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.

Why This Matters This is your challenge small group for Lesson 3.5. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

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 example

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

Mix A has 2 soap to 5 water. Mix B has 3 soap to 7 water. Which is stronger?

  1. Common multiple of 2 and 3: 6.
  2. Mix A × 3 = 6 : 15. Mix B × 2 = 6 : 14.
  3. Compare water: 14 < 15.

Answer: Mix B is stronger (less water for 6 soap)

Now you trySame steps, your turn

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

Store A sells 2 pens for $6. Store B sells 3 pens for $12. Which store has the better deal?

Answer:

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 out!A common mistake

A common mistake in Compare Ratios is thinking the ratio with the bigger raw number automatically wins

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.

Why This Matters This is your challenge small group for Lesson 3.5. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

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.

3-Point Exit Checklist: ☐ 1. Units & Labels Verified ☐ 2. Mathematical Reasoning Stated ☐ 3. Calculations Double-Checked
How did it go? ☐ 4 · I can teach it☐ 3 · I've got it☐ 2 · I need a hint☐ 1 · I need help