Unit 8 - Lesson 15 - Grade 8: Illustrative Mathematics

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14 Questions

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Grade 8 Unit 8
Lesson 15: Infinite Decimal Expansions
CC BY 2021 Illustrative Mathematics®

Instructions

Grade 8 Unit 8
Lesson 15: Infinite Decimal Expansions
CC BY 2021 Illustrative Mathematics®

Lesson: Infinite Decimal Expansions

Searching for Digits (Warm Up)

The first 3 digits after the decimal for the decimal expansion of 3/7 have been calculated. Find the next 4 digits.

Some Numbers Are Rational

Your teacher will give your group a set of cards. Each card will have a calculation side and an explanation side.

The cards show Noah’s work calculating the fraction representation of 

Arrange these in order to see how he figured out the following without needing a calculator.

Use Noah’s method to calculate the fraction representation of:

Some Numbers Are Not Rational

Why is \sqrt{2} between 1 and 2 on the number line?

Why is \sqrt{2} between 1.4 and 1.5 on the number line?

How can you figure out an approximation for \sqrt{2} accurate to 3 decimal places?

Label all of the tick marks. Plot \sqrt{2} on all three number lines. Make sure to add arrows from the second to the third number lines.

Elena notices a beaker in science class says it has a diameter of 9 cm and measures its circumference to be 28.3 cm. What value do you get for π using these values and the equation for circumference,

Diego learned that one of the space shuttle fuel tanks had a diameter of 840 cm and a circumference of 2,639 cm. What value do you get for π using these values and the equation for circumference,

10.

Label all of the tick marks on the number lines. Use a calculator to get a very accurate approximation of π and plot that number on all three number lines.

11.

How can you explain the differences between these calculations of π?

Cool Down: Repeating in Different Ways

Repeating in Different Ways

12.

Is x a rational number?

13.

Is y a rational number?

14.

Unit 8 - Lesson 15 - Grade 8: Illustrative Mathematics

Searching for Digits (Warm Up)

The first 3 digits after the decimal for the decimal expansion of 3/7 have been calculated. Find the next 4 digits.

Some Numbers Are Rational

Some Numbers Are Not Rational

Why is \sqrt{2} between 1 and 2 on the number line?

Why is \sqrt{2} between 1.4 and 1.5 on the number line?

How can you figure out an approximation for \sqrt{2} accurate to 3 decimal places?

Label all of the tick marks. Plot \sqrt{2} on all three number lines. Make sure to add arrows from the second to the third number lines.

Elena notices a beaker in science class says it has a diameter of 9 cm and measures its circumference to be 28.3 cm. What value do you get for π using these values and the equation for circumference,

Diego learned that one of the space shuttle fuel tanks had a diameter of 840 cm and a circumference of 2,639 cm. What value do you get for π using these values and the equation for circumference,

Label all of the tick marks on the number lines. Use a calculator to get a very accurate approximation of π and plot that number on all three number lines.

How can you explain the differences between these calculations of π?

Repeating in Different Ways

Is x a rational number?

Is y a rational number?

Which is larger, x or y?