Pythagorean Theorem and Volume

Lesson 5

Math

Unit 7

8th Grade

Lesson 5 of 16

Objective


Represent decimal expansions as rational numbers in fraction form.

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
  • 7.NS.A.3

Criteria for Success


  1. Understand that decimals that terminate or repeat are rational numbers and can be represented in the form $${a\over{b}}$$, where $$a$$ and $$b$$ are integers, and $$b\neq0$$.
  2. Write decimal expansions, those that terminate and those that repeat, as fractions. 
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Anchor Problems


Problem 1

Write each rational number in the form $${a\over{b}}$$, where $$a$$ and $$b$$ are integers, and $$b\neq0$$.

a.   $${0.3333}$$

b.   $${-5.05}$$

c.   $${\sqrt{64}}$$

e.   $${\sqrt{4\over25}}$$

f.   $${\sqrt{1.21}}$$

Guiding Questions

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Problem 2

A student wrote two repeating decimals as fractions using the strategy shown below. 

Given the decimal $$0.\overline{12}$$

Let $$x=0.\overline{12}$$

Then $$100x=12.\overline{12}$$

Given the decimal $$0.\overline{123}$$

Let $$x=0.\overline{123}$$

Then $$1000x=123.\overline{123}$$

a.   Describe the student’s strategy in your own words.

b.   Use the same strategy to write the two decimals below as fractions. 

  1.  $${0.\overline{54}}$$
  2. $${0.1\overline{23}}$$

Guiding Questions

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Problem 3

What is the sum of $${0.1}$$ and $${0.\overline3}$$ written as a fraction?

Guiding Questions

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Problem Set

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Target Task


Write each decimal expansion as a rational number in the form $${a\over b}$$, where $$a$$ and $$b$$ are integers.

a.   $${0.61313}$$

b.   $${0.6\overline{13}}$$

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.

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Lesson 4

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Lesson 6

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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