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.

Why This Matters This is your challenge small group for Lesson 3.7. 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 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 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's dog weighs 31 pounds. Flea medicine comes in a package for dogs from 10 to 25 kilograms. Does this package fit his dog? Use 1 pound ≈ 0.45 kilogram.

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

A common mistake converting between systems is comparing the bare numbers without converting at all

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.

Why This Matters This is your challenge small group for Lesson 3.7. 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.
    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.

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