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.
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 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)
- Write the conversion factor. 1 m ≈ 3.28 ft
- Ask which unit is BIGGER. A meter is bigger than a foot.
- A bigger unit becomes MORE of the smaller unit, so multiply. 5 × 3.28 = 16.4
- 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)
- Write the conversion factor. 1 kg ≈ lbs
- Which unit is bigger, a kilogram or a pound?
- Bigger unit → more of the smaller unit, so .
- Compute and check. 12 × ≈ lbs
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.
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.
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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 ___.