, form ordered pairs, and graph them on a coordinate plane?
Time Frame Standard Standard Description Content Resources (Suggested Number of Days)
(Jan)
Chapter 7 -
Expressions
and Patterns
(continued)
5.G.1
Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).
7-8: Ordered Pairs
Battle Ship Using Grid Paper [IMT]
Meerkat Coordinate Plane Task [IMT]
7-9: Graph Patterns
Pendulums – Swinging into Graphs (Science) [L]
SBAC Sample Questions Claim 1A: Numerical Expressions
SBAC Sample Questions Claim 1B: Patterns
SBAC Sample Questions Claim 1J: Coordinate Plane
5.G.2
Represent real-world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.
West Contra Costa Unified School District
Grade 5 Mathematics Curriculum Guide
On-line: CP=Content Presentation, L=Lesson, GMR=General Mathematics Resources, IMT = Illustrative Mathematics Task Page 10 of 16 WCCUSD 09/07/17
Grade Level/Course Title: Grade 5 Trimester 2 Academic Year: 2017-2018
Essential Questions for this Unit: How can students develop an understanding of fractions as division and use fraction equivalence to compare fractions?
Time Frame Standard Standard Description Content Resources (Suggested Number of Days)
(Jan)
Chapter 8 -
Fractions and
Decimals
(Approx.
9 days)
5.NF.3 Interpret a fraction as division of the numerator by the denominator (a/b = a÷b). Solve word problems involving division of whole numbers leading to answers in the form of fractions & mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3, & that when 3 wholes are shared equally among 4 people, each person has a share size of 3/4. If 9 people want to share a 50-pound sack of rice equally, how many pounds of rice should each person get? Between what two whole numbers does the answer lie?
Fractions as division with models
Prime factoring
Greatest Common Factor
Equivalent fractions (incl. simplest form
Least Common Multiple
Compare fractions
Multiplicative Identity Property
Equivalent forms of 1
Fractions and Decimals (9 days)
Progressions Document, Number and Operations - Fractions [GMR]
Parent Guide (English): Simplifying Fractions Parent Guide (Spanish): Simplificando
Fracciones
Fraction Bars [GMR] Chapter 8 - Fractions & Decimals (8 Lessons)
8-1: Fractions and Division
Number Lines, Fractions, and Bar Models [L]
Fractions Greater than 1 w/ Fractions Bars and Number Lines [L]
Converting Improper Fractions and Mixed Numbers [L] – Fractions as division.
8-2: Greatest Common Factor
Prime Factoring to find Least Common Multiple and Greatest Common Factor [L]
8-3: Simplest Form
8-4: Problem-Solving: Guess, Check, & Revise
8-5: Least Common Multiple
Bubble Method to find Least Common Multiple [GMR]
8-6: Compare Fractions
Decomposing Fractions [L]
8-7: Hands On: Use Models to Write Fractions
as Decimals
8-8: Write Fractions as Decimals
West Contra Costa Unified School District
Grade 5 Mathematics Curriculum Guide
On-line: CP=Content Presentation, L=Lesson, GMR=General Mathematics Resources, IMT = Illustrative Mathematics Task Page 11 of 16 WCCUSD 09/07/17
Grade Level/Course Title: Grade 5 Trimester 2 Academic Year: 2017-2018
Essential Questions for this Unit: 1. How can students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike denominators
(including mixed numbers) as equivalent calculations with like denominators? 2. How can students develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them?
Time Frame Standard Standard Description Content Resources (Suggested Number of Days)
(Jan-Feb)
Chapter 9 -
Add and
Subtract
Fractions
(Approx.
15 days)
5.NF.1
Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)
Round fractions
Decompose fractions
Add & subtract fractions with fraction tiles
Equivalent forms of 1
Equivalent fractions (incl. mixed numbers and improper fractions)
Least Common Multiple/Denominator (LCM/LCD)
Find common denominators using Multiplicative Identity Property
Use visual models to add and subtract, fractions and mixed numbers.
Add and Subtract Fractions (15 days) Chapter 9 – Add & Subtract Fractions (13 Lessons)
9-1: Round Fractions
9-2: Add Like Fractions
Adding Fractions with Unlike Denominators [CP]
9-3: Subtract Like Fractions
9-4: Hands On: Use Models to Add Unlike Fractions
9-5: Add Unlike Fractions
Do These Add Up? (Word problems for adding fractions with unlike denominators.) [IMT]
9-6: Hands On: Use Models to Subtract Unlike Fract.
