Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, "This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar." "We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger."
Official wording from the Common Core State Standards for Mathematics (© 2010 National Governors Association Center for Best Practices and Council of Chief State School Officers). View on thecorestandards.org
A unit rate tells you how much of one quantity goes with exactly one unit of another. If 4 notebooks cost $10, the unit rate is $2.50 per notebook; if a car travels 150 miles in 3 hours, the unit rate is 50 miles per hour. Sixth graders learn that every ratio a:b (with b not zero) comes with a unit rate a/b, found by dividing the first quantity by the second.
What students must get right is which quantity sits on top. From 4 notebooks for $10, the rate could be $2.50 per notebook or 0.4 notebooks per dollar, and both are true; the question decides which one is useful. Unit rates can be fractions too. A recipe with 3 cups of flour to 4 cups of sugar gives 3/4 cup of flour per cup of sugar. Using the word 'per' correctly, and attaching units to every rate, is part of meeting this standard, not an optional extra.
Students divide the bigger number by the smaller one out of habit. For 6 apples costing $3, the price per apple is 3 ÷ 6 = $0.50, not 6 ÷ 3.
An answer of '25' is meaningless without '25 words per minute'. Insist that every rate names both quantities.
Three pizzas shared by four friends gives 3/4 of a pizza per friend. Fractional and decimal unit rates are normal.
Knowing a car goes 50 miles per hour does not tell you how far it went. Students need the time as well before they can find a distance.
Store A sells 6 granola bars for $4.50. Store B sells 8 of the same bars for $5.60. Which store has the lower price per bar?
Answer: Store B is cheaper at $0.70 per bar, compared with $0.75 per bar at Store A.
Begin with situations where the unit rate is easy to see (5 tickets for $20) and ask 'how much for one?' before introducing the word unit rate. Double number lines are especially helpful, because the 1 on the bottom line lines up with the unit rate on the top line.
Assessments often hide the unit rate inside a comparison: which runner is faster, which bag is the better buy. Students who write the rate with units every time make far fewer mistakes on these items.
Original questions written for this standard. Choose an option or type your answer, then press Check. Every question has a worked explanation.
Answer: 30 (also accepted: 30 pages per minute)
Pages per minute means pages ÷ minutes: 90 ÷ 3 = 30 pages per minute.
Answer: C) $1.60
Price per pound is dollars ÷ pounds: 8 ÷ 5 = 1.60, so $1.60 per pound.
Answer: 2/5
Milk per cup of flour is milk ÷ flour: 2 ÷ 5 = 2/5 cup of milk for each cup of flour.
Answer: A) 60 words per minute
Words per minute = 240 ÷ 4 = 60. She types 60 words per minute.
Answer: 12 (also accepted: 12 mph, 12 miles per hour)
Miles per hour = 36 ÷ 3 = 12 miles per hour.
Answer: C) The cost is $0.75 per juice box
Dollars per box = 9 ÷ 12 = 0.75. You would get 12 ÷ 9, about 1.33 boxes, per dollar, not 0.75.
A full lesson with slides, activities and an exit ticket on unit rates, pitched to grade 6 and editable in PowerPoint or Google Slides.
Make a lesson →A printable, differentiated worksheet on 6.RP.A.2 with an answer key, ready in about a minute.
Make a worksheet →Turn unit rates into a quiz students answer online that marks itself, with a class summary for you.
Build a test →A unit rate is a rate for exactly one unit of the second quantity, such as $3 per pound or 45 miles per hour. For a ratio a:b it is a/b.
Yes. If 3 cups of oats make 4 batches, the rate is 3/4 cup per batch. Sixth graders work with whole-number, fraction and decimal unit rates.