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 try together: Let's factor 12 together. What is one way to split 12 into two factors? (You might say 3 × 4.) Is 3 prime? Yes, so we keep it. Is 4 prime? No — what is 4 split apart? (4 = 2 × 2.) So put the prime factors together: 12 = 2 × 2 × 3. Every factor is prime, so we are done.

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

   Show your work
2. 2

   Warm restartWhat is the LCM of 6 and 9?

   1. A18
   2. B54
   3. C3
   4. D27
3. 3

   Warm restartList the first four multiples of 7.

   1. A7, 14, 21, 28
   2. B1, 7, 14, 21
   3. C7, 7, 7, 7
   4. D7, 17, 27, 37
4. 4

   Warm restartWhat is the LCM of 5 and 10?

   1. A10
   2. B50
   3. C5
   4. D15

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 the prime factorization of 72?

   1. A2³ × 3²
   2. B2² × 3³
   3. C8 × 9
   4. D6 × 12

   Why is that the answer?

   I chose ___ because ___ .
2. 6

   Think it throughThe gardener wants a grid with 8 rows. How many pods in each row so all 72 are used?

   1. A9
   2. B6
   3. C12
   4. D64

   How do you know?

   I chose ___ because ___ .
3. 7

   Think it throughWhich 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

   Explain your thinking.

   I chose ___ because ___ .
4. 8

   Back to the modelHow did you decide whether a number is prime or composite? What strategy did you use?

   I know ___ is prime because its only factors are ___ and ___. I know ___ is composite because it has factors like ___.

Use the words

Fill each blank with a word from the bank.

• Writing a number as ___ numbers multiplied together is its prime factorization.
• A whole number greater than 1 with exactly two factors, 1 and itself, is a ___ number.
• A whole number greater than 1 that has more than two factors is a ___ number.
• A number that divides evenly into another number is called a ___.

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 Prime Factorization is stopping the factor tree too soon — leaving a composite number like 4, 6, 8, or 9 in the final answer instead of continuing to split it.
2. 10

   Say moreLook at your factor tree for 60. How did you decide which numbers to break apart first, and how do you know when to stop?

   I broke ___ into ___ because ___.
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 6.12. 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 prime factorization of 40?

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

   Explain your choice.

   I know it is ___ because ___ .
2. 13

   From Lesson 6.12Quick check — you've got this: What is the LCM of 9 and 12?

   1. A36
   2. B108
   3. C3
   4. D72
3. 14

   From Lesson 6.12How many packs of buns do you buy?

   1. A3
   2. B4
   3. C5
   4. D6

Be honest — this tells your teacher what to do next