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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: Suppose the student tickets cost 2³ dollars each instead of $2. The expression becomes 2 × 15 + 4 × 20 + 8 × 2³. Powers come before multiplying, so evaluate 2³ first: 2 × 2 × 2 = 8. Now multiply, left to right: 30 + 80 + 64. Then add: 30 + 80 + 64 = 174. The order now costs $174. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartWhat is the value of 6²?

   1. A36
   2. B12
   3. C62
   4. D8

   How do you know?
3. 3

   Warm restartWhat is the value of 4³?

   1. A64
   2. B12
   3. C43
   4. D7

   How do you know?
4. 4

   Warm restartIn 2⁵, which number is the base and which is the exponent?

   1. ABase 2, exponent 5
   2. BBase 5, exponent 2
   3. CBase 2, exponent 2
   4. DBase 5, exponent 5

   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 2.50 + 1.75(8)?

   1. A16.50
   2. B34.00
   3. C4.25
   4. D14.00

   Why is that the answer?
2. 6

   Think it throughWhat does the 2.50 represent?

   1. AA flat base fee charged no matter how far you go
   2. BThe cost of one mile
   3. CThe number of miles
   4. DThe tip

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

   Think it throughWhat does the 1.75 represent?

   1. AThe cost per mile, multiplied by the number of miles
   2. BThe base fee
   3. CThe total cost
   4. DThe number of miles

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

   Back to the modelTwo students evaluate 3 + 4 × 2 and get 14 and 11. Which one followed the order of operations, and why does the order have to be agreed on at all?

Sort it again — on paper this time

Write the letter of the group each one belongs in.

• 2² = 4
• 4 × 4 = 16
• 3 + 16 − 6 = 13
• Handle the exponent before anything else here
• Multiplication comes before addition
• Work left to right at the end

Use the words

Fill each blank with a word from the bank.

• Write the situation as an expression, then follow the ___ ___ ___ to value it.
• Numbers and operations with no equal sign and no variable form a ___ ___.
• To put numbers in for the letters and work out the value is to ___.
• Grouping symbols, then ___, then × and ÷, then + and −.

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 with powers is multiplying the base by the exponent: reading 3² as 3 × 2 = 6 instead of 3 × 3 = 9.
2. 10

   Say moreWhen you evaluate an expression like 4x² + 3, what order do you follow, and why must you square before you multiply?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: You are the music producer from the story. Your concert cost is given by the expression 150 + 12s, where s is the number of speakers you rent.

   Show your work

Last check

These two come from Lesson 6.3. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — Evaluate 2 × 15 + 8 × 2³.

   1. A94
   2. B124
   3. C736
   4. D150

   Explain your choice.
2. 13

   From Lesson 6.3Explain your thinking — What is the value of 3⁴?

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

   How do you know?
3. 14

   From Lesson 6.3Why 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

   How do you know?

Be honest — this tells your teacher what to do next