Newark Unified School District

Grade 5 Mathematics Curriculum Guide

GMR=General Math Resources (online) CP=Content Presentation (online) L=Lesson (online) Page 1 of 12 MCC@WCCUSD (NUSD) 06/28/14

1 The focus in this module is on the metric system to reinforce place value and writing measurements using mixed units. This standard is addressed again in later modules.

Grade Level/Course Title: Grade 5 Trimester 1 Academic Year: 2014-2015

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; and (3) developing understanding of volume.

Essential Questions for this Unit: 1. How can students use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal

multiplied by an appropriate power of 10 is a whole number), to understand and explain why the procedures for multiplying and dividing finite decimals make sense?

2. How can students compute products and quotients of decimals to hundredths efficiently and accurately?

Unit (Time) Standard Standard Description Content Resources (Suggested Number of Days)

Module 1:

Place Value

and Decimal

Fractions

( 20 days)

5.MD.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.1

Place value and

decimals:

Decomposition of

numbers

Expanded Notation

Estimating for

reasonability

Comparing values

Estimating using a

number line

Topic A: Multiplicative Patterns on the Place Value Chart (5 days) (5days) Topic B: Decimal Fractions and Place Value Patterns Topic C: Place Value and Rounding Decimal Fractions

Number Line Worksheets (GMR)

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 in the place to its left

5.NBT.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.

Use whole-number exponents to denote powers of 10.

5.NBT.3 Use place value understanding to round multi-digit whole numbers to

any place.

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.

Newark Unified School District

Grade 5 Mathematics Curriculum Guide

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Grade Level/Course Title: Grade 5 Trimester 1 Academic Year: 2014-2015

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; and (3) developing understanding of volume.

Essential Questions for this Unit: 1. How can students use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite decimal

multiplied by an appropriate power of 10 is a whole number), to understand and explain why the procedures for multiplying and dividing finite decimals make sense? 2. How can students compute products and quotients of decimals to hundredths efficiently and accurately?

Unit (Time) Standard Standard Description Content Resources(Suggested Number of Days)

Module 1:

Place Value and

Decimal

Fractions

( 20 days)

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

place.

Add & Subtract decimals

using

Base Ten blocks

Concrete models and

drawings

Number lines

Standard algorithm

Multiply & Divide decimals

using

Base Ten blocks

Concrete models and

drawings

Area models

Number lines

Partial products

Partial Quotients

Standard Algorithm

Powers of 10

(5days) Topic D: Adding and Subtracting Decimals Topic E: Multiplying Decimals

Decimal Operations (CP) Adding Decimals by Decomposition(L) Adding Whole Numbers and Decimals(L) Multiple Methods Mat (GMR) Rolling Numbers (GMR)

Topic F: Dividing Decimals (5days)

Conceptualizing Division (L) Dividing Decimals (L)

5.NBT.7 Add, subtract, multiply, and 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 the reasoning used.

MP.6 Attend to precision. Students express the units of the

base ten system as they work with decimal operations,

expressing decompositions and compositions with

understanding, e.g., “9 hundredths + 4 hundredths = 13

hundredths. I can change 10 hundredths to make 1

tenth.”

Newark Unified School District

Grade 5 Mathematics Curriculum Guide

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Grade Level/Course Title: Grade 5 Trimester 1 Academic Year: 2014-2015

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; and (3) developing understanding of volume.

Essential Questions for this Unit: 1. How can students develop understanding of why division procedures work based on the meaning of base-ten numerals and properties of operations? 2. How can students finalize fluency with multi-digit addition, subtraction, multiplication, and division? 3. How can students develop understanding of why division procedures work based on the meaning of base-ten numerals and properties of operations? 4. How can students use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite

decimal multiplied by an appropriate power of 10 is a whole number), to understand and explain why the procedures for multiplying and dividing finite decimals make sense?

5. How can students compute products and quotients of decimals to hundredths efficiently and accurately?

Unit (Time) Standard Standard Description Content Resources(Suggested Number of Days)

Module 2:

Multi-digit

Whole

number and

Decimal

Fraction

Operations

( 35 days)

5.OA.1 Use parentheses, brackets, or braces in numerical

expressions, and evaluate expressions with these symbols.

