6.RP.A.2Common CoreMathRatios and Proportional RelationshipsGrade 6
6.RP.A.2: Understanding Unit Rates and Rate Language
In plain English: 6.RP.A.2 is the Common Core grade 6 math standard that asks students to understand the unit rate a/b that goes with a ratio a:b, where b is not zero, and to use rate language such as "per" and "for each". For example, 3 cups of flour for every 4 cups of sugar means 3/4 cup of flour for each cup of sugar. It builds on the ratio ideas of 6.RP.A.1.
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 note: Expectations for unit rates in this grade are limited to non-complex fractions.
Common Core State Standards for Mathematics · Domain: Ratios and Proportional Relationships (RP) · Cluster: Understand ratio concepts and use ratio reasoning to solve problems. Also written as 6.RP.2 · Official standard
Students learn that every ratio a:b, with b not zero, has a unit rate a/b: the amount of the first quantity for 1 unit of the second quantity. A rate is a ratio that compares quantities with different units, such as dollars and hamburgers, and a unit rate tells how much for exactly 1, such as $5 per hamburger. Students use rate language: "per", "for each", "for every 1" and "each". They also see that a ratio has two unit rates, one for each order (a/b and b/a), and that a unit rate can be a fraction, as in the official example with 3/4 cup of flour for each cup of sugar.
Students explain why the standard says b ≠ 0: "per 0" has no meaning, because you cannot split an amount into 0 equal groups. They use double number lines (two number lines with matching marks lined up) and tape diagrams (bars split into equal boxes) to show a unit rate, and they choose which of the two unit rates answers a question. The official note limits grade 6 unit rates to non-complex fractions: both quantities in the ratio are whole numbers or decimals, never fractions divided by fractions (that comes in 7.RP.A.1). Solving longer unit rate problems is the work of 6.RP.A.3.
Learning Objectives
By the end of this lesson, students will be able to:
Find the unit rate a/b for a ratio a:b and say what it means with units
Write the two unit rates of one ratio and choose the one that answers a question
Use rate language ("per", "for each", "for every 1") to describe a ratio relationship
Explain why a unit rate a/b needs b ≠ 0
Recognize a unit rate that is a fraction, such as 3/4 cup per cup, and show it on a double number line
Prior Knowledge Required
Students should already be comfortable with:
Writing and describing ratios with ratio language 6.RP.A.1
Reading a fraction as division, such as 3/4 = 3 ÷ 4 5.NF.B.3
Dividing whole numbers with remainders written as fractions or decimals 5.NBT.B.6
Write the price on the board and ask students to answer two questions on a sticky note:
Warm-Up Prompt
"A pack of 6 juice boxes costs $3. How much does 1 juice box cost? How many juice boxes can you buy with $1?"
Collect answers: 1 juice box costs $3 ÷ 6 = $0.50, and $1 buys 6 ÷ 3 = 2 juice boxes. Both answers describe the same ratio of 6 juice boxes to $3. Explain that each answer is a unit rate: an amount for exactly 1 of the other quantity. "$0.50 per juice box" gives dollars for 1 juice box, and "2 juice boxes per dollar" gives juice boxes for $1. The word per means "for each" or "for every 1".
Direct Instruction15-20 minutes
Part 1: From a ratio to a unit rate. A rate is a ratio that compares two quantities with different units. For a ratio a:b, the unit rate is a/b, which is a ÷ b: the amount of the first quantity for 1 unit of the second. Show the official flour example with the double number line in Diagram 1: 4 cups of sugar split into 4 steps of 1 cup, and the 3 cups of flour split into the same 4 steps, so each step of flour is 3/4 cup.
Official example: a fraction unit rate
A recipe has a ratio of 3 cups of flour to 4 cups of sugar. How much flour is there for each cup of sugar? How much sugar for each cup of flour?
Equation: a:b = 3:4, so a/b = 3/4: there is 3/4 cup of flour for each cup of sugar. In the other order, 4/3 = 1 1/3 cups of sugar for each cup of flour
Official example: a price per item
We paid $75 for 15 hamburgers. What is the rate per hamburger?
Equation: 75/15 = 5, so the rate is $5 per hamburger. The other unit rate, 15/75 = 1/5, means 1/5 of a hamburger per dollar
A speed as a unit rate
A hiker walks 9 miles in 3 hours at a steady pace. Write both unit rates with units.
