Fifth Grade

MATHEMATICS Curriculum Map

2017 – 2018

Volusia County Schools

Mathematics Florida Standards

1 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department May 2017

2 Volusia County Schools Grade 1 Math Curriculum Map Mathematics Department May 2017

Elementary Instructional Math Block

Time Components Description

5-15 minutes

Number Talks

Short, daily fluency routine that engages students in meaningful conversations around purposefully crafted computation problems that are solved using number relationships and the structure of numbers. Students are asked to communicate their thinking when presenting and justifying solutions to problems they solve mentally while the teacher records their ideas with mathematical precision. These exchanges lead to the development of more accurate, efficient, and flexible strategies.

5 minutes

Opening: Hook/Coherence Connection

The teacher will engage students to create interest for the whole group lesson or review prerequisite standards to prepare students to make explicit connections that will allow students to apply and extend previous learning when interacting with the lesson’s grade-level content.

15 minutes

Whole Group: Mini Lesson/Guided Practice

Used prior to small group to introduce/practice new knowledge and skills or after small group to refine/practice strategies discovered by students.

The lesson focuses on the depth of grade-level cluster(s), grade-level content standard(s), or part(s) thereof, intentionally targeting the aspect(s) of rigor (conceptual understanding, procedural skill and fluency, application) called for by the standard(s) being addressed.

During this time, the teacher makes the mathematics of the lesson explicit using clear and correct explanations, representations, tasks, and/or examples. The teacher provides opportunities for all students to work with and practice grade-level problems and exercises, deliberately checking for understanding throughout the lesson and adapting the lesson according to student understanding. The teacher poses high-quality questions and problems that prompt students to share their developing thinking about the content of the lesson. Class created anchor charts are constructed by strategically adding key concepts throughout the topic’s lessons.

30-40 minutes

Small Collaborative Groups/ Independent Practice

The teacher encourages reasoning and problem solving by posing challenging problems that offer opportunities for student choice of appropriate tools and promote productive struggle. Students work in small, flexible collaborative groups to engage in mathematical tasks while the teacher circulates and asks questions to elicit thinking, providing support or extensions as needed. The teacher asks students to explain and justify work, connecting and developing students’ informal language to precise mathematical language appropriate to their grade, and provides feedback that helps students revise initial work. The teacher makes observations to select and sequence appropriate strategies for students to share during the class discussion.

5 minutes

Closure: Summarize

The teacher strengthens all students’ understanding of the content by strategically sharing a variety of students’ representations and solution methods. The teacher facilitates the summary of the mathematics with references to student work and by creating the conditions for student conversations where students are encouraged to talk about each other’s thinking in order to reinforce the purpose of the lesson.

Formative techniques occur throughout the framework to drive instruction, guide collaborative grouping, and evaluate which students will need intervention/enrichment.

Grade 5 Math Curriculum Map July 2017

3 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Year At A Glance

Unit 1: August 14 – October 13

Topic 1: Understanding Volume Topic 2: Developing multiplication and division strategies Topic 3: Using equivalency to add and subtract fractions with unlike denominators Topic 4: Expanding understanding of place value of decimals

Unit 2: October 17 – December 20

Topic 5: Understanding the concept of multiplying fractions by fractions Topic 6: Comparing and rounding decimals Topic 7: Interpreting multiplying fractions as scaling Topic 8: Developing the concept of dividing unit fractions

Unit 3: January 8 – March 8

Topic 9: Solving problems involving volume Topic 10: Performing operations with decimals Topic 11: Classifying two-dimensional geometric figures Topic 12: Solving problems with fractional quantities

Unit 4: March 19 – May 30

Topic 13: Representing algebraic thinking Topic 14: Exploring the coordinate plane Topic 15: Finalizing multiplication and division with whole numbers Topic 16: Finalizing expressions and exponents Topic 17: Finalizing operations on fractions with data presented in line plots Topic 18: Finalizing area of rectangles with fractional side lengths

4 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Unit 1 PACING: August 14 – October 13

Topic 1: Understanding Volume Pacing: August 14 – 25

Students expand their understanding of geometric measurement and spatial structuring to include volume as an attribute of three-­‐dimensional space. In this

topic, students develop this understanding using concrete models to discover strategies for finding volume, whereas in topic 9 students generalize this

understanding in real-­‐world problems and apply strategies and formulas. Volume is addressed in two topics (topic 1 and topic 9) because it is a major

emphasis in Grade 5. The connection to multiplication and addition provides an opportunity for students to start the year off by applying the mult iplication

and addition strategies they learned in previous grades in a new, interesting context.

Standards Academic Language

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.

MAFS.5.MD.3.3

attribute cubic units overlap rectangular prism unit cube volume

Students will:

• identify volume as an attribute of a solid figure.

• explain that a cube with 1 unit side length is “one cubic unit” of volume, and understand that this cubic unit is used to measure volume.

• explain that the volume of a solid figure can be found by filling it with unit cubes without gaps and overlaps.

Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units. MAFS.5.MD.3.4

Students will:

• measure the volume of a three-dimensional figure (i.e., rectangular prism and cube) by filling it with unit cubes and counting the number of unit cubes.

NOTE: Work with exponential notation will be introduced in topic 4, therefore all measurements in this topic should be labeled as “cubic units”. Units3 will not be used until topic 9.

3. Construct viable arguments and critique the reasoning of others. 7. Look for and make use of structure.

MAFS.K12.MP.3.1 MAFS.K12.MP.7.1

Topic Comments:

Students decompose and recompose geometric figures to make sense of the spatial structure of volume (MP.7). In particular, students explain their thinking and analyze others’ reasoning as they practice partitioning figures into layers and each layer into rows and each row into cubes (MP.3).

5 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 1 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

5.M

D.3

.3

Topic 1 No aligned resources

Teacher Guide: pp. 21-22

Daily Math Practice Journal: pp. 52, 54, 56, 58, 62

Pick a Problem: pp. 62, 64-68

How Did you Solve it?: 64-65

Volume Measurement Center box

How Do You Find the Volume? How Do We Determine Volume? Determining Volume

www.cpalms.org Building Rectangular Prisms

Hands-On! Rectangular Prisms

Manipulating Cubic Units

www.ixl.com/math/grade-5 No aligned resources

https://learnzillion.com/ Videos: Understanding volume

Identify the difference between a square unit and a cube unit.

Lessons: Identify objects that have volume

Understand that a cube with side length 1 unit is called a unit cube and measures volume

Identify cubic objects

5.M

D.3

.4

Topic 1 No aligned resources

Teacher Guide: pp. 21-22 Daily Math Practice Journal: pp. 50, 52, 54, 58, 60, 62 Pick a Problem: 64-65, 67 How Did you Solve it?: 66-67

Volume Measurement Center box

Find the Volume

Volume with Improvised Units Volume in Cubic Units Measuring Volume

www.cpalms.org Volume: It's All About the Count

Building Rectangular Prisms Part 2

Pump Up the Volume

www.ixl.com/math/grade-5 EE.11

https://learnzillion.com/ Videos: Find the volume of a rectangular prism by filling it with unit cubes.

Lessons: Pack rectangular prisms with unit cubes to find volume

Decompose and recompose solid figures by partitioning figures into layers

6 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 2: Developing multiplication and division strategies Pacing: August 28 – September 14 In this topic students build on their work from previous grade levels to refine their strategies for multiplication and division in order to reach fluency in multiplication by the end of the year. Students continue to develop more sophisticated strategies for division to become flexible and efficient with the standard algorithm in Grade 6. Students begin to find quotients with two‐digit divisors early in the year to build strategies for accurate computations.

Standards Academic Language

Fluently multiply multi-digit whole numbers using the standard algorithm. MAFS.5.NBT.2.5 area model dividend divisor factor inverse operation product quotient rectangular array standard algorithm

Students will:

• apply an understanding of multiplication, place value, and flexibility with multiple strategies to use the standard algorithm for multiplication.

NOTE: Computational fluency is defined as accuracy, efficiency, and flexibility. Grade 5 is the first grade level in which students are expected to be fluent with the standard algorithm for multiplication.

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.

MAFS.5.NBT.2.6

Students will:

• solve division of a multi-digit dividend by a two-digit divisor using strategies based on place value, 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.

NOTE: Use of the standard algorithm for division is a Grade 6 standard.

1. Make sense of problems and persevere in solving them. 8. Look for and express regularity in repeated reasoning.

MAFS.K12.MP.1.1 MAFS.K12.MP.8.1

Topic Comments:

In this topic 5.NBT.2.5 and 5.NBT.2.6 will focus on operations with whole numbers only. Operations with decimals will be introduced in topic 10. These standards will be finalized in topic 15, but should be practiced throughout the year to provide opportunities for students to develop proficiency with these operations. Students look for regularity in their work with multiplication and division, use their understanding of the structure (MP.8) to make sense of their solutions and understand the approaches of other students (MP.1).

7 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 2 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

5.N

BT

.2.5

Topic 2 No aligned resources

Daily Math Practice Journal: pp. 11,12, 13, 17, 21, 22, 23, 25, 29

Complete the Multiplication Problem Multiplying Using the Standard Algorithm More Multiplication Using the Standard Algorithm Find the Multiplication Error

www.cpalms.org Area Models to Algorithms

Multi-digit Multiplication Using Array Frames

Beach on a Budget

https://www.illustrativemathematics.org/content-standards No aligned resources

www.ixl.com/math/grade-5 C.12, C.13, C.14, C.15

https://learnzillion.com/ Lessons: Multiplication: From Partial Products to Standard Algorithm

Using the Standard Algorithm: Iterating Groups and Comparisons

5.N

BT

.2.6

Topic 2 No aligned resources

Teacher Guide: Multiplication and Division Whole Numbers p. 11

Reproducibles: p. 4

Daily Math Practice Journal: pp. 13, 18, 26, 29

How Did you Solve it?: 34-35

Giant place value blocks Whole number place value magnets

Dividing Using the Area Model with Larger Divisors

Dividing Using Place Value with Larger Divisors

Driving to Alaska

Analyzing and Applying to Division

www.cpalms.org Dividing for Equal Groups

Easy as Pie Division!

https://www.illustrativemathematics.org/content-standards Elmer’s Multiplication Error

www.ixl.com/math/grade-5 D.3, D.4, D.11, D.12, D.14

https://learnzillion.com/ Lessons:

Multiplication: From Partial Products to Standard Algorithm

Using the Standard Algorithm: Iterating Groups and Comparisons

8 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 3: Using equivalency to add and subtract fractions with unlike denominators Pacing: September 15 - 29 In this topic students use what they’ve learned in Grades 3 and 4 about equivalency in terms of visual models and benchmarks to extend understanding of adding

and subtracting fractions, including mixed numbers. They reason about size of fractions to make sense of their answers—e.g. they understand that the sum of 1

2

and 2

3 will be greater than 1. It is important to note that in some cases it may not be necessary to find least common denominator to add fractions with unlike

denominators. Students should be encouraged to use their conceptual understanding of fractions rather than just using the algorithm for adding fractions. There is no mathematical reason for students to write fractions in simplest form.

