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

Lesson 3.10Convert Measurement Units

Set B · Version ASecond form · supported practice

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

Learning target I can convert measurement units using ratios and conversion factors.

Why This Matters You're building a brand-new arcade cabinet! The blueprints use feet, but the parts catalog lists measurements in inches. The wiring instructions use yards, and the weight limits are in pounds — but the shipping labels use ounces. You need to convert between units to make sure everything fits and ships correctly. The blueprint says the cabinet is 6 feet tall, and the parts catalog lists a side panel that is 70 inches tall. Does the panel fit?

RememberConvert Measurement Units

Dimensional Analysis & Unit Conversions A unit is a standard amount used to measure, like a foot or an inch. A conversion factor is a ratio that relates two units, like 1 foot = 12 inches.

  1. Write the given measurement as a fraction over
  2. Multiply by conversion ratios arranged so unwanted units cancel diagonally.
  3. Multiply numerators, multiply denominators, and simplify the remaining unit

Words: Conversion Factor (Factor de conversión)Unit (Unidad)Equivalent (Equivalente)Ratio (Razón)Customary units (Unidades usuales (sistema inglés))

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

    Which ratio is equivalent to 8:12?

    1. A2:3
    2. B4:8
    3. C8:16
    4. D12:8
    Show your work
  2. 2Circle the letter of the best answer. Show how you know.

    Fill in the missing value: 5:9 = 20:___

    1. A24
    2. B32
    3. C36
    4. D45
    per 1
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?
  3. 3Circle the letter of the best answer. Show how you know.

    A ratio table shows 7:4 and 21:12. What was each part of 7:4 multiplied by?

    1. A3
    2. B4
    3. C7
    4. D14
    per 1
    1. 1LabelWrite what each column is.
    2. 2Find per 1Divide to get one.
    3. 3ScaleMultiply up to what is asked.
    4. 4CheckDoes the size make sense?
  4. 4Circle the letter of the best answer. Show how you know.

    Which pair of ratios is NOT equivalent?

    1. A3:7 and 9:21
    2. B4:6 and 10:15
    3. C5:8 and 15:25
    4. D6:10 and 9:15
    Show your work
  5. 5Circle the letter of the best answer. Show how you know.

    The arcade is ordering a new game cabinet. The doorway is 80 inches tall. The cabinet is listed as 7 feet. Your friend says it won't fit because 7 feet is 82 inches. How many inches are in 1 foot?

    1. A10
    2. B12
    3. C16
    4. D36
    Show your work
  6. 6Circle the letter of the best answer. Show how you know.

    The arcade is ordering a new game cabinet. The doorway is 80 inches tall. The cabinet is listed as 7 feet. Your friend says it won't fit because 7 feet is 82 inches. How many inches tall is the 7-foot cabinet?

    1. A19
    2. B70
    3. C82
    4. D84
    Show your work

Explain your thinkingHow do you decide whether to multiply or divide when converting units?

Sentence starter When converting from a ___ unit to a ___ unit, I ___ by the conversion factor because ___.

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 3.10Convert Measurement Units

Set B · Version BSecond form · core practice

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

Learning target I can convert measurement units using ratios and conversion factors.

Why This Matters You're building a brand-new arcade cabinet! The blueprints use feet, but the parts catalog lists measurements in inches. The wiring instructions use yards, and the weight limits are in pounds — but the shipping labels use ounces. You need to convert between units to make sure everything fits and ships correctly. The blueprint says the cabinet is 6 feet tall, and the parts catalog lists a side panel that is 70 inches tall. Does the panel fit?

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

    Equivalent Measurements

    1. 2 gallons of coolant
    2. 60 inches of trim
    3. 3,000 meters of cable
    4. 32 ounces of bolts
    5. 10 feet of railing
    • A8 quarts
    • B5 feet
    • C3 kilometers
    • D2 pounds
    • E120 inches
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    The arcade is ordering a new game cabinet. The doorway is 80 inches tall. The cabinet is listed as 7 feet. Your friend says it won't fit because 7 feet is 82 inches. Will the cabinet fit through the 80-inch doorway?

    1. ANo, because 84 > 80
    2. BYes, because 84 < 80
    3. CYes, because 7 feet is small
    4. DYou cannot tell without the width
    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    Leg 1: The joystick rod is 3 feet long, but the parts catalog lists it in inches. How many inches is that? (1 ft = 12 in)

    1. A15 inches
    2. B30 inches
    3. C33 inches
    4. D36 inches
    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    Leg 2: A power cable on the cabinet plan measures 2.5 kilometers across the whole arcade network. How many meters is that? (1 km = 1,000 m)

    1. A25 meters
    2. B250 meters
    3. C2,500 meters
    4. D25,000 meters
    Show your work
  4. 5Circle the letter of the best answer. Show how you know.

    Leg 3: The coin box weighs 5 pounds, but the shipping label needs the weight in ounces. How many ounces is that? (1 lb = 16 oz)

    1. A16 ounces
    2. B21 ounces
    3. C75 ounces
    4. D80 ounces
    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Level 2 Extension — Multiply or Divide?

    1. 1Convert 4 feet of side panel to inches4 feet → inches
    2. 2Use the conversion factor1 foot = 12 inches
    3. 3Operate4 ÷ 12 = 0.33 inches
    4. 4Final answer4 feet ≈ 0.33 inches

    Which step has the mistake? Explain what went wrong, then show the correct work.

    Correct work
    Correct answer:

Explain your thinkingHow do you decide whether to multiply or divide when converting units?

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