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Unit 7

Powers of Powers of 10

Exponents and Scientific Notation

Lesson 3

Expressions and Equations

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Let's look at powers of powers of 10.

Unit 7 ● Lesson 3

Learning

Goal

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Big Cube

Unit 7 ● Lesson 3 ● Activity 1

What is the volume of a giant cube that measures 10,000 km on each side?

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Warm-up

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Big Cube

Unit 7 ● Lesson 3 ● Activity 1

What patterns do you notice between (104)3 and 1012?

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Warm-up

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Raising Powers of 10 to Another Power

Unit 7 ● Lesson 3 ● Activity 2

    • Complete the table to explore patterns in the exponents when raising a power of 10 to a power. You may skip a single box in the table, but if you do, be prepared to explain why you skipped it.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Raising Powers of 10 to Another Power

Unit 7 ● Lesson 3 ● Activity 2

    • If you chose to skip one entry in the table, which entry did you skip? Why?
  • Use the patterns you found in the table to rewrite (10m)n as an equivalent expression with a single exponent, like 10⮹.
  • If you took the amount of oil consumed in 2 months in 2013 worldwide, you could make a cube of oil that measures 103 meters on each side. How many cubic meters of oil is this? Do you think this would be enough to fill a pond, a lake, or an ocean?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Raising Powers of 10 to Another Power

Unit 7 ● Lesson 3 ● Activity 2

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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How Do the Rules Work?

Unit 7 ● Lesson 3 ● Activity 3

Andre and Elena want to write 102 • 102 • 102 with a single exponent.

  • Andre says, “When you multiply powers with the same base, it just means you add the exponents, so

102 • 102 • 102 = 102 + 2 + 2 = 106.”

  • Elena says, 102 “ is multiplied by itself 3 times, so

102 • 102 • 102 = (102)3 = 102+3 = 105.”

Do you agree with either of them? Explain your reasoning.

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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How Do the Rules Work?

Unit 7 ● Lesson 3 ● Activity 3

  • Andre wrote 02 • 102 • 102 = 102 + 2 + 2 and Elena wrote

102 • 102 • 102 = (102)3. How are these ways of thinking different? How are they the same?

  • What is one way you could avoid making the kinds of mistake that happened in this problem?

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Powers of Powers of 10

Unit 7 ● Lesson 3

  • We looked at repeated multiplication of powers of 10. How would you write 104 • 104 • 104 with exponents instead of repeated multiplication?
  • Then how would you write (104)3 using a single exponent?
  • In general, why do you multiply the exponents when you write a power to a power with a single exponent? Give an example to show your reasoning.

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Lesson Synthesis

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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Unit 7 ● Lesson 3

I can explain and use a rule for raising a power of 10 to a power.

Learning

Targets

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Making a Million

Unit 7 ● Lesson 3 ● Activity 4

Here are some equivalent ways of writing 104:

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  • 10,000
  • 10 • 103
  • (102)2

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Write as many expressions as you can that have the same value as 106. Focus on using exponents and multiplication.

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Cool-down

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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base (of an exponent)

Unit 7 ● Lesson 3

In expressions like 53 and 82, the 5 and the 8 are called bases. They tell you what factor to multiply repeatedly. For example, 53 = 5 • 5 • 5, and 82 = 8 • 8.

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Glossary

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics

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Exponent Rules

Unit 7 ● Lesson 3

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Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Open Up Resources, with adaptations CC BY Illustrative Mathematics.

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This slide deck is copyright 2020 by Kendall Hunt Publishing, https://im.kendallhunt.com/, and is licensed under the Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0), https://creativecommons.org/licenses/by-nc/4.0/.

All curriculum excerpts are under the following licenses:

IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.

Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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The Illustrative Mathematics name and logo are not subject to the Creative Commons license and may not be used without the prior and express written consent of Illustrative Mathematics.

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