Equation: 9/3 = 3 miles per hour, and 3/9 = 1/3 hour per mile (20 minutes per mile)
Why b cannot be 0
A class of 24 students has 0 students absent today. Which unit rates exist for the ratio of students present to students absent, 24:0?
Equation: 24/0 has no meaning: "students present per absent student" asks how many students go with each of 0 absent students. In the other order, 0/24 = 0 absent students per student present, which does exist
Choosing the useful unit rate
Two gallons of paint cover 700 square feet of wall. How much wall does 1 gallon cover, and how much paint does 1 square foot need?
Equation: 700/2 = 350 square feet per gallon, and 2/700 = 1/350 gallon per square foot. The first rate is easier to use when planning a painting job
Part 2: Rate language. Post these sentence frames and use them for every example: "___ per ___"; "for each ___ there is ___"; "for every 1 ___ there are ___"; "each ___ costs (or takes, or holds) ___". The unit comes after "per": in "miles per hour", the hour is the 1 unit. Show the official hamburger example with the double number line in Diagram 2: the mark for 1 hamburger lines up with $5.
Part 3: Two unit rates, and why b ≠ 0. Every ratio a:b with both numbers not zero has two unit rates, a/b and b/a. One of them usually answers the question better: to find the cost of 1 item, use dollars per item. Then discuss the absent-students example. A unit rate asks "how much for each 1 of the second quantity?". If there are 0 of the second quantity, there is nothing to share out, so the division a ÷ 0 has no answer. That is why the standard says b ≠ 0. In grade 6, both numbers in the ratio are whole numbers or decimals, so every unit rate is a whole number, a decimal or a simple fraction such as 3/4.
Guided Practice15 minutes
Pairs complete the table below. For each row, they write both unit rates with units, then circle the one that answers the question in the last column. Pairs share one rate sentence per row.
Guided practice: write both unit rates for each ratio, then answer the question.
Ratio
Question
32 students in 4 vans
How many students ride in each van?
9 cups of flour for 6 loaves of bread
How much flour goes in 1 loaf?
$12 for 5 notebooks
What is the price of 1 notebook?
2 inches of rain in 8 hours
How much rain falls in each hour?
Answers: 8 students per van (and 1/8 van per student); 1 1/2 cups of flour per loaf (and 2/3 loaf per cup of flour); $2.40 per notebook (and 5/12 notebook per dollar); 1/4 inch of rain per hour (and 4 hours per inch of rain). Ask pairs which row has a unit rate less than 1 as its answer (the rain row) and whether that makes sense. Listen for pairs who divide in the wrong order and then attach the wrong unit.
Independent Practice10-15 minutes
Students work alone on four problems. (1) A leaky faucet drips 3 liters of water in 6 hours. Write the unit rate in liters per hour and in hours per liter. (1/2 liter per hour; 2 hours per liter.) (2) A softball team won 11 games and lost 0. Is there a unit rate of wins per loss? Is there a unit rate of losses per win? (No, because 11 ÷ 0 has no meaning; yes, 0/11 = 0 losses per win.) (3) Cherries cost $18 for 3 pounds. Write a rate sentence with the word "per". ($6 per pound.) (4) A bag of 50 balloons costs $4. Which unit rate tells the cost of 1 balloon, $0.08 per balloon or 12.5 balloons per dollar? Explain. ($0.08 per balloon, because it gives dollars for 1 balloon.)
Closure5 minutes
Exit ticket: (1) A 3D printer makes 14 keychains in 7 hours. Write both unit rates. (2 keychains per hour; 1/2 hour per keychain.) (2) A drink uses 3 cups of juice for every 5 cups of water. How much juice is there for each cup of water? (3/5 cup.) (3) In one sentence, explain why a ratio a:b needs b ≠ 0 to have the unit rate a/b.
