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.

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 exampleconverting between customary units

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

A bookshelf is 6 feet tall. How many inches is that? (1 foot = 12 inches)

  1. Write the conversion factor. 1 ft = 12 in
  2. Decide the direction. Feet → inches is LARGER to SMALLER, so multiply.
  3. Multiply. 6 × 12 = 72
  4. Check that it makes sense — inches are small, so the number got bigger. ✓

Answer: 6 feet = 72 inches.

Now you trySame steps, your turn

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

A box weighs 9 pounds. How many ounces is that? (1 pound = 16 ounces)

  1. Write the conversion factor. 1 lb = oz
  2. Larger unit to smaller unit, so I will .
  3. Compute. 9 × =
  4. Reasonable? Ounces are smaller, so the number should get .
Answer:ounces

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 outA common mistake

A common mistake when converting within a measurement system is choosing the operation by habit instead of by unit size — multiplying every time. Converting 36 inches to feet by multiplying gives 36 × 12 = 432 feet, taller than a 40-story building. Ask first which unit is smaller: it takes MORE small units to make the same amount, so going to a smaller unit multiplies, and going to a larger unit divides.

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.

  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.

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