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

Lesson 3.7Ratio Reasoning: Convert Measurements Between Systems

Start hereWords, worked example, and sentence starters

Name Date Period

Learning target I can use ratio reasoning to convert measurements between the customary and metric systems.

Why This Matters The academy's kitchen orders from suppliers in two different countries. One ships in pounds and quarts, the other in kilograms and liters. Compare measurements by converting with the appropriate factor. Some factors are exact; rounded factors give approximate results. One supplier ships 10 pounds of rice and the other ships 5 kilograms. Use 1 pound ≈ 0.45 kilogram to find which shipment is more.

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 a unit in one system to a unit in the other, such as 1 mile to about 1.609 kilometers. 1 m ≈ 3.28 ft
Customary systemSpanish: Sistema usual The measurement system used in the United States: inches, feet, miles, ounces, pounds, cups, quarts, gallons. in · ft · mi · oz · lb · qt · gal
Metric systemSpanish: Sistema métrico The measurement system used in most of the world, built on tens: centimeters, meters, kilometers, grams, kilograms, liters. cm · m · km · g · kg · mL · L
ApproximatelySpanish: Aproximadamente Close to, but not exactly equal. A rounded conversion factor gives an approximate result, written with ≈; an exact conversion uses =. ≈ means “about”
Ratio tableSpanish: Tabla de razones A table of equal ratios used to scale a conversion factor up to the amount you actually need. km: 1, 10, 100 · mi: 0.6, 6, 60
ReasonablenessSpanish: Sentido lógico Checking that the size of an answer makes sense for the situation. bigger unit → smaller number

How it worksWorked example

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

A bag weighs 44 pounds. About how many kilograms? (1 kg ≈ 2.2 lb)

  1. A kilogram is heavier, so the number gets smaller: divide.
  2. 44 ÷ 2.2 = 20.
  3. Check: 20 × 2.2 = 44.

Answer: 44 lb ≈ 20 kg

Now you trySame steps, your turn

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

Terrance needs flea medicine for a dog weighing 31 pounds, but the packages are labeled in kilograms.

Answer:

Say it and write itSentence starters

Finish each sentence out loud with a partner. Then use them in your writing.

  • I know 1 ≈ .
  • A is bigger than a , so I .
  • My answer is about .
  • This is reasonable because .

Word bank convertconversion factorapproximatelyaboutreasonablebiggersmallermultiplydividemetermilekilogram

Watch out!A common mistake

Compare measurements only after converting to a common unit. Also check whether the conversion factor is exact or rounded: 1 inch = 2.54 cm and 1 international mile = 1.609344 km are exact

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

Lesson 3.7Ratio Reasoning: Convert Measurements Between Systems

Version ASupported practice

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

Learning target I can use ratio reasoning to convert measurements between the customary and metric systems.

Why This Matters The academy's kitchen orders from suppliers in two different countries. One ships in pounds and quarts, the other in kilograms and liters. Compare measurements by converting with the appropriate factor. Some factors are exact; rounded factors give approximate results. One supplier ships 10 pounds of rice and the other ships 5 kilograms. Use 1 pound ≈ 0.45 kilogram to find which shipment is more.

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

    1 kilometer ≈ 0.6 mile. Complete the ratio table.

    KilometersMiles
    10.6
    10
    100

    Hint Row 1 is the conversion factor.

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

    1 kilometer ≈ 0.6 mile. About how many miles is 5 kilometers?

    1. A3 miles
    2. B5.6 miles
    3. C8 miles
    4. D30 miles

    Hint Write the conversion factor as a ratio: 1 : 0.6.

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

    1 pound ≈ 0.45 kilogram. About how many kilograms is 10 pounds?

    1. A4.5 kg
    2. B10.45 kg
    3. C22 kg
    4. D45 kg

    Hint The ratio is 1 lb : 0.45 kg.

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

    Which pair of units comes from two DIFFERENT measurement systems?

    1. AInches and feet
    2. BCups and quarts
    3. CGrams and kilograms
    4. DMiles and kilometers

    Hint Sort each unit as customary or metric.

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

    A sign in Mexico gives a distance of 80 kilometers. Using 1 km ≈ 0.6 mi, about how far is that in miles?

    1. AAbout 8 miles
    2. BAbout 48 miles
    3. CAbout 80 miles
    4. DAbout 133 miles

    Hint Scale the ratio 1 : 0.6 up to 80 kilometers.

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

    Find the error

    1. 1Setup1 kilometer ≈ 0.6 mile. About how many miles is 20 kilometers?
    2. 2Step 1The ratio is 1 : 0.6.
    3. 3Step 220 ÷ 0.6 = 33.3
    4. 4Step 320 kilometers ≈ 33.3 miles.

