Unit 5.3: Addition and Subtraction of Decimals and Fractions

Big Idea: The effects of the operations of addition and subtraction with decimals and fractions are the same as those with whole numbers.

Unless otherwise noted, SFUSD Math Core Curriculum is licensed under the Creative Commons Attribution 4.0 International License

Teacher-facing pages are green

Student-facing pages are white

notes for teachers are in the speaker notes

How to Use this Slide Deck

This slide deck contains all of the slides that can be adapted for teaching �Unit 5.3 live on Zoom.

5 lessons have been adapted for Unit 5.3. Each lesson can be taught over the course of two days.

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Important symbols

This slide deck is intended to be used during a synchronous class on Zoom. Teachers should use the Zoom Share Screen function so students see the slide deck. At different points in the lesson, the slide deck SHOULD be in Presentation Mode. At other times, the slide deck should NOT be in Presentation Mode so that the teacher can type directly onto a slide and/or model how to use digital manipulatives.

When a slide should be shown in Presentation Mode, �you will see this symbol →

When a slide has animations that the teacher can click through to reveal, you will see this symbol →

When a slide should NOT be in Presentation Mode, �you will see this symbol →

Table of Contents

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Use the links below to navigate to the lesson materials you need.

Table of Contents

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Use the links below to navigate to the lesson materials you need.

Entrance Slides

Teachers can use these slides to project at the beginning of Zoom class.

Welcome to Math Class

We will be starting in a few minutes!

To prepare for class, you can do the following:

• Make sure you’re in a comfortable place to do math work�
• Have a pair of headphones ready if you need them�
• Go to the bathroom before we start

Zoom Norms

• Encouraged to have cameras on

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• Mics generally off to avoid background noise; we’ll let you know when to turn mics on

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• We will be using the chat. If you have questions you can type them into the chat

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• Use other functions like raising hand as needed

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Math Norms

10

Errors are gifts that promote discussion.

Answers are important, but they are not the math.

Talk about each other’s thinking.

Ask questions until ideas make sense.

Use multiple strategies and multiple representations.

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SAN FRANCISCO UNIFIED SCHOOL DISTRICT

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Optional Tech Lesson

Using a digital Base 10 blocks

How to Use Digital Base 10 Blocks

Description: Some of the lessons in this unit require students to show their thinking using Base 10 blocks.

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Teachers might decide that students will draw the Base 10 blocks on paper and take a picture of their work. In that case, teachers might consider assigning this lesson S to students, which goes over how to take a picture and insert it into Google Slides.

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This lesson shows students how to use the Base 10 blocks app from Math Learning Center and copy and paste a screenshot of their work.

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Lesson Description

This lesson can be taught in one class period or combined with part of Lesson 1, which should be taught over the course of two days to allow students enough time to fully engage with the core math.

The following slides provide suggestions for how to adapt the Launch, Explore, and Summarize parts of the lesson for either synchronous or asynchronous teaching.

Lesson Description

Lesson Description

Lesson Description

Objective

In this lesson, you will be able to:

• learn how to use digital Base 10 blocks,�
• copy your work, �
• and paste it into a slide deck.

How to Use the Base 10 blocks app

Teacher either models how to use the app or shows this video

Teachers can assign this slide deck for students to complete the Explore

Activity Reflection

What did you like about using the digital Base 10 blocks?

What was difficult about using the digital Base 10 blocks?

Optional Tech Lesson

Using a Number line app

How to Use a Digital Number Line

Description: Some of the lessons in this unit require students to show their thinking using a number line.

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Teachers might decide that students will draw the number lines on paper and take a picture of their work. In that case, teachers might consider assigning this lesson S to students, which goes over how to take a picture and insert it into Google Slides.

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This lesson shows students how to use the Number line app from Math Learning Center and copy and paste a screenshot of their work.

Lesson Description

This lesson can be taught in one class period or combined with part of Lesson 1, which should be taught over the course of two days to allow students enough time to fully engage with the core math.

The following slides provide suggestions for how to adapt the Launch, Explore, and Summarize parts of the lesson for either synchronous or asynchronous teaching.