Multiply & Divide using

Base Ten blocks

Concrete models

and drawings

Arrays

Generic Rectangle

Area models

Number lines

Partial products

Partial Quotients

Standard Algorithm

(10 days)

Topic A: Mental Strategies for Multi-Digit

Whole Number Multiplication

Topic B: The Standard Algorithm for Multi-Digit

Whole Number Multiplication

Comparing Expressions (L)

Multiplying Multi-Digit Numbers (L)

(10 days)

Topic C: Decimal Multi-Digit Multiplication

Topic D: Measurement Word Problems with

Whole Number and Decimal Multiplication

Multiplying Decimals (L)

Measurement (L)

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.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 in the place to its left.

5.NBT.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. Use whole-number

exponents to denote power of 10

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

standard algorithm.

Newark Unified School District

Grade 5 Mathematics Curriculum Guide

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Grade Level/Course Title: Grade 5 Trimester 1 Academic Year: 2014-2015

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; and (3) developing understanding of volume.

Essential Questions for this Unit: 1. How can students develop understanding of why division procedures work based on the meaning of base-ten numerals and properties of operations? 2. How can students finalize fluency with multi-digit addition, subtraction, multiplication, and division? 3. How can students develop understanding of why division procedures work based on the meaning of base-ten numerals and properties of operations? 4. How can students use the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers (i.e., a finite

decimal multiplied by an appropriate power of 10 is a whole number), to understand and explain why the procedures for multiplying and dividing finite decimals make sense?

5. How can students compute products and quotients of decimals to hundredths efficiently and accurately?

Unit (Time) Standard Standard Description Content Resources(Suggested Number of Days)

Module 2:

Multi-digit Whole

number and

Decimal Fraction

operations

( 35 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.

Multiply &

Divide using:

Base Ten

blocks

Concrete

models and

drawings

Arrays

Generic

Rectangle

Area models

Number lines

Partial

products

Partial

Quotients

Standard

Algorithm

(10 days)

Topic E: Mental Strategies for Multi-Digit

Whole Number Division Topic F: Partial Quotients and Multi-Digit

Whole Number Division

Division — Multiple Representations (CP) Dividing by Decomposing Fractions (L) Division Algorithms (L)

Topic G: Partial Quotients and Decimal Multi-

Digit Division (5 days)

Decimal Operations (CP)

Topic H: Measurement Word Problems with

Multi-Digit Division (5 days)

Measurement (L)

Bar Model Customary Units (GMR)

Benchmark #1 Modules 1 & 2

(administered by 11/7/14)

5.NBT.7 Add, subtract, multiply, and 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 the reasoning used

5.MD.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.

End of Trimester 1

Newark Unified School District

Grade 5 Mathematics Curriculum Guide

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Grade Level/Course Title: Grade 5 Trimester 2 Academic Year: 2014-2015

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; and (3) developing understanding of volume.

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 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?

Unit (Time) Standard Standard Description Content Resources (Suggested Number of Days)

Module 3:

Addition and

Subtraction of

Fractions

( 22 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.)

Understanding:

Write equivalent

fractions using

equivalent forms of

1 and Fraction

chart

Converting

fractions and

mixed numbers

using bar models,

decomposition and

traditional

algorithm

Add/subtract

fractions using a

number line, visual

models, and

traditional

algorithm

Draw a visual

model to solve

word problems

(10 days)

Topic A: Equivalent Fractions

Topic B: Making Like Units Pictorially

Fraction Bars (GMR) Number Line Worksheets (GMR) Converting – Improper Fractions and

Mixed Numbers (L)

Topic C: Making Like Units

Numerically (5 days)

Adding Mixed Numbers (L) Subtracting Mixed Numbers (L) Adding Fractions with Unlike Denominators (L) Adding Fractions with Unlike Denominators (CP)

Topic D: Further Applications (5 days)

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.

4.NF.1 Explain why a fraction a/b is equivalent to a fraction (n x a)/(n x

b) by using visual fraction models, with attention to how the

number and size of the parts differ even though the two fractions

themselves are the same size. Use this principle to recognize and

generate equivalent fractions.

Newark Unified School District

Grade 5 Mathematics Curriculum Guide

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Grade Level/Course Title: Grade 5 Trimester 2 Academic Year: 2014-2015

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; and (3) developing understanding of volume.

1. How can students also use the meaning of fractions, of 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: this is limited to the case of dividing unit fractions by whole numbers and whole numbers by unit fractions.)

Unit (Time) Standard Standard Description Content Resources (Suggested Number of Days)

Module 4:

Multiplication

and Division

of Fractions

and Decimal

Fractions

( 22 days)

5.OA.1 Use parentheses, brackets, or braces in numerical expressions, and

evaluate expressions with these symbols.