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

    Hint Is a kilometer longer or shorter than a mile?

    Correct work
    Correct answer:

Explain your thinkingWhy does 1 inch = 2.54 cm use =, while 1 mile ≈ 1.609 km uses ≈? What does the rounding change?

Sentence starter The inch factor is ___ by definition. The mile factor shown is ___, so I write ___ for its result.

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 3.7Ratio Reasoning: Convert Measurements Between Systems

Version BCore practice

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

Learning target I can use ratio reasoning to convert measurements between the customary and metric systems.

Why This Matters The academy's kitchen orders from suppliers in two different countries. One ships in pounds and quarts, the other in kilograms and liters. Compare measurements by converting with the appropriate factor. Some factors are exact; rounded factors give approximate results. One supplier ships 10 pounds of rice and the other ships 5 kilograms. Use 1 pound ≈ 0.45 kilogram to find which shipment is more.

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

    1 pound ≈ 0.45 kilogram. Complete the ratio table, then use it to place a 31-pound dog.

    PoundsKilograms
    10.45
    10
    30
    40
    Show your work
  2. 2Write the name of the correct group on each line.

    Converting between systems: sort each conversion by what happens to the number.

    Groups: The number gets smaller The number gets bigger
    • Kilometers → miles
    • Miles → kilometers
    • Pounds → kilograms
    • Kilograms → pounds
    • Inches → centimeters
    • Centimeters → inches
  3. 3Mark and label each value on the number line.

    Using 1 km ≈ 0.6 mi, place the mile markers that match 0, 50, and 100 kilometers.

    0102030405060
    Show your thinking
Part 2Apply itreal-world problems
  1. 4Circle the letter of the best answer. Show how you know.

    A dog weighs 31 pounds. Flea medicine comes in packages for 4–10 kg, 10–25 kg, and 25–40 kg. Which package is correct?

    1. AThe 4–10 kg package
    2. BThe 10–25 kg package
    3. CThe 25–40 kg package
    4. DNone — 31 is above every range
    Show your work
  2. 5Circle the letter of the best answer. Show how you know.

    One of the academy's suppliers ships olive oil in 4-liter tins. Using 1 liter ≈ 1.06 quarts, about how many quarts of oil are in one tin?

    1. AAbout 3.77 quarts
    2. BAbout 4.24 quarts
    3. CAbout 5.06 quarts
    4. DAbout 42.4 quarts
    Show your work
Part 3Explain and correctreasoning
  1. 6Find the mistake. Explain it, then show the correct work.

    Find the error

    1. 1SetupA recipe calls for 2 pounds of flour. The scale is metric. (1 lb ≈ 0.45 kg)
    2. 2Step 1The conversion factor is 1 : 0.45.
    3. 3Step 20.45 × 2 = 0.9, so 2 pounds ≈ 0.9 kilogram.
    4. 4Step 32 pounds = 0.9 kilogram exactly.

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

    Correct work
    Correct answer:

Explain your thinkingWhy does 1 inch = 2.54 cm use =, while 1 mile ≈ 1.609 km uses ≈? What does the rounding change?

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 3.7Ratio Reasoning: Convert Measurements Between Systems

ChallengeExtension

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

Learning target I can use ratio reasoning to convert measurements between the customary and metric systems.

Why This Matters The academy's kitchen orders from suppliers in two different countries. One ships in pounds and quarts, the other in kilograms and liters. Compare measurements by converting with the appropriate factor. Some factors are exact; rounded factors give approximate results. One supplier ships 10 pounds of rice and the other ships 5 kilograms. Use 1 pound ≈ 0.45 kilogram to find which shipment is more.

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

    Complete the conversion table. The inch factor is exact. Round the other metric factors to three decimal places.

    CustomaryMetric equivalent
    1 inch2.54 cm (exact)
    1 mile
    1 pound
    1 United States liquid quart
    Show your work
Part 2Explain and correctreasoning
  1. 2Find the mistake. Explain it, then show the correct work.

    Find the error

    1. 1SetupWhich is longer, 5 kilometers or 5 miles? (1 km ≈ 0.6 mi)
    2. 2Step 1Both numbers are 5.
    3. 3Step 2The units are different, so I compare the numbers: they are equal.
    4. 4Step 35 kilometers is the same distance as 5 miles.

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

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

    The Golden Gate Bridge can hold about 35,924,000 pounds. An average midsize car weighs about 1,524 kilograms. Using 1 kilogram ≈ 2.2 pounds, about how many midsize cars could be on the bridge at one time? Explain each step, and say why your answer is an estimate.

    Write your answer

Explain your thinkingWhy does 1 inch = 2.54 cm use =, while 1 mile ≈ 1.609 km uses ≈? What does the rounding change?

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