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: Solve x ÷ 4 = 9. Is x multiplied or divided? It is divided by 4, so the inverse is multiplying both sides by 4. x = 9 × 4 = 36. Check: 36 ÷ 4 = 9. True?

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

   Show your work
2. 2

   Warm restartSolve: m − 11 = 25

   1. Am = 14
   2. Bm = 25
   3. Cm = 275
   4. Dm = 36
3. 3

   Warm restartSolve: n + 15 = 42

   1. An = 57
   2. Bn = 27
   3. Cn = 15
   4. Dn = 42
4. 4

   Warm restartSolve: y − 7 = 20

   1. Ay = 13
   2. By = 27
   3. Cy = 7
   4. Dy = 140

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 throughSolve 7k = 63.

   1. Ak = 9
   2. Bk = 70
   3. Ck = 56
   4. Dk = 441

   Why is that the answer?

   I chose ___ because ___ .
2. 6

   Think it throughWhich operation undoes multiplication?

   1. ADivision
   2. BAddition
   3. CSubtraction
   4. DMultiplication

   How do you know?

   I chose ___ because ___ .
3. 7

   Think it throughCheck: does 9 work?

   1. AYes — 7 × 9 = 63
   2. BNo — 7 × 9 = 56
   3. CNo — 7 + 9 = 16
   4. DOnly if kits cost $9

   Explain your thinking.

   I chose ___ because ___ .
4. 8

   Back to the modelHow do you decide whether to multiply or divide to solve an equation?

   When I see ___ in the equation, I know to ___ both sides because the inverse of ___ is ___.

Use the words

Fill each blank with a word from the bank.

• Undo a multiplication by ___ both sides by the same number.
• An operation that undoes another, like division undoing multiplication, is an ___.
• To undo dividing by a number, I ___ both sides by that number.
• To undo multiplying by a number, I ___ both sides by that number.

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 Solve Multiplication and Division Equations is applying the SAME operation again instead of the inverse — for example, seeing 6x = 42 and multiplying both sides by 6 to get x = 252, instead of dividing by 6 to get x = 7.
2. 10

   Say moreHow did you undo the multiplication in 3x = 21 (or the division in x / 4 = 9) to isolate the variable?

   I divided / multiplied both sides by ___, so the answer is ___.
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 8.2. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowQuick check — you've got this: Solve: w / 8 = 6

   1. Aw = 48
   2. Bw = 14
   3. Cw = 0.75
   4. Dw = 2

   Explain your choice.

   I know it is ___ because ___ .
2. 13

   From Lesson 8.2Quick check — you've got this: Solve: p + 2.8 = 9.1

   1. Ap = 6.3
   2. Bp = 11.9
   3. Cp = 7.7
   4. Dp = 3.25
3. 14

   From Lesson 8.2Check: does 7.5 work?

   1. AYes — 7.5 + 4.5 = 12
   2. BNo — 7.5 + 4.5 = 11
   3. CNo — 7.5 − 4.5 = 3
   4. DOnly if the trail is 11 miles

Be honest — this tells your teacher what to do next