Lesson 3.7Ratio Reasoning: Convert Measurements Between Systems
Start hereWords, worked example, and sentence starters
Learning target I can use ratio reasoning to convert measurements between the customary and metric systems.
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. 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 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
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; 1 mile ≈ 1.609 km is rounded. Use ≈ when the factor or the result has been rounded.
Lesson 3.7Ratio Reasoning: Convert Measurements Between Systems
Version ASupported practice
Learning target I can use ratio reasoning to convert measurements between the customary and metric systems.
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1Complete the table. Show how you found each value.
1 kilometer ≈ 0.6 mile. Complete the ratio table.
Kilometers Miles 1 0.6 10 100 Hint Row 1 is the conversion factor.
Show your work
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2Circle the letter of the best answer. Show how you know.
1 kilometer ≈ 0.6 mile. About how many miles is 5 kilometers?
- A3 miles
- B5.6 miles
- C8 miles
- D30 miles
Hint Write the conversion factor as a ratio: 1 : 0.6.
Show your work -
3Circle the letter of the best answer. Show how you know.
1 pound ≈ 0.45 kilogram. About how many kilograms is 10 pounds?
- A4.5 kg
- B10.45 kg
- C22 kg
- D45 kg
Hint The ratio is 1 lb : 0.45 kg.
Show your work -
4Circle the letter of the best answer. Show how you know.
Which pair of units comes from two DIFFERENT measurement systems?
- AInches and feet
- BCups and quarts
- CGrams and kilograms
- DMiles and kilometers
Hint Sort each unit as customary or metric.
Show your work -
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?
- AAbout 8 miles
- BAbout 48 miles
- CAbout 80 miles
- DAbout 133 miles
Hint Scale the ratio 1 : 0.6 up to 80 kilometers.
Show your work
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6Find the mistake. Explain it, then show the correct work.
Find the error
- 1Setup1 kilometer ≈ 0.6 mile. About how many miles is 20 kilometers?
- 2Step 1The ratio is 1 : 0.6.
- 3Step 220 ÷ 0.6 = 33.3
- 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 workCorrect 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.
Lesson 3.7Ratio Reasoning: Convert Measurements Between Systems
Version BCore practice
Learning target I can use ratio reasoning to convert measurements between the customary and metric systems.
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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.
Pounds Kilograms 1 0.45 10 30 40 Show your work -
2Write the name of the correct group on each line.
Converting between systems: sort each conversion by what happens to the number.
- Kilometers → miles
- Miles → kilometers
- Pounds → kilograms
- Kilograms → pounds
- Inches → centimeters
- Centimeters → inches
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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.
Show your thinking
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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?
- AThe 4–10 kg package
- BThe 10–25 kg package
- CThe 25–40 kg package
- DNone — 31 is above every range
Show your work
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5Find the mistake. Explain it, then show the correct work.
Find the error
- 1SetupA recipe calls for 2 pounds of flour. The scale is metric. (1 lb ≈ 0.45 kg)
- 2Step 1The conversion factor is 1 : 0.45.
- 3Step 20.45 × 2 = 0.9, so 2 pounds ≈ 0.9 kilogram.
- 4Step 32 pounds = 0.9 kilogram exactly.
Which step has the mistake? Explain what went wrong, then show the correct work.
Correct workCorrect answer:
Explain your thinkingWhy does 1 inch = 2.54 cm use =, while 1 mile ≈ 1.609 km uses ≈? What does the rounding change?
Lesson 3.7Ratio Reasoning: Convert Measurements Between Systems
ChallengeExtension
Learning target I can use ratio reasoning to convert measurements between the customary and metric systems.
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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.
Customary Metric equivalent 1 inch 2.54 cm (exact) 1 mile 1 pound 1 United States liquid quart Show your work
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2Find the mistake. Explain it, then show the correct work.
Find the error
- 1SetupWhich is longer, 5 kilometers or 5 miles? (1 km ≈ 0.6 mi)
- 2Step 1Both numbers are 5.
- 3Step 2The units are different, so I compare the numbers: they are equal.
- 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 workCorrect answer: -
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