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

Lesson 3.103.10 Small Group · Group 2

Start hereWords, worked example, and sentence starters

Name Date Period

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

A ribbon is 2 yards long. How many inches long is the ribbon? Use 1 yard = 3 feet and 1 foot = 12 inches.

  1. Find the inches in 1 yard: 3 × 12 = 36
  2. Find the scale factor: 2 ÷ 1 = 2
  3. Multiply the feet and inches by 2: 3 × 2 = 6; 36 × 2 = 72
  4. The ribbon is 72 inches long.

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. How many feet long is it? Use 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 3.103.10 Small Group · Group 2

Group 2Challenge practice

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

Learning target I can convert measurement units using ratios and conversion factors, 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.
    Yards13Feet3?Inches??× ?× ?
    Each column shows the same length in three units.

    A banner is 3 yards long. How many inches long is it? Use 1 yard = 3 feet and 1 foot = 12 inches.

    1. 11 foot is 12 inches. How many inches are in 1 yard?
    2. 2Find the scale factor from 1 yard to 3 yards.
    3. 3Multiply 3 feet by 3. How many feet?
    4. 4Multiply 36 inches by 3. How many inches?
    Final answer:
  2. 2Complete each step, then write the final answer.
    Yards1?Feet3?Inches?144× ?× ?

    A hallway is 144 inches long. How many yards long is it?

    1. 1How many inches are in 1 yard? Use 3 × 12.
    2. 2Find the scale factor from 36 inches to 144 inches.
    3. 3Multiply 1 yard by 4. How many yards?
    4. 4Why is the number of yards so much smaller than 144?
    Final answer:
  3. 3Complete each step, then write the final answer.
    YardsFeet________________

    A fence is 27 feet long. How many yards long is it?

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

    A board is 90 inches long. How many feet long is it? Write your answer as a decimal.

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

    One lap around a running track is 1,320 feet. How many yards is one lap?

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

    Dee changes 6 yards to inches. She multiplies 6 × 12 and gets 72 inches. What is the correct number of inches?

    Show your work
    Final answer:

Explain your thinkingDee used only one conversion factor. How do you know when a conversion needs two steps?

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