9-7: Subtract Unlike Fractions
Measuring Cups (Add & sub. w/ unlike denom.) [IMT]
9-8: Problem-Solv.: Determine Reasonable Answers
9-9: Estimate Sum and Differences
9-10: Hands On: Use Models to Add Mixed Numbers
9-11: Add Mixed Numbers
Adding Mixed Numbers [L]
9-12: Subtract Mixed Numbers
Subtracting Mixed Numbers [L]
9-13: Subtract with Renaming
SBAC Sample Questions Claim 1E: Add and
Subtraction Fractions
BENCHMARK 2 (Chapters 5 through 9)
5.NF.2
Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 by observing that 3/7 < 1/2.
West Contra Costa Unified School District
Grade 5 Mathematics Curriculum Guide
On-line: CP=Content Presentation, L=Lesson, GMR=General Mathematics Resources, IMT = Illustrative Mathematics Task Page 12 of 16 WCCUSD 09/07/17
Grade Level/Course Title: Grade 5 Trimester 3 Academic Year: 2017-2018
Essential Questions for this Unit: How can students use number sense; the meaning of fractions, multiplication and division; and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense? (Note: Division is limited to dividing unit fractions by whole numbers and whole numbers by unit fractions.)
Time Frame Standard Standard Description Content Resources (Suggested Number of Days)
(Mar)
Chapter 10 -
Multiply and
Divide
Fractions
(Approx.
15 days)
5.NF.4 Apply and extend previous understanding of multiplication to multiply a fraction or a whole number by a fraction. a. Interpret the product (a/b) x q as parts of a partition
of q into b equal parts, equivalently, as the result of a sequence of operations a x q ÷ b. For example, use a visual fraction model to show (2/3) x 4 = 8/3, and create a story context for this equation. Do the same with (2/3) x (4/5) = 8/15. (In general, (a/b) x (c/d) = ac/bd.)
b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.
( Multiply and Divide Fractions (15 days)
Parent Guide (English): Multiplying Fractions Parent Guide (Spanish): Multiplicando Fracciones
Chapter 10 - Multiply & Divide Fractions (12 Lessons)
10-1: Hands On: Part of a Number
10-2: Estimate Products of Fractions
10-3: Hands On: Model Fraction Multiplication
Multiplying Fractions [CP] & Multiplying Fractions [L]
10-4: Multiply Whole Numbers & Fractions
10-5: Hands On: Use Models to Multiply Fractions
10-6: Multiply Fraction
Cornbread Fundraiser (Full lesson for multiplying fractions – See end of Commentary section.) [IMT]
Painting a Wall (Multiply fractions.) [IMT]
10-7: Multiply Mixed Numbers
Chavone’s Bathroom Tiles (multiply mixed numbers with an area model) [IMT]
Cross Country Training (multiply mixed numb.) [IMT]
10-8: Hands On: Multiplication as Scaling
To Multiply or Not to Multiply (Word problems that require deciding to +, - or x fractions with unlike denominators. Problem e: Very challenging.) [IMT]
Calculator Trouble (Multiplication as scaling) [IMT]
Fundraising (Scaling and comparison) [IMT]
Scaling Up and Down [IMT]
5.NF.5 Interpret multiplication as scaling (resizing) by: a. Comparing the size of a product to the size of one
factor on the basis of the size of the other factor, without performing indicated multiplication.
b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n x a) / (n b) to the effect of multiplying a/b by 1.
West Contra Costa Unified School District
Grade 5 Mathematics Curriculum Guide
On-line: CP=Content Presentation, L=Lesson, GMR=General Mathematics Resources, IMT = Illustrative Mathematics Task Page 13 of 16 WCCUSD 09/07/17
Grade Level/Course Title: Grade 5 Trimester 3 Academic Year: 2017-2018
Essential Questions for this Unit: How can students use number sense; the meaning of fractions, multiplication and division; and the relationship between multiplication and division to understand and explain why the procedures for multiplying and dividing fractions make sense? (Note: Division is limited to dividing unit fractions by whole numbers and whole numbers by unit fractions.)