Lesson Description

Lesson Description

Lesson Description

Objective

In this lesson, you will be able to:

• learn how to use a web based number line,�
• copy your work, �
• and paste it into a slide deck.

How to Use the Number line App

Teacher either models how to use the app or shows this video

Teachers can assign this slide deck for students to complete the Explore

Activity Reflection

What did you like about using the web based number line?

What was difficult about using the web based number line?

Lesson 1

Adapted from 5.3 Entry Task

Adapted from 5.3 Entry Task

Core math: Decimal place value is an extension of whole number place value.

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Description: Students add decimals using base-10 blocks and an open number line. They estimate the sum of two decimals by rounding and using friendly numbers.

CCSS-M Standard(s)

Operations and Algebraic Thinking

Write and interpret numerical expressions.

5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 +921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

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Number and Operations in Base Ten

Perform operations with multi-digit whole numbers and with decimals to hundredths.

5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

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Lesson Description

This lesson should be taught over the course of two days to allow students enough time to fully engage with the core math.

The following slides provide suggestions for how to adapt the Launch, Explore, and Summarize parts of the lesson for either synchronous or asynchronous teaching.

Teachers can decide how they divide up the lesson over the two days.

Teachers can supplement with other activities or routines like Math Talks (Spanish).

Lesson 1 Description

Lesson 1 Description

Lesson 1 Description

Options for Continuing Activities

• Entry Task HW S. C.
• Tools for HW .S. C.
• This is a duplicate of Tools for CW; it provides visuals and tools that will help students with homework in this unit.

Objective

Today we are starting a unit on addition and subtraction of decimals and fractions. We will add decimals using tools that are familiar to us: base-10 blocks and an open number line.

Today’s Problem

There are 2 hiking loops in McLaren Park. One is 1.5 miles and one is 2.7 miles. If you hiked both trails, how many miles would you walk?

15

27

Compare and Contrast

There are 2 hiking loops in McLaren Park. One is 1.5 miles and one is 2.7 miles. If you hiked both trails, how many miles would you walk?

There are 2 hiking loops in McLaren Park. One is 15 miles and one is 27 miles. If you hiked both trails, how many miles would you walk?

Whole Numbers and Decimals

How is adding whole numbers the same as adding decimal numbers? ��How is it different?

Solving Today’s Problem

There are 2 hiking loops in McLaren Park. One is 1.5 miles and one is 2.7 miles. If you hiked both trails, how many miles would you walk?

1 whole

1 tenth

1 hundredth

Re-unitizing

There are 2 hiking loops in McLaren Park. One is 1.5 miles and one is 2.7 miles. If you hiked both trails, how many miles would you walk?

Which blocks would we use to represent 1.5 miles?

1 whole

5 tenths

Re-unitizing

There are 2 hiking loops in McLaren Park. One is 1.5 miles and one is 2.7 miles. If you hiked both trails, how many miles would you walk?

Which blocks would we use to represent 2.7 miles?

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2 wholes

7 tenths

Teachers can assign this slide deck for students to complete the Explore

What problem is represented by this number line? �How do you know?

Whole Numbers and Decimals

How is adding whole numbers the same as adding decimal numbers? ��How is it different?

Lesson 2

Adapted from 5.3 Lesson Series 1, Day 1

Adapted from 5.3 Lesson Series 1, Day 1

Core math: The effects of the operations of addition and subtraction with decimals are the same as those with whole numbers.

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Description: Students add and subtract decimals in a money context, using base-10 blocks and recording their work.

CCSS-M Standard(s)

Number and Operations in Base Ten

Perform operations with multi-digit whole numbers and with decimals to hundredths.

5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Lesson Description

This lesson should be taught over the course of two days to allow students enough time to fully engage with the core math.

The following slides provide suggestions for how to adapt the Launch, Explore, and Summarize parts of the lesson for either synchronous or asynchronous teaching.

Teachers can decide how they divide up the lesson over the two days.

Teachers can supplement with other activities or routines like Math Talks (Spanish).

