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.

   Try it together — then prove it: Solve x ÷ 4 = 9. Then explain the step you used. What is done to x? What is the inverse? (x is divided by 4. The inverse is multiplying by 4.) Multiply both sides by 4. What is x? (x = 9 × 4 = 36) Check: does 36 make the equation true? (Yes. 36 ÷ 4 = 9.) Why do we multiply by 4 and not divide by 4? (Multiplying undoes dividing. Dividing again would make the number smaller, not get x alone.)

   Show your work
2. 2

   Warm restartSolve: m − 11 = 25

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

   How do you know?
3. 3

   Warm restartSolve: n + 15 = 42

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

   How do you know?
4. 4

   Warm restartSolve: y − 7 = 20

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

   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 throughSolve 7k = 63.

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

   Why is that the answer?
2. 6

   Think it throughWhich operation undoes multiplication?

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

   How do you know? Give a second reason as well.
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. What would have to change for a different choice to be right?
4. 8

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

Use the words

Fill each blank with a word from the bank.

• 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.
• To get the variable alone on one side is to ___ it.

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?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Detective Park lines up 3 identical locked evidence boxes on a table. Together the 3 boxes hold 21 pieces of evidence, and each box holds the same amount.

   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 knowExplain your thinking — Solve: w / 8 = 6

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

   Explain your choice.
2. 13

   From Lesson 8.2Explain your thinking — Solve: p + 2.8 = 9.1

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

   How do you know?
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

   How do you know?

Be honest — this tells your teacher what to do next