Start here

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.

   Let's do one together: Find the value of 5². What is the base? What is the exponent? (The base is 5. The exponent is 2.) Write 5² as repeated multiplication. (5 × 5) What is the value? (5 × 5 = 25) Is 5² the same as 5 × 2? (No. 5 × 2 = 10, but 5² is 25.)

   My first step is ___ , because the problem asks for ___ .

   Show your work
2. 2

   Warm restart12 is 25% of what number?

   1. A3
   2. B37
   3. C48
   4. D300
3. 3

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

   1. A10 games
   2. B28 games
   3. C30 games
   4. D48 games
4. 4

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

   1. A0.02
   2. B4.5
   3. C45
   4. D50

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. A10
   2. B16
   3. C25
   4. D32

   Why is that the answer?

   I chose ___ because ___ .
2. 6

   Think it throughHow big is the file after 5 layers?

   1. A20 MB
   2. B40 MB
   3. C64 MB
   4. D128 MB

   How do you know?

   I chose ___ because ___ .
3. 7

   Think it throughWhy does the file grow so quickly?

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

   Explain your thinking.

   I chose ___ because ___ .
4. 8

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

   When the exponent increases by 1, the value is multiplied by ___ because the base is used as a factor ___ more time.

Use the words

Fill each blank with a word from the bank.

• 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 ___.
• To find the value of an expression, like 2³ = 8, is to ___ it.

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?

   When the exponent increases by 1, the value is multiplied by ___.
3. 11

   Change one numberGo back to Part 1 and pick one problem you already solved. Change one number in it, then solve your new version. Show every step.

   If ___ changed to ___ , then ___ .

   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 knowQuick check — you've got this: What is the value of 3⁴?

   1. A12
   2. B34
   3. C64
   4. D81

   Explain your choice.

   I know it is ___ because ___ .
2. 13

   From Lesson 6.2Quick check — you've got this: What is 5/6 ÷ 1/12?

   1. A5/72
   2. B5/6
   3. C10
   4. D72/5
3. 14

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

   1. A5
   2. B6
   3. C10
   4. D30

Be honest — this tells your teacher what to do next