Lesson 6: Ratio Reasoning: Convert Measurements within the Same System6.AT.3c

I can…

I can use ratio reasoning to convert between units within the same measurement system.

Key words

• Convert Measurements within the Same System — Switch to a new unit in the same system.
• Conversion factor — A ratio you use to change units.
• Unit ratio — A ratio for 1 unit, like 12 inches to 1 foot.
• Convert — Change to a new unit or form; the amount stays the same.
• Measurement system — A set of units that go together.
• Double number line — Two number lines side by side. Marks that line up go together.
• Ratio table — A table that lists equal ratios.
• Customary units — Units like inches, feet, and pounds.
• Metric units — Units like meters, liters, and grams.

Steps

1. A ride requires riders to be at or above 44 inches tall. A child is 4 feet tall. The two measurements use different units, so I cannot compare them yet.
2. Both units belong to the customary system, and there are 12 inches in one foot. That relationship is the conversion factor. As a ratio it is 12 : 1 — a unit ratio, because it compares an amount to exactly 1 foot.
3. Inches are smaller than feet, so there will be MORE of them: I multiply. 4 × 12 = 48.
4. The child is 48 inches tall. Now the comparison is fair: 48 inches is greater than 44 inches, so the child can go on the ride.

Try it

There are 3 feet in 1 yard. A jump rope is 6 yards long. How many feet long is the rope, and why?

Check your answer

18 feet, because feet are smaller so I multiply: 6 × 3

The unit ratio is 3 feet : 1 yard. A foot is smaller than a yard, so it takes more of them: 6 × 3 = 18 feet.

Sentence starter

I know ___ because ___.

Goal: I can explain a conversion using the words unit ratio, convert, measurement system, and per.