Curriculum  /  Math  /  4th Grade  /  Unit 6: Decimal Fractions  /  Lesson 7

Decimal Fractions

Lesson 7

Math

Unit 6

4th Grade

Lesson 7 of 13

Objective

Compare two decimals, recording the result of a comparison with the symbol >, =, or <, and justify the conclusion.

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. Understand that decimal comparisons are only valid when the two decimals refer to the same whole (MP.6).
  2. Compare decimal numbers written in decimal form.
  3. Record the result of a comparison with the symbol >, =, or <.
  4. Justify a comparison using a visual model or the meaning of a decimal as a fraction (MP.3).

Tips for Teachers

  • Number lines are a particularly helpful representation when comparing quantities, since given two numbers “and thus two points on the number line — the one to the left is said to be smaller and the one to its right is said to be larger” (NF Progression, p. 9). Students will also justify their conclusions using the meaning of a decimal as a fraction. While students could use area models to compare decimals in this unit, their disadvantage is that this argument does not generalize “to work with decimals in Grade 5 that have more than two digits” (NF Progression, p. 15). 
  • Standard 4.NF.7 notes that “comparisons are valid only when the two fractions refer to the same whole” (4.NF.2). Students encountered this idea when comparing fractions in third grade as well as comparing fraction in Unit 4 of this grade, and thus it is not explored explicitly in the Anchor Tasks or Problem Set. If you believe students would benefit from more discussion of this idea, you could include a warm-up related to this idea. For example, you could adapt this task from Illustrative Math so that it is comparing decimals, perhaps 0.1 and 0.01, incorrectly. You can also find additional problems in EngageNY, Grade 3, Module 5, Lesson 11, Problem Set and Homework (various problems), adapted to represent decimals rather than fractions.
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Anchor Tasks

25-30 minutes

Problem 1

a.   Locate and label these numbers on the number line.

0.2 0.95 0.61 1.12 0.08

b.   Use two numbers from Part (a) to complete each comparison statement so that it is true. 

  1. _____ is greater than _____.
  2. _____ is less than _____.
  3. _____ is the greatest number.

Guiding Questions

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Student Response

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References

Illustrative Mathematics Illustrative Math Grade 4 Unit 4 Lesson 3 — Activity 1

Illustrative Math Grade 4 Unit 4 Lesson 3, accessed on July 24, 2023, 10:42 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 2

Compare the numbers using <, >, or =. Can you think of a way to make comparisons without using a number line? Be prepared to explain your reasoning. 

a.   0.8 _____ 0.3

b.   0.01 _____ 0.11

c.   0.2 _____ 0.20

d.   0.6 _____ 0.41

e.   0.07 _____ 0.70

f.   0.57 _____ 0.75

Guiding Questions

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Student Response

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References

Illustrative Mathematics Using Place Value

Using Place Value, accessed on May 29, 2018, 12:03 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.
Illustrative Mathematics Illustrative Math Grade 4 Unit 4 Lesson 3 — Activity 2, #2

Illustrative Math Grade 4 Unit 4 Lesson 3, accessed on July 24, 2023, 10:42 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 3

Compare the numbers using <, >, or =. Justify your comparison.

a.   1.24 _____ 2.24

b.   2.38 _____ 2.83

c.   4.38 _____ 4.5

d.   6.37 _____ 6.3

e.   10.0 _____ 10.00

f.   15.2 _____ 15.02

Guiding Questions

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Student Response

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References

EngageNY Mathematics Grade 4 Mathematics > Module 6 > Topic C > Lesson 10 — Concept Development

Grade 4 Mathematics > Module 6 > Topic C > Lesson 10 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.

Problem Set

15-20 minutes

Discussion of Problem Set

  • How do the number lines in #1 support your statements? 
  • How would #3 be different if given area models to use to represent the values? Which is easier to use to model the values? Which is easier to use to compare? Why? 
  • Look at #4f. 1.9 has 2 digits and 1.21 has three digits, and yet 1.9 is greater than 1.21. Why? 
  • Why is 0.17 less than 0.2? How can looking at the numbers quickly instead of considering the size of the unit lead to mistakes when comparing? How can we rename 0.2 to compare it easily to 0.17? 
  • Would you rather have 2.7 pounds of strawberries or 2.34 pounds? Why? If you didn’t like strawberries, how might your answer change? 

Target Task

5-10 minutes

Problem 1

 Which comparisons are correct? Select the three correct answers.

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Student Response

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Problem 2

Choose one correct comparison from #1 and show or explain how you know it is correct. 

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

Compare two or more decimals written in various forms.

Lesson 8
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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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