Standards Academic Language

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.)

MAFS.5.NF.1.1

denominator equivalent fraction greater than

one ( 5

4 )

mixed number numerator

Students will:

• represent addition and subtraction of fractions, including mixed numbers and fractions greater than 1, with unlike denominators using concrete models, representations, and equations (denominators are limited to 1-20).

• apply concepts of factors, multiples, equivalent fractions, and decomposition of fractions to find like denominators to add and/or subtract.

NOTE: Students need to be able to recognize equivalent fractions, but will NOT use the language, “simplify, reduce or find lowest terms”.

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.

MAFS.5.NF.1.2

Students will:

• solve word problems involving addition and subtraction of fractions with like and unlike denominators.

• use benchmark fractions and number sense of fractions to estimate and assess reasonableness of answers.

2. Reason abstractly and quantitatively. 4. Model with mathematics.

MAFS.K12.MP.2.1 MAFS.K12.MP.4.1

Topic Comments:

In this topic, 5.NF.1.1 involves students using the same method from Grade 4 to generate equivalent fractions (4.NF.1.1). In topic 7

students will extend this understanding of equivalency to understand that multiplying by a fraction equivalent to 1 (e.g. 4

4) will result in

an equivalent fraction (5.NF.2.5b). Students use visual models and equations to solve problems involving the addition and subtraction of fractions, moving flexibly between the abstract and concrete representations (MP.2, MP.4).

9 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 3 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

5.N

F.1

.1

Topic 3 Fraction Time Fraction Action 4 Fraction Action 5 Fraction Action 9 Fraction Fringe

Teacher Guide: pp. 13- 14 Reproducibles: pp. 4, 9- 11 Daily Math Practice Journal: pp. 30, 32, 34, 36, 38, 40, 42, 44, 46, 48 Pick a Problem: 46-49 How Did you Solve it?: 38-40 Daily Dose of Fractions and Decimals: 1-75 Giant magnetic fraction circles and bars

Adding Fractions with Unlike Denominators Adding More Fractions with Unlike Denominators Subtracting Fractions Subtracting More Fractions

www.cpalms.org Adding and Subtracting Mixed Numbers with Unlike Denominators

Discovering Common Denominators

https://www.illustrativemathematics.org/content-standards Egyptian Fractions

Finding Common Denominators to Add

Finding Common Denominators to Subtract

Jog A Thon

Mixed Numbers with Unlike Denominators

www.ixl.com/math/grade-5: K.4, L.6, L.8, L.9, L.10, L.15,

L.19

https://learnzillion.com/ Lessons: Using multiplication arrays to solve division problems

Relating dividend, divisor, and quotient to a division problem

Partial quotients to solve division problems

Using multiplication and division in multistep word problems

http://achievethecore.org Leap frog fractions

Origo One Videos Exploring the Line Model of Fractions

Exploring the Length Model of Fractions

10 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

5.N

F.1

.2

Topic 3 Cindy's Carpet

Royal Rugs

Teacher Guide: pp. 15- 16 Reproducibles: pp. 4, 12 Daily Math Practice Journal: pp. 31, 33, 35, 36, 38, 43 Pick a Problem: 50, 54- 55 How Did you Solve it?: 41-43 Daily Dose of Decimals and Fractions: 7-9, 36- 39, 68, 70 Giant magnetic fraction circles and bars

Sarah’s Hike Maris Has a Party Just Run Baking Cakes

www.cpalms.org Babysitter's Club Fun with Fractions MEA

Let's Have a Fraction Party!

Fractions make the real WORLD problems go round

https://www.illustrativemathematics.org/content-standards Making Smores

www.ixl.com/math/grade-5 L.14

https://learnzillion.com/ Lessons: Sewing Shirts: Use benchmark fractions to solve problems

Paper Decorations: Solve problems with sums and differences of fractions with different sized pieces

11 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 4: Expanding understanding of place value of decimals Pacing: October 3 – 13 In this topic students expand their previous understanding of place value to include decimal numbers. Grade 5 is the last grade in which the NBT domain appears in the MAFS. Later work in the base-ten system relies on the meanings and properties of operations. This also contributes to deepening students’ understanding of computation and algorithms in the new domains that start in Grade 6.

Standards Academic Language

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.

MAFS.5.NBT.1.1 base-ten numeral decimal digit expanded form exponent hundredths multi-digit number names power of 10 tenths thousandths value

Students will:

• demonstrate with models that in a multi-digit number, a digit in one place represents ten times the value of the place to its right.

• demonstrate with models that a digit in one place is 1

10 the value of the place to its left.

E.g.,

• explain the relationship between the values of digits across multiple place values, using multiplicative comparison.

E.g., 1

10 × 6.4 = 0.64; the 6 in 0.64 represents 6 tenths which is

1

10 as much as the 6 ones in 6.4.

NOTE: While students may discover the pattern of adding a “0” at the end of a number, or “moving the decimal point”, they need to be able to justify this pattern in terms of place value. When you multiply a number by 10, the value becomes 10 times greater, so every digit shifts one place to the left, or in 10 x 0.04, ten groups of 4 hundredths is 40 hundredths, which is equivalent to 4 tenths, or 0.4.

12 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

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.

MAFS.5.NBT.1.2

Students will:

• express powers of 10 using whole-number exponents. E.g.,10¹=10, 10²=10 x 10=100, 10³=10 x 10 x 10=1,000

• explain the pattern for how and why the number of zeros in a product (when multiplying a whole number by a power of 10) relates to the power of 10.

E.g., 5 x 10² = 500 because multiplying by 10² is the same as multiplying by 10 two times (5 x 10 x 10) and every time a number is multiplied by 10 the digits shift one place to the left in the product, so multiplying by 10 two times shifts every digit 2 places to the left.

• explain the pattern in the placement of the decimal point when a decimal is multiplied by a power of 10 and how the placement of the decimal point relates to the power of 10.

E.g., 1.895 x 103=1,895 because multiplying by 103 is the same as multiplying by 10 three times (1.895 x 10 x 10 x 10) and every time a number is multiplied by 10 the digits shift one place to the left in the product, so multiplying by 10 three times shifts every digit 3 places to the left, resulting in the decimal point in the product being 3 places to the right of where it is in the factor.

• explain the pattern in the placement of the decimal point when a decimal is divided by a power of 10 and how the placement of the decimal point relates to the power of 10.

E.g., Every time a number is divided by 10, the digits shift one place to the right in the quotient, so when dividing by 10 two times such as in the expression 15.3 ÷ 102, every digit shifts 2 places to the right, resulting in the decimal point in the quotient being 2 places to the left of where it is in the dividend.

Read, write, and compare decimals to thousandths. a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded

form, e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1

10) + 9 x (

1

100) + 2 x (

1

1000).

MAFS.5.NBT.1.3

Students will:

• read and write decimals up to the thousandths place using base-ten numerals, number names and expanded form.

E.g., Some equivalent forms of 2.34 are:

2+0.30 + 0.04 2 x (1) + 3 x (0.1) + 4 x (0.01)

2 x (1) + 3 × (1

10) + 4 × (

1

100) 2 x (1) + 3 × (

1

10) + 4 × (

1

100) + 0 × (

1

1000)

2 x (1) + 34 x (0.01) 2 x (1) + 34 x (1

100)

6. Attend to precision. 7. Look for and make use of structure.

MAFS.K12.MP.6.1 MAFS.K12.MP.7.1

Topic Comments:

Powers of 10 is a fundamental aspect of the base‐ten system, thus 5.NBT.1.2 can help students extend their understanding of place value from millions to incorporate decimals to thousandths. 5.NBT.1.3a Students will be reading and writing decimals in this topic. Comparing decimals 5.NBT.1.3b will be addressed in topic 6.

Students use their understanding of structure of whole numbers to generalize this understanding to decimals (MP.7) and explain the relationship between the numerals (MP.6).

13 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 4 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

5.N

BT

.1.1

Topic 4 Modeling a Million

Teacher Guide: Place Value Detective p.5 Daily Math Practice Journal: pp.10, 12, 16, 26, 28 How Did you Solve it?: 21, 22 Whole Number Place Value Magnets

Walking to School Five Tenths Dylan’s Baseball Card Collection The Odometer

www.cpalms.org "Shift the Place, Shift the Value" - Understanding Adjacent Places in the Base-ten System

Predicting Place Value Patterns!

Wire We All Wet?

https://www.illustrativemathematics.org/content-standards Kipton’s Scale

Which Number is It?

Tenths and Hundredths

Millions and Billions of People

www.ixl.com/math/grade-5 A.2, G.4

https://learnzillion.com/ Lessons: Understand that digits in numbers represent 1/10 of what they represent in the place to the left

Compare the values of digits in numbers

Solve problems using place value understanding

5.N

BT

.1.2

Topic 4 No aligned resources

Daily Math Practice Journal: pp.10, 14, 16, 19, 20, 24, 27 Pick a Problem: 39, 40 How Did you Solve it?: 23, 24 Daily Dose of Fractions and Decimals: 76-150 (#1 only)

Multiplying by Ten Three Times How Many Zeros? The Error Using Whole Number Exponents

www.cpalms.org Seeking Patterns Using Base 10 and Powers of 10

What happens when you multiply by powers of 10?

https://www.illustrativemathematics.org/content-standards Watch out for parentheses

Bowling for Numbers

Using operations and parentheses

www.ixl.com/math/grade-5 C.3, C.4, D.6, I.2, J.1, J.2

https://learnzillion.com/ Lessons: (Discuss the appearance of the decimal moving) Understand how multiplication and division by 10 relate to place value

Practice shifting the positions of the digits in a number when multiplying and dividing by 10

Apply knowledge of the relationship between place value and multiplying/dividing by 10 (A)

14 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

5.N

BT

.1.3

Topic 4 Dealing with

Decimals Deducing Decimals

Teacher Guide: pp. 6-9 Reproducibles: pp. 5, 6, 7, 8 Daily Math Practice Journal: pp. 11, 14, 16, 22, 24

Decimal Place Value Magnets

Decimal Grids Tub

Decimals Activity Stations

Writing and Reading Decimals Decimals in Number Name Decimals in Expanded Form Decimals in Word and Expanded Form

www.cpalms.org Where's Your Place In the Kingdom of Decimals?

