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You did these with your group. Now do them on your own — the model above is yours to copy.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step.

   Try it together — then prove it: Now let's find 5². How many times do we multiply 5 by itself? The exponent is 2, so we write 5 × 5. What is 5 × 5? Yes, 25. So 5² = 25. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restart12 is 25% of what number?

   1. A48
   2. B3
   3. C37
   4. D300

   How do you know?
3. 3

   Warm restartA team won 18 games, which is 60% of the games it played. How many games did it play?

   1. A30 games
   2. B28 games
   3. C48 games
   4. D10 games

   How do you know?
4. 4

   Warm restartFind the whole: 15 = 0.30 × n. What is n?

   1. A50
   2. B4.5
   3. C45
   4. D0.02

   How do you know?

You answered these out loud. Now write them.

Answer, then say how you know — the reason is the part that counts.

1. 5

   Think it throughWhat is 2⁵?

   1. A32
   2. B10
   3. C25
   4. D16

   Why is that the answer?
2. 6

   Think it throughHow big is the file after 5 layers?

   1. A128 MB
   2. B40 MB
   3. C20 MB
   4. D64 MB

   How do you know? Give a second reason as well.
3. 7

   Think it throughWhy does the file grow so quickly?

   1. ABecause each layer doubles the size instead of adding a fixed amount
   2. BBecause 4 MB is already large
   3. CBecause 5 is a big exponent
   4. DBecause the studio records faster each time

   Explain your thinking. What would have to change for a different choice to be right?
4. 8

   Back to the modelHow does the value change when you increase the exponent by 1? Why?

Use the words

Fill each blank with a word from the bank.

• A power writes repeated multiplication with a base and an ___.
• The small raised number that shows how many times the base is multiplied is the ___.
• The number being multiplied repeatedly in a power, like the 3 in 3⁴, is the ___.
• A number written with a base and an exponent, like 3⁴, is a ___.

Explain the thinking

1. 9

   Find the mistakeAnother student made this exact mistake in this lesson. Explain why it is wrong, then write what they should have done.

   The mistake: A common mistake in Powers and Exponents is multiplying the base by the exponent instead of using the base as a repeated factor — for example, thinking 2³ = 2 × 3 = 6 instead of 2³ = 2 × 2 × 2 = 8.
2. 10

   Say moreLook at the table: when the exponent goes up by 1 (like from 2³ to 2⁴), what happens to the value, and why?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Each figure is built from square groups of tiles, and the groups grow larger from one figure to the next.

   Show your work

Last check

These two come from Lesson 6.2. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — What is the value of 3⁴?

   1. A81
   2. B12
   3. C34
   4. D64

   Explain your choice.
2. 13

   From Lesson 6.2Explain your thinking — What is 5/6 ÷ 1/12?

   1. A10
   2. B5/72
   3. C5/6
   4. D72/5

   How do you know?
3. 14

   From Lesson 6.2If each piece were 1/6 of a foot, how many pieces?

   1. A5
   2. B10
   3. C6
   4. D30

   How do you know?

Be honest — this tells your teacher what to do next