Differentiation Strategies
For Struggling Students
Give a double number line template with the 0 and 1 marks already drawn on the bottom line, so students only find the matching amount on the top line
Provide a "per" card: the word after "per" is the 1 unit, and it goes in the bottom of the division (dollars per hamburger = dollars ÷ hamburgers)
Start with ratios whose unit rates are whole numbers, such as 20 miles in 4 hours, before moving to fraction unit rates such as 3 cups for 4 people
For Advanced Students
Ask students to find two ratios with different numbers that have the same unit rate, such as 12 dollars for 3 pounds and 20 dollars for 5 pounds, and explain why
Ask: can a ratio have two unit rates that are both less than 1? Students test examples and explain why not (if a/b is less than 1, then b/a is more than 1)
Going further: give a rate built from fractions, such as 1/2 mile in 1/4 hour, and ask what makes it harder. These complex fractions are part of grade 7 (7.RP.A.1), not this standard
Assessment Guidance
What to Look For
Check that every unit rate carries its units and that the unit after "per" matches the number students divided by. Ask students to name both unit rates of a ratio and to say which one answers the question. Look for correct fraction unit rates, such as 3/5 cup per cup, instead of a flipped fraction. Students should explain b ≠ 0 in words (there is nothing to share each amount among), not only as a rule. On double number lines, the 1 mark must line up with the unit rate.
02
Classroom Activities
3 Activities
1
Two Rates from One Ratio
15 minPairs
Each pair receives 6 ratio cards. For every card, pairs write both unit rates with units, then write one rate sentence that uses "per" and one that uses "for each".
Ratio Cards (6 cards)
C1: 12 pencils for $3 (4 pencils per dollar; $0.25 per pencil)
C2: 5 laps of the school track in 10 minutes (1/2 lap per minute; 2 minutes per lap)
C3: 4 cups of water for 2 cups of rice (2 cups of water per cup of rice; 1/2 cup of rice per cup of water)
C4: 150 words typed in 3 minutes (50 words per minute; 1/50 minute per word)
C5: 3 pizzas for 12 students (1/4 pizza per student; 4 students per pizza)
C6: 7 lemons for 2 pitchers of lemonade (3 1/2 lemons per pitcher; 2/7 pitcher per lemon)
Procedure
Partner A finds the unit rate in the order the card is written (first quantity per 1 of the second); partner B finds the other unit rate
Partners check each other by multiplying: for C1, 4 pencils per dollar × $3 = 12 pencils
Write the two rate sentences on the back of the card and underline the 1 unit in each
Discussion Questions
On which two cards is the unit rate in the written order less than 1? (C2 and C5)
Why is one of the two unit rates always 1 or more? (If a/b is less than 1, then b/a is more than 1.)
For C5, which unit rate helps a teacher order pizza for a larger class? Why?
Modification for Distance Learning
Post the 6 cards on a shared slide, one per page. Pairs type both unit rates and their two sentences in the speaker notes, then the class compares the notes for C2 and C5.
2
Measure Your Walking Rate
20 minGroups of 3
Groups mark a 20-meter course in the hallway or on the playground with masking tape. Each student walks the course at a normal pace while a partner times the walk and another counts steps. Students then write unit rates for their own walk.
Procedure
Measure 20 meters with a measuring tape or meter sticks and mark the start and finish with tape
Walker: walk the course at your normal pace. Timer: record the time in seconds. Counter: count the steps
Rotate roles until everyone has walked
Each student writes three unit rates: meters per second, seconds per meter, and steps per meter
Sample Results (invented, for the teacher)
An invented walker covers 20 meters in 16 seconds with 28 steps. Unit rates: 20 ÷ 16 = 1.25 meters per second; 16 ÷ 20 = 0.8 second per meter; 28 ÷ 20 = 1.4 steps per meter. Typical walking speeds for students are about 1.1 to 1.5 meters per second, so results far outside that range are worth re-timing.
Discussion Questions
Who in your group had the highest meters per second? Did that person also have the fewest seconds per meter? Why must that happen?
What would "steps per meter" mean for someone with longer legs?
Why can't anyone have a rate of "meters per 0 seconds"?
Challenge Variation
Groups walk the course a second time at a fast pace and compare the two meters-per-second rates. They write one sentence comparing the rates with the word "per".
3
Recipe Rewrite with Unit Rates
15 minPairs
Pairs rewrite a granola bar recipe as unit rates, the way the official example rewrites 3 cups of flour to 4 cups of sugar as 3/4 cup of flour for each cup of sugar.
