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

Lesson 3.63.6 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can use ratio reasoning to convert between units within the same measurement system, explain why the method works, and use it on a problem I have not seen before.

Why This Matters This is your challenge small group for Lesson 3.6. 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
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 ft = 12 in
Unit ratioSpanish: Razón unitaria A ratio that compares an amount to exactly 1 unit of another quantity, like 12 inches to 1 foot. 12 : 1 — twelve inches for every one foot
ConvertSpanish: Convertir To change a measurement from one unit to another without changing how much it is. 6 ft → 72 in
Measurement systemSpanish: Sistema de medidas A family of units that go together — customary units like inches and feet, or metric units like milliliters and liters. Customary: 12 in = 1 ft · Metric: 1,000 mL = 1 L
Double number lineSpanish: Recta numérica doble Two number lines lined up so matching tick marks show two units for the same amount. Liters 0, 1, 2, 3, 4 above milliliters 0, 1,000, 2,000, 3,000, 4,000
Ratio tableSpanish: Tabla de razones A table of equal ratios that lets you scale a conversion up or down one row at a time. 1 ft : 12 in, 2 ft : 24 in, 4 ft : 48 in

How it worksWorked example

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

A pitcher holds 2 quarts. How many fluid ounces? (1 qt = 4 cups, 1 cup = 8 fl oz)

  1. Quarts to cups: 2 × 4 = 8 cups.
  2. Cups to fl oz: 8 × 8 = 64 fl oz.
  3. Check: 64 ÷ 8 ÷ 4 = 2 quarts.

Answer: 2 quarts = 64 fluid ounces

Now you trySame steps, your turn

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

Diamond wants to drink 4 liters of water. Her bottle holds 500 milliliters. How many times does she fill the bottle?

Answer:

Say it and write itSentence starters

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

  • I know 1 = .
  • I because I am going from a unit to a unit.
  • My answer is .
  • This is reasonable because .

Word bank convertconversion factorcustomarymultiplydividelargersmallerinchfootyardpoundgallon

Watch out!A common mistake

A common mistake when converting within a measurement system is choosing the operation by habit instead of by unit size

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

Lesson 3.63.6 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can use ratio reasoning to convert between units within the same measurement system, explain why the method works, and use it on a problem I have not seen before.

Why This Matters This is your challenge small group for Lesson 3.6. 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.

  1. 1Complete each step, then write the final answer.
    Inches1242Feet1?× ?× ?
    Find the feet that match 42 inches.

    A rug is 42 inches long. How many feet long is the rug?

    1. 1How many inches are in 1 foot?
    2. 2What scale factor takes 12 inches to 42 inches?
    3. 3Multiply 1 foot by 3.5. How many feet long is the rug?
    4. 43 feet is 36 inches. How many inches are left over?
    Final answer:
  2. 2Complete each step, then write the final answer.
    Meters1,0007,500Kilometers1?× ?× ?

    A runner ran 7,500 meters. How many kilometers did she run?

    1. 1How many meters are in 1 kilometer?
    2. 2What scale factor takes 1,000 meters to 7,500 meters?
    3. 3Multiply 1 kilometer by 7.5. How many kilometers did she run?
    4. 4Why must the number of kilometers be much less than 7,500?
    Final answer:
  3. 3Complete each step, then write the final answer.
    InchesFeet________________

    A plank is 51 inches long. How many feet long is it? Write your answer as a decimal.

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.
    PoundsOunces________________

    Bag A of rice weighs 2 pounds. Bag B weighs 30 ounces. How many more ounces does the heavier bag weigh?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.
    OuncesPounds________________

    A project needs 800 ounces of sand. Sand comes in 40-pound bags. How many bags must you buy?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.
    InchesFeet________________

    Ana says 2 feet 6 inches is 2.6 feet. What is the correct length in feet, as a decimal?

    Show your work
    Final answer:

Explain your thinkingAna thought 6 inches was 0.6 foot. How do you decide to multiply or divide, and how do you check that your answer makes sense?

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