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

Lesson 3.10Convert Measurement Units

Start hereWords, worked example, and sentence starters

Name Date Period

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

Start hereWords for this lesson

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

WordWhat it meansExample
Conversion FactorSpanish: Factor de conversión A ratio that helps you change one unit into another. 1 foot = 12 inches, so the factor is 12
UnitSpanish: Unidad A standard amount used to measure, like an inch or a liter. Inches, feet, pounds, ounces
EquivalentSpanish: Equivalente Having the same value, just in different units. 2 feet = 24 inches
RatioSpanish: Razón A way to compare two amounts, like 3 to 2. 12 inches per 1 foot
Customary unitsSpanish: Unidades usuales (sistema inglés) The U.S. way of measuring, like inches, feet, and pounds. 12 inches = 1 foot, 3 feet = 1 yard, 16 ounces = 1 pound
Metric unitsSpanish: Unidades métricas A way of measuring by 10s, like meters, liters, and grams. 1 meter = 100 centimeters, 1 kilogram = 1,000 grams

How it worksWorked example

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

The cabinet is 5 feet tall. I want to know how many inches that is.

  1. My conversion factor is 1 foot = 12 inches.
  2. Inches are smaller than feet, so I multiply: 5 × 12 = 60.
  3. So 5 feet = 60 inches.

Now you trySame steps, your turn

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

A wire is 4 yards long. The factor is 1 yard = 3 feet.

Answer:

Say it and write itSentence starters

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

  • When converting from a unit to a unit, I by the conversion factor because .

Word bank Conversion FactorUnitEquivalentRatioCustomary unitsMetric unitslargersmallermultiplydivideconversion factorratio

Watch outA common mistake

A common mistake in Convert Measurement Units is applying the conversion factor in the wrong direction — for example, converting 4 feet to inches by dividing (4 ÷ 12 = 0.33 inches) instead of multiplying (4 × 12 = 48 inches), or converting 80 ounces to pounds by multiplying (80 × 16 = 1,280 pounds) instead of dividing (80 ÷ 16 = 5 pounds). Before you answer, ask: am I changing to a SMALLER unit (there will be MORE of them, so multiply) or a BIGGER unit (there will be FEWER of them, so divide)?

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

Lesson 3.10Convert Measurement Units

Version ASupported practice

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

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

Part 1Understand the ideamodels and meaning
  1. 1Complete the table. Show how you found each value.

    Complete the conversion table using the given conversion factors.

    GivenConversion FactorAnswer
    2 feet1 ft = 12 in24 inches
    6 yards1 yd = 3 ft
    3 pounds1 lb = 16 oz

    Hint Each row hands you the conversion factor — the finished row shows 2 feet × 12 = 24 inches.

    Show your work
Part 2Apply itreal-world problems
  1. 2Circle the letter of the best answer. Show how you know.

    How many inches are in 7 feet?

    1. A70 inches
    2. B72 inches
    3. C84 inches
    4. D96 inches

    Hint The key fact: 1 foot = 12 inches. You have 7 feet and want inches.

    Show your work
  2. 3Circle the letter of the best answer. Show how you know.

    How many feet are in 3 yards?

    1. A6 feet
    2. B9 feet
    3. C12 feet
    4. D36 feet

    Hint The key fact: 1 yard = 3 feet. You have 3 yards and want feet.

    Show your work
  3. 4Circle the letter of the best answer. Show how you know.

    How many ounces are in 4 pounds?

    1. A16 ounces
    2. B32 ounces
    3. C48 ounces
    4. D64 ounces

    Hint The key fact: 1 pound = 16 ounces. You have 4 pounds and want ounces.

    Show your work
  4. 5Circle the letter of the best answer. Show how you know.

    Convert 24 inches to feet.

    1. A2 feet
    2. B3 feet
    3. C12 feet
    4. D24 feet

    Hint This one goes the OTHER direction: inches (small) to feet (big), so the number of units gets smaller.

    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Convert 2 yards of rope to feet2 yards → feet
    2. 2Use the conversion factor1 yard = 3 feet
    3. 3Operate2 ÷ 3 = 0.67 feet
    4. 4Final answer2 yards ≈ 0.67 feet

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

    Hint You are going from a bigger unit (yards) to a smaller unit (feet). Should the number get bigger or smaller?

    Correct work
    Correct answer:

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 ___.

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

Version BCore practice

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

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

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

    Match each measurement to its equivalent value.

    1. 3 yards
    2. 4 feet
    3. 5 pounds
    4. 2 yards
    5. 36 inches
    6. 3 pounds
    • A9 feet
    • B48 inches
    • C80 ounces
    • D72 inches
    • E3 feet
    • F48 ounces
  2. 2Complete the table. Show how you found each value.

    An arcade cabinet has parts measured in different units. Convert each to the target unit.

    PartMeasurementTarget UnitConverted
    Power cord2 yardsinches
    Top panel54 inchesfeet
    Weight96 ouncespounds
    Side rail5 feetinches
    Show your work
  3. 3Write the name of the correct group on each line.

    When converting, do you multiply or divide? Sort each conversion by the correct operation.

    Groups: Multiply Divide
    • Feet → inches
    • Yards → feet
    • Pounds → ounces
    • Inches → feet
    • Ounces → pounds
    • Feet → yards
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    A shelf is 30 inches long. How many feet and inches is that?

    1. A1 foot 18 inches
    2. B2 feet 6 inches
    3. C2 feet 8 inches
    4. D3 feet 0 inches
    Show your work
Part 3Explain and correctreasoning
  1. 5Find the mistake. Explain it, then show the correct work.

    Spot the Common Mistake

    1. 1Convert 80 ounces of bolts to pounds80 ounces → pounds
    2. 2Use the conversion factor1 pound = 16 ounces
    3. 3Operate80 × 16 = 1,280 pounds
    4. 4Final answer80 ounces = 1,280 pounds

    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?

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

ChallengeExtension

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

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

Part 1Understand the ideamodels and meaning
  1. 1Mark and label each value on the number line.

    Place these lengths on a number line in inches: A = 1 foot, B = 1.5 feet, C = 2 feet, D = 1 yard

    0612182430364248
    Show your thinking
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find the Conversion Error

    1. 1Convert 6 feet to yards6 feet → yards
    2. 2Use conversion factor1 yard = 3 feet
    3. 3Multiply6 × 3 = 18 yards
    4. 4Final answer6 feet = 18 yards

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

    Correct work
    Correct answer:
  2. 3Answer in complete sentences.

    A recipe says you need 5 feet of ribbon, but the store only sells ribbon in inches. Another recipe says you need 2 yards of fabric, but your ruler measures in feet. Convert both measurements and explain the steps you used. Which conversion factor did you use each time?

    Write your answer

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

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