Lesson 2 Description

Lesson 2 Description

Lesson 2 Description

Options for Continuing Activities

• Day 1 HW S. C.

Objective

Today we will add and subtract decimals in a money context, using base-10 blocks to represent this.

Representing Decimals

How can you represent $0.47 more efficiently? ��How many different coin combinations can you make that would equal $0.47?��How many more do you need to make a whole (dollar)?

Representing Decimals

How can you represent $0.47 more efficiently? ��How many different coin combinations can you make that would equal $0.47?��How many more do you need to make a whole (dollar)?

Example Modeling:

How would we represent $2.34?

Note:

At this point the teacher should model the next problem using the Math Learning Center Base 10 Blocks App. The first problem was modelled on Google Slides so that students could see the place value mat.

When the teacher models the next problem, they should remind students of the quantity that each block represents.

See this video as an example.

Representing subtraction

How would we represent a problem like $5.23 – $2.40?

We are going to represent this problem using the app that you used in the previous lesson.

We’ll see some features of the app that make subtracting Base 10 blocks a little bit more efficient.

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Teachers can assign this slide deck for students to complete the Explore

• “I wonder …” �
• “I don’t understand…”�
• “How did you …?”

Ask questions until ideas make sense.

Whole Numbers and Decimals

How is adding/subtracting whole numbers the same as adding/subtracting decimal numbers? ��How is it different?

Is the student correct?

Belinda said that �$0.52 + $0.3 = $0.55. ��Is she correct? ��How do you know?

Example: Modeling with Base 10 Blocks

Lesson 3

Adapted from 5.3 Lesson Series 1, Day 2

Adapted from 5.3 Lesson Series 1, Day 2

Core math: The effects of the operations of addition and subtraction with decimals are the same as those with whole numbers.

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Description: Students add and subtract decimals to solve a puzzle, using base-10 blocks and an open number line and recording their work.

CCSS-M Standard(s)

Number and Operations in Base Ten

Perform operations with multi-digit whole numbers and with decimals to hundredths.

5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

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Lesson Description

This lesson should be taught over the course of two days to allow students enough time to fully engage with the core math.

The following slides provide suggestions for how to adapt the Launch, Explore, and Summarize parts of the lesson for either synchronous or asynchronous teaching.

Teachers can decide how they divide up the lesson over the two days.

Teachers can supplement with other activities or routines like Math Talks (Spanish).

Lesson 3 Description

Lesson 3 Description

Lesson 3 Description

Options for Continuing Activities

• Day 2 Three Read HW S. C.

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Apprentice Task

• Book Catalog BLM S. C.
• Book Club Shopping Order .S. C.
• Apprentice HW S. C.

Objective

Today we will add and subtract decimals to solve a puzzle, using base-10 blocks and an open number line.

Magic Square

To this Magic Square, the magic number is 9.0

The sum of every row, column, and diagonal is 9.0

What strategies could we use to find the value of the ?

Visualizing Our Thinking.

To solve for the value of the ? we can use base 10 blocks or an open number line.

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Teachers can assign this slide deck for students to complete the Explore

Is the student correct? How do you know?

To solve for the next missing number, Elsa wrote wrote the following:

First need to add 9.00 + 6.

9.00 + 6 = 9.06

Then we need to subtract 11.25 - 9.06 to find the missing number.

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Lesson 4

Adapted from 5.3 Lesson Series 2, Day 1

Adapted from 5.3 Lesson Series 2, Day 1

Core math: When two fractions are equivalent, they name the same number.

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Description: Students create fraction kits to review part-to-whole relationships and equivalent fractions. Students use their kits to visualize addition and subtraction of fractions with different denominators.

CCSS-M Standard(s)

Number and Operations—Fractions�Use equivalent fractions as a strategy to add and subtract fractions.

• 5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

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Lesson Description

This lesson should be taught over the course of two days to allow students enough time to fully engage with the core math.

The following slides provide suggestions for how to adapt the Launch, Explore, and Summarize parts of the lesson for either synchronous or asynchronous teaching.

