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

Lesson 3.73.7 Small Group · Group 2

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, 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 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. Conversions between systems are almost always approximate, so they use the ≈ sign. ≈ 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
Ratio and Rate Problem SolvingSpanish: Resolución de problemas de razones y tasas Use ratios and rates to compare quantities and solve real-world problems. Cost = number of items × cost per item.

How it worksWorked exampleconverting across the two systems

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

A room is 5 meters wide. How many feet is that? (1 meter ≈ 3.28 feet)

  1. Write the conversion factor. 1 m ≈ 3.28 ft
  2. Ask which unit is BIGGER. A meter is bigger than a foot.
  3. A bigger unit becomes MORE of the smaller unit, so multiply. 5 × 3.28 = 16.4
  4. Check reasonableness: 16.4 ft is more than 5 — correct direction. ✓

Answer: 5 meters ≈ 16.4 feet.

Now you trySame steps, your turn

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

A crate weighs 12 kilograms. How many pounds is that? (1 kg ≈ 2.2 lbs)

  1. Write the conversion factor. 1 kg ≈ lbs
  2. Which unit is bigger, a kilogram or a pound?
  3. Bigger unit → more of the smaller unit, so .
  4. Compute and check. 12 × ≈ lbs
Answer:pounds

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 outA common mistake

A common mistake converting between systems is comparing the bare numbers without converting at all — deciding that 5 kilometers and 5 miles are the same distance because both say 5. They are not: 5 kilometers ≈ 3 miles. A second mistake is writing = instead of ≈. Conversion factors between systems are rounded (1 mile is about 1.609344 kilometers), so the result is approximate no matter how carefully you multiply.

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

Lesson 3.73.7 Small Group · Group 2

Group 2Challenge 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, 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.
    Kilometers (km)1?Miles (mi)0.69× ?× ?
    Find the factor from 0.6 to 9.

    A hike is 9 miles long. Use 1 kilometer ≈ 0.6 mile. About how many kilometers long is the hike?

    1. 1Write the conversion fact in the first column.
    2. 2What is the scale factor from 0.6 mi to 9 mi? Find 9 ÷ 0.6.
    3. 3Multiply the 1 km by the same factor. How many kilometers is the hike?
    4. 4Check: what is 15 × 0.6?
    Final answer:
  2. 2Complete each step, then write the final answer.
    Pounds (lb)1?Kilograms (kg)0.459× ?× ?
    Find the factor from 0.45 to 9.

    A puppy has a mass of 9 kilograms. Use 1 pound ≈ 0.45 kilogram. About how many pounds does the puppy weigh?

    1. 1Write the conversion fact in the first column.
    2. 2What is the scale factor from 0.45 kg to 9 kg? Find 9 ÷ 0.45.
    3. 3Multiply the 1 lb by the same factor. About how many pounds is it?
    4. 4Why is the number of pounds greater than the number of kilograms?
    Final answer:
  3. 3Complete each step, then write the final answer.
    Kilometers (km)Miles (mi)________________

    Use 1 kilometer ≈ 0.6 mile. About how many kilometers is 21 miles?

    Show your work
    Final answer:
  4. 4Complete each step, then write the final answer.
    Kilometers (km)Miles (mi)________________

    Race A is 8 kilometers. Race B is 5 miles. Use 1 kilometer ≈ 0.6 mile. About how many miles is Race A?

    Show your work
    Final answer:
  5. 5Complete each step, then write the final answer.
    Kilograms (kg)Pounds (lb)________________

    A dog weighs 66 pounds. Medicine comes in a package for dogs from 20 to 40 kilograms. Use 1 kilogram ≈ 2.2 pounds. About how many kilograms does the dog weigh?

    Show your work
    Final answer:
  6. 6Complete each step, then write the final answer.
    Inches (in.)Centimeters (cm)________________

    Kim changes 6 inches to centimeters. Use 1 inch = 2.54 centimeters. She divides and gets about 2.4 centimeters. What is the correct number of centimeters?

    Show your work
    Final answer:

Explain your thinkingTo change kilometers to miles, do you multiply or divide by 0.6? How do you decide which way to go?

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