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

Lesson 3.53.5 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can compare ratios by finding unit rates or using equivalent ratios, 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
Unit rateSpanish: Tasa unitaria A rate for just 1 of something, like cost for 1 item. $3 per 1 pound → unit rate is $3/lb
Equivalent ratioSpanish: Razón equivalente Two ratios that mean the same thing. 4:6 and 2:3 are equivalent (both simplify to 2:3)
CompareSpanish: Comparar To look at ratios and see which is bigger, smaller, or equal. 3:4 vs. 2:5 — which has more of the first ingredient per unit?
SimplifySpanish: Simplificar To write a ratio with smaller numbers that still compares the same way. 6:8 and 3:4 are the same ratio. 8:12 → divide both by 4 → 2:3
Common denominatorSpanish: Denominador común A bottom number that two fractions can share so you can compare them. To compare 3/5 and 4/7, use LCD 35: 21/35 vs 20/35
Common multipleSpanish: Múltiplo común A number that both terms can be scaled to. 2 and 3 both reach 6

How it worksWorked examplecomparing two mixes fairly

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

Mix P is 2 cocoa to 5 milk. Mix Q is 3 cocoa to 7 milk. Which is more chocolatey?

  1. Pick the quantity to match — cocoa. Find the LCM of 2 and 3 → 6.
  2. Scale Mix P. ×3 → 6 cocoa : 15 milk
  3. Scale Mix Q. ×2 → 6 cocoa : 14 milk
  4. Same cocoa, so compare the milk. LESS milk = more chocolatey.

Answer: Mix Q is more chocolatey: for 6 cocoa it has only 14 milk.

Now you trySame steps, your turn

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

Juice A is 3 scoops to 8 cups water. Juice B is 4 scoops to 10 cups water. Which is stronger?

  1. Match the scoops. LCM of 3 and 4 =
  2. Scale A. × → scoops : cups
  3. Scale B. × → scoops : cups
  4. Same scoops, so compare the water. LESS water = stronger. Juice
Answer:the stronger juice

Say it and write itSentence starters

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

  • I scaled both ratios to .
  • Mix has and Mix has .
  • is stronger because .
  • You cannot compare them directly because .

Word bank common multipleleast common multiplescalematchcomparestrongerweakerlessmoresamefor everyfair

Watch outA common mistake

A common mistake in Compare Ratios is thinking the ratio with the bigger raw number automatically wins — like assuming Chef Tran's 8 tablespoons of cocoa must be more chocolatey than Chef Reyes's 6 tablespoons, without checking that the milk amounts (14 oz vs. 10 oz) are different. Never compare the raw numbers alone — always scale both ratios to the same amount or find each unit rate first.

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

Lesson 3.53.5 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can compare ratios by finding unit rates or using equivalent ratios, explain how I can tell, and judge a case I have not seen before.

Part 1Understand the ideamodels and meaning
  1. 1Circle the letter of the best answer. Show how you know.
    First numberSecond number________________________________
    7:10: first two columns. 3:4: last two.

    Ty says the ratio 7:10 is greater than 3:4, because 7 > 3. Which statement is true?

    1. A3:4 is greater
    2. B7:10 is greater
    3. CThey are equal
    Show your work
Part 2Apply itreal-world problems
  1. 2Complete each step, then write the final answer.
    Oats (cups)4?6?Milk (cups)6?10?× ?× ?× ?× ?
    Recipe A: first two columns. Recipe B: last two.

    Recipe A uses 4 cups of oats for 6 cups of milk. Recipe B uses 6 cups of oats for 10 cups of milk. Recipe B uses more oats. Does it have more oats for each cup of milk?

    1. 1What is the least common multiple of 6 and 10?
    2. 2Scale Recipe A to 30 cups of milk. How many cups of oats?
    3. 3Scale Recipe B to 30 cups of milk. How many cups of oats?
    Final answer:
  2. 3Complete each step, then write the final answer.
    Time (hours)6181Pay ($)45?52?÷ ?÷ ?÷ ?÷ ?
    Sam: first two columns. Lia: last two.

    Sam earns $45 for 6 hours of work. Lia earns $52 for 8 hours of work. Who earns more per hour?

    1. 1Divide Sam's table by 6. What is his pay for 1 hour?
    2. 2Divide Lia's table by 8. What is her pay for 1 hour?
    3. 3Lia earns more in all. Why does Sam still earn more per hour?
    Final answer:
  3. 4Complete each step, then write the final answer.
    Powder (scoops)Water (cups)________________________________
    Drink A: first two columns. Drink B: last two.

    Drink A uses 3 scoops of powder for 5 cups of water. Drink B uses 5 scoops for 8 cups of water. Scale both to 40 cups of water. For 40 cups of water, how many scoops does the stronger drink use?

    Show your work
    Final answer:
  4. 5Complete each step, then write the final answer.
    Juice (cups)Water (cups)________________________

    Mix A uses 4 cups of juice for 10 cups of water. Mix B uses 6 cups of juice for ? cups of water. The two mixes taste the same. Find the missing number.

    Show your work
    Final answer:
  5. 6Complete each step, then write the final answer.
    Gas (gal)Distance (mi)________________________________
    Car A: first two columns. Car B: last two.

    Car A goes 165 miles on 5 gallons of gas. Car B goes 192 miles on 6 gallons. How many more miles per gallon does the better car get?

    Show your work
    Final answer:

Explain your thinkingRecipe B used more oats, but it was not the oatier recipe. How do you pick a common amount to compare two ratios fairly?

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