Decimals Have a Point!

Fraction Frenzy! (Division/Fractional Word Problems)

Picture This! Fractions as Division

https://www.illustrativemathematics.org/content-standards Are these equivalent to 9.52?

www.ixl.com/math/grade-5 G.1, G.2, G.3, G.5, G.14

https://learnzillion.com/ Lessons: Write decimal numbers in expanded notation

Write decimal numbers in expanded notation (part 2)

15 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Unit 2 PACING: October 17 – December 20

Topic 5: Understanding the concept of multiplying fractions by fractions Pacing: October 17 – November 2 In this topic students extend their understanding of multiplying a fraction by a whole number to multiplying fractions by fractions. In previous grades, students have developed understanding of fractions as numbers. In this grade level, students develop an understanding of the connection between fractions and division. They will use this understanding to explore the relationship of multiplication and division when multiplying fractions as explained in 5.NF.2.4a.

Standards Academic Language

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?

MAFS.5.NF.2.3

area denominator fraction mixed number numerator partition rectangular array tiling unit fraction

Students will:

• illustrate that the numerator represents the total amount being divided (dividend) and that the denominator represents the number of equal portions needed (divisor).

• explain that fractions (𝑎

𝑏) can be represented as division of the numerator by the denominator (a ÷ b). For example,

5

3 = 5 ÷ 3.

• solve word problems involving the division of whole numbers resulting in a fractional or mixed number quotient.

E.g., Show how 3 ÷ 7 can also be represented as 3

7.

Sara has 3 sub sandwiches. She would like to split the sandwiches equally between 7 people. What fraction of 1 sandwich will each person receive?

o Divide each of 3 rectangles into 7 equal parts resulting in a total of 21 one-seventh sized pieces. o Divide the 21 one-seventh sized pieces into 7 equal groups.

1

7

1

1

7

1

1

7

1

1

7

2

1

7

2

1

7

2

1

7

3

1

7

3

1

7

3

1

7

4

1

7

4

1

7

4

1

7

5

1

7

5

1

7

5

1

7

6

1

7

6

1

7

6

1

7

7

1

7

7

1

7

7

o The result is 3 one-seventh sized pieces per group. 3 x 1

7 =

3

7. So, 3 ÷ 7 =

3

7

16 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

a. Interpret the product (𝑎

𝑏) × q as a parts of a partition of q into b equal parts; equivalently, as the

result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2

3) ×

4 = 8

3, 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.)

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.

MAFS.5.NF.2.4

Students will:

• use visual fraction models (e.g., fraction strips, arrays, area models, fraction multipliers, number lines, etc.) to interpret multiplication of a whole number by a fraction

E.g., 2

3 of 5 (i.e.,

2

3 x 5) is 2 parts when 5 is partitioned into 3 equal parts.

• use visual fraction models (e.g., fraction strips, arrays, area models, fraction multipliers, number lines, etc.) to interpret multiplication of a fraction by a fraction

E.g., Extend the reasoning that since 2

3 of 5 is 2 parts when 5 is partitioned into 3 equal parts to understand that

2

3 of

5

6 (i.e.,

2

3 x

5

6 )

is 2 parts when 5

6 is partitioned into 3 equal parts.

• create story contexts for problems involving multiplication of whole number by a fraction or multiplication of two fractions.

• use unit squares with fractional sides to find the area of a rectangle with fractional side lengths by tiling it, and use this tiling to prove that the area is the same as would be found by multiplying the side lengths.

• multiply fractional side lengths to find areas of rectangles.

• represent fraction products as rectangular areas.

E.g., 2

3 x

4

5 represented using an area model:

17 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

1. Make sense of problems and persevere in solving them. 4. Model with mathematics. 5. Use appropriate tools strategically.

MAFS.K12.MP.1.1 MAFS.K12.MP.4.1 MAFS.K12.MP.5.1

Topic Comments:

NF.2.4 When labeling areas with exponential units for, students will use their understanding of exponents (NBT.1.2) from topic 4

to see that units2 is the result of multiplying units x units.

Representing multiplication of fractions with visual and concrete models is fundamental to this topic in order for students to make sense of multiplying fractions by fractions (MP.1, MP.4). Students select and use a variety of tools to explore these concepts (MP.5).

18 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 5 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

5.N

F.2

.3

Topic 5 No aligned resources

Teacher Guide: p.16 Daily Math Practice Journal: pp. 31, 36, 46, 48 Pick a Problem: 49, 53, 54 How Did you Solve it?: 44-45 Daily Dose of Fractions and Decimals: 1-5 (#3), 10 (#1), 16-25 (#3), 31 (#3), 41-45 (#3), 60 (#1), 66-67 (#1), 69 (#1)

Sharing Pizzas Sharing Brownies Two Thirds Five Thirds

www.cpalms.org Fraction Frenzy! (Division/Fractional Word Problems)

Picture This! Fractions as Division

https://www.illustrativemathematics.org/content-standards What is 23/5?

Converting Fractions of a Unit into a Smaller Unit

How much is pie? Sharing Lunches

www.ixl.com/math/grade-5 K.2

https://learnzillion.com/ Lessons: Fractions as division

Understand fractions as division

Practice connecting fractions and division

Pet Palace: Reporting results of division as fractions

http://achievethecore.org Sharing chocolate

https://www.khanacademy.org/math/cc-fifth-grade-math/cc-5th-fractions-topic/cc-5th-fractions-as-division/v/fractions-as-division

5.N

F.2

.4

Topic 5 Fair Squares Fraction Action p.109-118

Teacher Guide: p.16 Daily Math Practice Journal: pp. 31, 36, 46, 48 Pick a Problem: 49, 53, 54 How Did you Solve it?: 44-45 Daily Dose of Fractions and Decimals: 1-5 (#3), 10 (#1), 16-25 (#3), 31 (#3), 41-45 (#3), 60 (#1), 66-67 (#1), 69 (#1)

Multiplying Fractions by Whole Numbers Using Visual Fraction Models Multiplying Fractions by Fractions The Rectangle

www.cpalms.org Multiplying a Fraction by a Fraction

Real-World Fractions

https://www.illustrativemathematics.org/content-standards Conner and Makayla Discuss Multiplication

Folding Strips of Paper

Chavone’s Bathroom Tiles

Connecting the Area Model to Context

www.ixl.com/math/grade-5 M.12, M.13, M.14

https://learnzillion.com/ Lessons: Understand multiplying with fractions

Find a fraction of a whole number

Find the area of a rectangle with fractional side lengths

Apply multiplication of fractions to find area

Origo One Videos Exploring the Area Model of Fractions

19 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 6: Comparing and rounding decimals Pacing: November 3 – 16

In this topic students apply both their understanding of comparing fractions and their understanding of place value to compare decimals.

Standards Academic Language

Read, write, and compare decimals to thousandths. a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form,

e.g., 347.392 = 3 x 100 + 4 x 10 + 7 x 1 + 3 x (1

10) + 9 x (

1

100) + 2 x (

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.

MAFS.5.NBT.1.3

base-ten numeral decimal expanded form hundredths number names tenths thousandths whole

Students will:

• read and write decimals up to the thousandths place using base-ten numerals, number names and expanded form.

• compare two decimals up to the thousandths using place value and record the comparison using symbols <, >, or =.

Use place value understanding to round decimals to any place. MAFS.5.NBT.1.4

Students will:

• use place value to round decimals to any place, including the nearest whole number.

6. Attend to precision. 7. Look for and make use of structure.

MAFS.K12.MP.6.1 MAFS.K12.MP.7.1

Topic Comments:

Students apply their understanding of the structure within the base-ten system and fraction‐decimal equivalencies to precisely communicate their understanding of relative sizes of decimal numbers (MP.6, MP.7).

20 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 6 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

5.N

BT

.1.3

Topic 6 Dealing with Decimals Deducing Decimals

Teacher Guide: pp. 6-9

Reproducibles: pp. 5, 6, 7, 8

Daily Math Practice Journal: pp. 11, 14, 16, 22, 24

Pick a Problem: 41-45

How Did you Solve it?: 25, 26, 27, 28, 29

Daily Dose of Fractions and Decimals: 76-90 (#5), 106-120 (#5),

Decimal Place Value Magnets

Decimal Grids Tub

Comparing Decimals Writing and Reading Decimals Decimals in Number Name Decimals in Expanded Form Decimals in Word and Expanded Form

www.cpalms.org Tacking on Decimals

Batting a Thousand(th)

Solar Cooking

https://www.illustrativemathematics.org/content-standards Drawing Pictures to Illustrate Comparisons

Comparing Decimals on a Number line

Placing Thousandths on the Number Line

www.ixl.com/math/grade-5 G.9, G.10

https://learnzillion.com/ Lessons: Comparing decimals with different numbers of digits

Comparing decimals with different numbers of digits

Using understanding of place value to compare decimals of different digits

Gumball Machine: Comparing decimals extending to different place values in word problems

5.N

BT

.1.4

Topic 6 No aligned resources

Teacher Guide: pp. 9-11

Daily Math Practice Journal: pp. 10, 12, 15, 17, 18, 20, 22, 26, 28

Pick a Problem: 26-29, 41, 44-46

How Did you Solve it?: 30, 31

Daily Dose of Fractions and Decimals: 76-150 (#2) Decimal Place

Decimal Grids Tub

Rounding to the Nearest Whole Number Rounding to the Tenths Place Rounding to the Thousandths Place Shopping for Produce (Hundredths)

www.cpalms.org Beach on a Budget

Which Cell Phone for Mia?

https://www.illustrativemathematics.org/content-standards Rounding to Tenths and Hundredths

www.ixl.com/math/grade-5 G.9, G.10

https://learnzillion.com/ Lessons: Daniel's Race: Rounding decimals

Rounding decimals to the nearest tenth

Rounding decimals to the nearest hundredth or thousandth

Mystery Number: Using understanding of place value to round decimals in word problems

21 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 7: Interpreting multiplying fractions as scaling Pacing: November 17 – December 7

In this topic students build on their work with “compare” problems in Grade 4 (4.OA.1.1) to develop a foundational understanding of multiplication as

scaling. They interpret, represent, and explain situations involving multiplication of fractions. Students apply their whole number work with multiplication

to develop conceptual understanding of multiplying a fraction by a fraction. Scaling is foundational for developing an understanding of ratios and proportion

in future grade levels.