Time Frame Standard Standard Description Content Resources (Suggested Number of Days)
(Mar)
Chapter 10 -
Multiply and
Divide
Fractions
(continued)
5.NF.6 Solve real word problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
Parent Guide (English): Dividing Fractions Parent Guide (Spanish): Dividiendo Fracciones
10-9: Hands On: Division with Unit Fractions
10-10: Divide Whole Numbers by Unit Fractions
Modeling Division of Whole Numbers by Unit Fractions [L]
How Many Servings of Oatmeal? (Divide a whole number by a unit fraction) [IMT]
How Many Marbles? (Complements How Many Servings of Oatmeal?) [IMT]
10-11: Divide Unit Fractions by Whole Numbers
Modeling Division of a Fraction by a Fraction (only part that covers dividing unit fractions by whole numbers) [L]
Painting a Room (Divide a unit fraction by a whole number) [IMT]
10-12: Problem Solving: Draw a Diagram
Problem Solving with Multiplication and Division [L]
Salad Dressing (Add fractions with unlike denominators then divide) [IMT]
Dividing by One Half (Word problems that require deciding to multiply or divide by 1/2.) [IMT]
SBAC Sample Questions Claim 1F: Multiply and Divide
Fractions
5.NF.7 Apply and extend previous understanding of division to divide unit fractions by whole numbers and whole numbers by unit fractions.
a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) x 4 = 1/3.
b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 x (1/5) = 4.
c. Solve real word problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb. of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?
West Contra Costa Unified School District
Grade 5 Mathematics Curriculum Guide
On-line: CP=Content Presentation, L=Lesson, GMR=General Mathematics Resources, IMT = Illustrative Mathematics Task Page 14 of 16 WCCUSD 09/07/17
Grade Level/Course Title: Grade 5 Trimester 3 Academic Year: 2017-2018
Essential Questions for this Unit: 1. How can students understand how units within the same measurement system (customary or metric) are related? 2. How can students make a line plot from a list of data in fractional units and use operations to solve problems involving the data?
Time Frame Standard Standard Description Content Resources (Suggested Number of Days)
(Mar-Apr)
Chapter 11 -
Measurement
(incl. Line
Plots)
(Approx.
16 days)
5.MD.1
Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05m), and use these conversions in solving multi-step, real world problems.
Multiplying and dividing to convert U.S. customary and metric units
Use rulers, balance scales, and containers to create tables to determine equivalents in U.S. customary and metric units
Analyzing and displaying data using line plots
Equivalent forms of 1
Equivalent fractions
Use visual models to add and divide fractions and mixed numbers.
Use bar models to add and divide fractions and mixed numbers
Use function tables to convert U.S. customary and metric units
Measurement (incl. Line Plots) (16 days)
Progressions Document, Geometric Measurement
(Measurement Conversion and Volume) [GMR]
Progressions Document, Measurement and Data (Line
Plots) [GMR]
Chapter 11 Measurement (incl. Line Plots) (13 Lessons) 11-1: Hands On: Measure with a Ruler
Measurement [L]
Bar Models for Customary Units [GMR]
11-2: Convert Customary Units of Length
11-3: Problem Solving: Use Logical Reasoning
11-4: Hands On: Estimate & Measure Weights
11-5: Convert Customary Units of Weight
11-6: Hands On: Estimate & Measure Capacity
11-7: Convert Customary Units of Capacity
11-8: Display Measurement Data on a Line Plot
Line Plots [L]
Fractions on a Line Plot (Game) [IMT]
11-9: Hands On: Metric Rulers
11-10: Convert Metric Units of Length
11-11: Hands On: Estimate & Measure Metric Mass
11-12: Convert Metric Units of Mass
11-13: Convert Metric Units of Capacity
SBAC Sample Questions Claim 1G: Measurement
SBAC Sample Questions Claim 1H: Line Plots
5.MD.2
Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in the line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all beakers were redistributed equally.
