NY Next Generation Math NY-7.RP.1

Math7th GradeAnalyze proportional relationships and use them to solve real-world and mathematical problems.

The Standard

Compute unit rates associated with ratios of fractions.

New York State Next Generation Mathematics Learning Standards

Teacher's field guide

What Students Need to Do: Students divide one fractional quantity by another to find an amount per one unit. They identify what the resulting unit rate measures and label it correctly.
What Mastery Looks Like: A student finds that 3/4 mile in 1/2 hour is 3/2 miles per hour. The student can explain why dividing by 1/2 doubles the amount.
Common Misconceptions: Students may reverse the two quantities, invert the wrong fraction, or omit the unit. They may also divide numerators and denominators separately instead of using fraction division correctly.
How to Assess It: A cyclist travels 2 1/4 miles in 3/4 hour. Ask students to find the miles per hour and show how the units guide the division.

Lesson moves

Mark 3/4 meter of tape and time a 1/2-minute walk, then calculate meters per minute from the two measurements.
Ask, "Why is 3/4 divided by 1/2 greater than 3/4?"
Match ratio cards such as 2/3 cup in 1/4 batch with their unit-rate cards, then justify each match.
Compare prices for fractional-pound packages and calculate each item's cost per pound.

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