Lesson 3.6Metric Unit Conversions
Start hereWords, worked example, and sentence starters
Learning target I can use ratio reasoning to convert between units within the same measurement system.
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 two units in the same measurement system, such as 12 inches to 1 foot. Within one system it is exact. | 1 ft = 12 in. · 1 L = 1,000 mL · 1 lb = 16 oz |
| Unit ratioSpanish: Razón unitaria | A ratio that compares an amount to exactly 1 unit of another quantity, like 12 inches to 1 foot. | 12 : 1 — twelve inches for every one foot |
| ConvertSpanish: Convertir | To change a measurement from one unit to another without changing how much it is. | 7 km → 7,000 m |
| Measurement systemSpanish: Sistema de medidas | A family of units that go together — customary units like inches and feet, or metric units like milliliters and liters. | Customary: 12 in = 1 ft · Metric: 1,000 mL = 1 L |
| Double number lineSpanish: Recta numérica doble | Two number lines lined up so matching tick marks show two units for the same amount. | Liters 0, 1, 2, 3, 4 above milliliters 0, 1,000, 2,000, 3,000, 4,000 |
| Ratio tableSpanish: Tabla de razones | A table of equal ratios that lets you scale a conversion up or down one row at a time. | 1 ft : 12 in, 2 ft : 24 in, 4 ft : 48 in |
How it worksWorked exampleconverting metric units with powers of 10
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A race route is 7 kilometers long. How many meters is that? (1 km = 1,000 m)
- Write the conversion factor. 1 km = 1,000 m
- Decide the direction. km → m is LARGER to SMALLER, so multiply.
- Multiply by 1,000 — shift the decimal 3 places right. 7 → 7,000
- Check: meters are small, so the number got bigger. ✓
Answer: 7 kilometers = 7,000 meters.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A cooler holds 6 liters. How many milliliters is that? (1 L = 1,000 mL)
- Write the conversion factor. 1 L = mL
- Larger unit to smaller unit, so I will .
- Shift the decimal places to the . 6 →
- Reasonable? mL are smaller, so the number should get .
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- I know 1 = .
- I by because .
- I shifted the decimal places to the .
- My answer is reasonable because .
Word bank convertmetrickilo-centi-milli-metergramlitermultiplydividedecimalpowers of 10
Watch outA common mistake
A common mistake when converting within a measurement system is choosing the operation by habit instead of by unit size — multiplying every time. Converting 36 inches to feet by multiplying gives 36 × 12 = 432 feet, taller than a 40-story building. Ask first which unit is smaller: it takes MORE small units to make the same amount, so going to a smaller unit multiplies, and going to a larger unit divides.
Lesson 3.6Metric Unit Conversions
Apply Day · Version ASupported practice
Learning target I can use ratio reasoning to convert between units within the same measurement system.
-
1Complete each step, then write the final answer.
How many inches are in 2 feet?
Show your workHint Each foot is 12 inches. Find 2 × 12.
Final answer: -
2Complete each step, then write the final answer.
There are 1,000 meters in 1 kilometer. How many meters are in 6 kilometers?
Show your workHint Meters are smaller than kilometers, so multiply by 1,000.
Final answer: -
3Complete each step, then write the final answer.
A rope is 5 yards long. There are 3 feet in 1 yard. How many feet long is the rope?
Show your workHint Feet are smaller than yards, so multiply: 5 × 3.
Final answer:
Lesson 3.6Metric Unit Conversions
Apply Day · Version BCore practice
Learning target I can use ratio reasoning to convert between units within the same measurement system.
-
1Complete each step, then write the final answer.
Leo says 24 inches is 288 feet, because 24 × 12 = 288. Is he right? How many feet is 24 inches?
Show your workFinal answer: -
2Complete each step, then write the final answer.
A plank is 51 inches long. How many feet long is it? Write your answer as a decimal.
Show your workFinal answer: -
3Complete each step, then write the final answer.
How many inches are in 8 feet?
Show your workFinal answer:
Lesson 3.6Metric Unit Conversions
Apply Day · ChallengeExtension
Learning target I can use ratio reasoning to convert between units within the same measurement system.
-
1Circle the letter of the best answer. Show how you know.
A rope measures 7 feet. Using 1 foot = 12 inches, how long is the rope in inches?
- A0.58 inches
- B7 inches
- C19 inches
- D84 inches
Show your work -
2Complete each step, then write the final answer.
Ana says 2 feet 6 inches is 2.6 feet. What is the correct length in feet, as a decimal?
Show your workFinal answer: -
3Complete each step, then write the final answer.
A table is 66 inches long. How many feet long is it? Write your answer as a decimal.
Show your workFinal answer: