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

Stuck? Start here. Read the steps, try the problem, then check your answer.

I can…

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

Convert Measurements within the Same System — Rewriting a measurement in a different unit of the SAME system, such as feet into inches or liters into milliliters.
Conversion factor — The ratio that links two units in the same measurement system, such as 12 inches to 1 foot. Within one system it is exact.
Unit ratio — A ratio that compares an amount to exactly 1 unit of another quantity, like 12 inches to 1 foot.
Convert — To change a measurement from one unit to another without changing how much it is.
Measurement system — A family of units that go together — customary units like inches and feet, or metric units like milliliters and liters.
Double number line — Two number lines lined up so matching tick marks show two units for the same amount.
Ratio table — A table of equal ratios that lets you scale a conversion up or down one row at a time.

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.
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.
Inches are smaller than feet, so there will be MORE of them: I multiply. 4 × 12 = 48.
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.

There are 4 cups in 1 quart. A soup recipe calls for 5 quarts of broth. How many cups is that, and why?

20 cups, because cups are smaller so I multiply: 5 × 4

The unit ratio is 4 cups : 1 quart. A cup is smaller than a quart, so it takes more of them: 5 × 4 = 20 cups.

I know ___ because ___.

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