West Contra Costa Unified School District
Grade 5 Mathematics Curriculum Guide
On-line: CP=Content Presentation, L=Lesson, GMR=General Mathematics Resources, IMT = Illustrative Mathematics Task Page 15 of 16 WCCUSD 09/07/17
Grade Level/Course Title: Grade 5 Trimester 3 Academic Year: 2017-2018
Essential Questions for this Unit: 1. How can students understand the properties of two-dimensional figures? 2. How can students understand that two-dimensional figures are classified in a hierarchy based on their properties? 3. How can students recognize volume as an attribute of three-dimensional space? 4. How can students understand that volume can be measured by finding the total number of same-size units required to fill the space without gaps or overlaps
and understand that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume? 5. How can students decompose 3-dimensional shapes made of multiple right rectangular prisms by viewing them as decomposed into layers of arrays of cubes? 6. How can students find volume to solve real-world and mathematical problems?
Time Frame Standard Standard Description Content Resources (Suggested Number of Days)
(Apr-May)
Chapter 12 -
Geometry
(incl. Volume)
(Approx.
15 days)
5.G.3
Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles & squares are rectangles, so all squares have 4 right angles..
Attributes of 2D geometric shapes
Categories and subcategories of 2D shapes
Volume of rectangular prisms
Volume formulas:
Length (l) x width x height: V = lwh
Area of base (B) x height(h): V = Bh
Solve real-world problems involving volume
Geometry (15 days)
Progressions Document, Geometry (incl. Volume) [GMR] Chapter 12 – Geometry (12 Lessons)
12-1: Polygons
12-2: Hands On: Sides and Angles of Triangles
12-3: Classify Triangles
12-4: Hands On: Sides and Angles of Quadralaterals
12-5: Classify Quadrilaterals
12-6: Hands On: Build 3-D Figures
12-7: Three-Dimensional Figures
SBAC Sample Questions Claim 1K: Classify 2-
Dimensional Figures
5.G.4
Classify two-dimensional figures in a hierarchy based on properties.
5.MD.3
Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. A cube with side length of 1 unit, called
a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.
b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
5.MD.4
Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.
Standards continued on next page.
West Contra Costa Unified School District
Grade 5 Mathematics Curriculum Guide
On-line: CP=Content Presentation, L=Lesson, GMR=General Mathematics Resources, IMT = Illustrative Mathematics Task Page 16 of 16 WCCUSD 09/07/17
Grade Level/Course Title: Grade 5 Trimester 3 Academic Year: 2017-2018
Essential Questions for this Unit: 1. How can students understand the properties of two-dimensional figures? 2. How can students understand that two-dimensional figures are classified in a hierarchy based on their properties? 3. How can students recognize volume as an attribute of three-dimensional space? 4. How can students understand that volume can be measured by finding the total number of same-size units required to fill the space without gaps or overlaps and
understand that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume? 5. How can students decompose 3-dimensional shapes made of multiple right rectangular prisms by viewing them as decomposed into layers of arrays of cubes? 6. How can students find volume to solve real-world and mathematical problems?
Time Frame Standard Standard Description Content Resources (Suggested Number of Days)
(Apr-May
Chapter 12 -
Geometry
(incl. Volume)
(continued)
5.MD.5
Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. a. Find the volume of a right rectangular prism
with whole-number side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold whole-number products as volumes, e.g., to represent the associative property of multiplication.
b. Apply the formulas V = l x w x h and V = B x h for rectangular prisms with whole-
number edge lengths in the context of solving real world and mathematical problems.
c. Recognize volume as additive. Find volumes of solid figures composed of two non-overlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying the technique to solve real world problems.
12-8: Hands On: Use Models to Find Volume
Definition of Volume (interactive) [from mathisfun.com)
Volume Activity (building rectangular prisms unit-by-unit or layer-by-layer with connection to nets) [from NCTM Illuminations]
Volume: A Foundation in Unit Cubes [L]
12-9: Volume of Prisms
12-10: Hands On: Build Composite Figures
12-11: Volume of Composite Figures
Breaking Apart Composite Solids [IMT]
12-12: Problem-Solving: Make a Model
You Can Multiply Three Numbers in Any Order (Volume and Commutative Property of Multiplication) [IMT]
Using Volume to Understand the Associative Property of Multiplication (with linker cubes) [IMT]
SBAC Sample Questions Claim 1I: Volume
BENCHMARK 3 (Chapters 10 through 12) CUMULATIVE REVIEW FOR SBAC ASSESSMENT (10 days)
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