# Decimal Fractions

## Objective

Compare two or more decimals written in various forms.

## Common Core Standards

### Core Standards

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• 4.NF.C.7 — Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

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• 3.NF.A.2

• 4.NF.A.2

## Criteria for Success

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1. Make sense of a three-act task and persevere in solving it (MP.1).
2. Order a list of decimals from least to greatest or greatest to least.
3. Compare and order decimals written in different forms (e.g., unit form).
4. Generate a decimal value that lies between two other decimal values.
5. Record the result of a comparison with the symbol >, =, or <.
6. Justify a comparison using a visual model or reasoning (MP.3).

## Tips for Teachers

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• Because the Common Core State Standards do not explicitly ask for students to compare any more than two decimals written in decimal form, today’s lesson is optional. However, tasks asking students to order a list of decimals just require numerous comparisons to be performed in a single task, providing extensive practice of a skill students already have. Students are also asked to compare and order decimals in various forms in this lesson, a review and synthesis of already-acquired skills.
• If instead you’d like students to have more practice with the skills that 4.NF.7 entails, you could modify Illustrative Mathematics’ “Comparing Fractions Game,” so that students are asked to compare decimals instead. It’s at your discretion to include visual models, such as area models or number lines, on the task cards or not, similar to the Grade 3 version.
• As a supplement to the Problem Set, students can play a modified version of the game Decimal Point Pickle, on the blog Math Hombre. To modify the game, have students create decimals up to two places rather than three. Otherwise the rules can remain unchanged.

#### Fishtank Plus

• Problem Set
• Student Handout Editor
• Vocabulary Package

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### Problem 1

Act 1: Watch the video "Act 1" from Final Lap.

Who won the race?

#### References

Questioning My Metacognition Final Lap

Final Lap by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed May 29, 2018, 1:25 p.m..

Modified by The Match Foundation, Inc.

### Problem 2

Act 2: Use the following information to solve.

#### References

Questioning My Metacognition Final Lap

Final Lap by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed May 29, 2018, 1:25 p.m..

Modified by The Match Foundation, Inc.

### Problem 3

Act 3: Reveal the answer. (Watch Act 3 video from Final Lap.)

#### References

Questioning My Metacognition Final Lap

Final Lap by Graham Fletcher is made available on Questioning My Metacognition under the CC BY-SA 4.0 license. Accessed May 29, 2018, 1:25 p.m..

Modified by The Match Foundation, Inc.

### Problem 4

List the following values in order from greatest to least.

1.0, 3 tenths, 0.2, 0.17, $\frac{34}{100}$, 0, $\frac{4}{10}$, 13 hundredths

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 6 > Topic C > Lesson 11Concept Development

Grade 4 Mathematics > Module 6 > Topic C > Lesson 11 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

## Discussion of Problem Set

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• How much frozen yogurt might the recipe call for in #2e? What other possible values could it be?
• How did the number line help you to order—or to check the order of—the numbers from least to greatest? Do you think it could be useful to use the number line to order numbers from greatest to least like in #5? Why or why not?
• What made #3c more challenging than #3a and #3b? How did you determine what the value of the unlabeled tick marks were?
• How could a place value chart help you solve #5a? What other models or tools have we used this year that might help you with #5?
• In #5b, which numbers did you start ordering first? How did ordering some numbers help you with the remaining numbers?

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### Problem 1

List the following numbers in order from greatest to least.

1 one and 1 tenth,  ${{13\over10}}$,  1 one and 20 hundredths,  ${{129\over100}}$,  1.11,  ${{102\over100}}$

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 6 > Topic C > Lesson 11Exit Ticket, Question #1

Grade 4 Mathematics > Module 6 > Topic C > Lesson 11 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

### Problem 2

Explain how you can use a number line to list the following numbers in order from least to greatest.

5.6,  6.05,  6.15,  5.10,  5.16,  6.5

#### References

EngageNY Mathematics Grade 4 Mathematics > Module 6 > Topic C > Lesson 11Exit Ticket, Question #2

Grade 4 Mathematics > Module 6 > Topic C > Lesson 11 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by The Match Foundation, Inc.

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