Understanding:

Drawing area

models

Visual models

fraction

tiles/number line

Arrays

Bar Models

(5 days)

Topic A: Line Plots of Fraction

Measurements

Topic B: Fractions as Division

Line Plots (L)

Topic C: Multiplication of a Whole

Number by a Fraction (5 days)

Bar Models – Percents and Fractions

(L)

Problem Solving with Multiplication

and Division (L)

Multiplying Fractions (CP)

Topic D: Fraction Expressions and

Word Problems (5 days)

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.NBT.7 Add, subtract, multiply, and 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

the reasoning used.

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 or 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, and that

when 3 wholes are shared equally among 4 people 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?

Newark Unified School District

Grade 5 Mathematics Curriculum Guide

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Grade Level/Course Title: Grade 5 Trimester 2 Academic Year: 2014-2015

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; and (3) developing understanding of volume.

1. How can students also use the meaning of fractions, of 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: this is limited to the case of dividing unit fractions by whole numbers and whole numbers by unit fractions.)

Unit (Time) Standard Standard Description Content Resources (Suggested Number of Days)

Module 4:

Multiplication

and Division

of Fractions

and Decimal

Fractions

( 22 days)

5.NF.4 Apply and extend previous understandings of multiplication to

multiply a fraction or whole number by a fraction.

a. Interpret the product of (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, and create a story context for this equation. Do the same

with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

Understanding:

Prime

Factorization

Decompose and

simplify using

equivalent forms

of one

Division/Fraction

relationship

Topic E: Multiplication of a Fraction by

a Fraction (10 days)

Multiplying Fractions (L)

Multiplying Mixed Numbers (L)

Topic F: Multiplication with Fractions

and Decimals as Scaling and Word

Problem (5 days)

Converting Fractions, Decimals, and

Percents (L)

Topic G: Division of Fractions and

Decimal Fractions (10 days)

Modeling Division of a Whole Number

by a Fraction (L)

Modeling Division of a Fraction by a

Fraction (L)

Dividing Fractions (CP)

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 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); 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×a)/(n×b) to the effect of multiplying a/b by 1.

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.

5.MD.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.

Newark Unified School District

Grade 5 Mathematics Curriculum Guide

GMR=General Math Resources (online) CP=Content Presentation (online) L=Lesson (online) Page 8 of 12 MCC@WCCUSD (NUSD) 06/28/14

Grade Level/Course Title: Grade 5 Trimester 2 Academic Year: 2014-2015

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; and (3) developing understanding of volume.

1. How can students also use the meaning of fractions, of 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: this is limited to the case of dividing unit fractions by whole numbers and whole numbers by unit fractions.)

Unit (Time) Standard Standard Description Content Resources (Suggested Number of

Days)

Module 4:

Multiplication

and Division

of Fractions

and Decimal

Fractions

( 22 days)

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

whole numbers and whole numbers by unit fractions. (Students able to multiple

fractions in general can develop strategies to divide fractions in general, by reasoning

about the relationship between multiplication and division. But division of a fraction

by a fraction is not a requirement at this grade level.)

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) × 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 × (1/5) = 4.

c. Solve real world 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?

Topic H: Interpretation of

Numerical Expressions (5 days)

Benchmark #2

(administered by 2/27/15)

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 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 the beakers were redistributed equally.

End of Trimester 2

Newark Unified School District

Grade 5 Mathematics Curriculum Guide

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Grade Level/Course Title: Grade 5 Trimester 3 Academic Year: 2014-2015

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; and (3) developing understanding of volume.

Essential Questions for this Unit: 1. How can students recognize volume as an attribute of three-dimensional space? 2. How can students understand that volume can be measured by finding the total number of same-size units of volume required to fill the space without gaps or

overlaps? 3. How can students understand that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume? 4. How can students select appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume? 5. How can students decompose three-dimensional shapes and find volumes of right rectangular prisms by viewing them as decomposed into layers of arrays of

cubes? 6. How can students measure necessary attributes of shapes in order to determine volumes to solve real-world and mathematical problems?

Unit (Time) Standard Standard Description Content Resources (Suggested Number of Days)

Module 5:

Addition and

Multiplication

with Volume

and Area

( 25 days)

5.NF.4 Apply and extend previous understandings of multiplication to

multiply a fraction or whole number by a fraction.

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.