Teachers can decide how they divide up the lesson over the two days.

Teachers can supplement with other activities or routines like Math Talks (Spanish).

Lesson 4 Description

Lesson 4 Description

Lesson 4 Description

Options for Continuing Activities

• Day 1 HW S. C.
• Extension Fraction Kit Games Add Up and Take Down BLM S. C.

Objective

Today we will use digital fraction kits.

You might have built fraction kits in 3rd or 4th grade. There are actually some fraction kits that exist online! So this year we will use these kits to models adding, subtracting, multiplying, and dividing fractions.

What do you notice? What do you wonder?

Example Modeling:

Using the Online Fraction Kit

Teachers can assign this slide deck for students to complete the Explore

Equivalent Fractions

What do you notice about the size of the ⅛ pieces in comparison to the ¼ piece?

Equivalent Fractions

What patterns do you see in the table?

Equivalent Fractions

How can we prove that ¼ = 2/8?

Lesson 5

Adapted from 5.3 Lesson Series 2, Day 2

Adapted from 5.3 Lesson Series 2, Day 2

Core math: Fractions with unlike denominators can be renamed as equivalent fractions with like denominators to add and subtract. Equivalent fractions can be generated by multiplying or dividing the numerator and denominator by the same number.

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Description: Students add and subtract fractions with like and unlike denominators using fraction kits, and record their work with an equivalent fraction written method.

CCSS-M Standard(s)

Number and Operations—Fractions

Use equivalent fractions as a strategy to add and subtract fractions.

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• 5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

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• 5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < ½.

Lesson Description

This lesson should be taught over the course of two days to allow students enough time to fully engage with the core math.

The following slides provide suggestions for how to adapt the Launch, Explore, and Summarize parts of the lesson for either synchronous or asynchronous teaching.

Teachers can decide how they divide up the lesson over the two days.

Teachers can supplement with other activities or routines like Math Talks (Spanish).

Lesson 5 Description

Lesson 5 Description

Lesson 5 Description

Options for Continuing Activities

• Day 2 Situation HW S. C.
• Pizza With Friends Assessment S. C.
• This assessment is the first part of an FAL (Formative Assessment Lesson) called Pizza with Friends. This can be assigned for asynchronous completion.
• Students will complete the second part in Lesson 6.
• For more information about FALs, see the MTT at www.sfusdmath.org/formative-assessment-lessons

In 4th grade math…

In 4th grade math, you learned how to add fractions with like (same) denominators.

2/4

1/4

+

3/4

=

Review

How would we add these fractions together?

3/8

2/8

+

5/8

=

Unlike Fractions

Now we are going to try adding unlike fractions. What would be your strategy here?

3/8

1/4

+

?

=

Objective

Today we will add and subtract fractions with like and unlike denominators using fraction kits. We will also record our work with the equivalent fraction written method.

Example Modeling:

Unlike Fractions

Now are are going to solve this problem with a fraction kit.

3/8

1/4

+

?

=

Teachers can assign this slide deck for students to complete the Explore

Talk about each other’s thinking.

Here is an example of an estimate one student provided.

What was the student thinking here? How would they have gotten the estimate ¾ ?

Talk about each other’s thinking.

Here is an example of a solution one student provided.

What was this student’s strategy?

Does it always work?

Is it easy?

Is it efficient?

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Talk about each other’s thinking.

Here is an example of a solution one student provided.

What was the student thinking here?

What suggestions would you give this student?

Lesson 6

Adapted from 5.3 Lesson Series 2, Day 5

Adapted from 5.3 Lesson Series 2, Day 5

Core math: Fractions with unlike denominators can be rewritten as equivalent fractions with like denominators to add and subtract.

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Description: Students work in pairs to match word problems and two fraction models. After a whole class debrief, students return to their original assessment task and revise their responses.

CCSS-M Standard(s)

Number and Operations—Fractions

Use equivalent fractions as a strategy to add and subtract fractions.

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• 5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

​

• 5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < ½.

Lesson Description

This lesson should be taught over the course of two days to allow students enough time to fully engage with the core math.

