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: Are 2x + 3x and 5x equivalent? Test x = 2. Then explain why they always match. Substitute x = 2 into both expressions. (2 × 2 + 3 × 2 = 10 and 5 × 2 = 10) Combine the like terms in 2x + 3x. (2x + 3x is 5x.) Why does 2x + 3x match 5x for every x, not just 2? (2 groups of x plus 3 groups of x is 5 groups of x. That is true for any number x.)

   Show your work
2. 2

   Warm restartEvaluate 4n + 3 when n = 5.

   1. A23
   2. B27
   3. C35
   4. D45

   How do you know?
3. 3

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

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

   How do you know?
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

   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 throughSimplify 4h + 2h + 30.

   1. A4h + 32
   2. B6h + 30
   3. C6h + 30h
   4. D36h

   Why is that the answer?
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? Give a second reason as well.
3. 7

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

   1. AA = 50 and B = 60
   2. BBoth equal 60
   3. CA = 60 and B = 55
   4. DBoth equal 90

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

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

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?
3. 11

   Write your ownWrite your own problem about this situation, then solve it and show the answer. The situation: The same square is shown two ways — broken into green strips and yellow unit squares on the left, and as one whole red square on the right.

   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 knowExplain your thinking — Which expression is equivalent to 6n + 4 + 3n − 1?

   1. A9n + 3
   2. B9n + 5
   3. C18n + 4
   4. D63n

   Explain your choice.
2. 13

   From Lesson 6.5Explain your thinking — 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

   How do you know?
3. 14

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

   1. A25
   2. B8
   3. Ch
   4. D25h

   How do you know?

Be honest — this tells your teacher what to do next