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

Lesson 3.53.5 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can compare ratios by finding unit rates or using equivalent ratios — one step at a time, with support.

Start hereWords for this lesson

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

Word	What it means	Example
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?

Pick the quantity to match — cocoa. Find the LCM of 2 and 3 → 6.
Scale Mix P. ×3 → 6 cocoa : 15 milk
Scale Mix Q. ×2 → 6 cocoa : 14 milk
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?

Match the scoops. LCM of 3 and 4 =
Scale A. × → scoops : cups
Scale B. × → scoops : cups
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 1

Group 1Supported practice

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target With my small group, I can compare ratios by finding unit rates or using equivalent ratios — one step at a time, with support.

1Complete each step, then write the final answer.
Juice A: first two columns. Juice B: last two.
Juice A uses 2 cups of mango for 3 cups of water. Juice B uses 3 cups of mango for 4 cups of water. Which juice tastes more like mango?
1. 1What amount of water can both juices reach? Use 3 × 4.
2. 2Scale Juice A by 4. How many cups of mango?
3. 3Scale Juice B by 3. How many cups of mango?
4. 4Same water. Which juice has more mango?
Final answer:
2Complete each step, then write the final answer.
Store A: first two columns. Store B: last two.
Store A sells 4 muffins for $6. Store B sells 5 muffins for $8. Which store has the lower price for 1 muffin?
1. 1Divide Store A's table by 4. What does 1 muffin cost?
2. 2Divide Store B's table by 5. What does 1 muffin cost?
3. 3Which store has the better deal?
Final answer:
3Complete each step, then write the final answer.

Pack A: first two columns. Pack B: last two.
Pack A has 2 apples for $1. Pack B has 5 apples for $3. What is the lower price for 1 apple?
Show your work
Hint Divide each cost by the number of apples. Then compare.
Final answer:
4Complete each step, then write the final answer.

Reyes: first two columns. Tran: last two.
Chef Reyes uses 2 tablespoons of cocoa for 3 ounces of milk. Chef Tran uses 3 tablespoons for 5 ounces of milk. Scale both to 15 ounces of milk. Whose cocoa is more chocolatey?
Show your work
Hint Multiply each recipe so the milk is 15 ounces. Then compare the cocoa.
Final answer:
5Complete each step, then write the final answer.

Tom: first two columns. Ana: last two.
Tom runs 3 miles in 27 minutes. Ana runs 4 miles in 32 minutes. Who takes less time to run 1 mile?
Show your work
Hint Divide each time by the miles. That is the minutes for 1 mile.
Final answer:
6Circle the letter of the best answer. Show how you know.
Box A: first two columns. Box B: last two.
Box A has 10 granola bars for $4. Box B has 12 granola bars for $6. Which box is the better buy?
1. ABox A — $0.40 per bar
2. BBox B — $0.50 per bar
3. CBox B — it has more bars
4. DThey cost the same per bar
Hint Find the price for 1 bar in each box.
Show your work

Explain your thinkingJuice B has 3 cups of mango and Juice A has 2. Why can't you just compare 3 and 2?

Sentence starter I cannot compare 3 and 2 yet because the ___ is different. · To compare fairly, I make ___ the same, or I find ___.

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