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

Lesson 3.6Ratio Reasoning: Convert Measurements within the Same System

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.

Why This Matters Chef Reyes writes every recipe in the units the supplier uses, but the kitchen's measuring tools are marked in different units of the same system. A stock order lists quarts; the pot is marked in cups. A height rule at the county fair ride is posted in inches; the sign-up sheet lists feet. Your job is to convert between units without changing the amount. The stock order lists 3 quarts, but the pot is marked in cups. The height rule at the ride says 48 inches, but the sign-up sheet lists feet.

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 example

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

A pitcher holds 2 quarts. How many fluid ounces? (1 qt = 4 cups, 1 cup = 8 fl oz)

  1. Quarts to cups: 2 × 4 = 8 cups.
  2. Cups to fl oz: 8 × 8 = 64 fl oz.
  3. Check: 64 ÷ 8 ÷ 4 = 2 quarts.

Answer: 2 quarts = 64 fluid ounces

Now you trySame steps, your turn

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

Diamond wants to drink 4 liters of water. Her bottle is marked in milliliters.

Answer:

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 out!A common mistake

A common mistake when converting within a measurement system is choosing the operation by habit instead of by unit size

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

Lesson 3.6Ratio Reasoning: Convert Measurements within the Same System

Version ASupported 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.

Why This Matters Chef Reyes writes every recipe in the units the supplier uses, but the kitchen's measuring tools are marked in different units of the same system. A stock order lists quarts; the pot is marked in cups. A height rule at the county fair ride is posted in inches; the sign-up sheet lists feet. Your job is to convert between units without changing the amount. The stock order lists 3 quarts, but the pot is marked in cups. The height rule at the ride says 48 inches, but the sign-up sheet lists feet.

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

    There are 4 cups in 1 quart. Complete the conversion table.

    QuartsCups
    14
    3
    6

    Hint Row 1 is the unit ratio: 1 quart is 4 cups.

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

    There are 12 inches in 1 foot. How many inches are in 5 feet?

    1. A7 inches
    2. B17 inches
    3. C50 inches
    4. D60 inches

    Hint Write the unit ratio first: 12 inches : 1 foot.

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

    There are 1,000 milliliters in 1 liter. How many milliliters are in 3 liters?

    1. A30 mL
    2. B300 mL
    3. C1,003 mL
    4. D3,000 mL

    Hint The unit ratio is 1,000 mL : 1 L.

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

    There are 16 ounces in 1 pound. How many pounds is 48 ounces?

    1. A3 pounds
    2. B32 pounds
    3. C64 pounds
    4. D768 pounds

    Hint Which unit is larger, an ounce or a pound?

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

    A child is 4 feet tall. A ride requires 44 inches. Can the child ride?

    1. ANo, because 4 is less than 44
    2. BYes, because 4 feet = 44 inches exactly
    3. CYes, because 4 feet = 48 inches, which is more than 44
    4. DYou cannot compare feet and inches

    Hint You cannot compare two different units directly.

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

    Find the error

    1. 1SetupConvert 5 feet to inches.
    2. 2Step 1There are 12 inches in 1 foot.
    3. 3Step 25 ÷ 12 = 0.42
    4. 4Step 3So 5 feet is about 0.42 inches.

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

    Hint Is an inch bigger or smaller than a foot?

    Correct work
    Correct answer:

Explain your thinkingWhy does converting to a smaller unit always make the NUMBER bigger, even though the amount stays exactly the same?

Sentence starter When the unit gets ___, it takes ___ of them to make the same amount, so I ___.

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

Lesson 3.6Ratio Reasoning: Convert Measurements within the Same System

Version BCore 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.

Why This Matters Chef Reyes writes every recipe in the units the supplier uses, but the kitchen's measuring tools are marked in different units of the same system. A stock order lists quarts; the pot is marked in cups. A height rule at the county fair ride is posted in inches; the sign-up sheet lists feet. Your job is to convert between units without changing the amount. The stock order lists 3 quarts, but the pot is marked in cups. The height rule at the ride says 48 inches, but the sign-up sheet lists feet.

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

    There are 1,000 milliliters in 1 liter. Complete the double number line as a table.

    LitersMilliliters
    11,000
    2
    4
    Show your work
  2. 2Use the model to solve. Show your work.
    TotalQuart 1Quart 2Quart 3

    A 3-quart stockpot is filled using a 1-cup scoop. There are 4 cups in 1 quart. Use the bar model to show how many scoops fill the pot.

    Show your work
    Answer:
  3. 3Write the name of the correct group on each line.

    Sort each conversion by what happens to the NUMBER.

    Groups: The number gets bigger The number gets smaller
    • 7 feet → inches
    • 84 inches → feet
    • 2 liters → milliliters
    • 5,000 milliliters → liters
    • 3 pounds → ounces
    • 64 ounces → pounds
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    Diamond needs 4 liters of water. Her bottle holds 500 milliliters. How many times must she fill it?

    1. A2 times
    2. B4 times
    3. C8 times
    4. D40 times
    Show your work
  2. 5Circle the letter of the best answer. Show how you know.

    Chef Reyes's stock order lists 3 quarts of broth, but her measuring cup is marked in cups. There are 4 cups in 1 quart. How many cups of broth is that?

    1. A7 cups
    2. B0.75 cup
    3. C12 cups
    4. D3 cups
    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Find the error

    1. 1SetupA recipe needs 2 pounds of flour. The scale reads in ounces (16 oz = 1 lb).
    2. 2Step 1The unit ratio is 16 ounces : 1 pound.
    3. 3Step 22 × 16 = 32, so 2 pounds = 32 ounces.
    4. 4Step 3The scale reads 40 ounces, so there is not enough flour.

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

    Correct work
    Correct answer:

Explain your thinkingWhy does converting to a smaller unit always make the NUMBER bigger, even though the amount stays exactly the same?

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

Lesson 3.6Ratio Reasoning: Convert Measurements within the Same System

ChallengeExtension

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.

Why This Matters Chef Reyes writes every recipe in the units the supplier uses, but the kitchen's measuring tools are marked in different units of the same system. A stock order lists quarts; the pot is marked in cups. A height rule at the county fair ride is posted in inches; the sign-up sheet lists feet. Your job is to convert between units without changing the amount. The stock order lists 3 quarts, but the pot is marked in cups. The height rule at the ride says 48 inches, but the sign-up sheet lists feet.

Part 1Understand the ideamodels and meaning
  1. 1Decide whether each pair balances. Check Yes or No, then explain.

    1 foot / 12 inches = 7 feet / x inches → x = 84 inches

    Left sideRight sideBalanced?
    Explain your choice
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find the error

    1. 1SetupConvert 4 liters to milliliters, then find how many 250-mL cups it fills.
    2. 2Step 14 × 1,000 = 4,000 mL
    3. 3Step 24,000 × 250 = 1,000,000
    4. 4Step 3It fills 1,000,000 cups.

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

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

    Michael's mother is setting four fence posts. Each post needs 250 ounces of concrete mix, one bag holds 80 ounces, and each bag needs 1 quart of water. How many bags and how many cups of water does she need? Show your conversions.

    Write your answer

Explain your thinkingWhy does converting to a smaller unit always make the NUMBER bigger, even though the amount stays exactly the same?

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