Curriculum  /  Math  /  4th Grade  /  Unit 6: Decimal Fractions  /  Lesson 8

Decimal Fractions

Lesson 8

Math

Unit 6

4th Grade

Lesson 8 of 13

Objective

Compare two or more decimals written in various forms.

Common Core Standards

Core Standards

  • 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.

Foundational Standards

  • 3.NF.A.2
  • 4.NF.A.2

Criteria for Success

  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

  • 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.
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Anchor Tasks

25-30 minutes

Problem 1

Act 1: Watch the video Act 1.

a.   What do you notice? What do you wonder?

b.   What order did they finish the race in? Make a prediction.

Guiding Questions

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Student Response

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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 Fishtank Learning, Inc.

Problem 2

Act 2: Use the following information to solve.

Guiding Questions

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Student Response

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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 Fishtank Learning, Inc.

Problem 3

Act 3: Watch Act 3 Final Lap to see the solution. 

Was your prediction correct? If not, change the finishing times of various cars so that their order would match your prediction.

Guiding Questions

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Student Response

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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 Fishtank Learning, Inc.

Problem 4

Mr. Balboni’s class records how much rainwater, in inches, they each got overnight at their homes. The information is recorded in the table below. 

Student

Amount of Rainwater (in inches)
Maja 1.0
Patricia 3 tenths
Anselm 0.2
Jacob $$\frac{24}{100}$$
Byron  $$\frac{4}{10}$$
Fiona 0
Evelyn 0.17
Clark 13 hundredths
Liz $$\frac{6}{100}$$

a.   List the amount of rainwater recorded in order from least to greatest.

b.   Which student recorded an amount of rainwater closest to the amount of rainwater Anselm recorded? Explain.

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 4 Mathematics > Module 6 > Topic C > Lesson 11 — Concept 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 Fishtank Learning, Inc.
MCAS Digital Item Library MCAS 2019 Grade 4 Released Item #3

MCAS 2019 Grade 4 Released Item #3 from the MCAS Digital Item Library is made available by the Massachusetts Department of Elementary and Secondary Education. © 2018 Pearson 2018. Accessed July 15, 2023, 3:55 p.m..

Problem Set

15-20 minutes

Discussion of Problem Set

  • 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 drawing base ten blocks 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? 

Target Task

5-10 minutes

Problem 1

List the following numbers in order from greatest to least.

$$22\over 10$$,  2 ones and 10 hundredths, $$203\over 100$$,  2.23,  2 ones and 3 tenths, $$216\over 100$$

Student Response

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Problem 2

List the following numbers in order from least to greatest. Explain your answer with a picture.

7.18,  8.7,  8.17,  7.10,  8.07,  7.8

Student Response

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Additional Practice

The Extra Practice Problems can be used as additional practice for homework, during an intervention block, etc. Daily Word Problems and Fluency Activities are aligned to the content of the unit but not necessarily to the lesson objective, therefore feel free to use them anytime during your school day.

Word Problems and Fluency Activities

Word Problems and Fluency Activities

Help students strengthen their application and fluency skills with daily word problem practice and content-aligned fluency activities.

Next

Add tenths with hundredths written as decimal fractions.

Lesson 9
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Understanding Tenths

Topic B: Understanding Tenths and Hundredths

Topic C: Decimal Comparison

Topic D: Decimal Addition

Topic E: Money as a Decimal Amount

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