Understanding:

Find Volume by

using unit cubes

Use of Formulas

Unit conversion

Use area

models/generic

rectangle to find area

Solve multi-step

problems

Solve using visual

models and or

equations

Classify 2D Figures Using:

•Shape attributes

•Categories & Sub

Categories

(10 days)

Topic A: Concepts of Volume

Topic B: Volume and the Operations

of Multiplication and Addition

Volume: A Foundation in Unit

Cubes (L)

Rectangular Prisms (L)

(15 days)

Topic C: Area of Rectangular Figures

with Fractional Side Lengths

Topic D: Drawing, Analysis, and

Classification of Two-Dimensional

Shapes

Quadrilaterals (CP)

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.

5.MD.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 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.

Newark Unified School District

Grade 5 Mathematics Curriculum Guide

GMR=General Math Resources (online) CP=Content Presentation (online) L=Lesson (online) Page 10 of 12 MCC@WCCUSD (NUSD) 06/28/14

Grade Level/Course Title: Grade 5 Trimester 3 Academic Year: 2014-2015

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; and (3) developing understanding of volume.

Essential Questions for this Unit: 1. How can students recognize volume as an attribute of three-dimensional space? 2. How can students understand that volume can be measured by finding the total number of same-size units of volume required to fill the space without gaps or

overlaps? 3. How can students understand that a 1-unit by 1-unit by 1-unit cube is the standard unit for measuring volume? 4. How can students select appropriate units, strategies, and tools for solving problems that involve estimating and measuring volume? 5. How can students decompose three-dimensional shapes and find volumes of right rectangular prisms by viewing them as decomposed into layers of arrays of

cubes? 6. How can students measure necessary attributes of shapes in order to determine volumes to solve real-world and mathematical problems?

Unit (Time) Standard Standard Description Content Resources (Suggested Number of Days)

Module 5:

Addition and

Multiplication

with Volume

and Area

( 25 days)

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 × w × h and V = b × h for rectangular prisms to

find volumes of right 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 this technique to solve real world problems.

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 and squares are rectangles, so all squares have four

right angles.

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

Newark Unified School District

Grade 5 Mathematics Curriculum Guide

GMR=General Math Resources (online) CP=Content Presentation (online) L=Lesson (online) Page 11 of 12 MCC@WCCUSD (NUSD) 06/28/14

Grade Level/Course Title: Grade 5 Trimester 3 Academic Year: 2014-2015

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; and (3) developing understanding of volume.

Essential Questions for this Unit: 1. How can students use their knowledge of number lines to define a coordinate system and use it to represent real world and math problems?

Unit (Time) Standard Standard Description Content Resources (Suggested Number of

Days)

Module 6:

Problem

Solving with

the

Coordinate

Plane

(40 days)

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.

Understanding:

Number lines

Graphing on a coordinate plane

Plot points using two coordinates

Explore relationships between points

Generate 2 number patterns from 2 different rules

Interpret data from a line graph

Use visual models to solve problems

(15 days)

Topic A: Coordinate Systems Topic B: Patterns in the Coordinate Plane and Graphing Number Patterns from Rules

(10 days)

Topic C: Drawing Figures in the Coordinate Plane Topic D: Problem Solving in the Coordinate Plane Patterns: Foundations of Functions (L) Interpreting Data in Graphs (L)

(15 days)

Topic E: Multi-Step Word Problems Topic F: The Years In Review: A Reflection on A Story of Units

Benchmark #3 (Modules 5 & 6)

Administered by 5/29/15

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.

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.

5.NF.7c Solve real world 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?

Newark Unified School District

Grade 5 Mathematics Curriculum Guide

GMR=General Math Resources (online) CP=Content Presentation (online) L=Lesson (online) Page 12 of 12 MCC@WCCUSD (NUSD) 06/28/14

Grade Level/Course Title: Grade 5 Trimester 3 Academic Year: 2014-2015

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; and (3) developing understanding of volume.

Essential Questions for this Unit:

1. How can students use their knowledge of number lines to define a coordinate system and use it to represent real world and math problems?

Unit (Time) Standard Standard Description Content Resources (Suggested Number of Days)

Module 6:

Problem

Solving with

the

Coordinate

Plane

(40 days)

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., -axis and -coordinate, -axis and

-coordinate).

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.

5.MD.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.

MP.1 Make sense of problems and persevere in solving them. Students make

sense of problems as they use tape diagrams and other models, persevering

to solve complex, multi-step word problems. Students check their work

and monitor their own progress, assessing their approach and its validity

within the given context and altering their method when necessary.

End of Trimester 3