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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: Clue: "A number plus 5 equals 9." Write an equation. Then test n = 3 and n = 4. Let n be the number. Write the equation. (n + 5 = 9) Test n = 3. Is it a solution? (No. 3 + 5 = 8, and 8 is not 9.) Test n = 4. Is it a solution? (Yes. 4 + 5 = 9.) Why does substituting tell you if a value is a solution? (A solution must make both sides equal. Substituting shows if the two sides match.)

   Show your work
2. 2

   Warm restartReflect the point (4, 3) across the x-axis. What are the new coordinates?

   1. A(3, 4)
   2. B(4, −3)
   3. C(−4, 3)
   4. D(−4, −3)

   How do you know?
3. 3

   Warm restartReflect the point (−2, 5) across the y-axis.

   1. A(2, 5)
   2. B(−2, −5)
   3. C(2, −5)
   4. D(5, −2)

   How do you know?
4. 4

   Warm restartWhen you reflect a point across the x-axis, which coordinate changes sign?

   1. AThe y-coordinate
   2. BThe x-coordinate
   3. CBoth of them
   4. DNeither of them

   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 p + 14 = 37.

   1. Ap = 14
   2. Bp = 23
   3. Cp = 37
   4. Dp = 51

   Why is that the answer?
2. 6

   Think it throughWhy subtract 14 from BOTH sides?

   1. ATo keep the equation balanced while isolating p
   2. BBecause subtraction is easier than addition
   3. CBecause 14 is the smaller number
   4. DTo make the answer a whole number

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

   Think it throughCheck 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

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

   Back to the modelHow did you decide what expression to put on each side of the balance?

Use the words

Fill each blank with a word from the bank.

• A math sentence that says two amounts are equal, with an = sign, is an ___.
• A letter that stands for an unknown number is a ___.
• The symbol = that shows two amounts are the same is the ___.
• A group of numbers and variables with no equal sign is an ___.

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 Write Equations is writing subtraction and division clues in the wrong order — putting the number from the clue first instead of the variable first.
2. 10

   Say moreOn the balance scale you put n + 8 on one side and 20 on the other. How did you decide what belongs on each side of the equal sign?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: Detective Ruiz pins a clue to the case board: 'A number of stolen gems, plus 8 more found in the safe, equals 20 gems in all.'

   Show your work

Last check

These two come from Lesson 7.9. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowExplain 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

   Explain your choice.
2. 13

   From Lesson 7.9Explain your thinking — What is the reflection of (-5, 2) over the y-axis?

   1. A(-5, -2)
   2. B(2, -5)
   3. C(5, -2)
   4. D(5, 2)

   How do you know?
3. 14

   From Lesson 7.9Reflecting over the y-axis changes which coordinate?

   1. AOnly the y-coordinate
   2. BOnly the x-coordinate
   3. CBoth coordinates
   4. DNeither coordinate

   How do you know?

Be honest — this tells your teacher what to do next