Overview

Module 5: Fraction Equivalence, Ordering and Operations

Students build on their Grade 3 work with unit fractions as they explore fraction equivalence and extend this understanding to mixed numbers. This leads to the comparison of fractions an mixed numbers and the representation of both in a variety of models. Benchmark fractions play an important part in students’ ability to generalize and reason about relative fraction and mixed number sizes. Students then have the opportunity to apply what they know to be true for whole number operations to the new concepts of fraction and mixed number operations

Topic A: Decomposition and Fraction Equivalence

Topic B: Fraction Equivalence Using Multiplication and Division

Topic D: Fraction Addition and Subtraction

Topic E: Extending Fraction Equivalence to Fractions Greater Than 1

Topic F: Addition and Subtraction of Fractions by Decomposition

Topic G: Repeated Addition of Fractions as Multiplication

Topic H: Exploring a Fraction Pattern

Advanced Preparation

- Fraction strips (made from paper, folded, and used to model equivalent fractions)
- Rulers

Math Schedule of Assessed Standards (SAS)

Module Tip Sheet for Parents

These documents provide parents an opportunity to see what their children are learning in the current module including:

- Standards
- Key vocabulary
- Example Problems
- Pictorial Models
- Ideas for how to can help children at home
- Coherence of learning with past and future modules

For guides in Spanish, go here (Module 6 guide is unavailable)

Week 1: February 5

Standards Addressed in Week's Lessons

Topic B:

4.NF.1

4.NF.3b

Topic C:

4.NF.2

Notes:

Lesson 10

This lesson builds on Lesson 9. Students continue to use the area model and division to show the equivalence of two fractions. During the "Counting Fractions" fluency, couple numbers on the board with prepared visuals to support students who might struggle to keep up with this activity. During the Concept Development, allow students to share how they have drawn different area models, and be accepting of those that are mathematically correct.

Lesson 11

Explain fraction equivalence using a tape diagram and the number line, and relate that to the use of multiplication and division. The Application Problem in this lesson places equivalent fractions into a context that may be familiar to students. Multiple solution strategies are possible. The first solution models the equivalency learned in Lessons 7 and 8. The second solution uses number bonds to find unit fractions, reviewing Topic A content. Students need rulers for the Concept Development.

Lessons 12

Reason using benchmarks to compare two fractions on the number line. This lesson's Application Problem reviews equivalent fractions and bridges to today’s lesson, in which students use reasoning and benchmarks to compare fractions. Students need the number line template for the Application and Concept Development.

Lessons 13

This lesson builds on Lesson 12. Students continue to reason using benchmarks to compare two fractions on the number line. During the "Divide in Different Ways" fluency that reviews Module 3, you can choose to alternatively have students solve the division problems using any one of the three methods that works for them (place value disks, area model, standard algorithm). Students need blank number lines with midpoint (template) for the Concept Development.

Week 2: February 12

Assessment:

Bi-Weekly 1: Lesson 14 Exit Ticket

Standards Addressed in Week's Lessons

Topic C:

4.NF.2

Topic D:

4.NF.3ad

4.NF.1

4.MD.2

Notes:

Lessons 14

Find common units or number of units to compare two fractions. This objective is continued in Lesson 15. To accurately compare two fractions using a tape diagram, both tape diagrams must be the same length and aligned precisely. Providing a template of two blank parallel tape diagrams of equal length may be helpful in assisting students.

Lesson 15

This lesson is a continuation of Lesson 14. Students continue to find common units or number of units to compare two fractions. The "Counting by Equivalent Fractions" builds fluency and the progression builds in complexity. Work students up to the highest level of complexity at which they can confidently participate. During the Concept Development, consider modeling the two fractions with different denominators differently (one horizontally and one vertically) before decomposing to create a common unit.

Lesson 16

Use visual models to add and subtract two fractions with the same units. This lesson is a critical foundation for moving to Lesson 17, where students will subtract from one whole. This lesson's fluency activity "Comparing Fractions" is a direct review of the previous lesson. Students need blank number line (template) for the Concept Development.

Lesson 17

Use visual models to add and subtract two fractions with the same units, including subtracting from one whole. During the Concept Development, student modeling of subtraction and addition on the number line may vary slightly depending on how students solve. For example, students working below grade level may model counting down with an arrow representing a series of hops. Encourage part–whole thinking and modeling by means of modeling with the number bond before the number line, if beneficial.