The following slides provide suggestions for how to adapt the Launch, Explore, and Summarize parts of the lesson for either synchronous or asynchronous teaching.

Teachers can decide how they divide up the lesson over the two days.

Teachers can supplement with other activities or routines like Math Talks (Spanish).

Lesson 6 Description

Lesson 6 Description

Lesson 6 Description

Options for Continuing Activities

• Day 5 Subtracting Fractions HW S. C
• If teachers had assigned Pizza With Friends Assessment S. C, they can return the assignment to students and have them revise their work.

Example Modeling

Pizza With Friends

Jack and Ellen ordered five whole pizzas for their class party. The shaded region below shows the amount of pizza left after the party.

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Pizza With Friends

Jack and Ellen ordered five whole pizzas for their class party. The shaded region below shows the amount of pizza left after the party.

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​

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What fractions represent the amounts of pizza left over?

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​

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¼

⅙

⅙

⅙

⅙

Pizza With Friends

Jack and Ellen ordered five whole pizzas for their class party. The shaded region below shows the amount of pizza left after the party.

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​

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Ellen predicts that there is one whole pizza left over for them to share.

What strategies could we use to determine if Ellen is correct?

​

​

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¼

⅙

⅙

⅙

⅙

Objective

Today you will match word problems to two fraction models.

You’ll then be able to use this models to compare, add, and subtract fractions with unlike denominators.

Example Modeling:

Before assigning the Explore activity to students, the teacher should modeling how students are expected to show their work by completing Problem #1 with the class.

This Explore activity requires students to cut/paste images and to use hyperlinks to navigate between slides.

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Shaded pieces

In all of the models that you will see in the Explore, the SHADED parts all represent the amount that was eaten.

This is different from how we just visualized the previous problem.

Check for Understanding

Alex and Laura each bought their own pizza. Alex ate ⅓ of his, and Laura ate ¼ of hers.

Which visual representation matches this scenario?

Remember, the SHADED parts all represent the amount that was eaten.

Check for Understanding

Jose and Maria each bought their own pizza. Jose ate ⅔ of his, and Maria ⅚ ate of hers.

Which visual representation matches this scenario?

Remember, the SHADED parts all represent the amount that was eaten.

Teachers can assign this slide deck for students to complete the Explore

Talk about each other’s thinking.

What did this student understand about the problem?

Talk about each other’s thinking.

How could this student find exactly how much pizza Fiona ate?

Example Summarize

Lesson 7

Adapted from 5.3 Lesson Series 2, Day 6

Adapted from 5.3 Lesson Series 2, Day 6

Core math: Fractions with unlike denominators can be rewritten as equivalent fractions with like denominators to add and subtract. Fractions can be compared using greater than, less than, or equal to.

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Description: Students play the Fraction Equations Game. They determine the best placement of 8 fractions to form 3 equations (addition, subtraction, and comparison).

CCSS-M Standard(s)

Number and Operations—Fractions

Use equivalent fractions as a strategy to add and subtract fractions.�

• 5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)�
• 5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < ½.

Lesson Description

This lesson should be taught over the course of two days to allow students enough time to fully engage with the core math.

The following slides provide suggestions for how to adapt the Launch, Explore, and Summarize parts of the lesson for either synchronous or asynchronous teaching.

Teachers can decide how they divide up the lesson over the two days.

Teachers can supplement with other activities or routines like Math Talks (Spanish).

Lesson 7 Description

Lesson 7 Description

Lesson 7 Description

Options for Continuing Activities

• Day 6 Three Read HW S. C.

Objective

Today we will play a game that involves:

• adding and subtracting fractions with �like denominators �
• adding and subtracting fractions with unlike denominators �
• and comparing fractions.

+

+

<

=

=

Fraction Equations

Game directions:

• Spin a series of spinners to generate 8 different fractions. �
• Place as many of those 8 fractions in the blank squares to make true equations. �
• Show how you knew that those 8 fractions were correctly placed into the blank squares.

