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 prime factors to find the GCF of 48 and 36.
   2. Use the factor tree. Write 48 as a product of primes. (2 × 2 × 2 × 2 × 3)
   3. Write 36 as a product of primes. (2 × 2 × 3 × 3)
   4. Which primes do both numbers share? (Two 2s and one 3.)
   5. Multiply the shared primes. What is the GCF? (2 × 2 × 3 = 12)

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

   Show your work
2. 2

   Quick reviewWhich expression is equivalent to 5x + 2x? 🔊 Listen 💡 Hint

   1. A7x
   2. B7x²
   3. C10x
   4. D52x
3. 3

   Quick reviewAre 3(n + 2) and 3n + 6 equivalent? Test with n = 4. 🔊 Listen 💡 Hint

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

   Quick reviewSimplify 6a + 4 − 2a. 🔊 Listen 💡 Hint

   1. A2a + 4
   2. B4a + 4
   3. C4a
   4. D8a

Try these on your own

Choose an answer. Then explain how you know.

1. 5

   Think it throughWhat is the GCF of 48 and 36? 🔊 Listen 💡 Hint

   1. A4
   2. B6
   3. C12
   4. D144

   Why is that the answer?

   I chose ___ because ___ .
2. 6

   Think it throughWhat is the LCM of 6 and 8? 🔊 Listen 💡 Hint

   1. A2
   2. B14
   3. C24
   4. D48

   How do you know?

   I chose ___ because ___ .
3. 7

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

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

   Explain your thinking.

   I chose ___ because ___ .
4. 8

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

   If the problem ___ something into equal groups, I use the ___. If it asks when things ___ again, I use the ___.

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.

• 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 ___ ___ ___.
• The smallest number both numbers reach is their ___ ___ ___.

Explain the thinking

1. 9

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

   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? 🔊 Listen 💡 Hint

   The common factors are ___.
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 6.6. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowQuick check — you've got this: 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? 🔊 Listen 💡 Hint

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

   Explain your choice.

   I know it is ___ because ___ .
2. 13

   From Lesson 6.6Quick check — you've got this: Which expression is equivalent to 6n + 4 + 3n − 1? 🔊 Listen 💡 Hint

   1. A9n + 3
   2. B9n + 5
   3. C18n + 4
   4. D63n
3. 14

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

   1. AA = 50 and B = 60
   2. BBoth equal 60
   3. CA = 60 and B = 55
   4. DBoth equal 90

Check your progress

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