Start here

Use the model to solve the first problem. Then try these quick review questions from earlier lessons.

1. 1

   Same stepsFinish what the group started. Use the model above, step for step. 🔊 Listen 💡 Hint

   Let's do one together:

   1. Use the distributive property to find 2(8 + 3).
   2. The 2 multiplies each term. Write the two products. (2 × 8 + 2 × 3)
   3. Find each product. (2 × 8 = 16 and 2 × 3 = 6)
   4. Add the products. What is 2(8 + 3)? (16 + 6 = 22)

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

   Show your work
2. 2

   Quick reviewWhat is the prime factorization of 24? 🔊 Listen 💡 Hint

   1. A2 × 2 × 2 × 3
   2. B2 × 12
   3. C3 × 8
   4. D4 × 6
3. 3

   Quick reviewWhich number is prime? 🔊 Listen 💡 Hint

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

   Quick reviewA factor tree for 36 ends with which prime factors? 🔊 Listen 💡 Hint

   1. A2 × 2 × 3 × 3
   2. B2 × 18
   3. C3 × 12
   4. D6 × 6

Try these on your own

Choose an answer. Then explain how you know.

1. 5

   Think it throughDistribute: 8(12 + 9) = ? 🔊 Listen 💡 Hint

   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? 🔊 Listen 💡 Hint

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

   How do you know?

   I chose ___ because ___ .
3. 7

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

   1. AThey added instead of multiplying
   2. BThey used the wrong prices
   3. CThey forgot to multiply the 9 by 8 as well
   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? 🔊 Listen 💡 Hint

   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 mistakeRead the mistake. Explain what went wrong, then show the correct step. 🔊 Listen 💡 Hint

   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? 🔊 Listen 💡 Hint

   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. 🔊 Listen 💡 Hint

   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)? 🔊 Listen 💡 Hint

   1. A7x + 21
   2. B7x + 3
   3. C7x + 10
   4. Dx + 21

   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? 🔊 Listen 💡 Hint

   1. A2 × 2 × 2 × 5
   2. B2 × 20
   3. C4 × 10
   4. D5 × 8
3. 14

   From Lesson 6.13Which grid would NOT use exactly all 72 seed pods? 🔊 Listen 💡 Hint

   1. A3 by 24
   2. B4 by 18
   3. C5 by 14
   4. D6 by 12

Check your progress

Choose the box that best describes how you feel about each skill.