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Example Modeling

Using the Digital Spinners

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My 8 Fractions

Our goal is to use the fractions above to create a true addition statement, subtraction statement, and comparison statement.

What would be your strategy for accomplishing this?

Example Modeling

Should students need support in coming up with a strategy for attempting this activity, teachers might consider modeling how to create equivalent fractions.

Teachers might remind students to use their (digital) fraction kits to help them with this.

Showing Your Thinking

Today you’ll be completing your work on a piece of paper and taking a picture of it to upload onto Google Slides.

Example Modeling

Should students need support in organizing their work on a piece of paper or in understanding how to get started, teachers might do a think aloud of how they would have used the fractions they got from the spinner to complete this task.

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Showing Your Thinking

On your piece of paper, make sure you include the following:

• The 8 fractions that you got from the spinners
• Calculations and/or models that demonstrate how you thought about adding, subtracting, and comparing the fractions

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Teachers can assign this slide deck for students to complete the Explore

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Teachers should tell students that they will complete this task on a piece of paper and upload a picture. If students have not yet practiced this skill of taking photos and uploading it into Google Slides, teachers might consider assigning this lesson. S

Talk about each other’s thinking.

This student was able to use 5 of their 8 fractions to create two statements.

How can we prove that the student’s two statements are correct?

Talk about each other’s thinking.

This student says that the remaining fractions of 11/6, 1/16, and 5/8 cannot be used to make a true statement.

Do you agree with this student? Why or why not?

Lesson 8

Adapted from 5.3 Lesson Series 3, Day 1

Adapted from 5.3 Lesson Series 3, Day 1

Core math: Mixed numbers are fractions that are greater than a whole and are written as a composite of a whole number part and a fractional part. Mixed numbers can be added by adding the whole parts and the fractional parts separately, or by using equivalent fractions greater than one.

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Description: Students add mixed numbers with like and unlike denominators using strategies they developed in the previous lesson series, and thinking of mixed numbers as a combination of a whole and a fraction.

CCSS-M Standard(s)

Number and Operations—Fractions

Use equivalent fractions as a strategy to add and subtract fractions.�

• 5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)�
• 5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < ½.

Lesson Description

This lesson should be taught over the course of two days to allow students enough time to fully engage with the core math.

The following slides provide suggestions for how to adapt the Launch, Explore, and Summarize parts of the lesson for either synchronous or asynchronous teaching.

Teachers can decide how they divide up the lesson over the two days.

Teachers can supplement with other activities or routines like Math Talks (Spanish).

Lesson 8 Description

Lesson 8 Description

Lesson 8 Description

Options for Continuing Activities

• Fraction Grab HW S. C.
• Fraction Grab Gameboard HW S. C.

Amounts less than 1 whole

So far in this unit, we have worked on adding and subtracting quantities less than 1 whole.

We describe these quantities that are less than 1 whole as fractions.

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How much water?

How would you describe the total amount of water represented in this picture?

We might represent this amount of water as 1 ¼ or 5/4.

Objective

Today we will think of mixed numbers as a combination of a whole number and a fraction.

We will add mixed numbers with like and unlike denominators using strategies from previous lessons.

1 ¼

Animations in this Lesson

The Launch for this lesson includes several animations.

In this video, you’ll see when animations should appear in the class discussion.

For the questions that appear throughout the Launch, teachers should provide wait time for students to think to themselves and then solicit responses from students.

Today’s Problem

A recipe calls for 1¼ cups of white flour and 2¼ cups of whole wheat flour. How much flour is that all together?

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Today’s Problem

A recipe calls for 1¼ cups of white flour and 2¼ cups of whole wheat flour. How much flour is that all together?

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1 + 2 = 3 whole cups

1/4 + 1/4 = 2/4 cup

3 ²/4 cups

Another Mixed Number Problem

How could we find the total amount of water represented here?

2

3

2

3

2 + 3 = 5 whole cups

3/8 + 6/8 = 9/8 cups

5 ⁹/8 cups

Is there a different way we can represent the same quantity of 5 ⁹/8 ?

5 ⁹/8 cups

What would happen if we combined the 3/8 cup of water�with the 6/8 cup of water?

