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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: Let's expand 2(8 + 3). Where does the 2 go? We multiply the 2 by each term: 2 × 8 + 2 × 3. That is 16 + 6 = 22. So 2(8 + 3) = 22. 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 prime factorization of 24?

   1. A2 × 2 × 2 × 3
   2. B4 × 6
   3. C2 × 12
   4. D3 × 8

   How do you know?
3. 3

   Warm restartWhich number is prime?

   1. A19
   2. B21
   3. C27
   4. D33

   How do you know?
4. 4

   Warm restartA factor tree for 36 ends with which prime factors?

   1. A2 × 2 × 3 × 3
   2. B6 × 6
   3. C2 × 18
   4. D3 × 12

   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 throughDistribute: 8(12 + 9) = ?

   1. A8 × 12 + 8 × 9
   2. B8 × 12 + 9
   3. C8 + 12 × 9
   4. D8 × 21 × 8

   Why is that the answer?
2. 6

   Think it throughWhat is the total cost for 8 practice rooms?

   1. A$168
   2. B$105
   3. C$96
   4. D$21

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

   Think it throughA student wrote 8(12 + 9) = 8 × 12 + 9 = 105. What went wrong?

   1. AThey forgot to multiply the 9 by 8 as well
   2. BThey added instead of multiplying
   3. CThey used the wrong prices
   4. DThey distributed too many times

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

   Back to the modelWhat pattern do you see when you expand an expression using the distributive property?

Use the words

Fill each blank with a word from the bank.

• a(b + c) = ab + ___ — the factor reaches ___ term.
• The rule that a(b + c) = ab + ac is the ___.
• To rewrite a sum as a product, like 3x + 12 = 3(x + 4), is to ___.
• To multiply out a product over a sum, like 3(x + 4) = 3x + 12, is to ___.

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: The most common mistake in The Distributive Property is multiplying the outside factor by only the FIRST term inside the parentheses and forgetting the second — for example, writing 3(x + 4) = 3x + 4 instead of 3x + 12.
2. 10

   Say moreWhen you expand 5(2x + 4), why must the 5 multiply BOTH terms inside the parentheses?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: The studio manager is ordering merch bundles for 9 band members going on tour. Each bundle includes a t-shirt ($18) and a strap ($7). The order form writes the cost two ways: 9(18 + 7) and 9 × 18 + 9 × 7.

   Show your work

Last check

These two come from Lesson 6.13. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — Which expression is equivalent to 7(x + 3)?

   1. A7x + 21
   2. B7x + 3
   3. Cx + 21
   4. D7x + 10

   Explain your choice.
2. 13

   From Lesson 6.13Explain your thinking — What is the prime factorization of 40?

   1. A2 × 2 × 2 × 5
   2. B4 × 10
   3. C5 × 8
   4. D2 × 20

   How do you know?
3. 14

   From Lesson 6.13Which grid would NOT use exactly all 72 seed pods?

   1. A6 by 12
   2. B4 by 18
   3. C5 by 14
   4. D3 by 24

   How do you know?

Be honest — this tells your teacher what to do next