Week 3: February 19

Notes:

Lesson 18

Add and subtract more than two fractions. One way to differentiate the "Counting by Equivalent Fractions" fluency activity for students working above grade level is to grant them more autonomy. Students may enjoy this as a partner activity in which students take turns leading and counting. Students can make individualized choices about when to convert larger units, counting forward and backward, and speed. Students need Adding and Subtracting Fractions practice sheet during Concept Development.

Lesson 19

Solve word problems involving addition and subtraction of fractions. The Concept Development in this lesson requires the Problem Set and suggests you follow this sequence to instruct: Model the Problem (in pairs, with two pairs working at the board), Calculate to Solve, Assess the Solution for Reasonableness.

Lesson 20

Part 1 of 2-part lesson. Use visual models to add two fractions with related units using the denominators 2, 3, 4, 5, 6, 8, 10, and 12. In Lessons 20 and 21, students add fractions with related denominators where one denominator is a factor of the other. Note on progression of standards: Because students are able to generate equivalent fractions (4.NF.1) from their work in Topics A, B, and C and are very familiar with the idea that units must be the same to be added, this work makes sense and prepares them well for work with decimals in Module 6 where tenths are converted to hundredths and added to hundredths

Week 4: February 26

Notes:

Lesson 21

Part 2 of 2-part lesson. Students continue to use visual models to add two fractions with related units using the denominators 2, 3, 4, 5, 6, 8, 10, and 12. Prioritize the last two debrief questions.

One day provided for Mid-Module Assessment after Lesson 21.

Lesson 22

Add a fraction less than 1 to, or subtract a fraction less than 1 from, a whole number using decomposition and visual models. During the "Counting by Equivalent Fractions" fluency, some learners may benefit from counting again and again until they gain fluency. You can also differentiate as suggested in Lesson 18 and let students above and below grade level work in partners with more autonomy over units, counting forward and backward, and speed.

Lesson 23

Add and multiply unit fractions to build fractions greater than 1 using visual models. During Concept Development, it might help to model drawing groups of 2 on the number line for the first example.

Standards Addressed in Week's Lessons

Topic D:

4.NF.3ad

4.NF.1

4.MD.2

Topic E:

4.NF.2

4.NF.3

4.MD.4

4.NBT.6

4.NF.1

4.NF.4a

Standards Assessed in Assessment

Mid-Module

4.NF.1

4.NF.2

4.NF.3abd

4.NF.4a

Standards from Week's Lessons not Assessed before ANet

4.NF.3

4.MD.4

4.NBT.6

4.NF.1

Week 5: March 5

Standards Addressed in Week's Lessons

Topic E:

4.NF.2

4.NF.3

4.MD.4

4.NBT.6

4.NF.1

4.NF.4a

Notes:

Lesson 24

Part 1 of 2-part lesson. Decompose and compose fractions greater than 1 to express them in various forms. During Concept Development, some learners may need explicit instructions for counting by 3 thirds and later by 5 fifths. It might be helpful to scaffold the count by directing students to first count by threes. Then, have them count by 3 thirds. If needed, do the same for counting by 5 fifths.

Lesson 25

Part 2 of 2-part lesson. Students continue to decompose and compose fractions greater than 1 to express them in various forms. This Application Problem builds on Lesson 24 where students learned to convert a fraction to a mixed number. Knowing how to make this conversion leads to today’s lesson in which students use what they know about mixed numbers to convert to a fraction greater than 1.

Lesson 26

Compare fractions greater than 1 by reasoning using benchmark fractions. During the Concept Development, it might help to scaffold questioning to convert fraction to mixed number (see notes directly in lesson guide for question examples).

Lesson 27

Compare fractions greater than 1 by creating common numerators or denominators. Because precision in modeling is critical when comparing, it may be helpful to provide aligned parallel tape diagram templates of equal length that students can partition.

Week 6: March 12

Module

Notes:

Lesson 28

Solve word problems with line plots. The Problem Set is used in the Concept Development. Scaffold the word problems on the Problem Set for students working below grade level with questioning. For example, for Problem 2(d) ask, “What was the longest distance run? The shortest? What is the difference, in miles, between the longest and shortest distance run?” Additionally, students may benefit from organizing data in a table before solving Problem 2(b).