Recipe Card
4 cups of rolled oats
1 cup of honey
2 cups of chopped nuts
3 cups of dried fruit
Procedure
Write these unit rates as sentences with "for each": oats per cup of honey, honey per cup of oats, nuts per cup of dried fruit, and dried fruit per cup of nuts
Draw a double number line for nuts and dried fruit, with the dried fruit on the bottom line and marks at 0, 1, 2 and 3 cups
Choose two more ingredient pairs and write their unit rates
Answer Key
4 cups of oats for each cup of honey; 1/4 cup of honey for each cup of oats; 2/3 cup of nuts for each cup of dried fruit; 1 1/2 cups of dried fruit for each cup of nuts.
Discussion Questions
Name two ingredient pairs whose unit rate is exactly 2. (Oats per cup of nuts, and nuts per cup of honey.)
Which unit rate is the largest one you can make from this recipe? (4 cups of oats per cup of honey)
Why do fraction unit rates appear when the second amount is larger than the first?
03
Diagrams & Visual Aids
2 diagrams
Diagram 1: The Official Flour and Sugar Example on a Double Number Line
A double number line has two number lines with matching marks lined up. Sugar is on the bottom line, in steps of 1 cup, and flour is on the top line. The ratio 3:4 of flour to sugar puts 3/4 cup of flour above 1 cup of sugar, so the unit rate is 3/4 cup of flour for each cup of sugar. Marks are drawn to scale.
Diagram 2: The Official Hamburger Example on a Double Number Line
The bottom line counts hamburgers and the top line counts dollars, both drawn to scale. $75 lines up with 15 hamburgers, and dividing both by 15 gives $5 above 1 hamburger: a rate of $5 per hamburger.
04
Homework Assignment
~30 min
6.RP.A.2 Homework: Unit Rates and Rate Language
Directions: Write every unit rate with its units, such as "cups of broth per cup of vegetables". Show the division you used. Draw a double number line when a problem asks for one.
Part 1: Unit Rates from Ratios (Problems 1-2)
A soup recipe uses 7 cups of broth for every 4 cups of vegetables. (a) Find the unit rate of broth per cup of vegetables. (b) Find the unit rate of vegetables per cup of broth. (c) Write each unit rate in a sentence with "for each".
A family paid $48 for 6 movie tickets, all at the same price. (a) What is the rate per ticket? (b) What is the other unit rate, in tickets per dollar? (c) Which unit rate would you use to find the price of 1 ticket, and why?
Part 2: Using Rate Language (Problems 3-4)
A school printer prints 90 pages in 5 minutes. (a) Write the ratio of pages to minutes. (b) Find the unit rate in pages per minute and write a sentence with "per". (c) Find the unit rate in minutes per page, and explain what it tells you.
A car travels 110 miles on 4 gallons of gas. Decide whether each statement is true or false, and explain: (a) The car goes 27.5 miles per gallon. (b) The car uses 2/55 gallon per mile. (c) The car goes 27.5 gallons per mile. (d) For every 1 gallon, the car goes 106 miles.
Part 3: Explaining Unit Rates (Problems 5-6)
A chess club has 8 boys and 0 girls. Mia says, "The ratio of boys to girls is 8:0, so the unit rate is 8 boys per girl." Explain why Mia is wrong. Is there a unit rate of girls per boy? If so, what is it?
A smoothie uses 2 cups of yogurt for every 5 cups of fruit. Kai says there is 2/5 cup of yogurt for each cup of fruit. Lea says there are 2 1/2 cups of fruit for each cup of yogurt. Who is right? Draw a double number line with the fruit on the bottom line to support your answer.
Rubric
Criterion
Full Credit (2 pts)
Partial Credit (1 pt)
No Credit (0 pts)
Finding Unit Rates
Both unit rates found correctly, including fraction unit rates
One unit rate correct, or the division is right but not simplified
Unit rates missing or found by subtracting
Units and Rate Language
Every rate has correct units and a clear sentence with "per" or "for each"
Correct numbers but a missing or reversed unit
No units or sentences
Choosing and Explaining
Chooses the useful unit rate and explains b ≠ 0 in words
Correct choice or explanation, but not both
No explanation
Double Number Lines
Marks are evenly spaced and the 1 mark lines up with the unit rate
Correct numbers but uneven spacing
Diagram missing or incorrect
05
Quiz: 20 Questions
Interactive, with answers
Instructions
Work through the questions in order. Your score updates as you answer, and Reset quiz clears everything so you or your students can try again.
