Overview

Module 4: Multiplication and Division of Fractions and Decimal Fractions

Topic A: Line Plots of Fraction Measurements: In topic A students compare line plots and explain how changing the accuracy of unit of measure affects the distribution of points to building foundation understanding of measurement, as well as growing conceptual knowledge of fractional relationships.

Topic B: Fractions as Division: Students will explore equal sharing area models to building understanding of how division of whole numbers relates to fractions and mixed numbers. Tape diagrams are used to provide linear models of real world problems involving fractions.

Topic C: Multiplication of a Whole Number by a Fraction: Students will interpret finding fractional sets (ex. 3/4 of 24) to build their understanding of how division by whole numbers is equivalent to multiplying by its reciprocal. Students will use the communicative property to relate repeated addition of fractions to multiplying fractions, ultimately reasoning through various strategies for multiplying fractions and whole numbers.

Topic D: Fraction Expressions and Word Problems: Students will learn to interpret numerical expressions (ex. 3 times the difference between 2/3 and 1/5), and generate word problems that lead to the same calculations. This will allow students to apply their new fraction knowledge into real world situations.

Topic E: Multiplication of a Fraction by a Fraction: Students use area models, rectangular arrays, and tape diagrams to model multiplication of two fractions (first unit fractions, then non-unit fractions). Students then build connections between dividing with whole numbers, fractions, and decimals, finding the intersection between all three.

Topic F: Multiplication with Fractions and Decimals as Scaling and Word Problems: Students build their understanding of multiplication to include scaling, using fractional relationships to denote size comparison. Fractions are limited to factors of 10, 100, or 1000. Students then apply the concepts to real-world scenarios.

Topic G: Division of Fractions and Decimal Fractions: Students use tape diagrams to build understanding of division of whole numbers by a unit fraction, and dividing a unit fraction by a whole number. From here, students are introduced to decimal fraction divisors and use equivalent fraction and place value thinking to reason about the side of quotients, calculate quotients, and sensibly place decimals in quotients.

Topic H: Interpretation of Numerical Expressions: Students use their knowledge from the previous topics to create and solve word problems involving both multiplication and division of fractions and decimal points.

Advanced Preparation:

- Personal white boards
- Fraction tiles

2016-2017 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

Week 1: February 6

Standards Addressed in Week's Lessons

Topic D

5.NF.A.1 (16)

5.NF.A.2 (16)

Topic A

5.MD.2 (1)

Topic B

5.NF.3 (2, 3, 4)

Standards Assessed in Assessment

End of Module

5.NF.A.1

5.NF.A.2

Notes:

Lesson 16

Tape diagrams continue to be an important tool throughout k-8 learning with Eureka math. Continue to assess student comfort in using these models to perform fraction problems. Emphasizing the "part to whole" language will be important for their understanding of ratios in 6th grade

One day this week is provided for End of Module Assessment

Lesson 1

This lesson builds knowledge for the entire unit. Do entire lesson. During CD and SD, emphasize that when we measure, this is usually an estimate, and is more accurate depending on how precise we are with our unit of measure.

Lesson 2

In CD, emphasize the 2 ways of sharing (using wholes and using equal parts) as well as the relationship between division and fractions. If short on time, do PS 1, 2, 4

Week 2: February 13

Assessment:

Biweekly 1:

Exit Ticket from Lesson 5

This lesson was chosen to give a view into student understanding of topic B before moving forward. It assesses students' ability to apply the learning of the first 5 lessons in a real world problem.

Notes:

Lesson 3

Look for students to start to transition from pictorial to conceptual understanding

Lesson 4 Omit

Omit lesson 4 and use tape diagrams to model fractions as division in lesson 5.

Lesson 5

Note the change in CD, make sure to teach the problem solving protocol, help students reason whether to use diagram or algorithm to solve, especially as they close this topic

Lesson 6

Emphasize the use of tape diagrams to build understanding of multiplying fractions, they will need this understanding in order to do lesson 7, and it also aligns to 6th grade concepts with ratios. Push students to PS #2 to build this understanding

Lesson 7

The use of tape diagrams is important in this lesson and beyond. For students who struggle with fine motor, or to save time, consider using graph paper in the personal white board or a sleeve protector to give a guide while making the tape diagrams. You may also need to provide concrete models, since this lesson requires finding fraction of whole numbers that are not a multiple of the denominator.

Standards Addressed in Week's Lessons

Topic B

5.NF.3 (5)

Topic C

5.NF.4a (6, 7, 8)

Week 3: February 20

Standards Addressed in Week's Lessons

Topic C

5.NF.4a (9)

Topic D

5.NF.4a (12)

5.NF.6 (12)

Notes:

Lesson 8

Consider continuing to use tape diagrams and models to assist students who need extra support. Build understanding between the difference when multiplying with a proper or improper fraction

Lesson 9

Students will use reference sheet from lesson 8

Lesson 10

If short on time, omit lesson 10. This lesson builds 5.OA.1, 2 to include writing expressions with fractions. However, this will not be assessed on A3 or A4

Week 4: February 27

Assessment:

Biweekly 2

Mid-Module Assessment (Given after lesson 12)

Administer the complete Mid-Module assessment. Use problem #6 from the Mid-Module as the data point for the biweekly #2. This problem assess students' ability to apply their learning into a real world problem and explain their thinking.

Notes:

Lesson 11 & 12 Combine.

