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

Lesson 3.7Ratio Reasoning: Convert Measurements Between Systems

Set B · Version ASecond form · supported practice

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

Learning target I can use ratio reasoning to convert measurements between the customary and metric systems.

Why This Matters The academy's kitchen orders from suppliers in two different countries. One ships in pounds and quarts, the other in kilograms and liters. Compare measurements by converting with the appropriate factor. Some factors are exact; rounded factors give approximate results. One supplier ships 10 pounds of rice and the other ships 5 kilograms. Use 1 pound ≈ 0.45 kilogram to find which shipment is more.

RememberRatio Reasoning: Convert Measurements Between Systems

Converting Measurements Between Systems Kilometers and miles both measure distance, but they come from different measurement systems, so the numbers cannot be compared directly. A conversion factor links the two systems, and a ratio table scales it up to the amount you need.

  1. Identify the conversion ratio connecting systems (e.g. 1 in = 2.54 cm, 1 kg ≈ 2.2 lbs).
  2. Set up a ratio table or proportion aligning customary and metric units.
  3. Multiply or divide by the conversion factor to compute the equivalent measurement

Words: Conversion factor (Factor de conversión)Customary system (Sistema usual)Metric system (Sistema métrico)Approximately (Aproximadamente)Ratio table (Tabla de razones)

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

    The other supplier sells flour by the kilogram. The academy kitchen needs 22 pounds of flour. Using 1 kg ≈ 2.2 lb, about how many kilograms should it order?

    1. AAbout 48.4 kg
    2. BAbout 19.8 kg
    3. CAbout 100 kg
    4. DAbout 10 kg

    Hint Write the ratio 1 kg : 2.2 lb.

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

    A recipe from the U.S. supplier uses 3 cups of milk per batch. The academy buys milk in liters, and 1 cup ≈ 0.24 liter. About how many liters of milk do 5 batches need?

    1. AAbout 3.6 liters
    2. BAbout 0.72 liter
    3. CAbout 62.5 liters
    4. DAbout 36 liters

    Hint How many cups do 5 batches need?

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

    How many cups are in 3 quarts? (1 quart = 4 cups)

    1. A3/4 cup
    2. B7 cups
    3. C12 cups
    4. D16 cups
    Show your work
  4. 4Circle the letter of the best answer. Show how you know.

    A rope is 240 centimetres long. How many metres is that? (1 m = 100 cm)

    1. A0.24 m
    2. B2.4 m
    3. C24 m
    4. D240 m
    My work — one step per lineWhat I did to both sides
    1. 1LookWhat is done to the variable?
    2. 2UndoDo the opposite — both sides.
    3. 3SimplifyOne side at a time.
    4. 4CheckPut it back in.
  5. 5Circle the letter of the best answer. Show how you know.

    Which conversion factor changes feet into inches?

    1. A1 ft / 12 in
    2. B1 in / 12 ft
    3. C3 ft / 1 yd
    4. D12 in / 1 ft
    Show your work
  6. 6Circle the letter of the best answer. Show how you know.

    A jug holds 5 litres. How many millilitres is that? (1 L = 1,000 mL)

    1. A0.005 mL
    2. B50 mL
    3. C500 mL
    4. D5,000 mL
    My work — one step per lineWhat I did to both sides
    1. 1LookWhat is done to the variable?
    2. 2UndoDo the opposite — both sides.
    3. 3SimplifyOne side at a time.
    4. 4CheckPut it back in.

Explain your thinkingWhy does 1 inch = 2.54 cm use =, while 1 mile ≈ 1.609 km uses ≈? What does the rounding change?

Sentence starter The inch factor is ___ by definition. The mile factor shown is ___, so I write ___ for its result.

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

Lesson 3.7Ratio Reasoning: Convert Measurements Between Systems

Set B · Version BSecond form · core practice

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

Learning target I can use ratio reasoning to convert measurements between the customary and metric systems.

Why This Matters The academy's kitchen orders from suppliers in two different countries. One ships in pounds and quarts, the other in kilograms and liters. Compare measurements by converting with the appropriate factor. Some factors are exact; rounded factors give approximate results. One supplier ships 10 pounds of rice and the other ships 5 kilograms. Use 1 pound ≈ 0.45 kilogram to find which shipment is more.

Part 1Understand the ideamodels and meaning
  1. 1Write the letter of the matching item on each line.

    Match each customary unit with its metric equivalent. The inch conversion is exact; the other factors shown are rounded.

    1. 1 inch
    2. 1 mile
    3. 1 pound
    4. 1 United States liquid quart
    • A2.54 centimeters
    • B1.609 kilometers
    • C0.454 kilogram
    • D0.946 liter
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    Evelyn is driving in Canada. The highway sign reads 100 kilometers per hour. She is used to speed limits in miles per hour, and 1 kilometer is about 0.6 mile. Using 1 km ≈ 0.6 mi, about how many miles is 10 kilometers?

    1. A0.06 mile
    2. B6 miles
    3. C16 miles
    4. D60 miles
    per 1
  2. 3Circle the letter of the best answer. Show how you know.

    Evelyn is driving in Canada. The highway sign reads 100 kilometers per hour. She is used to speed limits in miles per hour, and 1 kilometer is about 0.6 mile. Using 1 lb ≈ 0.45 kg, about how many kilograms is a 30-pound dog?

    1. A4.5 kg
    2. B13.5 kg
    3. C30.45 kg
    4. D66 kg
    per 1
  3. 4Circle the letter of the best answer. Show how you know.

    Evelyn is driving in Canada. The highway sign reads 100 kilometers per hour. She is used to speed limits in miles per hour, and 1 kilometer is about 0.6 mile. Why does a conversion using the rounded factor 1 mile ≈ 1.609 km use ≈?

    1. ABecause metric units are always bigger
    2. BBecause the amounts are actually different
    3. CBecause ratios cannot be exact
    4. DThe conversion factors are rounded approximations
    Show your work
  4. 5Circle the letter of the best answer. Show how you know.

    One inch equals exactly 2.54 cm. How many centimeters are in 4 inches?

    1. A1.57 cm
    2. B6.54 cm
    3. C10.16 cm
    4. D254 cm
    Show your work
  5. 6Circle the letter of the best answer. Show how you know.

    Which unit is metric?

    1. AQuart
    2. BLiter
    3. CGallon
    4. DPint
    Show your work

Explain your thinkingWhy does 1 inch = 2.54 cm use =, while 1 mile ≈ 1.609 km uses ≈? What does the rounding change?

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