Grade 6 Mathematics · Unit 3: Ratios & RatesStandard 6.AT.2

Lesson 3.23.2 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can find a unit rate to compare prices and decide the better buy, explain how I can tell, and judge a case I have not seen before.

Start hereWords for this lesson

Read each word before you begin. Say it out loud.

WordWhat it meansExample
Rates and Unit RatesSpanish: Tasas y tasas unitarias A rate compares different units; a unit rate compares a quantity to 1 unit. 180 miles in 3 hours = 60 miles per 1 hour.
RateSpanish: Tasa A ratio comparing two amounts with different units, like miles per hour. 96 pages / 3 hours
Unit RateSpanish: Tasa unitaria A rate for just 1 of something, like cost for 1 item. 32 pages per 1 hour
PerSpanish: Por For each one. Example: 5 dollars per book. miles per hour, cost per pound
RatioSpanish: Razón A way to compare two amounts, like 3 to 2. 5 to 3 or 5:3
Unit priceSpanish: Precio unitario A unit rate that gives the cost of exactly 1 item, like $0.60 per game. $3 for 5 games → $0.60 per 1 game

How it worksWorked examplefinding a unit rate

These numbers are not on your problems. The steps are. Follow them with your own numbers.

A reader finishes 96 pages in 3 hours at a steady speed. Find the pages per hour.

  1. Write the rate as a fraction. 96 pages / 3 hours
  2. Divide to make the bottom number 1. 96 ÷ 3 = 32
  3. Say it with the word PER. 32 pages per 1 hour
  4. Use it to predict. in 5 hours: 5 × 32 = 160 pages

Answer: The unit rate is 32 pages per hour.

Now you trySame steps, your turn

The steps are the same as the worked example. The numbers are yours. Do the work.

A train covers 84 kilometers in 4 hours at a steady speed.

  1. Write the rate as a fraction. km / hours
  2. Divide to make the bottom number 1. 84 ÷ =
  3. Say it with PER. km per 1 hour
  4. Predict 6 hours. 6 × = km
Answer:unit rate and the distance in 6 hours

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • The rate is for every .
  • I divided by to find the unit rate.
  • The unit rate is per .
  • To find the amount for , I .

Word bank rateunit ratepereachdividemultiplyfor everyspeedpredictconstanthourpound

Watch outA common mistake

A common mistake in Rates and Unit Rates is comparing total costs instead of unit rates: a student sees Pack X at $4.00 for 10 tokens and Pack Y at $6.00 for 16 tokens and picks Pack X just because $4.00 is the smaller number, without dividing to find the cost per token ($0.40 for Pack X vs. $0.375 for Pack Y — Pack Y is actually the better buy). A second common mistake is dividing backwards — finding tokens ÷ cost instead of cost ÷ tokens — which turns 'dollars per token' into 'tokens per dollar' and gives an answer that looks reasonable but answers the wrong question. Always divide the total cost by the number of items, and check that your unit rate answers 'the cost for ONE item,' not the reverse.

Grade 6 Mathematics · Unit 3: Ratios & RatesStandard 6.AT.2

Lesson 3.23.2 Small Group · Group 2

Group 2Challenge practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice
Name Date Period

Learning target I can find a unit rate to compare prices and decide the better buy, explain how I can tell, and judge a case I have not seen before.

  1. 1Complete each step, then write the final answer.
    Hours21?Miles90?315÷ ?÷ ?× ?× ?
    Find the miles for 1 hour first.

    A bus travels 90 miles in 2 hours. It keeps the same speed. How many hours does it take to travel 315 miles?

    1. 1Divide both by 2. How many miles in 1 hour?
    2. 2What scale factor takes 45 miles to 315 miles?
    3. 3Multiply 1 hour by 7. How many hours?
    4. 4Check with multiplication.
    Final answer:
  2. 2Complete each step, then write the final answer.
    Bottles101?Cost$4.00?$1.00÷ ?÷ ?× ?× ?
    Two unit rates from one deal.

    A store sells 10 bottles of water for $4. Find the cost per bottle and the bottles per dollar.

    1. 1Divide both by 10. What is the cost for 1 bottle?
    2. 2What scale factor takes $0.40 to $1.00? Use it on 1 bottle.
    3. 3Which rate helps you find the cost of 25 bottles? Why?
    Final answer:
  3. 3Complete each step, then write the final answer.
    HoursMiles________________

    A cyclist rides 36 miles in 3 hours at the same speed. How many miles does she ride per hour?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.
    HoursMiles________________________

    A train travels 240 miles in 4 hours. It keeps the same speed. How many hours does it take to travel 360 miles?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.
    Juices61106-pack cost$4.20?10-pack cost?$6.50÷ ?÷ ?× ?× ?

    A 6-pack of juice costs $4.20. A 10-pack of the same juice costs $6.50. What is the lower unit price?

    Show your work
    Final answer:
  6. 6Circle the letter of the best answer. Show how you know.
    Games10116Booth X cost$8.00?Booth Y cost?$10.00÷ ?÷ ?× ?× ?

    Booth X charges $8 for 10 games. Booth Y charges $10 for 16 games. Mo says Booth X is the better buy because $8 is less than $10. Which booth is the better buy?

    1. ABooth Y — $0.625 per game
    2. BBooth X — $0.80 per game
    3. CBooth X — it costs less in all
    Show your work

Explain your thinkingIs a lower total price always the better buy? Use a unit price to defend your answer.

ChallengeWrite your own problem

Write a new word problem that uses this lesson's idea. Then solve it and show every step.

How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help