Lesson 7: Ratio Reasoning: Convert Measurements Between Systems6.AT.3c

I can…

I can use ratio reasoning to convert measurements between the customary and metric systems.

Key words

• Convert Measurements Between Systems — Change US units to metric units, or back.
• Conversion factor — A ratio you use to change units.
• Customary system — Units like inches and pounds, used in the US.
• Metric system — Units like meters, grams, and liters, used in most of the world.
• Approximately — Close to, but not exactly equal.
• Ratio table — A table that lists equal ratios.
• Reasonableness — Checking that an answer makes sense.
• Multi-step problem — A problem that takes more than one step.

Steps

1. Evelyn sees a Canadian highway sign reading 100 kilometers per hour and wonders whether that is faster or slower than 100 miles per hour.
2. Kilometers are metric and miles are customary, so 100 and 100 cannot be compared as they stand. Both measure distance, so a conversion factor links them: 1 kilometer ≈ 0.6 mile, or the ratio 1 : 0.6.
3. I build a ratio table from that unit ratio. Kilometers 1, 10, 100 pair with miles 0.6, 6, 60 — each column multiplies both numbers by the same factor.
4. So 100 kilometers ≈ 60 miles, which means 100 kilometers per hour ≈ 60 miles per hour.
5. Now the comparison is fair: 100 miles per hour is faster, because in one hour you would travel 100 miles instead of only about 60.

Try it

A bag of rice from a market in Mexico weighs 5 kilograms. Using 1 kg ≈ 2.2 lb, is the bag heavier or lighter than 5 pounds?

Check your answer

Heavier — 5 kg is about 11 lb

Scale the conversion factor: 2.2 × 5 = 11, so 5 kilograms ≈ 11 pounds — heavier than 5 pounds.

Sentence starter

I know ___ because ___.

Goal: I can explain a conversion between systems using the words conversion factor, approximately, customary, and metric.