Standards Academic Language

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.

MAFS.5.NF.2.5

equivalent fraction factor fraction greater than 1 mixed number product scale factor

Students will:

• interpret the relationship between the size of the factors and the size of the product without performing the actual multiplication.

NOTE: Whole number factors should be greater than 1,000.

E.g.,

• explain why multiplying a given number by a scale factor greater than 1 (i.e., a whole number, a fraction greater than 1, or a mixed number) results in a product greater in size than the given number.

• explain why multiplying a given number by a scale factor less than 1 results in a product less in size than the given number.

• explain why multiplying a given fraction by a fraction that is equivalent to 1 as a scale factor results in a product that is equivalent in size to the given fraction.

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

MAFS.NF.2.6

Students will:

• solve real world problems involving multiplication of fractions and mixed numbers.

Example 1:

How does the product of 3,225 x 6,000 compare to the product of 3,225 x 3,000? How do you know? Since 3,000 is half of 6,000, the product of 3,225 x 6000 will be double or twice the product of 3,225 x 3000.

Example 2:

Two newspapers are comparing sales from last year. o The Post sold 34,859 copies. o The Tribune sold one-and-a-half times as many copies as the Post.

Write an expression which describes the number of newspapers the Tribune sold.

11

2 x 34,859

22 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

2. Reason abstractly and quantitatively. 4. Model with mathematics. 6. Attend to precision.

MAFS.K12.MP.2.1 MAFS.K12.MP.4.1 MAFS.K12.MP.6.1

Topic Comments:

In this topic, 5.NF.2.5a and 5.NF.2.5b involve only multiplication by fractions. Division by unit fractions will be introduced in topic

8. In 5.NF.2.6 students should have opportunities to work with all problem types.

Students reason abstractly about the size of factors and practice communicating their thinking about the relationship between

scale factors and factors (MP.2, MP.6). They use number lines and other visual models to interpret real world situations (MP.4).

23 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 7 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

5.N

F.2

.5

Topic 7 No aligned resources

Teacher Guide: p.18 Daily Math Practice Journal: pp. 30, 33, 39, 40, 42, 45, 48 Pick a Problem: 47-49, 51-52, 54-55 How Did you Solve it?: 51-52 Daily Dose of Fractions and Decimals: 46-50 (#1) Fraction Multipliers Tub

Multiplying by a Fraction Greater Than One Multiplying by a Fraction Less Than One More Than or Less Than 2 Miles Estimating Products

www.cpalms.org Looking for Patterns in a Sequence of Fractions

Real-World Fractions

https://www.illustrativemathematics.org/content-standards Running a Mile

Reasoning About Multiplication

Grass Seedlings

Fundraising

Calculator Trouble

www.ixl.com/math/grade-5 M.17, M.18, M.19

https://learnzillion.com/ Lessons: Understand that scaling does not always make numbers larger

Practice scaling down

Apply scaling down to a real-world situation

Practice multiplying by 1

Using multiplying by one to maintain equivalence and to solve problems

5.N

F.2

.6

Topic 7 No aligned resources

Daily Math Practice Journal: pp. 32, 34, 37, 38, 41, 42, 49 Pick a Problem: 50-57 How Did you Solve it?: 53-54 Daily Dose of Fractions and Decimals: 71-73 (#1)

Pizza Party Box Factory Half of a Recipe Candy at the Party

www.cpalms.org Wazzup Charter Schools Playground Dilemma MEA

Garden Variety Fractions

https://www.illustrativemathematics.org/content-standards Scaling Up and Down

Running to School

www.ixl.com/math/grade-5 No aligned resources.

https://learnzillion.com/ Lessons: Using multiplication arrays to solve division problems

Relating dividend, divisor, and quotient to a division problem

Partial quotients to solve division problems

Using multiplication and division in multistep word problems

24 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 8: Developing the concept of dividing unit fractions Pacing: December 8 – 20 In this topic students will use their understanding of the relationship of multiplication and division to develop a conceptual understandin g of division with fractions (division of a whole number by a unit fraction or a unit fraction by a whole number).

Standards Academic Language

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply 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.)

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 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?

MAFS.5.NF.2.7

dividend divisor quotient unit fractions

Students will:

• apply an understanding of the division of whole numbers to the concept of dividing whole numbers by unit fractions (e.g., 4÷1

3 can

be interpreted as 4 inches of ribbon being cut into 1

3 inch pieces) and dividing unit fractions by whole numbers (e.g.,

1

3 ÷ 4 can be

interpreted as sharing 1

3 of a school pizza with 4 people).

• interpret and solve problems involving the division of whole numbers by unit fractions (e.g., 4÷1

3 can be thought of as how many

groups of 1

3 can be made from 4 wholes) using visual models and story contexts.

• interpret and solve problems involving the division of unit fractions by whole numbers (e.g., 1

3 ÷ 4 can be thought of as

1

3 being

divided into 4 equal parts) using visual models and story contexts.

• solve real world problems involving division of unit fractions and whole numbers using fraction models and equations.

NOTE: Division of a fraction by a fraction is a Grade 6 standard.

1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively.

MAFS.K12.MP.1.1 MAFS.K12.MP.2.1

Topic Comments:

In this topic it is critical for students to use concrete objects or pictures to help conceptualize, create, and solve proble ms (MP.1, MP.2).

25 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 8 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

5.N

F.2

.7

Topic 8 No aligned resources

Teacher Guide: pp.18- 19 Reproducibles: pp.13-14 Daily Math Practice Journal: pp.41, 43, 45, 47, 49 Pick a Problem: 50-60 How Did you Solve it?: 55-57 Daily Dose of Fractions and Decimals: 15 (#5), 63 (#2)

Whole Numbers Divided by Fractions Bags of Fudge Fractions Divided by Whole Numbers Relay Race

www.cpalms.org Real-World Fractions

It's My Party and I'll Make Dividing by Fractions Easier if I Want to!

https://www.illustrativemathematics.org/content-standards Drinking Juice

Half of a recipe

Making Cookies

To multiply or not to multiply

To multiply or not to multiply variation 2

www.ixl.com/math/grade-5 N.1, N.2, N.3, N.4

https://learnzillion.com/ Lessons: Find the area of a rectangle with fractional side lengths

Solve problems involving non-unit fractions

http://achievethecore.org Mini Assessment (Multiplying and Dividing Fractions)

Banana Pudding

26 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Unit 3 PACING: January 8 – March 8

Topic 9: Solving problems including volume Pacing: January 8 – 19 This topic calls for students to apply their understanding of volume to real-­world problems. They develop efficient strategies, including the use of formulas, to compute volumes of right rectangular prisms or other three-­dimensional figures that can be broken down into non-­overlapping right rectangular prisms.

Standards Academic Language

Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. 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.

a. Represent threefold whole-number products as volumes, e.g.,to represent the associative property of multiplication.

b. Apply the formula V= l x w x h and V= B x 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 non-overlapping parts, applying this technique to solve real world problems.

MAFS.5.MD.3.5

additive associative property B= area of base cubic units edge formula height length rectangular prism unit cube volume width

Students will:

• 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 or multiplying the height by the area of the base.

• relate finding the product of three numbers (length, width, and height) using the associative property of multiplication to finding volume.

• calculate volume of rectangular prisms and cubes, with whole number edge lengths, using the formula for volume (V = l x w x h or V = B x h) in real world and mathematical problems.

E.g., 1. Find the area of the base by multiplying its length by its width (B = l × w). 2. Multiply the area of the base by the height (V = B × h).

• recognize that volume is additive by decomposing a composite solid into non-overlapping rectangular prisms to find the volume of the solid by finding the sum of the volumes of each of the decomposed prisms.

(3 x 2) represents the number of cubic units on the first layer

(3 x 2) x 5 represents the number of 3 x 2 layers

(3 x 2) + (3 x 2) + (3 x 2) + (3 x 2) + (3 x 2) represents 5 layers with 6 cubic units each

5 x 6 = 30 cubic units

27 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

• solve real world problems involving finding the volume of solid figures composed of two non-overlapping right rectangular prisms.

E.g., What is the volume of water needed to fill the pool in the diagram?

NOTE: Labels may include cubic units (i.e. cubic centimeters, cubic feet, etc.) or exponential units (i.e., cm3, ft3, etc.).

5. Use appropriate tools strategically. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

MAFS.K12.MP.5.1 MAFS.K12.MP.7.1 MAFS.K12.MP.8.1

Topic Comments:

When labeling volumes with exponential units, students will use their understanding of exponents (NBT.1.2) from topic 4 to see

that units3 is the result of multiplying units x units x units.

Students pack the figures with unit cubes (MP.5) and connect this structure to multiplicative reasoning (MP.7). They solve

problems by applying the generalized formulas (MP.8).

The deep end of the pool measures 14 ft. × 10 ft. × 5 ft. making the volume 700 ft3. The shallow end of the pool measures 6 ft. × 5 ft. × 5 ft. making the volume 150 ft3. 700 ft3+ 150 ft3= 850 ft3

28 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 9 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

5.M

D.3

.5

Topic 9 Luggage Limits Teacher Guide: pp. 21- 22 Daily Math Practice Journal: pp. 50, 52, 56, 58, 60, 62 Pick a Problem: 62, 64- 69 How Did you Solve it?: 68-74 Volume Measurement Center box

Determining and Interpreting Volume Using Additive Reasoning When Finding Volume Determining Dimensions Volume Two Ways

www.cpalms.org Building Rectangular Prisms Part 2

Volume: Let’s Be Efficient

Lunchbox Volume

https://www.illustrativemathematics.org/content-standards Cari’s Aquarium

You can multiply 3 numbers in any order.

Understand the Associative property of multiplication

Breaking apart composite solids

www.ixl.com/math/grade-5 E.11, E.12, E.13

https://learnzillion.com/ Lessons: Understand that volume can be measured by packing objects with unit cubes

http://achievethecore.org Box of clay

29 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 10: Performing operations with decimals Pacing: January 23 – February 6 Measurement is used in this topic as a context for operations with decimals. In Grade 4, students converted measurements given in a larger unit to a smaller unit. Students’ previous experiences with decimal fractions and fraction computations are applied here to provide multiple ways of thinking about operations with decimals. Students can use their understanding of decimal-­fraction equivalencies, concrete or visual models, and place value to reason about decimal quantities and operations.

Standards Academic Language

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.

MAFS.5.NBT.2.7

conversion convert customary units decimal hundredths metric units tenths thousandths

Students will:

• add decimals to hundredths, using concrete models, drawings, strategies based on place value, and/or properties of operations.

