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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.

   Let's try together: Let's check 2x + 3x and 5x. Try x = 2. 2(2) + 3(2) = 4 + 6 = 10, and 5(2) = 10. Same answer. So 2x + 3x and 5x are equivalent.

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

   Show your work
2. 2

   Warm restartEvaluate 4n + 3 when n = 5.

   1. A23
   2. B35
   3. C27
   4. D45
3. 3

   Warm restartWhich expression means '7 more than a number x'?

   1. Ax + 7
   2. B7x
   3. Cx − 7
   4. D7 − x
4. 4

   Warm restartA ticket costs $9. Which expression gives the cost of t tickets?

   1. A9t
   2. Bt + 9
   3. C9 + t
   4. Dt ÷ 9

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 throughSimplify 4h + 2h + 30.

   1. A6h + 30
   2. B6h + 30h
   3. C36h
   4. D4h + 32

   Why is that the answer?

   I chose ___ because ___ .
2. 6

   Think it throughAre the two pricing formulas equivalent?

   1. AYes — 4h + 2h + 30 simplifies to exactly 6h + 30
   2. BNo — Client A pays more
   3. CNo — Client B pays more
   4. DOnly when h = 0

   How do you know?

   I chose ___ because ___ .
3. 7

   Think it throughTest it: what does each expression equal when h = 5?

   1. ABoth equal 60
   2. BBoth equal 90
   3. CA = 60 and B = 55
   4. DA = 50 and B = 60

   Explain your thinking.

   I chose ___ because ___ .
4. 8

   Back to the modelHow did you decide which expressions belong in the same group? What strategies did you use?

   I knew ___ and ___ are equivalent because when I ___ the terms, I got the same expression.

Use the words

Fill each blank with a word from the bank.

• Expressions with the same value for ___ allowed number are equivalent.
• Expressions that always have the same value are ___.
• Rewriting an expression in a shorter form that is still equal to it is to ___ it.
• Terms with the same variable raised to the same power, like 4x and 9x, are ___.

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 Equivalent Expressions is adding the exponents instead of the coefficients when combining like terms — writing 3x + 2x as 5x² instead of 5x.
2. 10

   Say moreHow can you prove 2(n + 4) and 2n + 8 are equivalent? What two strategies could you use?

   They are equivalent because distributing 2(n + 4) gives ___.
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 6.5. If they are shaky, that is the lesson to revisit — not this one.

1. 12

   Show what you knowQuick check — you've got this: Which expression is equivalent to 6n + 4 + 3n − 1?

   1. A9n + 3
   2. B9n + 5
   3. C63n
   4. D18n + 4

   Explain your choice.

   I know it is ___ because ___ .
2. 13

   From Lesson 6.5Quick check — you've got this: A club orders one $4.25 shirt for each student plus a one-time $23.50 shipping fee. Write the expression for s students, then find the cost for 30 students.

   1. A4.25s + 23.50; for s = 30 the cost is $151.00
   2. B4.25s + 23.50; for s = 30 the cost is $832.50
   3. C4.25 + 23.50s; for s = 30 the cost is $709.25
   4. D27.75s; for s = 30 the cost is $832.50
3. 14

   From Lesson 6.5In 25 + 8h, what is the coefficient?

   1. A8
   2. B25
   3. Ch
   4. D25h

Be honest — this tells your teacher what to do next