Pythagorean Theorem and Volume

Lesson 4

Math

Unit 7

8th Grade

Lesson 4 of 16

Objective


Represent rational numbers as decimal expansions.

Common Core Standards


Core Standards

  • 8.NS.A.1 — Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

Foundational Standards

  • 7.NS.A.2.D

Criteria for Success


  1. Understand that every rational number has a decimal expansion that either terminates or repeats.
  2. Write the decimal expansion of rational numbers, including those that terminate and those that repeat. 
  3. Approximate the location of a repeating decimal expansion on a number line. 

Tips for Teachers


  • Students have prior experience from seventh grade with writing decimal expansions for rational numbers using long division (for reference, see 7th Grade Unit 2, Lesson 16). This lesson reviews and extends on this concept.
  • Students should not have access to calculators for this lesson.
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Anchor Problems

25-30 minutes


Problem 1

All rational numbers have a decimal expansion. Write the decimal expansion of the rational numbers below. 

a.   $${{2\over5}}$$

b.   $${{9\over8}}$$

c.   $${-{7\over25}}$$

d.   $${{108\over125}}$$

e.   $${-{492\over10,000}}$$

f.   $${\sqrt{16}}$$

g.   $${\sqrt{0.16}}$$

h.   $${\sqrt{1\over16}}$$

Guiding Questions

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Student Response

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Problem 2

Follow the directions to approximate the location of $${{{{{{{{{{{{{{2\over11}}}}}}}}}}}}}}$$on the number lines below.

  1. On the topmost number line, label the tick marks. Next, find the first decimal place of $${{{{{{{{{{{{{{2\over11}}}}}}}}}}}}}}$$ using long division and estimate where $${{{{{{{{{{{{{{2\over11}}}}}}}}}}}}}}$$ should be placed on the top number line. 
  2. Label the tick marks of the second number line. Find the next decimal place of $${{{{{{{{{{{{{{2\over11}}}}}}}}}}}}}}$$ by continuing the long division and estimate where $${{{{{{{{{{{{{{2\over11}}}}}}}}}}}}}}$$ should be placed on the second number line. Add arrows from the second to the third number line to zoom in on the location of $${{{{{{{{{{{{{{2\over11}}}}}}}}}}}}}}$$.
  3. Repeat the earlier step for the remaining number lines. 
  4. What do you think the decimal expansion of $${{{{{{{{{{{{{{2\over11}}}}}}}}}}}}}}$$ is? 

Guiding Questions

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Student Response

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References

Open Up Resources Grade 8 Unit 8 Lesson 1414.4

Grade 8 Unit 8 Lesson 14 is made available by Open Up Resources under the CC BY 4.0 license. Copyright © 2017 Open Up Resources. Download for free at openupresources.org. Accessed March 30, 2018, 6:55 p.m..

Modified by Fishtank Learning, Inc.

Problem Set

15-20 minutes


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes


Problem 1

Which of the rational numbers have a terminating decimal expansion? Select all that apply.

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Student Response

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Problem 2

What is the decimal expansion of $$\frac{167}{6}$$?

Student Response

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Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

Next

Represent decimal expansions as rational numbers in fraction form.

Lesson 5
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Lesson Map

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

Topic A: Irrational Numbers and Square Roots

Topic B: Understanding and Applying the Pythagorean Theorem

Topic C: Volume and Cube Roots

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