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

Lesson 3.63.6 Small Group · Group 1

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target With my small group, I can use ratio reasoning to convert between units within the same measurement system — one step at a time, with support.

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 1

Group 1Supported practice

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

Learning target With my small group, I can use ratio reasoning to convert between units within the same measurement system — one step at a time, with support.

  1. 1Complete each step, then write the final answer.
    Feet13Inches12?× ?× ?
    Start with the fact: 1 foot is 12 inches.

    A shelf is 3 feet long. A box is 40 inches long. Does the box fit on the shelf?

    1. 1How many inches are in 1 foot?
    2. 2What scale factor takes 1 foot to 3 feet?
    3. 3How many inches long is the shelf?
    4. 4Compare 40 inches and 36 inches. Does the box fit?
    Final answer:
  2. 2Complete each step, then write the final answer.
    Kilograms12Grams1,000?× ?× ?
    Start with the fact: 1 kilogram is 1,000 grams.

    A bag of flour has a mass of 2 kilograms. A recipe needs 1,500 grams of flour. Is there enough flour?

    1. 1How many grams are in 1 kilogram?
    2. 2What scale factor takes 1 kilogram to 2 kilograms?
    3. 3Grams are smaller. How many grams are in 2 kilograms?
    4. 4Compare 2,000 grams and 1,500 grams. Is there enough flour?
    Final answer:
  3. 3Complete each step, then write the final answer.
    FeetInches________________

    How many inches are in 6 feet?

    Show your work

    Hint Each foot is 12 inches. Inches are smaller, so multiply.

    Final answer:
  4. 4Complete each step, then write the final answer.
    PoundsOunces________________

    There are 16 ounces in 1 pound. How many ounces are in 5 pounds?

    Show your work

    Hint Ounces are smaller than pounds. Will you get more or fewer ounces?

    Final answer:
  5. 5Complete each step, then write the final answer.
    LitersMilliliters________________

    A water jug holds 3 liters. How many 250-milliliter cups can you fill from the jug?

    Show your work

    Hint First change 3 liters to milliliters. Then see how many 250s fit.

    Final answer:
  6. 6Complete each step, then write the final answer.
    InchesFeet________________

    Leo says 24 inches is 288 feet, because 24 × 12 = 288. Is he right? How many feet is 24 inches?

    Show your work

    Hint Feet are larger than inches. Should there be more feet or fewer feet?

    Final answer:

Explain your thinkingWhen you change feet to inches, why does the number get bigger? Use Leo's mistake to explain.

Sentence starter I multiply when I change to a smaller unit because ___. · Leo should divide because ___.

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