What would happen if we combined the 3/8 cup of water�with the 6/8 cup of water?

We would have another whole cup and ¹/8, which we can represent as 1¹/8.

5 ⁹/8 cups

6 ¹/8 cups

Two Ways of Writing Mixed Numbers

In the Explore today, you will be adding together mixed numbers.

As we just saw, there is more than one way to write a mixed number that represents the same quantity.

5 ⁹/8 cups

6 ¹/8 cups

is the same as

Teachers can assign this slide deck for students to complete the Explore

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Teachers should tell students that they will complete this task on a piece of paper and upload a picture. If students have not yet practiced this skill of taking photos and uploading it into Google Slides, teachers might consider assigning this lesson. S

Errors are gifts that promote discussion.

This student has some thinking that is correct and some thinking that is not. ��What does the student understand well?

Where has the student made an error?

Errors are gifts that promote discussion.

This student has some thinking that is correct and some thinking that is not. ��What does the student understand well?

Where has the student made an error?

Lesson 9

Adapted from 5.3 Lesson Series 3, Day 2

Adapted from 5.3 Lesson Series 3, Day 2

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Core math: Mixed numbers are fractions that are greater than a whole and are written as a composite of a whole number part and a fractional part. Mixed numbers can be subtracted by subtracting the whole parts and the fractional parts separately, or by using equivalent fractions greater than one.

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Description: Students explore different ways to express a fraction that is more than one whole, and use this to subtract fractions with unlike denominators that require regrouping.

CCSS-M Standard(s)

Number and Operations—Fractions

Use equivalent fractions as a strategy to add and subtract fractions.

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• 5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)�
• 5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < ½.

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Lesson Description

This lesson should be taught over the course of two days to allow students enough time to fully engage with the core math.

The following slides provide suggestions for how to adapt the Launch, Explore, and Summarize parts of the lesson for either synchronous or asynchronous teaching.

Teachers can decide how they divide up the lesson over the two days.

Teachers can supplement with other activities or routines like Math Talks (Spanish).

Lesson 9 Description

Lesson 9 Description

Lesson 9 Description

Options for Continuing Activities

• Day 2 HW S. C.

Equivalent Mixed Numbers

In the previous lesson, we saw that we can represent the same quantity with equivalent mixed numbers.

Let’s review how 5 ⁹/8 is equivalent to 6¹/8.

5 ⁹/8 cups

6 ¹/8 cups

is the same as

Equivalent Mixed Numbers

How do you see 5 ⁹/8 in this model?

Equivalent Mixed Numbers

How do you see 6 ¹/8 in this model?

Equivalent Mixed Numbers

How do you see 6 ¹/8 in this model?

More Equivalent Mixed Numbers

What are other ways that we could break up these circles to create fractions or mixed numbers that are equivalent to 4 ¹/2?

Equivalent Mixed Numbers

⁹/2

Equivalent Mixed Numbers

4 ²/4

Equivalent Mixed Numbers

All of these are equivalent mixed numbers. They are different ways of writing a number that represents the same quantity.

Subtracting Mixed Numbers

Yesterday we added mixed numbers. Today we are going to subtract mixed numbers. Using what you already know about mixed numbers, how would you think about solving the problem 8 - ½?

Subtracting Mixed Numbers

How would you think about solving the problem 8 - ½?

How do we record our work?

First we started with this image.

We wanted to solve the problem 8 - ½.

Then we broke up 1 whole into ²/2.

So we can rewrite the problem as 7 ²/2 - ½.

We then took away one of the ½’s to get the image below.

So we can then record our work as

7 ²/2 - ½ = 7 ½

Objective

Today we will solve subtraction problems with mixed numbers.

To solve these subtraction problems, we will trade whole numbers for equivalent fractions or convert fractions to equivalent fractions with like denominators.

Teachers can assign this slide deck for students to complete the Explore

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Teachers should tell students that they will complete this task on a piece of paper and upload a picture. If students have not yet practiced this skill of taking photos and uploading it into Google Slides, teachers might consider assigning this lesson. S

Talk about each other’s thinking.