• subtract decimals to hundredths, using concrete models, drawings, strategies based on place value, properties of operations and/or the relationship between addition and subtraction.

• multiply decimals using rectangular arrays, area models, and/or an understanding of place value and properties of operations.

• divide decimals using rectangular arrays, area models, an understanding of place value and properties of operations, and/or the relationship between multiplication and division.

• represent and explain strategies and reasoning used to solve problems including decimals.

E.g., Use a model to solve 3 – 0.6.

NOTE: This standard requires students to extend the models and strategies previously developed for conceptual understanding of operations with whole numbers. Using the standard algorithms for adding, subtracting, multiplying, and dividing decimals is Grade 6 standard.

Convert among different-sized standard measurement units (i.e., km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec) 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. NOTE: This standard has been amended in Florida to include specific units of measure.

MAFS.5.MD.1.1

Students will:

NOTE: Students need to be provided with the Grade 5 FSA Mathematics Reference Sheet (see pg. 57) in order to practice using the tool.

• convert units (required units are listed on Grade 5 FSA Mathematics Reference Sheet) within the same system (customary to customary and metric to metric).

• apply knowledge of length, weight, mass, and time to solve multi-step word problems using measurement conversions.

NOTE: Measurement values may be fractional, decimal, or whole number values.

30 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others.

MAFS.K12.MP.2.1 MAFS.K12.MP.3.1

Topic Comments:

5.MD.1.1 provides measurement conversion as a context for not only working with decimals but a deeper understanding for place

value and the connection to the metric system.

Instead of just computing answers, students reason about both the relationship between fraction and decimal operations and the relationship between whole number computation and fractional/decimal computation (MP.2, MP.3).

31 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 10 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

5.N

BT

.2.7

Topic 10 Operation Decimals

Pack and Post

Teacher Guide: p. 12 Daily Math Practice Journal: pp. 14, 19, 23, 28

Pick a Problem: 26-38, 82 How Did you Solve it?: 36, 37

Daily Dose of Fractions and Decimals: 76-150 (#3-4)

Decimal Place Value Magnets

Decimal Grids Tub

Decimal Activity

Stations

Write and Wipe Graphing Boards

Running a Race (addition) Tony's Lunchbox (subtraction) Buying Candy Bars (multiplication)

Running (division)

www.cpalms.org To Oregon By Wagon

The 20 Second Game

https://www.illustrativemathematics.org/content-standards Value of Education

www.ixl.com/math/grade-5 B.4, D.15, J.3, J.4, J.5, H.1, H.2, H.3 H.4, H.5, O.5, O.6, S.1, S.2, I.3, I.4, I.5, I.6, I.8, I.9

https://learnzillion.com/ Lessons: Adding decimals using base ten blocks

Use an area model to multiply a decimal by a decimal

Divide decimals

5.M

D.1

.1

Topic 10 Measure for Measure Straw Planes

No aligned resources

Converting Metric Measurement Units (first question only)

Converting Customary Measurement Units (2nd and 3rd problems)

Candy and Ribbon

www.cpalms.org Metric Length Madness

Conversion Excursion

Where On Earth Is …

https://www.illustrativemathematics.org/content-standards Converting Fractions of a unit into a smaller unit (also aligns to NF.2.3)

www.ixl.com/math/grade-5 Y.1, Z.5, Z.13, Z.15

https://learnzillion.com/ No aligned resources

http://achievethecore.org No aligned resources

32 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 11: Classifying two-dimensional geometric figures Pacing: February 7 – 21 In this topic the emphasis is on the hierarchical relationship among 2-­dimensional geometric figures. Students have had previous experience classifying shapes using defining attributes, and this topic extends this concept to set a foundation for understanding the propagation of properties.

Standards Academic Language

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.

MAFS.5.G.2.3

defining attribute category classify congruent parallel perpendicular polygons right angles subcategory two-dimensional figures Venn diagram

Students will: categorize two-dimensional figures (i.e., triangle, quadrilateral, rectangle, square, rhombus, trapezoid) according to their defined attributes.

NOTE: Geometric (defining) attributes include number and properties of sides (i.e., parallel, perpendicular, congruent) and number and properties of angles (i.e., type of angle, measurement of angle, congruency of angles).

• relate certain categories of two-dimensional figures as subcategories of other categories

E.g., rectangles are a subcategory of parallelograms because they are both quadrilaterals with two pairs of sides that are parallel and congruent, therefore all rectangles are also parallelograms.

• explain that the attributes belonging to one category of two-dimensional figures also belong to all subcategories of that category.

E.g, Squares are a subcategory of rectangles, therefore if rectangles have four right angles and two pairs of sides that are parallel and congruent, it can be inferred that squares have four right angles and two pairs of sides that are parallel and congruent.

33 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Classify and organize two-dimensional figures into Venn diagrams based on the attributes of the figures. NOTE: This standard has been amended in Florida to include Venn diagrams.

MAFS.5.G.2.4

Students will:

• classify two-dimensional figures (i.e., triangle, quadrilateral, rectangle, square, rhombus, trapezoid) based on defining attributes.

• organize two-dimensional figures into a Venn diagram (graphic organizer) based on defining attributes.

E.g.,

3. Construct viable arguments and critique the reasoning of others. 7. Look for and make use of structure.

MAFS.K12.MP.3.1 MAFS.K12.MP.3.1

Topic Comments:

Students make use of structure to build a logical progression of statements and explore hierarchical relationships among 2-­dimensional shapes (MP.3, MP.7).

34 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 11 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

5.G

.2.3

Topic 11 Classifying Quadrilaterals Lines to Design

Teacher Guide: pp. 23- 24 Reproducibles: pp. 4, 15 Daily Math Practice Journal: pp. 64, 66, 68, 70 Pick a Problem: 97, 98, 99, 100 How Did you Solve it?: 83, 84, 85, 86 2-D Geometric Shapes Tub Giant Magnetic Pattern Blocks

Classifying Squares What Do You Know About Rectangles? Guess My Shape Shape Clues

www.cpalms.org Calling All Quads!

https://www.illustrativemathematics.org/content-standards Always Sometimes, Never

www.ixl.com/math/grade-5 BB.4

https://learnzillion.com/ Lessons: Organize shapes into a hierarchy

5.G

.2.4

Topic 11

Teacher Guide: pp. 23- 24

Reproducibles: pp. 4, 15

Daily Math Practice Journal: pp. 64, 66, 68, 70

How Did you Solve it?: 87, 88, 89, 90

2-D Geometric Shapes Tub

Giant Magnetic Pattern Blocks

Where Do They Belong? Classifying Shapes Classifying Quadrilaterals Trapezoids

www.cpalms.org Where in the Venn are the Quadrilaterals?

https://www.illustrativemathematics.org/content-standards What is a trapezoid? Part 2

What do these shapes have in common?

https://learnzillion.com/ Lessons: Use and create organized structures for categories of shapes

35 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 12: Solving problems with fractional quantities Pacing: February 22 – March 8 In this topic students use data and other contexts to solve real world problems involving fractional computations. All of the problem types in the Common Addition and Subtraction and Multiplication and Division Situations Tables (see pages 55 and 56) should be addressed in this topic.

Standards Academic Language

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.

MAFS.5.MD.2.2

data set dividend divisor line plot quotient unit fraction wholes

Students will:

• create a line plot recording measurement data including fraction units of halves, quarters, and eighths.

• use the measurement data on a line plot to solve multistep problems involving fractions and draw conclusions about the data.

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Students able to multiply 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.)

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 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?

MAFS.5.NF.2.7

Students will:

• apply an understanding of the division of whole numbers to the concept of dividing whole numbers by unit fractions (e.g., 4÷1

3 can be

interpreted as 4 inches of ribbon being cut into 1

3 inch pieces) and dividing unit fractions by whole numbers (e.g.,

1

3 ÷ 4 can be

interpreted as sharing 1

3 of a school pizza with 4 people).

• interpret and solve problems involving the division of whole numbers by unit fractions (e.g., 4÷1

3 can be thought of as how many

groups of 1

3 can be made from 4 wholes) using visual models and story contexts.

• interpret and solve problems involving the division of unit fractions by whole numbers (e.g., 1

3 ÷ 4 can be thought of as

1

3 being divided

into 4 equal parts) using visual models and story contexts.

• use data to solve real world problems involving division of unit fractions and whole numbers using fraction models and equations.

2. Reason abstractly and quantitatively. 5. Use appropriate tools strategically.

MAFS.K12.MP.2.1 MAFS.K12.MP.5.1

36 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic Comments:

5.MD.2.2 is included here so measurement line plots can be used as a context for students to apply fraction computation strategies. Students use line plots and other tools/technology to reason about problem situations (MP.5). Students attend to the underlying meaning of the quantities and operations when solving problems rather than just how to compute answers (MP.2).

Topic 12 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

5.M

D.2

.2

Topic 12 No aligned resources

Teacher Guide: p. 20-21 Reproducibles: p.4 Daily Math Practice Journal: pp.51, 53, 55, 57, 59, 61, 63 Pick a Problem:70-74 How Did you Solve it?: pp. 62-63

Rock Measurement Part One Rock Measurement Part Two Bulk Candy Part One Bulk Candy Part Two

www.cpalms.org Line Plotting with Fractions Chicago Pizza Style

What’s in the Plot?

April Showers Bring May Flowers – Line Plots

https://www.illustrativemathematics.org/content-standards Fractions on a line plot

www.ixl.com/math/grade-5 W.10, W.11, W.12

https://learnzillion.com/ Lessons: Solve Multi-step problems using information in a line plot

Use data from a line plot to solve real world problems

Represent and interpret data on a line plot

5.N

F.2

.7

Topic 12 No aligned resources

Teacher Guide: pp.18-19

Reproducibles: pp.13-14

Daily Math Practice Journal: pp.41, 43, 45, 47, 49

Pick a Problem: 50-60

How Did you Solve it?: 55-57

Daily Dose of Fractions and Decimals: 15 (#5), 63 (#2)

Whole Numbers Divided by Fractions Bags of Fudge Fractions Divided by Whole Numbers Relay Race

https://www.illustrativemathematics.org/content-standards Origami Stars

Banana Pudding

www.ixl.com/math/grade-5 N.1, N.2, N.3, N.4

https://learnzillion.com/ Lessons: Find the area of a rectangle with fractional side lengths

Solve problems involving non-unit fractions

http://achievethecore.org Mini Assessment (Multiplying and Dividing Fractions)

Banana Pudding

37 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Unit 4 PACING: March 19 – May 30

Topic 13: Representing algebraic thinking Pacing: March 19 - 30 In this topic students explore numerical expressions more formally to represent and interpret calculations involving whole numbers, fractions, and decimals. They apply their understanding of the different algebraic properties of operations and explain the relationships between the quantities with the written expressions. This topic includes opportunities to both evaluate expressions and reason about expressions without calculating a solution.