Multiple choice: pick an option to check it. Short answer: write your answer, then reveal the model answer.
0 of 20 answered · 0 correct
Question 1 of 20 · Multiple Choice
A punch recipe uses 10 cups of juice for every 2 cups of soda. What is the unit rate of juice per cup of soda?
Answer: D
Juice per cup of soda is 10 ÷ 2 = 5 cups of juice per cup of soda. Choice A divides in the wrong order: 2 ÷ 10 = 1/5 is soda per cup of juice. Choice B subtracts, 10 - 2 = 8. Choice C adds, 10 + 2 = 12.
Question 2 of 20 · Multiple Choice
A club paid $36 for 4 pizzas, all at the same price. What is the rate per pizza?
Answer: B
The rate per pizza is $36 ÷ 4 = $9 per pizza. Check: 4 × $9 = $36. Choice A subtracts, 36 - 4 = 32. Choice C multiplies, 36 × 4 = 144. Choice D divides 4 ÷ 36 ≈ 0.11, which is pizzas per dollar, then labels it with the wrong units.
Question 3 of 20 · Multiple Choice
Dana hikes 11 miles in 4 hours at a steady pace. What is her unit rate in miles per hour?
Answer: B
Miles per hour means miles ÷ hours: 11 ÷ 4 = 11/4 = 2 3/4 miles per hour, a steady hiking pace. Choice A divides 4 ÷ 11, which gives hours per mile, not miles per hour. Choice C subtracts, 11 - 4 = 7. Choice D multiplies, 11 × 4 = 44.
Question 4 of 20 · Multiple Choice
A salad dressing uses 2 tablespoons of vinegar for every 3 tablespoons of oil. How much vinegar is there for each tablespoon of oil?
Answer: A
The ratio of vinegar to oil is 2:3, so the unit rate is 2/3: there is 2/3 tablespoon of vinegar for each tablespoon of oil. Choice B is 3/2, the oil for each tablespoon of vinegar. Choice C is the difference, 3 - 2 = 1. Choice D divides the vinegar by all 2 + 3 = 5 tablespoons.
Question 5 of 20 · Multiple Choice
Sam typed 240 words in 4 minutes. Which sentence uses rate language correctly?
Answer: C
Words per minute is 240 ÷ 4 = 60, so Sam typed 60 words per minute. Choice A has the right number but swaps the units. Choice B uses the other unit rate, 4/240 = 1/60, but it is minutes per word, not words per minute. Choice D forgets to divide by the 4 minutes.
Question 6 of 20 · Multiple Choice
For which ratio of cats to dogs is there NO unit rate of cats per dog?
Answer: C
Cats per dog is cats ÷ dogs. With 0 dogs, 5 ÷ 0 has no meaning: there are no dogs to share the cats among. This is why the standard says b ≠ 0. Choice B does have a unit rate: 0 ÷ 4 = 0 cats per dog. Choice A gives 3 cats per dog, and choice D gives 1 cat per dog.
Question 7 of 20 · Multiple Choice
A class paid $84 for 12 T-shirts, all at the same price. Which statement is true?
Answer: A
$84 ÷ 12 = $7, so the rate is $7 per T-shirt. Choice B subtracts, 84 - 12 = 72. Choice C has the right number but the wrong units: the other unit rate is 12/84 = 1/7 T-shirt per dollar, not 7. Choice D adds, 84 + 12 = 96.
Question 8 of 20 · Multiple Choice
A car goes 150 miles on 5 gallons of gas. The unit rate 150 ÷ 5 = 30 is measured in which units?
Answer: B
The division is miles ÷ gallons, so 30 means 30 miles per gallon: for each gallon, the car goes 30 miles. Choice A swaps the units; gallons per mile would be 5 ÷ 150 = 1/30. Choices C and D use hours, but the problem gives no time.
Question 9 of 20 · Multiple Choice
A rice recipe uses 4 cups of rice and 6 cups of water. Which pair lists both unit rates correctly?
