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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: A factor tree breaks each number into primes. 48 = 2 × 2 × 2 × 2 × 3, and 36 = 2 × 2 × 3 × 3. Now look at what the two share: two 2s and one 3. Multiply the shared primes: 2 × 2 × 3 = 12. Same answer as the lists, 12 — which is the check. For big numbers, the factor tree is usually the faster road. Now prove it: say why that move had to work at all — not just that it did.

   Show your work
2. 2

   Warm restartWhich expression is equivalent to 5x + 2x?

   1. A7x
   2. B10x
   3. C7x²
   4. D52x

   How do you know?
3. 3

   Warm restartAre 3(n + 2) and 3n + 6 equivalent? Test with n = 4.

   1. AYes — both equal 18
   2. BNo — one is 18 and one is 14
   3. CYes, but only when n = 0
   4. DYou cannot test with a number

   How do you know?
4. 4

   Warm restartSimplify 6a + 4 − 2a.

   1. A4a + 4
   2. B8a
   3. C2a + 4
   4. D4a

   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 the GCF of 48 and 36?

   1. A12
   2. B6
   3. C144
   4. D4

   Why is that the answer?
2. 6

   Think it throughWhat is the LCM of 6 and 8?

   1. A24
   2. B48
   3. C2
   4. D14

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

   Think it throughA problem asks when two repeating schedules meet again. Which do you use?

   1. AThe least common multiple
   2. BThe greatest common factor
   3. CEither one works
   4. DNeither — you list factors

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

   Back to the modelBoth problems say “common.” How do you decide whether a problem wants the GCF or the LCM?

Sort it again — on paper this time

Write the letter of the group each one belongs in.

• What is the largest number of identical combo packs?
• When will both classes fall in the same week again?
• How many equal groups can I split both stocks into?
• Hot dogs come in 10s and buns in 8s — when do they match?
• The answer is never bigger than either number
• The answer is never smaller than either number

Use the words

Fill each blank with a word from the bank.

• Factors ___ a number; multiples are what it ___.
• A number that divides another exactly, with no remainder, is a ___.
• What you land on counting by a number are its ___.
• The largest number that divides both is their ___ ___ ___.

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 is reaching for the wrong tool: listing FACTORS for a problem about repeating cycles.
2. 10

   Say moreHow did you find the factors that 24 and 36 share, and how did you decide which one is the GCF?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Mission Control sorted the factors of 56 and the factors of 48 into two overlapping rings. The numbers that divide BOTH 56 and 48 sit in the middle, where the rings cross.

   Show your work

Last check

These two come from Lesson 6.6. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — Two supply runs repeat every 6 weeks and every 8 weeks, and both happen this week. When will they next happen in the same week?

   1. AWeek 24, the least common multiple of 6 and 8
   2. BWeek 2, the greatest common factor of 6 and 8
   3. CWeek 48, because 6 × 8 = 48
   4. DWeek 14, because 6 + 8 = 14

   Explain your choice.
2. 13

   From Lesson 6.6Explain your thinking — Which expression is equivalent to 6n + 4 + 3n − 1?

   1. A9n + 3
   2. B9n + 5
   3. C63n
   4. D18n + 4

   How do you know?
3. 14

   From Lesson 6.6Test it: what does each expression equal when h = 5?

   1. ABoth equal 60
   2. BBoth equal 90
   3. CA = 60 and B = 55
   4. DA = 50 and B = 60

   How do you know?

Be honest — this tells your teacher what to do next