This is

foundational for further work with number in later grades.

Standards Academic Language

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. MAFS.5.OA.1.1 braces brackets evaluate numerical expression operation parentheses value

Students will:

• evaluate expressions which include parentheses, brackets, and/or braces by performing operations in the conventional order (Order of Operations).

E.g.,

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 x (8 + 7). Recognize that 3 x (18932 + 921) as three times as large as 18932 + 921, without having to calculate the indicated sum or product.

MAFS.5.OA.1.2

Students will:

• apply an understanding of operations and grouping symbols to write numerical expressions.

• apply an understanding of operations and grouping symbols to interpret the meaning of numerical expressions without evaluating (i.e.,calculating) them.

6. Attend to precision. MAFS.K12.MP.6.1

Topic Comments:

The expressions described in 5.OA.1.1 include the use of parentheses but should not contain nested grouping symbols. Teachers should use caution when introducing mnemonic devices such as PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction) for remembering Order of Operations because they have the potential to cause students to focus on the device, rather than on the underlying mathematical meaning of an expression. This can lead to serious misconceptions in future study.

The expressions described in 5.OA.1.2 should be no more complex than the expressions one finds in an application of the associative or distributive property. Students discuss the meaning of symbols and interpret numerical expressions precisely (MP.6).

38 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 13 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

5.O

A.1

.1

Topic 13 No aligned resources

Teacher Guide: Parenthesis, Brackets, and Braces p.3 Order of Operations p.3 Reproducibles: pp. 3,4 Daily Math Practice Journal: pp.2, 3, 4, 5, 7, 8 Pick a Problem: 19-22 How Did you Solve it?: 1-7

With or Without Parentheses Evaluating Expressions More Expressions Place the Parentheses

www.cpalms.org Exploring Krypto (Order of Operations)

https://www.illustrativemathematics.org/content-standards Watch out for parentheses

Bowling for Numbers

Using operations and parentheses

www.ixl.com/math/grade-5 O.4

https://learnzillion.com/ Lessons: Determine if Parenthesis change the value of an expression

Using grouping symbols to make an equation true

5.O

A.1

.2

Topic 13 Picturing Clues (partially aligned) Who Has?

Teacher Guide: Order of Operations p.3 Reproducibles: p.4 Daily Math Practice Journal: pp.2, 4-9 Pick a Problem: 23-25 How Did you Solve it? 8-15

Brayden's Video Game Write the Expression Comparing Products How Much Greater is the Product?

https://www.illustrativemathematics.org/content-standards Comparing Products

Words to expressions 1

Video Game Scores

Seeing is Believing

www.ixl.com/math/grade-5 O.3

https://learnzillion.com/ Lessons: Write a numerical expression to represent a verbal description of a calculation

Represent a real world situation as a numerical expression

39 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 14: Exploring the coordinate plane Pacing: April 2 – April 13 In this topic students are introduced to the coordinate plane, applying their knowledge of the number line to understand the relationship of the two dimensions of a point in the coordinate plane. Students connect their work with numerical patterns to form ordered pairs and graph these ordered pairs in the first quadrant of a coordinate plane. Students use this model to make sense of and explain the relationships within the numerical patterns they generate. This prepares students for future work with functions and proportional relationships in the middle grades.

Standards Academic Language

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.

MAFS.5.OA.2.3

axes coordinate plane coordinates corresponding terms horizontal plot rule ordered pairs origin point quadrant vertical x-axis y-axis x- and y-coordinates

Students will:

• generate two numerical patterns using two given rules.

• explain the relationship between the two numerical patterns by comparing the relationship between each of the corresponding terms from each pattern.

• form ordered pairs out of corresponding terms from each pattern.

• graph the ordered pairs on a coordinate plane.

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).

MAFS.5.G.1.1

Students will:

• draw a coordinate plane with two intersecting perpendicular lines.

• identify the intersection as the origin and the point where 0 lies on each of the number lines.

• label the horizontal axis as the x-axis, and the vertical axis as the y-axis.

• explain that when plotting points on a coordinate plane the first number in an ordered pair (the x-coordinate) indicates how far to travel from the origin in the direction of the x-axis and that the second number (y-coordinate) indicates how far to travel in the direction of the y-axis.

E.g., When graphing the ordered pair (3,2), 3 is the x-coordinate so you move 3 units from 0 on the x-axis and then, since 2 is the y-coordinate, you move up 2 units in the direction of the y-axis.

NOTE: Students are only expected to utilize the first quadrant which includes only positive numbers.

40 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

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.

MAFS.5.G.1.2

Students will:

• determine when a mathematical problem has a set of ordered pairs.

• represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane.

E.g., Students plan to draw a symmetric figure in which they plot coordinates that are then connected by line segments.

• interpret coordinate values of points in the context of the situation.

NOTE: Students need to be able to use directional language or a compass rose and cardinal directions. (i.e., North, South, East, or West)

6. Attend to precision. 7. Look for and make use of structure.

MAFS.K12.MP.6.1 MAFS.K12.MP.7.1

Topic Comments:

Students precisely describe the coordinates of points and the relationship of the coordinate plane to the number line (MP.6). Students both generate and identify relationships in numerical patterns, using the coordinate plane as a way of representing these relationships and patterns (MP.7).

41 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 14 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

5.O

A.2

.3

Topic 14 Just Drop It Willie the Wheel Man

Teacher Guide: p. 4 Daily Math Practice Journal: pp. 2, 5, 6, 9 Pick a Problem: How Did you Solve it?: 16, 17, 18, 19, 20, 81, 82 Write and Wipe Graphing Boards

Generating Two Patterns Exploring Related Patterns Comic Books Choo Choo Trains Company

www.cpalms.org Cool School

Chameleon Graphing

https://www.illustrativemathematics.org/content-standards Sidewalk patterns

www.ixl.com/math/grade-5 V.8, V.9, V.10

https://learnzillion.com/ Lessons: Generate patterns and recognize relationships in corresponding terms

Apply knowledge of patterns in corresponding terms in the real-world

5.G

.1.1

Topic 14 No aligned resources

Teacher Guide: p. 23 Reproducibles: p. 4 Daily Math Practice Journal: pp. 65, 67, 69,71 Write and Wipe Graphing Boards

What Do the Coordinates Mean? Understanding Coordinates Properties of Coordinate Planes Coordinates

www.cpalms.org “Design a Town” Coordinates

Quadrant Shuffle

Human Ordered Pairs

https://www.illustrativemathematics.org/content-standards Using battleship grid paper

www.ixl.com/math/grade-5 U.1, U.2

https://learnzillion.com/ Lessons: Locate and name points on a coordinate plane

Identify and plot ordered pairs on a coordinate plane.

42 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

5.G

.1.2

Topic 14 Plotting Planes

Hurkle Hide and Seek Captain Kid's Grid Space Shuttle Coordinates Mark My Words

Teacher Guide: p. 23 Reproducibles: p. 4 Daily Math Practice Journal: pp. 65, 67, 69, 71 Pick a Problem: 86, 87, 88, 89, 90, 91, 92, 93 How Did you Solve it?: 75, 76, 77, 78, 79, 80 Write and Wipe Graphing Boards

Name the Ordered Pair On the Coordinate Plane Mowing the Lawn Making Bracelets

www.cpalms.org Graphy, Graphy

Map It Out

Property Picking Pickle

https://www.illustrativemathematics.org/content-standards Meerkat Coordinate Plane Task

www.ixl.com/math/grade-5 U.3, U.4

https://learnzillion.com/ Lessons: Interpret coordinate values of points in the context of a situation

Represent and solve real world and mathematical problems by graphing points in the coordinate plane

43 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 15: Revisiting multiplication and division with whole numbers Pacing: April 16 – 27 These standards were introduced in topic 2 to provide opportunities throughout the year for students to work towards fluency. In this topic students demonstrate fluency in multiplication with whole numbers and continue to practice division with whole numbers using various s trategies.

Standards Academic Language

Fluently multiply multi-digit whole numbers using the standard algorithm. MAFS.5.NBT.2.5 area model dividend divisor factor product quotient rectangular array standard algorithm

(multiplication)

Students will:

• multiply multi-digit whole numbers using the standard algorithm.

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.

MAFS.5.NBT.2.6

Students will:

• solve division of a multi-digit dividend by a two-digit divisor using strategies based on place value, 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.

1. Make sense of problems and persevere in solving them. 8. Look for and express regularity in repeated reasoning.

MAFS.K12.MP.1.1 MAFS.K12.MP.8.1

Topic Comments:

5.NBT.2.6 is a milestone along the way to reaching fluency with the standard algorithm in Grade 6 (6.NS.2.2). Students use efficient strategies and look for shortcuts to multiply and divide whole numbers with accuracy (MP.1, MP.8).

44 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 15 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

5.N

BT

.2.5

Topic 15 No aligned resources

Daily Math Practice Journal: pp. 11,12, 13, 17, 21, 22, 23, 25, 29

Multiplying Using the Standard Algorithm

More Multiplication Using the Standard Algorithm

Complete the Multiplication Problem

Find the Multiplication Error

www.cpalms.org Cameras on Campus There are many MEAs (Model Eliciting Activities) offered for this standard. Choose one based on your students’ interests.

www.ixl.com/math/grade-5 C.12, C.13, C.14, C.15

https://learnzillion.com/ Lessons: Multiplication: From Partial Products to Standard Algorithm

Using the Standard Algorithm: Iterating Groups and Comparisons

5.N

BT

.2.6

Topic 15 Party Planning Teacher Guide: Multiplication and Division Whole Numbers p. 11 Reproducibles: p. 4 Daily Math Practice Journal: pp. 13, 18, 26, 29 How Did you Solve it?: 34-35 Giant place value blocks Whole number place-value magnets

Dividing Using an Area Model with Larger Divisors Dividing Using Place Value with Larger Divisors Driving to Alaska Analyzing and Applying Division

www.cpalms.org Diving Deeper into Division There are also many MEAs (Model Eliciting Activities) offered for this standard. Choose one based on your students’ interests.

https://www.illustrativemathematics.org/content-standards Minutes and Days (task listed in previous NBT.2.6 topics)

www.ixl.com/math/grade-5 D.3, D.4, D.11, D.12, D.14

https://learnzillion.com/ Lessons: Using multiplication arrays to solve division problems

Relating dividend, divisor, and quotient to a division problem

Partial quotients to solve division problems

Using multiplication and division in multistep word problems

45 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 16: Revisiting expressions and exponents Pacing: April 30 – May 14 This is a culminating topic in which students continue their work from topic 13 to solidify an understanding of using numerical expressions to represent and interpret calculations involving whole numbers, fractions, and decimals. Students gain further experience with investigating and applying properties of operations in numerical contexts, such as the associative, distributive, and commutative properties. Students also move forward with their work from topic 4 using whole-number exponents to denote bases of 10.

