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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 - Challenge Me

NameDate

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

  1. Esme finds a puzzle taped to the door. Which expression is equal to 2(3x − 1) + x + 5?

    • 7x + 4
    • 10x
    • 7x + 7
    • 7x + 3

  2. Luz opens an envelope that holds one tiny puzzle. Luz writes 1.5x + 4.5 = 1.5(x + ?). What number replaces the question mark so the sides are equivalent?

  3. Ren spots a puzzle at the back of a book. Ren writes x/3 + 4/3 = (x + ?)/3. What number replaces the question mark so the sides are equivalent?

  4. Tala has one minute on the clock, and it ticks loudly. Tala writes x/4 + 3/2 = (x + ?)/4. What number replaces the question mark so the sides are equivalent?

  5. Bo builds a kite frame with two sides of x cm and two sides of y cm. Which form of the whole way around shows half of it inside one set of parentheses?

    • x + y
    • 2x + 2y
    • 2x + y
    • 2(x + y)

  6. Esme tests x = -1 on paper: 2x + 3 and 3x + 4 both give 1. Esme says they are equivalent. What is wrong with that?

    • Nothing. They match at x = -1, so they match for every x.
    • One test with a bigger number would prove they are equivalent.
    • They differ at x = 0: 2x + 3 gives 3 and 3x + 4 gives 4.
    • Nothing. Both are linear, so they are equivalent.

  7. Jun tests x = 1 on paper: x/2 + 3 and 2x + 1.5 both give 3.5. Jun says they are equivalent. What is wrong with that?

    • They differ at x = 2: x/2 + 3 gives 4 and 2x + 1.5 gives 5.5.
    • Nothing. Both are linear, so they are equivalent.
    • Nothing. They match at x = 1, so they match for every x.
    • One test with a bigger number would prove they are equivalent.

  8. Luz has a rectangle x long and y wide, so the way around is 2x + 2y. What does 2y stand for?

    • one short side
    • the two long sides together, on top and bottom
    • the two short sides together
    • the whole way around

  9. Each level gives Noah x points and costs 3 points to puddles. After 5 levels the total is 5x − 15. What does the 15 stand for?

    • the points won in all 5 levels
    • the points lost in one level
    • the number of levels
    • the points lost in all 5 levels

  10. Each level gives Pia x points and costs 2 points to puddles. After 6 levels the total is 6(x − 2). What does (x − 2) stand for?

    • the points lost in one level
    • the points from all 6 levels
    • the number of levels
    • the points from one level
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7th grade Equivalent expressions and what each form tells you worksheet – printable
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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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