They both use the word problem solving protocol. From lesson 11 include problems 1 and 4 as part of lesson 12. Use problems 4 and 5 on lesson 12 as challenge/extension problems for early finishers. Use exit ticket and problem set from lesson 12.

One day this week is provided to administer Mid Module assessment.

Lesson 13

Consider using concrete models to assist students if they are having challenges with pictorial models

Lesson 14

If students have solid understanding of lesson 13, consider omitting CD 1&2 for time

Standards Addressed in Week's Lessons

Topic D

5.NF.4a (12)

5.NF.6 (12)

Topic E

5.NF.4a (13, 14, 15)

5.NF.5b (14)

Standards Assessed in Assessment

Mid Module

5.OA.1

5.OA.2

5.NF.3

5.NF.4

5.NF.6

5.MD.1

5.MD.2

Week 5: March 6

Standards Addressed in Week's Lessons

Topic E

5.NF.6 (16, 19)

5.NBT.7 (17, 18)

5.MD.1 (19)

Notes:

Lesson 15

If students have good understanding of lesson 14, consider omitting CD 2&3 for time

Lesson 16

There is no AP for this lesson to allow time to teach the new method of using the tape diagram. Students can use PS #1 as the AP

Lessons 17

This lesson build connections back to the work in the first two modules, as well as connecting fractions and decimals. Teach lesson in it's entirety if possible. Work on finding estimates to help students reason the placement of the decimal point.

Lesson 18

This lesson build connections back to the work in the first two modules, as well as connecting fractions and decimals. Teach lesson in it's entirety if possible. Work on finding estimates to help students reason the placement of the decimal point.

Week 6: March 13

Module

Notes:

Lesson 19

Have centimeter rulers and meter sticks prepared for students to use to solve the problems. This will also help them transfer their learning of measurement into a real world context. You may consider posting a chart with common conversions to support students with their word problems

Lesson 20

If you haven't already done so, posting conversion charts in the room will support students in completing these problems. For students who struggle with basic conversions, you may consider giving these to them individually as a support, and assessing their ability to use the conversions in their completion of the problems. You may also consider a chart highlighting common abbreviations used for measurement.

Lesson 21 Omit

This lesson has been omitted for pacing considerations. Multiplying fractions will be continuously experienced throughout topic F. Use Sprint in lesson 22.

Lessons 22

Include fluency practice from omitted lesson 21.

Lesson 23

This lesson pushes for conceptual understanding, so consider spending more time on student discussion, building reasoning of how scale factors affect size of a model

Assessment:

Biweekly 3

Use exit ticket from Lesson 19

Standards Addressed in Week's Lessons:

Topic E

5.NF.6 (20)

Topic F

5.NF.5a (21, 22, 23)

5.NF.5b (21, 22, 23)

Week 7: March 20

Module

Notes:

Lesson 24

This lesson returns to the problem solving protocol, omitting AP

Lesson 25

This lesson builds the conceptual understanding of dividing fractions, so it will be helpful to use the paper models

*Only two lessons due to consideration of PARCC Administration

Assessment:

PARCC

Standards Addressed in Week's Lessons

Topic F

5.NF.5a (24)

5.NF.6 (24)

Topic G

5.NF.7a (25)

5.NF.7b (26)

5.NF.7c (27)

Week 8: March 27

Module

Topic

Notes:

Lesson 26

This lesson pushes students from concrete to pictorial understanding, where appropriate, emphasize the use of modeling

Lesson 27

This lesson returns to PS protocol. Emphasize SMP 3: Constructing viable arguments and critiquing the reasoning of others. Consider projecting student work and using that to build a discussion

Lesson 28 Omit

This lesson is largely review, so it may be omitted or used as a review, using the tape diagrams to deepen understanding

Lesson 29

This lesson is moving from understanding division with fractions to decimal fractions. Emphasize saying the decimals aloud to show the connection between decimals and fractions, and how many tenths and hundredths are in each number, which will help with lesson 30

One day this week provided for administering ANET test.

Assessment:

ANet

Standards Addressed in Week's Lessons

Topic G

5.NF.7b (29)

5.NF.7c (28)

5.NF.7 (30, 31)

Standards in Assessment

ANet

Major

5.NF.B.3

5.NF.B.4a

5.NF.B.5a

5.NF.B.5b

5.NF.B.6

5.NF.7a

5.NF.7b

5.NF.7c

Supporting

5.MD.2

Review

5.NBT.5

5.NBT.6

5.NBT.7

5.NF.1

5.NF.2

Week 9: April 3

Assessment:

End of Module Assessment

Administer after lesson 31

Standards Addressed in Week's Lessons

Topic G

5.NF.7b (29)

5.NF.7c (28)

5.NF.7 (30, 31)

Standards in Assessment

End of Module

5.OA.1

5.OA.2

5.NBT.7

5.NF.3

5.NF.4

5.NF.5

5.NF.6

5.NF.7

5.MD.1

5.MD.2

Notes:

Lesson 30

For time, consider only doing PS 1 and 2, since word problems will be taught in future lessons

Lesson 31

Consider teaching this lesson over two days. One day emphasize finding estimations of the answers, the second day finding exact answers.

Lessons 32 & 33 Omit

Omit for pacing consideration. If time showcase equivalent expression Problem Set questions during small group time.

One additional day is given to administer the End of Module Assessment.