Revisiting these concepts will further prepare students for working with algebraic expressions and

numerical expressions with whole-number exponents in Grade 6.

Standards Academic Language

Use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols. MAFS.5.OA.1.1 braces brackets evaluate exponent numerical expression operation parentheses value

Students will:

• evaluate expressions which include parentheses, brackets, and/or braces by performing operations in the conventional order.

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 x (8 + 7). Recognize that 3 x (18932 + 921) as three times as large as 18932 + 921, without having to calculate the indicated sum or product.

MAFS.5.OA.1.2

Students will:

• apply an understanding of operations and grouping symbols to write numerical expressions.

• apply an understanding of operations and grouping symbols to interpret the meaning of numerical expressions without evaluating them.

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.

MAFS.5.NBT.1.2

• express powers of 10 using whole-number exponents. E.g., 10¹=10, 10²=10 x 10=100, 10³=10 x 10 x 10=1,000

2. Reason abstractly and quantitatively. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning.

MAFS.K12.MP.2.1 MAFS.K12.MP.7.1 MAFS.K12.MP.8.1

Topic Comments:

5.OA.1.1 and 5.OA.1.2 are pre-requisite standards for 6.EE.1.2 (write, read, and evaluate expressions in which letters stand for numbers) and 6.EE.1.3 (apply the properties of operations to generate equivalent expressions).

5.NBT.1.2 is a pre-requisite standard for 6.EE.1.1 (write and evaluate numerical expressions involving whole-number exponents). For this reason, work on this standard will only focus on using whole-number exponents to denote powers of 10 at this time. As students apply properties of operations to represent and evaluate expressions, they must reason abstractly and quantitatively (MP.2) while looking for and making use of structure (MP.7). Working with exponents is a tool for expressing regularity in repeated reasoning (MP.8).

46 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 16 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

5.O

A.1

.1

Topic 16 No aligned resources

Teacher Guide: Parenthesis, Brackets, and Braces p.3 Order of Operations p.3 Reproducibles: pp. 3,4 Daily Math Practice Journal: pp.2, 3, 4, 5, 7, 8 Pick a Problem: 19-22 How Did you Solve it?: 1-7

With or Without Parentheses Evaluating Expressions More Expressions Place the Parentheses

www.cpalms.org Everything Balances Out in the End: Balancing Algebraic Understanding

https://www.illustrativemathematics.org/content-standards Watch out for parentheses

Bowling for Numbers Using operations and parentheses

www.ixl.com/math/grade-5 O.4

https://learnzillion.com/ Lessons: Determine if Parenthesis change the value of an expression

Using grouping symbols to make an equation true

5.O

A.1

.2

Topic 16 Picturing Clues (partially aligned) Who Has?

Teacher Guide: Order of Operations p.3 Reproducibles: p.4 Daily Math Practice Journal: pp.2, 4-9 Pick a Problem: 23-25 How Did you Solve it? 8-15

Brayden's Video Game Write the Expression Comparing Products How Much Greater is the Product?

https://www.illustrativemathematics.org/content-standards Comparing Products

Words to expressions 1

Video Game Scores

Seeing is Believing

www.ixl.com/math/grade-5 O.3

https://learnzillion.com/ Lessons: Write a numerical expression to represent a verbal description of a calculation

Represent a real world situation as a numerical expression

5.N

BT

.1.2

Topic 16 No aligned resources

Daily Math Practice Journal: pp. 27

Multiplying by Ten Three Times How Many Zeros? Using Whole Number Exponents

www.cpalms.org Seeking Patterns Using Base 10 and Powers of 10

What happens when you multiply by powers of 10?

No aligned resources

47 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 17: Revisiting operations on fractions with data presented in line plots Pacing: May 15 – 22 This is a culminating topic in which students continue their work from topic 12 using line plots to solve multistep problems involving fractions. Revisiting these concepts will further prepare students for representing and analyzing numerical data sets and continued operations with fractions in grade 6.

Standards Academic Language

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.

MAFS.5.MD.2.2

data set line plot

Students will:

• create a line plot recording measurement data including fraction units of halves, quarters, and eighths.

• use the measurement data on a line plot to solve multistep problems involving fractions and draw conclusions about the data.

2. Reason abstractly and quantitatively. 5. Use appropriate tools strategically.

MAFS.K12.MP.2.1 MAFS.K12.MP.5.1

Topic Comments:

5.MD.2.2 is a pre-requisite standard for 6.SP.2.4 (display numerical data in plots on a number line, including dot plots, histograms, and box plots). It also provides a context for students to continue to apply fraction computation strategies. Students use line plots and other tools/technology to reason about problem situations (MP.5). Students attend to the underlying meaning of the quantities and operations when solving problems rather than just how to compute answers (MP.2).

48 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 17 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

5.M

D.2

.2

Topic 17 Teacher Guide: p. 20-21 Reproducibles: p.4 Daily Math Practice Journal: pp.51, 53, 55, 57, 59, 61, 63 Pick a Problem:70-74 How Did you Solve it?: pp. 62-63

Rock Measurement Part One Rock Measurement Part Two Bulk Candy Part One Bulk Candy Part Two

www.cpalms.org Line Plotting with Fractions Chicago Pizza Style

What’s in the Plot?

April Showers Bring May Flowers – Line Plots

https://www.illustrativemathematics.org/content-standards Fractions on a line plot

www.ixl.com/math/grade-5 W.10, W.11, W.12

https://learnzillion.com/ Lessons: Solve Multi-step problems using information in a line plot

Use data from a line plot to solve real world problems

Represent and interpret data on a line plot

49 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 18: Revisiting area of rectangles with fractional side lengths Pacing: May 23 – May 30 This is a culminating topic in which students continue their work from topic 5, focusing on applying an understanding of finding area of rectangles with fractional side lengths. Revisiting these concepts will further prepare students to extend this understanding to finding the volume of rectangular prisms with fractional side lengths using the formula V=Bh (where B is the area of the rectangular base) in grade 6. In this final topic, multiplication of a fraction by fraction is again solidified through the context of area measures.

Standards Academic Language

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.

MAFS.5.NF.2.4

area denominator fraction numerator partition rectangular array tiling unit fraction

Students will:

• use unit squares with fractional sides to prove the area found by tiling a rectangle with fractional side lengths is the same as would be found by multiplying the side lengths.

• multiply fractional side lengths to find areas of rectangles.

• represent fraction products as rectangular areas.

6. Attend to precision. MAFS.K12.MP.6.1

Topic Comments:

Applying the formula to find areas with fractional edge lengths requires that students attend to the degree of precision appropriate for a given situation (MP.6).

50 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Topic 18 Suggested Instructional Resources

MAFS Module AIMS Lakeshore MFAS Internet

5.N

F.2

.4.b

Topic 18 Fair Squares Fraction Action p.109-118

Teacher Guide: p.16 Daily Math Practice Journal: pp. 31, 36, 46, 48 Pick a Problem: 49, 53, 54 How Did you Solve it?: 44-45 Daily Dose of Fractions and Decimals: 1-5 (#3), 10 (#1), 16-25 (#3), 31 (#3), 41-45 (#3), 60 (#1), 66-67 (#1), 69 (#1)

Multiplying Fractions by Whole Numbers Using Visual Fraction Models Multiplying Fractions by Fractions The Rectangle

www.cpalms.org Multiplying a Fraction by a Fraction

Real-World Fractions

https://www.illustrativemathematics.org/content-standards Conner and Makayla Discuss Multiplication

Folding Strips of Paper

Chavone’s Bathroom Tiles

Connecting the Area Model to Context

www.ixl.com/math/grade-5 M.12, M.13, M.14

https://learnzillion.com/ Lessons: Understand multiplying with fractions

Find a fraction of a whole number

Find the area of a rectangle with fractional side lengths

Apply multiplication of fractions to find area

Origo One Videos Exploring the Area Model of Fractions

51 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Critical Areas for Mathematics in Grade 5

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 (i.e., 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) Students apply their understanding of fractions and fraction models to represent the addition and subtraction of fractions with unlike

denominators. They develop fluency in calculating sums and differences of fractions, and make reasonable estimates of them. 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.)

(2) Students develop understanding of why division procedures work based on the meaning of base-ten numerals and properties of operations. They finalize fluency with multi-digit addition, subtraction, multiplication, and division. They apply their understandings of models for decimals, decimal notation, and properties of operations to add and subtract decimals to hundredths. They develop fluency in these computations, and make reasonable estimates of their results. 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. They compute products and quotients of decimals to hundredths efficiently and accurately.

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

52 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Grade 5 Major, Supporting, and Additional Work

Topic Title Major Work Supporting Work Additional Work

1 Understanding volume

5.MD.3.3, 5.MD.3.4

2 Developing multiplication and division strategies

5.NBT.2.5, 5.NBT.2.6

3 Using equivalency to add and subtract fractions with unlike denominators

5.NF.1.1, 5.NF.1.2

4 Expanding understanding of place value of decimals 5.NBT.1.1, 5.NBT.1.2,

5.NBT.1.3 (a)

5 Understanding the concept of multiplying fractions by fractions

5.NF.2.3, 5.NF.2.4

6 Comparing and rounding decimals

5.NBT.1.3, 5.NBT.1.4

7 Interpreting multiplying fractions as scaling

5.NF.2.5, 5.NF.2.6

8 Developing the concept of dividing unit fractions

5.NF.2.7

9 Solving problems involving volume

5.MD.3.5

10 Performing operations with decimals

5.NBT.2.7 5.MD.1.1

11 Classifying two-dimensional geometric figures

5.G.2.3, 5.G.2.4

12 Solving problems with fractional quantities 5.NF.2.7 5.MD.2.2

13 Representing algebraic thinking

5.OA.1.1, 5.OA.1.2

14 Exploring the coordinate plane

5.OA.2.3, 5.G.1.1, 5.G.1.2

15 Revisiting multiplication and division with whole numbers

5.NBT.2.5, 5.NBT.2.6

16 Revisiting expressions and exponents

5.NBT.1.2 5.OA.1.1, 5.OA.1.2

17 Revisiting operations on fractions with data presented in line plots

5.MD.2.2

18 Revisiting area of rectangles with fractional side lengths

5.NF.2.4 (b)

53 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Standards for Mathematical Practice Grade 5 students will:

1. Make sense of problems and persevere in solving them. (SMP.1) Mathematically proficient students in Grade 5 solve problems by applying their understanding of operations with whole numbers, decimals, and fractions including mixed numbers.