Answer: D
Rice per cup of water is 4/6 = 2/3, and water per cup of rice is 6/4 = 3/2 = 1 1/2. Choice A swaps the two numbers. Choice B divides each amount by the total 4 + 6 = 10 cups. Choice C uses the difference, 6 - 4 = 2, for both rates.
Question 10 of 20 · Multiple Choice
A ratio is 9:4. What is the unit rate a/b associated with this ratio?
Answer: C
For a ratio a:b, the unit rate is a/b, so 9:4 gives 9/4 = 2 1/4: 9/4 of the first quantity for each 1 of the second. Choice A is b/a, the unit rate for the other order. Choice B subtracts, 9 - 4 = 5. Choice D adds, 9 + 4 = 13.
Question 11 of 20 · Multiple Choice
Jon read 45 pages in 60 minutes. Which unit rate tells how many pages he read in each minute?
Answer: A
Pages per minute is 45 ÷ 60 = 45/60 = 3/4 page per minute. A unit rate can be less than 1. Choice B divides 60 ÷ 45 = 1 1/3, which is minutes per page, and gives it the wrong units. Choice C subtracts, 60 - 45 = 15. Choice D adds, 45 + 60 = 105.
Question 12 of 20 · Multiple Choice
18 students share 6 lab tables equally. Which describes this with rate language?
Answer: D
Students per table is 18 ÷ 6 = 3, so there are 3 students per table. Choice A divides 6 ÷ 18 = 1/3, which is tables per student, and labels it as students per table. Choice B subtracts, 18 - 6 = 12. Choice C has the right number but swaps the units.
Question 13 of 20 · Multiple Choice
A garden hose fills a 60-liter tub in 5 minutes. Which gives the rate and its meaning?
Answer: A
Liters per minute is 60 ÷ 5 = 12 liters per minute, so each minute adds 12 liters. Choice B divides 5 ÷ 60 = 1/12, which is minutes per liter, not liters per minute. Choice C subtracts, 60 - 5 = 55. Choice D multiplies, 60 × 5 = 300.
Question 14 of 20 · Multiple Choice
A pancake recipe uses 5 cups of flour for every 4 cups of milk. Which statement is correct?
Answer: C
Milk per cup of flour is 4 ÷ 5 = 4/5, so there is 4/5 cup of milk for each cup of flour. (In the other order, there are 5/4 = 1 1/4 cups of flour for each cup of milk.) Choice A uses 4/5 but calls it flour per cup of milk. Choice B uses 5/4 but calls it milk per cup of flour. Choice D is the difference, 5 - 4 = 1.
Question 15 of 20 · Short Answer
A school garden grew 42 tomatoes on 6 plants. Find the unit rate of tomatoes per plant and the unit rate of plants per tomato. Write a sentence with "per" for the more useful one.
Tomatoes per plant: 42 ÷ 6 = 7 tomatoes per plant. Plants per tomato: 6 ÷ 42 = 1/7 plant per tomato. The more useful sentence is "The garden grew 7 tomatoes per plant", because it tells how much one plant produces.
Question 16 of 20 · Short Answer
A lemonade mix uses 3 scoops of powder for every 8 cups of water. How much powder is there for each cup of water? How much water is there for each scoop of powder?
Powder per cup of water: 3/8 = 3/8 scoop for each cup of water. Water per scoop: 8/3 = 2 2/3 cups of water for each scoop. The two unit rates come from the same ratio, 3:8, in the two orders.
Question 17 of 20 · Short Answer
Explain in words what "a speed of 55 miles per hour" means. Then write two different ratios of miles to hours that have this unit rate.
It means that for each hour of driving, the car goes 55 miles. Any ratio of miles to hours whose unit rate is 55 works, for example 110 miles in 2 hours and 165 miles in 3 hours, because 110 ÷ 2 = 55 and 165 ÷ 3 = 55.
Question 18 of 20 · Short Answer
Six students are waiting at a bus stop, and 0 buses have arrived. Use this situation to explain why the ratio 6:0 of students to buses has no unit rate of students per bus.
"Students per bus" asks how many students go with each bus, which means sharing the 6 students among the buses. With 0 buses there is nothing to share them among, so 6 ÷ 0 has no answer, and the unit rate a/b does not exist. That is why the standard requires b ≠ 0.
