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.

Why This Matters This is your challenge small group for Lesson 3.10. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

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 out!A common mistake

A common mistake in Convert Measurement Units is applying the conversion factor in the wrong direction

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.

Why This Matters This is your challenge small group for Lesson 3.10. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.

  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.

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