Lesson 3.7Multi-Step System Conversions & Dosage
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 lb ≈ 0.45 kg · 1 in = 2.54 cm |
| 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 =. | 1 km ≈ 0.6 mi, not exactly 0.6 |
| 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. | A bigger unit should give a smaller number. |
How it worksWorked examplesolving a two-step conversion
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A dog weighs 66 pounds. The medicine dose is 4 mg for every 1 kg. (1 kg ≈ 2.2 lbs)
- — convert to the unit the rate uses. 66 ÷ 2.2 = 30 kg
- Do NOT skip to the dose — the rate is per KILOGRAM, not per pound.
- — apply the rate. 30 × 4 = 120
- Label the answer with its unit. 120 mg
Answer: The dog needs a 120 mg dose.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A cat weighs 11 pounds. The dose is 6 mg for every 1 kg. (1 kg ≈ 2.2 lbs)
- — convert to the unit the rate uses. 11 ÷ = kg
- Why can you not multiply 11 by 6?
- — apply the rate. × 6 =
- Label the answer with its unit.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- First I converted to .
- I because .
- Then I multiplied by to get .
- My answer is , and it is reasonable because .
Word bank convertdoseperroundfirstthenmulti-stepkilogrampoundmilligrammultiplydivide
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 3.7Multi-Step System Conversions & Dosage
Apply Day · Version ASupported practice
Learning target I can use ratio reasoning to convert measurements between the customary and metric systems.
-
1Complete each step, then write the final answer.
Use 1 kilometer ≈ 0.6 mile. About how many miles is 60 kilometers?
Show your workHint Find the scale factor from 1 to 60. Multiply 0.6 by the same factor.
Final answer: -
2Complete each step, then write the final answer.
Use 1 kilogram ≈ 2.2 pounds. About how many pounds is 3 kilograms?
Show your workHint Find the scale factor from 1 to 3. Multiply 2.2 by the same factor.
Final answer: -
3Complete each step, then write the final answer.
Use 1 pound ≈ 0.45 kilogram. About how many kilograms is 40 pounds?
Show your workHint Find the scale factor from 1 to 40. Multiply 0.45 by the same factor.
Final answer:
Lesson 3.7Multi-Step System Conversions & Dosage
Apply Day · Version BCore practice
Learning target I can use ratio reasoning to convert measurements between the customary and metric systems.
-
1Complete 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 workFinal answer: -
2Complete each step, then write the final answer.
Use 1 kilometer ≈ 0.6 mile. About how many kilometers is 21 miles?
Show your workFinal answer: -
3Complete each step, then write the final answer.
Use 1 kilometer ≈ 0.6 mile. About how many miles is 70 kilometers?
Show your workFinal answer:
Lesson 3.7Multi-Step System Conversions & Dosage
Apply Day · ChallengeExtension
Learning target I can use ratio reasoning to convert measurements between the customary and metric systems.
-
1Circle the letter of the best answer. Show how you know.
A backpack weighs 5 kilograms. Using 1 kilogram ≈ 2.2 pounds, about how much does it weigh in pounds?
- A2.27 pounds
- B7.2 pounds
- C10 pounds
- D11 pounds
Show your work -
2Complete each step, then write the final answer.
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 workFinal answer: -
3Complete each step, then write the final answer.
Use 1 kilometer ≈ 0.6 mile. About how many kilometers is 4.2 miles?
Show your workFinal answer: