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Unit 8 - Lesson 3 - Grade 8: Illustrative Mathematics

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Grade 8 Unit 8
Lesson 3: Rational and Irrational Numbers
CC BY 2021 Illustrative Mathematics®
Grade 8 Unit 8
Lesson 3: Rational and Irrational Numbers
CC BY 2021 Illustrative Mathematics®
Lesson: Rational and Irrational Numbers

Algebra Talk: Positive Solutions (Warm Up)

Find a positive solution to each equation:
1.

2.

3.

4.

Three Squares

5.

  1. Draw 3 squares of different sizes with vertices aligned to the vertices of the grid.
  2. For each square:
  • Label the area.
  • Label the side length.
  • Write an equation that shows the relationship between the side length and the area.

Looking for a Solution

6.

Are any of these numbers a solution to the equation x2 = 2? Explain your reasoning.
  • 1
  • 1/2
  • 3/2
  • 7/5

Looking for \sqrt{2}



A rational number is a fraction or its opposite (or any number equivalent to a fraction or its opposite).
7.

Find some more rational numbers that are close to \sqrt{2}.


8.

Can you find a rational number that is exactly \sqrt{2}.

Cool Down: Types of Solutions

Types of Solutions

9.

In your own words, say what a rational number is. Give at least three different examples of rational numbers.


10.

In your own words, say what an irrational number is. Give at least two examples.