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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.

   Let's try together: 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.

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

   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
3. 3

   Warm restartWhich number is prime?

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

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?

   I chose ___ because ___ .
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?

   I chose ___ because ___ .
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.

   I chose ___ because ___ .
4. 8

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

   When I distribute, I multiply the outside factor ___ by each term ___. The operation inside the parentheses ___ stays the same.

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?

   I distribute the 5 to ___ and ___, so 5(2x + 4) = ___.
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 6.13. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowQuick check — you've got this: Which expression is equivalent to 7(x + 3)?

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

   Explain your choice.

   I know it is ___ because ___ .
2. 13

   From Lesson 6.13Quick check — you've got this: What is the prime factorization of 40?

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

Be honest — this tells your teacher what to do next