They solve problems related to volume and measurement conversions. Students seek the meaning of a problem and look for efficient ways to represent and solve it. They may

check their thinking by asking themselves, “What is the most efficient way to solve the problem?”, “Does this make sense?"

2. Reason abstractly and quantitatively. (SMP.2) Mathematically proficient students in Grade 5 recognize that a number represents a specific quantity. They extend this understanding from whole numbers to work with fractions and

decimals. This involves two processes- decontexualizing and contextualizing. Grade 5 students decontextualize by taking a real-world problem and writing and solving equations

based on the word problem. For example, consider the task, “There are 2 2/3 of a yard of rope in the shed. If a total of 4 1/6 yard is needed for a project, how much more rope is

needed?” Students decontextualize the problem by writing the equation 4 1/6 – 2 2/3 = ___ and then solving it. Further, students contextualize the problem after they find the answer,

by reasoning that 1 3/6 or 1 ½ yards of rope is the amount needed. Further, Grade 5 students write simple expressions that record calculations with numbers and represent or round

numbers using place value concepts.

3. Construct viable arguments and critique the reasoning of others. (SMP.3) Mathematically proficient students in Grade 5 construct arguments using representations, such as objects, pictures, and drawings. They explain calculations based upon models and

properties of operations and rules that generate patterns. They demonstrate and explain the relationship between volume and multiplication. They refine their mathematical

communication skills as they participate in mathematical discussions involving questions like “How did you get that?” and “Why is that true?” They explain their thinking to others and

respond to others’ thinking through discussions or written responses.

4. Model with mathematics. (SMP.4)

Mathematically proficient students in Grade 5 experiment with representing problem situations in multiple ways including numbers, words (mathematical language), drawing pictures,

using objects, making a chart, list, or graph, creating equations, etc. Students need opportunities to connect the different representations and explain the connections. They should

be able to use all of these representations as needed. Fifth graders should evaluate their results in the context of the situation and whether the results make sense. They also

evaluate the utility of models to determine which models are most useful and efficient to solve problems.

5. Use appropriate tools strategically. (SMP.5) Mathematically proficient students in Grade 5 consider the available tools (including estimation) when solving a mathematical problem and decide when certain tools might be

helpful. For instance, they may use unit cubes to fill a rectangular prism and then use a ruler to measure the dimensions. They use graph paper to accurately create graphs and

solve problems or make predictions from real world data.

6. Attend to precision. (SMP.6)

Mathematically proficient students in Grade 5 continue to refine their mathematical communication skills by using clear and precise language in their discussions with others and in

their own reasoning. Students use appropriate terminology when referring to expressions, fractions, geometric figures, and coordinate grids. They are careful about specifying units

of measure and state the meaning of the symbols they choose. For instance, when figuring out the volume of a rectangular prism they record their answers in cubic units.

7. Look for and make use of structure. (SMP.7)

Mathematically proficient students in Grade 5 look closely to discover a pattern or structure. For instance, students use properties of operations as strategies to add, subtract,

multiply and divide with whole numbers, fractions, and decimals. They examine numerical patterns and relate them to a rule or a graphical representation.

8. Look for and express regularity in repeated reasoning. (SMP.8)

Mathematically proficient students in Grade 5 use repeated reasoning to understand algorithms and make generalizations about patterns. Students connect place value and their prior work with operations to understand algorithms to fluently multiply multi-digit numbers and perform all operations with decimals to hundredths. Students explore operations with fractions with visual models and begin to formulate generalizations.

54 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Common Addition and Subtraction Situations Table

Result Unknown Change Unknown Start Unknown

Add to

Two bunnies sat on the grass. Three more bunnies hopped there. How many bunnies are on the grass now?

2 + 3 = ?

Two bunnies were sitting on the grass. Some more bunnies hopped there. Then there were five bunnies. How many bunnies hopped over to the first two?

2 + ? = 5

Some bunnies were sitting on the grass. Three more bunnies hopped there. Then there were five bunnies. How many bunnies were on the grass before?

? + 3 = 5

Take from

Five apples were on the table. I ate two apples. How many apples are on the table now?

5 – 2 = ?

Five apples were on the table. I ate some apples. Then there were three apples. How many apples did I eat?

5 - ? = 3

Some apples were on the table. I ate two apples. Then there were three apples. How many apples were on the table before?

? – 2 = 3

Total Unknown Both Addends Unknown1 Addend Unknown2

Put Together/

Take Apart

Three red apples and two green apples are on the table. How many apples are on the table?

3 + 2 = ?

Grandma has five flowers. How many can she put in her red vase and how many in her blue vase?

5 = ? + ? 5 = 0 + 5, 5 = 5 + 0 5 = 1 + 4, 5 + 4 + 1 5 = 2 + 3, 5 = 3 + 2

Five apples are on the table. Three are red and the rest are green. How many apples are green?

3 + ? = 5 5 – 3 = ?

Difference Unknown Bigger Unknown Smaller Unknown

Compare

“How many more?” version:

Lucy has two apples. Julie has five apples. How many more apples does Julie have than Lucy?

“How many fewer?” version:

Lucy has two apples. Julie has five apples. How may fewer apples does Lucy have than Julie?

2 + ? = 5 5 – 2 = ?

“More” version suggests operation:

Julie has 3 more apples than Lucy. Lucy has two apples. How many apples does Julie have?

“Fewer” version suggests operation:

Julie has three more apples than Lucy. Julie has five apples. How many apples does Lucy have?

“Fewer” version suggests wrong operation:

Lucy has three fewer apples than Julie. Lucy has two apples. How many apples does Julie have?

2 + 3 = ? 3 + 2 = ?

“More” version suggests wrong operation: Lucy has three fewer apples than Julie. Julie has five apples. How many apples does Lucy have?

5 – 3 = ? ? + 3 = 5

Darker shading indicates the four Kindergarten problem subtypes. Grade 1 and 2 students work with all subtypes and variants. Unshaded (white) problems are the four difficult subtypes or variants that students should work with in Grade 1 but need not master until Grade 2. Adapted from CCSS, p. 88, which is based on Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity, National Research Council, 2009, pp. 32–33.

1 This can be used to show all decompositions of a given number, especially important for numbers within 10. Equations with totals on the left help children understand that = does not always mean “makes” or “results in” but always means “is the same number as.” Such problems are not a problem subtype with one unknown, as is the Addend Unknown subtype to the right. These problems are a productive variation with two unknowns that give experience with finding all the decompositions of a number and reflecting on the patterns involved.

2 Either addend can be unknown; both variations should be included.

55 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Common Multiplication and Division Situations Table1

1 The first examples in each cell are examples of discrete things. These are easier for students and should be given before the measurement examples. 2 The language in the array examples shows the easiest form of array problems. A harder form is to use the terms rows and columns: The apples in the grocery window are in 3 rows and 6 columns. How many apples are in there? Both forms are valuable. 3 Area involves arrays of squares that have been pushed together so that there are no gaps or overlaps, so array problems include these especially important measurement situations. 4 Multiplicative Compare problems appear first in Grade 4, with whole-number values for A, B, and C, and with the “times as much” language in the table. In Grade 5, unit fractions language such as “one third as much” may be used. Multiplying and unit fraction language change the subject of the comparing sentence, e.g., “A red hat costs A times as much as the blue hat” results in the same comparison as “A blue hat

costs 1

𝑎 times as much as the red hat,” but has a different subject.

Unknown Product

Group Size Unknown (“How many in each group?” Division)

Number of Groups Unknown (“How many groups?” Division)

3 × 6 = ? 3 × ? = 18 and 18 ÷ 3 = ? ? × 6 = 18 and 18 ÷ 6 = ?

Equal Groups

There are 3 bags with 6 plums in each bag. How many plums are there in all? Measurement example. You need 3 lengths of string, each 6 inches long. How much string will you need altogether?

If 18 plums are shared equally into 3 bags, then how many plums will be in each bag? Measurement example. You have 18 inches of string, which you will cut into 3 equal pieces. How long will each piece of string be?

If 18 plums are to be packed 6 to a bag, then how many bags are needed? Measurement example. You have 18 inches of string, which you will cut into pieces that are 6 inches long. How many pieces of string will you have?

Arrays2, Area3

Unknown Product Unknown Factor Unknown Factor There are 3 rows of apples with 6 apples in each row. How many apples are there? Area example. What is the area of a 3 cm by 6 cm rectangle?

If 18 apples are arranged into 3 equal rows, how many apples will be in each row? Area example. A rectangle has area 18 square centimeters. If one side is 3 cm long, how long is a side next to it?

If 18 apples are arranged into equal rows of 6 apples, how many rows will there be? Area example. A rectangle has area 18 square centimeters. If one side is 6 cm long, how long is a side next to it?

Compare4

Larger Unknown Smaller Unknown Multiplier Unknown A blue hat costs $6. A red hat cost 3 times as much as the blue hat. How much does the red hat cost? Measurement example. A rubber band is 6 cm long. How long will the rubber band be when it is stretched to be 3 times as long?

A red hat costs $18 and that is 3 times as much as a blue hat costs. How much does the blue hat cost? Measurement example. A rubber band is stretched to be 18 cm long and that is 3 times as long as it was at first. How long was the rubber band at first?

A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue hat? Measurement example. A rubber band was 6 cm long at first. Now it is stretched to be 18 cm long. How many times as long is the rubber band now as it was at first?

Smaller Unknown 1

3 x 18 = ?

Larger Unknown 1

3 x ? = 6

Multiplier Unknown ? x 18 = 6

A red hat costs $18. A blue hat costs 1

3 as

much as the red hat. How much does the blue hat cost?

A blue hat costs $6 and that is 1

3 of the cost of a

red hat. How much does a red hat cost?

A red hat costs $18 and a blue hat costs $6. What fraction of the cost of the red hat is the cost of the blue hat?

General a × b = ? a × ? = p and p ÷ a = ? ? × b = p and p ÷ b = ?

56 Volusia County Schools Grade 5 Math Curriculum Map Mathematics Department July 2017

Grade 5 Math Curriculum Map July 2017