Converting units

What is this skill?

Converting units means expressing the same measurement in a different unit, such as 3.5 kilometers as 3,500 meters. The measurement itself does not change, only the size of the unit we count with. When changing to a smaller unit, there are more of them, so we multiply. When changing to a bigger unit, there are fewer, so we divide.

The practice uses the common conversions: meters to centimeters (100), kilometers to meters (1,000), liters to milliliters (1,000), kilograms to grams (1,000), feet to inches (12), yards to feet (3), pounds to ounces (16), gallons to quarts (4), hours to minutes (60) and miles to feet (5,280). Metric conversions are all powers of ten, which links back to moving the decimal point. Customary conversions have to be learned, and children are expected to know them or look them up. For example, 2 gallons is 8 quarts, and 48 ounces is 3 pounds.

Why it matters

Measurement is everywhere in real life, in recipes, travel, sports and science projects, and it often arrives in mixed units. Children who can convert easily can compare a 2-liter bottle with 1,500 milliliters of juice, or work out how many minutes are in a 3-hour trip.

Conversion also puts multiplication and division to use on something meaningful, and it makes a good check for sense. A measurement in a smaller unit should always be a larger number. If it is not, the conversion went the wrong way.

Common mistakes

• Multiplying when the problem calls for dividing, or the other way around. Asking whether the new number should be bigger or smaller catches this.
• Mixing up the conversion factors, such as using 100 for kilometers to meters or 10 for feet to inches.
• Confusing the metric prefixes: kilo means thousand, centi means hundredth, milli means thousandth.
• Moving the decimal the wrong way in metric conversions, or by the wrong number of places.
• Forgetting the unit in the answer. A number with no unit is not a measurement.

How to help at home

• Make a small reference card of the common conversions and keep it on the fridge. Familiarity comes from seeing them often.
• Cook with recipes that use several units and let your child convert between them.
• Ask the direction question each time: “Are we going to a smaller unit or a bigger unit? Will there be more of them or fewer?”
• Measure the same item in two units, like a table in feet and in inches, and compare the numbers.
• Tie metric to money: 1,000 meters in a kilometer is like 100 cents in a dollar. Different units, same structure.

Worked examples

These are real questions from the Tutorsaurus converting units practice, with the answers worked out.

1. Example 1

   72 inches = ? feet

   Answer: 6 feet. 12 inches make 1 foot. 72 ÷ 12 = 6.

2. Example 2

   10 hours = ? minutes

   Answer: 600 minutes. 1 hour = 60 minutes; 10 × 60 = 600.

3. Example 3

   8.4 meters = ? centimeters

   Answer: 840 centimeters. 1 meter = 100 centimeters; 8.4 × 100 = 840.