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7th grade · Math · Unit 17 of 20

Rewriting Expressions

Same value, clearer meaning

What your child practices

Writing the same expression in a different form to see what it means: a 6% increase as 1.06p, 20% off as 0.8p, and 4t + 4s as 4(t + s), what each friend spends times 4.

New York State Learning Standards learning standard: NY-7.EE.2 · rewriting expressions in different forms to show how the quantities in a problem are related

How we explain it

Children can open this short lesson before they practice.

  1. Equivalent expressions have the same value, but each form can show something different.
  2. p + 0.06p = 1.06p shows a 6% increase in one step.
  3. 4t + 4s = 4(t + s) shows 4 groups of t + s.

Example: A price p is 20% off. Write the sale price as one term. The discount is 0.2p, so the sale price is p − 0.2p. 1p − 0.2p = 0.8p: you pay 80% of the price. Answer: 0.8p

Rewriting Expressions in New York

In the New York State Learning Standards, this is unit 17 of 20 in 7th grade Math, after Scale Drawings and before One Triangle, Many or None?.

Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.

Source: New York State Education Department (NYSED)

Sample questions

A taste of this unit. In the app, questions change every time and get easier or harder to match your child.

  1. Question 1

    A jacket costs p dollars and is 40% off. Which expression gives the sale price?

    • 1.4p
    • 0.6p
    • p − 40
    • 0.4p

  2. Question 2

    A salary p goes up by 3%. The new salary is p + 0.03p. Which expression is the same?

    • 0.03p
    • 1.3p
    • 1.03p
    • p + 3

  3. Question 3

    a + a + a + a is the same as 4a. What does 4a show more clearly?

    • that a is 4
    • that there are 4 equal amounts
    • that the total is a
    • that there are 4 different amounts

  4. Question 4

    A sale price is written as 0.97p. What does this tell you?

    • The price is 0.97 dollars off
    • The price went up by 3%
    • The price is 97% off
    • The price is 3% off

  5. Question 5

    9 friends each buy a ticket and a snack. The total cost is 9(t + s). What does t + s stand for?

    • the number of friends
    • what one friend spends
    • what all the friends spend
    • the cost of all the tickets

  6. Question 6

    A sale price is written as 0.95p. What does this tell you?

    • The price is 95% off
    • The price is 0.95 dollars off
    • The price is 5% off
    • The price went up by 5%

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