This student has represented their thinking using both a visual model and an equation.

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What connections do you seen between the visual model and the equation?

Talk about each other’s thinking.

This student has represented their thinking with visual models and words.

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What does this student understand about the problem?

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Talk about each other’s thinking.

What does this student still need help with?

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Talk about each other’s thinking.

What would you tell that student to do next?

Lesson 10

Adapted from 5.3 Milestone

Adapted from 5.3 Milestone

Core math: Real-life problems can be solved using addition and subtraction of decimals and fractions. The effects of the operations of addition and subtraction with decimals and fractions are the same as those with whole numbers.

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Description: Students write expressions and solve problems involving addition and subtraction of decimals and fractions with unlike denominators.

CCSS-M Standard(s)

Operations and Algebraic Thinking

Write and interpret numerical expressions.

• 5.OA.2 Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2” as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

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Number and Operations in Base Ten

Perform operations with multi-digit whole numbers and with decimals to hundredths.

• 5.NBT.7 Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

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Number and Operations—Fractions

Use equivalent fractions as a strategy to add and subtract fractions.

• 5.NF.1 Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)�
• 5.NF.2 Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < ½.

Lesson Description

This lesson should be taught over the course of two days to allow students enough time to fully engage with the core math.

The following slides provide suggestions for how to adapt the Launch, Explore, and Summarize parts of the lesson for either synchronous or asynchronous teaching.

Teachers can decide how they divide up the lesson over the two days.

Teachers can supplement with other activities or routines like Math Talks (Spanish).

Lesson 10 Description

Lesson 10 Description

Lesson 10 Description

Options for Continuing Activities

• Milestone Task HW S. C.

Objective

Today you will show what you have learned during this unit. You will solve problems related to decimal and fraction addition and subtraction.

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End of the Launch; Beginning of Student Facing Slides

There are no discussion prompts included in the Launch to this Milestone.

Teachers tell students that today’s task is an opportunity to demonstrate everything they have learned in this unit about decimal and fraction addition and subtraction. Teachers should read through the task and answer any questions.

Teachers should tell students that they will complete this task on a piece of paper and upload a picture. Teachers might remind students of how to do that or show this video.

Reflection

How was this task for you?

Which part(s) were the easiest?

Which parts(s) were the most challenging for you?

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Talk about each other’s thinking.

This student has represented their thinking using both a visual model and an equation.

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What connections do you seen between the visual model and the equation?

Errors are gifts that promote discussion.

This student has some thinking that is correct and some thinking that is not. ��What does the student understand well?

Where has the student made an error?

Talk about each other’s thinking.

This student has represented their thinking using both a visual model and an equation.

​

What connections do you seen between the visual model and the equation?

Talk about each other’s thinking.

This student has represented their thinking using both a visual model and an equation.

​

What connections do you seen between the visual model and the equation?

Breakout Room Slides

Teachers can use these slides to prepare students to be in Zoom breakout rooms

What should you have up on your Screen?

Looking at Zoom and your work together.

About ⅔ of your screen.

About ⅓ of your screen.

Breakout Rooms

Work Expectations Template

Teachers can use these slides to review expectations for independent, partner, or group work

Independent Work Expectations

Teacher writes in the student facing expectations that will support student learning:

Suggestions:

• Type questions into the chat if you get stuck.
• Turn on your mic and ask me a question if you get stuck.
• Refer back to the examples if you get stuck.

Partner Work Expectations

Teacher writes in the student facing expectations that will support student learning:

Suggestions:

• Click on the link that matches your Breakout room number.
• Click on the “Ask for help” button on Zoom if you get stuck.
• Keep conversations focused on the math.
• Refer back to the examples if you get stuck.

Example of document that can be shared in Google Classroom if students are working in pairs:

Appreciations

Teachers can use these slides to structure appreciations at the end of class

Appreciations

“I appreciate ____ for (teacher selects an action related to the focus norm or standard for mathematical practice the class focused on today)”�

“I appreciate ____ for explaining _____”

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