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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: Solve x − 4 = 9. Then explain the step you used. What is done to x? What is the inverse? (4 is subtracted from x. The inverse is adding 4.) Add 4 to both sides. What is x? (x = 9 + 4 = 13) Check: does 13 make the equation true? (Yes. 13 − 4 = 9.) Why do we add 4 to both sides, not just one side? (The two sides are equal. If we add 4 to both, they stay equal.)

   Show your work
2. 2

   Warm restartWhich equation represents: 'Three times a number equals 21'?

   1. An + 3 = 21
   2. Bn − 3 = 21
   3. C3n = 21
   4. Dn / 3 = 21

   How do you know?
3. 3

   Warm restartWhich equation represents: 'Seven less than a number is 18'?

   1. A7 − n = 18
   2. Bn − 7 = 18
   3. Cn + 7 = 18
   4. Dn / 7 = 18

   How do you know?
4. 4

   Warm restartWhich equation represents: 'A number plus 12 equals 30'?

   1. An − 12 = 30
   2. B12n = 30
   3. Cn + 12 = 30
   4. Dn / 12 = 30

   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 d + 4.5 = 12.

   1. Ad = 4.5
   2. Bd = 7.5
   3. Cd = 8.5
   4. Dd = 16.5

   Why is that the answer?
2. 6

   Think it throughWhich operation undoes addition?

   1. AMultiplication
   2. BDivision
   3. CSubtraction
   4. DSquaring

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

   Think it throughCheck: 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

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

   Back to the modelWhy do you have to subtract 19 from BOTH sides, not just one?

Use the words

Fill each blank with a word from the bank.

• A math sentence with an equal sign showing two equal amounts is an ___.
• An operation that undoes another, like subtraction undoing addition, is an ___.
• To get the variable alone on one side of the equation is to ___ it.
• The value of the variable that makes the equation true is the ___.

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 applying the same operation instead of the inverse — for example, solving x − 7 = 15 by subtracting 7 from both sides (getting the wrong x = 8) instead of adding 7 to both sides (the correct x = 22).
2. 10

   Say moreWhat inverse operation did you use to solve n + 23 = 58, and why must you do it to BOTH sides of the balance?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: The top row shows two baseballs and a bat with a total of 50. The bottom row shows one baseball and a bat with a total of 45. Compare the two rows.

   Show your work

Last check

These two come from Lesson 8.1. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain your thinking — Solve: p + 2.8 = 9.1

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

   Explain your choice.
2. 13

   From Lesson 8.1Explain your thinking — Which value is the solution of n + 5 = 9, and how do you know?

   1. An = 3, because 3 is close to 4
   2. Bn = 4, because 4 + 5 = 9 is true
   3. Cn = 5, because 5 appears in the equation
   4. Dn = 14, because 9 + 5 = 14

   How do you know?
3. 14

   From Lesson 8.1Check your answer: does 23 work?

   1. AYes — 23 + 14 = 37
   2. BNo — 23 + 14 = 47
   3. CNo — 23 − 14 = 9
   4. DYou cannot check an equation

   How do you know?

Be honest — this tells your teacher what to do next