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

Lesson 3.23.2 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can find a unit rate to compare prices and decide the better buy — one step at a time, with support.

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 1

Group 1Supported practice

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

Learning target With my small group, I can find a unit rate to compare prices and decide the better buy — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    Games41Cost$6.00?÷ ?÷ ?
    Find the cost for 1 game.

    A booth charges $6 for 4 games. What is the unit price, the cost for 1 game?

    1. 1What do we divide 4 games by to get 1 game?
    2. 2Divide $6 by 4 too. What is the cost for 1 game?
    3. 3Write the unit rate with both units.
    Final answer:
  2. 2Complete each step, then write the final answer.
    Days41Pages36?÷ ?÷ ?
    Find the pages for 1 day.

    Ana reads 36 pages in 4 days. She reads the same number each day. How many pages does she read per day?

    1. 1What do we divide 4 days by to get 1 day?
    2. 2Divide 36 pages by 4 too. How many pages?
    3. 3Write the unit rate with both units.
    Final answer:
  3. 3Complete each step, then write the final answer.
    PencilsCost________________

    A pack of 5 pencils costs $2. What is the cost for 1 pencil?

    Show your work

    Hint Divide the cost by the number of pencils.

    Final answer:
  4. 4Complete each step, then write the final answer.
    GamesCost________________

    Booth C at the fair charges $4.50 for 6 games. What is the unit price?

    Show your work

    Hint The unit price is the cost for 1 game. Divide the cost by the games.

    Final answer:
  5. 5Complete each step, then write the final answer.
    GallonsMiles________________

    A car travels 150 miles on 5 gallons of gas. How many miles does it travel per gallon?

    Show your work

    Hint Per gallon means for 1 gallon. Divide the miles by the gallons.

    Final answer:
  6. 6Circle the letter of the best answer. Show how you know.
    Games510Booth A cost$4.00?Booth B cost$6.00× ?× ?
    Compare both booths at 10 games.

    Booth A charges $4 for 5 games. Booth B charges $6 for 10 games. Which booth is the better buy?

    1. ABooth B — $0.60 per game
    2. BBooth A — $0.80 per game
    3. CBooth A — it costs less in all
    4. DThey cost the same per game

    Hint Find the cost for 1 game at each booth. Then compare.

    Show your work

Explain your thinkingBooth A costs less in all. Why can Booth B still be the better buy? Use the unit prices.

Sentence starter To find the unit price, I divide ___ by ___. · Booth ___ is the better buy because ___.

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