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

Lesson 3.73.5 · 3.6 · 3.7 · 3.9 Catch-Up

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can show I am caught up on Lessons 3.5 · 3.6 · 3.7 · 3.9 by using each lesson's big idea in mixed practice.

Why This Matters Missed a lesson — or just want a refresher? This catch-up station reviews Lessons 3.5 · 3.6 · 3.7 · 3.9: 3.5 Compare Ratio Relationships, 3.6 Ratio Reasoning: Convert Measurements within the Same System, 3.7 Ratio Reasoning: Convert Measurements Between Systems, 3.9 Equivalent Ratios. Work one example from each lesson, then prove you're caught up in the mixed practice.

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
Conversion factorSpanish: Factor de conversión	The ratio that links two units in the same measurement system, such as 12 inches to 1 foot. Within one system it is exact.	1 m ≈ 3.28 ft

How it worksWorked example

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

A bag weighs 44 pounds. About how many kilograms? (1 kg ≈ 2.2 lb)

A kilogram is heavier, so the number gets smaller: divide.
44 ÷ 2.2 = 20.
Check: 20 × 2.2 = 44.

Answer: 44 lb ≈ 20 kg

Now you trySame steps, your turn

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

Pack A has 3 apples for $3. Pack B has 4 apples for $6. Which pack costs less for 1 apple?

Answer:

Say it and write itSentence starters

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

I know 1 ≈ .
A is bigger than a , so I .
My answer is about .
This is reasonable because .

Word bank convertconversion factorapproximatelyaboutreasonablebiggersmallermultiplydividemetermilekilogram

Watch out!A common mistake

A common mistake in Equivalent Ratios is ADDING the scale factor to one part instead of MULTIPLYING both parts by it. For example, scaling 2:5 by a factor of 4 should give 8:20 (2×4 and 5×4)

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

Lesson 3.73.5 · 3.6 · 3.7 · 3.9 Catch-Up

Catch-UpSkill bridge

Mastery check☐ Exceeds☐ Meets target☐ Needs practice

Name Date Period

Learning target I can show I am caught up on Lessons 3.5 · 3.6 · 3.7 · 3.9 by using each lesson's big idea in mixed practice.

1Complete each step, then write the final answer.

Shop A: first two columns. Shop B: last two.
Shop A sells 2 cookies for $4. Shop B sells 3 cookies for $9. What is the lower price for 1 cookie?
Show your work
Hint Divide each cost by the number of cookies.
Final answer:
2Complete each step, then write the final answer.

Drink A: first two columns. Drink B: last two.
Drink A uses 1 cup of juice for 2 cups of water. Drink B uses 2 cups of juice for 3 cups of water. Scale both to 6 cups of water. Which drink has more juice?
Show your work
Hint With the same water, the drink with more juice wins.
Final answer:
3Complete each step, then write the final answer.

How many inches are in 2 feet?
Show your work
Hint Each foot is 12 inches. Find 2 × 12.
Final answer:
4Complete each step, then write the final answer.

There are 1,000 meters in 1 kilometer. How many meters are in 6 kilometers?
Show your work
Hint Meters are smaller than kilometers, so multiply by 1,000.
Final answer:
5Complete each step, then write the final answer.

Use 1 kilometer ≈ 0.6 mile. About how many miles is 60 kilometers?
Show your work
Hint Find the scale factor from 1 to 60. Multiply 0.6 by the same factor.
Final answer:
6Complete each step, then write the final answer.

Use 1 kilogram ≈ 2.2 pounds. About how many pounds is 3 kilograms?
Show your work
Hint Find the scale factor from 1 to 3. Multiply 2.2 by the same factor.
Final answer:
7Complete each step, then write the final answer.

A ratio is 1:4. Multiply both numbers by 3. The new ratio is 3 : ?. What is the missing number?
Show your work
Hint Multiply the second number by 3: 4 × 3.
Final answer:
8Complete each step, then write the final answer.

A ratio is 3:2. Use a scale factor of 5. The new ratio is ? : 10. What is the missing number?
Show your work
Hint Multiply the first number by 5: 3 × 5.
Final answer:

Explain your thinkingHow did you find the missing values in Chef Montoya's table? How can you PROVE two of your rows are equivalent ratios?

Sentence starter I multiplied ___ and ___ by the same number, ___, so the ratio ___ is equivalent to 3:2.

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