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.

Start hereWords for this lesson

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

WordWhat it meansExample
Compare RatiosSpanish: Comparar razones Decide which ratio is greater, less, or equal by using equivalent ratios or unit rates. Compare 6:2 and 8:4 using unit rates: 3 > 2.
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

How it worksWorked exampleconverting across the two systems

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

A room is 5 meters wide. How many feet is that? (1 meter ≈ 3.28 feet)

  1. Write the conversion factor. 1 m ≈ 3.28 ft
  2. Ask which unit is BIGGER. A meter is bigger than a foot.
  3. A bigger unit becomes MORE of the smaller unit, so multiply. 5 × 3.28 = 16.4
  4. Check reasonableness: 16.4 ft is more than 5 — correct direction. ✓

Answer: 5 meters ≈ 16.4 feet.

Now you trySame steps, your turn

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

A crate weighs 12 kilograms. How many pounds is that? (1 kg ≈ 2.2 lbs)

  1. Write the conversion factor. 1 kg ≈ lbs
  2. Which unit is bigger, a kilogram or a pound?
  3. Bigger unit → more of the smaller unit, so .
  4. Compute and check. 12 × ≈ lbs
Answer:pounds

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 outA 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) — not 6:9 (2+4 and 5+4). Adding changes the taste of the recipe (and the value of the ratio); only multiplying or dividing both numbers by the same amount keeps it equivalent.

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.

  1. 1Circle the letter of the best answer. Show how you know.

    (Lesson 3.5) Chef A uses 2 cups of cheese for every 8 crackers. Chef B uses 3 cups of cheese for every 9 crackers. Who uses more cheese per cracker?

    1. AChef B
    2. BChef A
    3. CThey use the same amount
    4. DCannot determine

    Hint You can't compare 2 cups and 3 cups directly — the chefs use different numbers of crackers.

    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    (Lesson 3.5) Which ratio is greater: 3:4 or 5:8?

    1. A5:8
    2. BThey are equal
    3. C3:4
    4. DCannot determine

    Hint The second numbers (4 and 8) don't match, so the ratios aren't ready to compare yet.

    Show your work
  3. 3Circle the letter of the best answer. Show how you know.

    (Lesson 3.6) There are 12 inches in 1 foot. How many inches are in 5 feet?

    1. A7 inches
    2. B17 inches
    3. C50 inches
    4. D60 inches

    Hint Write the unit ratio first: 12 inches : 1 foot.

    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    (Lesson 3.6) There are 1,000 milliliters in 1 liter. How many milliliters are in 3 liters?

    1. A30 mL
    2. B300 mL
    3. C1,003 mL
    4. D3,000 mL

    Hint The unit ratio is 1,000 mL : 1 L.

    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    (Lesson 3.7) 1 kilometer ≈ 0.6 mile. About how many miles is 5 kilometers?

    1. A3 miles
    2. B5.6 miles
    3. C8 miles
    4. D30 miles

    Hint Write the conversion factor as a ratio: 1 : 0.6.

    Show your work

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.

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