Lesson 29 Omit

This lesson focuses on estimation. For pacing considerations, we suggest skipping this lesson and embedding estimation into your regular questioning during the Application Problem, Concept Development and Student Debrief as much as possible during other lessons.

Lesson 30

Add a mixed number and a fraction. Consider preceding the "Compare Fractions" fluency activity with a counting by fifths, thirds, and fourths activity to increase student confidence and participation.

Lesson 31

Add mixed numbers. Prioritize questions 1, 4 and 5 in the Student Debrief.

Lesson 32

Subtract a fraction from a mixed number. Students who struggle during this lesson might be better off working with the decomposition that will be modeled in Lesson 34 since it most closely resembles regrouping with whole number subtraction.

Assessment:

Biweekly 3: Lesson 30 Exit Ticket

Standards Addressed in Week's Lessons

Topic E:

4.NF.2

4.NF.3

4.MD.4

4.NBT.6

4.NF.1

4.NF.4a

Topic F:

4.NF.3c

4.MD.2

Week 7: March 19

Module

Topic

Notes:

*Only two lessons due to consideration of PARCC Administration

Lesson 33: Subtract a mixed number from a mixed number. A note on the progression of standards: student use of the ten in Grade 1 has evolved into a place value strategy in Grade 2. Here in Grade 4, it evolves yet again as students use fractional units rather than place value units.

Lesson 34: Subtract mixed numbers. The strategy presented in the Concept Development involves the decomposition of a higher value unit, the same process used in the standard algorithm when 8 tens 1 one would be renamed as 7 tens 11 ones to subtract 2 tens 8 ones. This connection is made in the Debrief. Students who struggle with this strategy may benefit from calling out the connection sooner if their understanding of renaming with whole number subtraction has a conceptual foundation.

Assessment:

PARCC

Standards Addressed in Week's Lessons

Topic F:

4.NF.3c

4.MD.2

Week 8: April 2

Module

Topic

Notes:

*Only three lessons due to ANet

Lesson 35

Part 1 of 2-part lesson. Represent the multiplication of n times a/b as (n × a)/b using the associative property and visual models. During the "Add and Subtract" fluency, some learners may benefit from using grid paper or a place value chart to organize numbers up to 1 million as they add and subtract.

Lesson 36

Part 2 of 2-part lesson. Students continue to represent the multiplication of n times a/b as (n × a)/b using the associative property and visual models. Adjust the Application Problem to challenge students working above grade level. For example, ask, “How many total hours and minutes did Rhonda exercise?”

Lesson 37

Part 1 of 2-part lesson. Find the product of a whole number and a mixed number using the distributive property. During Concept Development, grid paper may help learners draw appropriately proportioned, though not meticulously precise, tape diagrams.. For example: the bar for 3 should be longer than the bar 1/5.

Assessment:

ANet

Standards Addressed in Week's Lessons

Topic G:

4.NF.4

4.OA.2

4.MD.2

4.MD.4

Standards Assessed in Assessment

ANet

Major

4.NF.A.1

4.NF.A.2

4.NF.B.3

4.NF.B.4

Supporting

4.MD.B.4

Review

4.NBT.B.5

4.NBT.B.6

4.OA.A.3

Week 9: April 9

Assessment:

End-of-Module Assessment

Standards Addressed in Week's Lessons

Topic G:

4.NF.4

4.OA.2

4.MD.2

4.MD.4

Topic H:

4.OA.5

Standards Assessed in Assessment

End of Module

4.OA.5

4.NF.1

4.NF.2

4.NF.3

4.NF.4

4.MD.4

Notes:

Lesson 38 Omit

This whole lesson reviews Lesson 37.

Lesson 39

Solve multiplicative comparison word problems involving fractions. As in Lesson 19 of this module, this lesson's Concept Development requires the Problem Set and suggests you follow this sequence to instruct: Model the Problem (in pairs, with two pairs working at the board), Calculate to Solve, Assess the Solution for Reasonableness.

Lesson 40

Solve word problems involving the multiplication of a whole number and a fraction including those involving line plots. The Concept Development requires the Problem Set and suggests you follow the same sequence to walk through the problems as in the lesson prior, debriefing as you go.

Lesson 41 Omit

This is a pattern lesson on adding all fractions within 1. It is a good exploration and opportunity for students to critique the reasoning of others, but it is not crucial for the new content and has been omitted for pacing considerations.

One day provided for End-of-Module Assessment after Lesson 40.