Lesson 3.73.7 Small Group · Group 1
Start hereWords, worked example, and sentence starters
Learning target With my small group, I can use ratio reasoning to convert measurements between the customary and metric systems — one step at a time, with support.
Why This Matters This is your support small group for Lesson 3.7. We're going to slow this down and build it together, one step at a time. You can ask a question any time — that's what this group is for.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| 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)
- A kilogram is heavier, so the number gets smaller: divide.
- 44 ÷ 2.2 = 20.
- 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.
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
Lesson 3.73.7 Small Group · Group 1
Group 1Supported practice
Learning target With my small group, I can use ratio reasoning to convert measurements between the customary and metric systems — one step at a time, with support.
Why This Matters This is your support small group for Lesson 3.7. We're going to slow this down and build it together, one step at a time. You can ask a question any time — that's what this group is for.
-
1Complete each step, then write the final answer.
Find the factor. Do the same to both rows. A bike race is 40 kilometers long. Use 1 kilometer ≈ 0.6 mile. About how many miles long is the race?
- 1Write the conversion fact in the first column.
- 2What is the scale factor from 1 km to 40 km?
- 3Multiply 0.6 by the same factor. About how many miles is 40 km?
Final answer: -
2Complete each step, then write the final answer.
Find the factor. Do the same to both rows. A suitcase has a mass of 20 kilograms. Use 1 kilogram ≈ 2.2 pounds. An airline allows 50 pounds. Is the suitcase under the limit?
- 1Write the conversion fact in the first column.
- 2What is the scale factor from 1 kg to 20 kg?
- 3Multiply 2.2 by the same factor. About how many pounds is 20 kg?
- 4Is 44 pounds less than 50 pounds?
Final answer: -
3Complete each step, then write the final answer.
Use 1 kilometer ≈ 0.6 mile. About how many miles is 25 kilometers?
Show your workHint Find the scale factor from 1 to 25. Multiply 0.6 by the same factor.
Final answer: -
4Complete each step, then write the final answer.
A dog weighs 60 pounds. Use 1 pound ≈ 0.45 kilogram. About how many kilograms does the dog weigh?
Show your workHint Find the scale factor from 1 to 60. Multiply 0.45 by the same factor.
Final answer: -
5Complete each step, then write the final answer.
Maya's run is 5 miles long. Her phone shows distance in kilometers. Use 1 mile ≈ 1.6 kilometers. About how many kilometers will her phone show?
Show your workHint Find the scale factor from 1 to 5. Multiply 1.6 by the same factor.
Final answer: -
6Complete each step, then write the final answer.
A sign says the next town is 50 kilometers away. Sam says that is 50 miles. Use 1 kilometer ≈ 0.6 mile. About how many miles away is the town?
Show your workHint Kilometers and miles are different units. Convert before you say how far it is.
Final answer:
Explain your thinkingSam thought 50 kilometers is 50 miles. Why is the number of miles smaller? Use the ratio 1 : 0.6 to explain.
Sentence starter The number of miles is smaller because ___. · 50 kilometers is about ___ miles because ___.