Grade 7 · Math

7th grade Equivalent expressions and what each form tells you worksheet

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Equivalent expressions and what each form tells you

Grade 7 Math Worksheet

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Circle the best answer, or write your answer on the line.

1.
In each level, Pia wins x points from stars and loses 3 points to puddles. There are 4 levels. Which expression for all the levels shows the points from one level?
- 4(x − 3)
- 4x − 12
- 4x − 3
- -8x
2.
In each level, Ren wins x points from stars and loses 2 points to puddles. There are 5 levels. Which expression counts the points from stars and the points lost separately, for all the levels?
- 5x − 2
- 5x − 10
- 5(x − 2)
- -5x
3.
Each of Bo's 3 buckets holds x shells and 5 pebbles, so the total is 3x + 15. What does the 15 stand for?
- the pebbles in one bucket
- the number of buckets
- the shells in all 3 buckets
- the pebbles in all 3 buckets
4.
Each level gives Esme x points and costs 5 points to puddles. After 4 levels the total is 4(x − 5). What does (x − 5) stand for?
- the number of levels
- the points from all 4 levels
- the points lost in one level
- the points from one level
Kira reads a puzzle painted on a castle wall. Kira writes 2.5x + 10 = 2.5(x + ?). What number replaces the question mark so the sides are equivalent?
Luz reads a puzzle by flashlight in a tent. Luz writes -3x + 12 = -3(x + ?). What number replaces the question mark so the sides are equivalent?
Milo solves a puzzle on the bus, bumps and all. Milo writes 3.5x + 14 = 3.5(x + ?). What number replaces the question mark so the sides are equivalent?
Noah finds a puzzle on top of the piano. Noah writes 5(x − 4) = 5x − ?. What number replaces the question mark so the sides are equivalent?
Pia ties a puzzle card to a kite. Pia writes 1.5(x + 6) = 1.5x + ?. What number replaces the question mark so the sides are equivalent?
Ren gets a puzzle from a toy rocket. Ren writes -3(x + 2) = -3x + ?. What number replaces the question mark so the sides are equivalent?

7th grade Equivalent expressions and what each form tells you worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Equivalent expressions and what each form tells you. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can say why 2x + 6 and 3x + 5 are not equivalent even though they match at x = 1.
I can tell which form shows one box (the parentheses) and which form counts each kind separately (the expanded form).
I can find the missing number that makes two forms equal, like 6x + 42 = 6(x + ?), and say what a part of a form stands for in the story.

Standard: 7.EE.A.2

Words to know

equivalent: Two expressions are equivalent if they give the same number for every x.

form: One way of writing an expression, like 3(x + 2) or 3x + 6.

expanded form: A form with no parentheses, like 3x + 6, that counts each kind of piece separately.

parentheses form: A form like 3(x + 2) that shows one group and how many groups there are.

coefficient: The number multiplying the letter. In 3x + 4 it is 3.

test value: A number put in for x to compare two expressions.

Common mistakes

Your child rewrote an expression in parentheses by multiplying only the first term, so the second term was counted once.

Your child added the plain numbers into the x pieces, so numbers with no letter became extra x's.

Your child multiplied all the numbers together and put the answer on x, so the plain piece turned into more x's.

What to say

Ask: how many bars have the second piece? Draw them and count.

Ask: can a plain piece and an x piece go into one pile?

Ask: which piece is x, and which piece is just a number?

Questions parents ask

What is the most common mistake with equivalent expressions and what each form tells you?

Your child rewrote an expression in parentheses by multiplying only the first term, so the second term was counted once.

How can I help my child with equivalent expressions and what each form tells you?

Ask: how many bars have the second piece? Draw them and count.

Are these 7th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More grade 7 math

See all grade 7 math

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