Question 19 of 20 · Short Answer
A school paid $540 for 30 calculators, all at the same price. Write the unit price as a rate sentence. Then explain what the other unit rate, 30/540 = 1/18, means.
$540 ÷ 30 = $18, so the school paid $18 per calculator. The other unit rate, 1/18 calculator per dollar, means each dollar buys 1/18 of a calculator. Both describe the same ratio, but the price per calculator is easier to use.
Question 20 of 20 · Short Answer
A craft project uses 10 feet of ribbon for 4 bows. Write both unit rates with units. Which one tells how much ribbon one bow needs?
Ribbon per bow: 10 ÷ 4 = 2 1/2 feet per bow. Bows per foot: 4 ÷ 10 = 2/5 bow per foot. The first rate, 2 1/2 feet per bow, tells how much ribbon one bow needs.
0 of 20 answered · 0 correct
06
Frequently Asked Questions
10 Questions
What does 6.RP.A.2 mean?
6.RP.A.2 means students understand that a ratio a:b has a unit rate a/b and can describe it with rate language such as "per". The unit rate is the amount of the first quantity for 1 unit of the second. For 20 dollars for 4 pounds of apples, the unit rate is $5 per pound.
What is a unit rate in 6th grade math?
A unit rate is a rate for exactly 1 unit of the second quantity. If a runner covers 12 laps in 24 minutes, the unit rates are 1/2 lap per minute and 2 minutes per lap. In grade 6, unit rates come from whole numbers or decimals, so they are whole numbers, decimals or simple fractions.
What is the difference between a ratio and a unit rate?
A ratio compares two quantities, and a unit rate is the ratio rewritten for 1 unit of the second quantity. The ratio 30 students to 5 tables becomes the unit rate 6 students per table. A unit rate is one number with units, while a ratio has two numbers.
Why does 6.RP.A.2 say b ≠ 0?
Because the unit rate a/b means a ÷ b, and you cannot divide by 0. In words, "per 0" makes no sense: if a store had 10 apples and 0 bags, there would be no bags to put the apples in, so "apples per bag" has no value. The other order, 0/10 = 0 bags per apple, is fine.
Does every ratio have two unit rates?
Yes, when both numbers are not zero. The ratio 5 cups of water to 3 cups of oats gives 5/3 = 1 2/3 cups of water per cup of oats and 3/5 cup of oats per cup of water. Students should choose the one that answers the question, usually the one with "per 1" of the thing the question asks about.
What does "per" mean in a rate?
"Per" means "for each" or "for every 1". In "$3 per pound", the pound is the 1 unit and $3 goes with it. When you compute a rate, the quantity after "per" is the number you divide by: dollars per pound is dollars ÷ pounds.
Can a unit rate be a fraction?
Yes. The official example gives 3/4 cup of flour for each cup of sugar. The official note says grade 6 unit rates are limited to non-complex fractions, so students divide whole numbers or decimals, like 3 ÷ 4. Rates made from fractions, such as 1/2 mile in 1/4 hour, belong to grade 7 (7.RP.A.1).
How is 6.RP.A.2 different from 6.RP.A.3?
6.RP.A.2 is about understanding what a unit rate is and describing it; 6.RP.A.3 is about using unit rates to solve problems. In 6.RP.A.2 students explain that $75 for 15 hamburgers means $5 per hamburger. In 6.RP.A.3 they use rates like that to compare prices, solve constant speed problems and convert units.
What are common mistakes with unit rates?
A common mistake is dividing in the wrong order and keeping the original units, for example writing 4 ÷ 20 = 0.2 "dollars per pound" for $20 for 4 pounds. Another is subtracting the two numbers instead of dividing. Many students also drop the units, which hides which unit rate they found.
How can parents help with unit rates at home?
Look for rates on shelf tags, gas pumps and nutrition labels, and ask your child what the "per" part means. At the store, ask for the price per item or per ounce, then the other rate (items per dollar), and ask which one is more useful. Ask your child to check a rate by multiplying back.
07
Related Standards
5 standards
These standards connect to 6.RP.A.2: prerequisites to review first, parallel standards at the same level, and next steps that build on it.
Before this lesson
6.RP.A.1Prerequisite
Understand ratios and use ratio language to describe two related quantities
