Measurement is always made of two parts: a number and a unit. The number tells how many, and the unit tells what kind of amount we are measuring. For example, 12 inches, 3 feet, 5 square meters, and 8 cubic centimeters are all measurements because each one includes both a number and a unit.

In this topic, we focus on how to move between units. Sometimes converting means multiplying, and sometimes it means dividing. A helpful way to decide is to think about the size of the units. When we change from larger units to smaller units, the number usually gets larger. When we change from smaller units to larger units, the number usually gets smaller.

We will also look at how units can guide our work. When several conversions are needed, we can set up one large multiplication problem so that unwanted units cancel and the desired unit remains. This helps students see unit conversion as reasoning, not just memorizing rules.

Finally, we will discuss why square and cubic units behave differently from regular length units. Converting feet to inches is different from converting square feet to square inches, because area measures two dimensions and volume measures three dimensions. As future teachers, it is important to help students understand what the units mean so they can choose conversion strategies that make sense.

 

Student Learning Goals

By the end of this topic, students should be able to:

  • Explain that a measurement includes both a number and a unit.

  • Convert between units of length, area, and volume.

  • Decide when to multiply and when to divide during a unit conversion.

  • Use unit cancellation to organize multi-step conversions.

  • Explain why square unit conversions are different from length conversions.

  • Explain why cubic unit conversions are different from length and area conversions.

  • Check whether a converted measurement makes sense.

Key Vocabulary

  • Measurement - A number paired with a unit.

  • Unit - The label that tells what is being measured, such as inches, feet, grams, or liters.

  • Conversion - Rewriting a measurement using a different unit.

  • Conversion Factor - A ratio equal to 1 that compares two equivalent measurements.

  • Unit Cancellation - A method where units divide out, helping us track conversions.

  • Square Unit - A unit for area, such as square inches or square feet.

  • Cubic Unit - A unit for volume, such as cubic centimeters or cubic feet.

  • Dimension - A direction of measurement, such as length, width, or height.

Multiply or Divide?

  • Larger unit to smaller unit - Feet to inches - Number gets larger - 3 feet = 36 inches

  • Smaller unit to larger unit - Inches to feet - Number gets smaller - 36 inches = 3 feet

  • Larger area unit to smaller area unit - Square feet to square inches

  • Number gets much larger1 ft² = 144 in²

  • Larger volume unit to smaller volume unit - Cubic feet to cubic inches - Number gets much, much larger1 ft³ = 1,728 in³

Teacher Connection

Unit conversion is often taught as a set of procedures, but students understand it better when they think about the meaning of the units. Before calculating, it helps to ask: “Am I changing to a smaller unit or a larger unit?” This helps students predict whether the number should increase or decrease.

Square and cubic units are especially important because they reveal whether students truly understand measurement. A student may know that 1 foot equals 12 inches, but still incorrectly think that 1 square foot equals 12 square inches. Visual models, grid drawings, and cubes can help make the difference clear.

Helpful teacher questions include:

  • What are we measuring: length, area, or volume?

  • What unit do we start with?

  • What unit do we want?

  • Is the new unit larger or smaller?

  • Should the number get larger or smaller?

  • What conversion factor equals 1?

  • Which units cancel?

  • Does the final answer make sense?

Quick Reflection Question

Why is 1 ft² equal to 144 in², not 12 in²? What drawing or model could you use to help students understand this?