Overview

Equivalence is a fundamental idea that underlies work in many mathematical areas. Equivalence is central for understanding and working with fractions, as well as for other areas of mathematics, like: algebra (e.g., when solving equations equivalent equations are created), place value (e.g., that 73 is the same as 6 tens and 13 ones), or geometry (e.g., two angles with a difference that is a multiple of 360 degrees are equivalent).

Processes for generating equivalent fractions can be challenging for students to understand. One way to help students make sense of numerical procedures is to connect them to a representation.

This part focuses on representing equivalence and explaining the processes through which equivalent fractions can be generated.

Key Points

When considering which representations to use when explaining fraction concepts and procedures, it can be useful to consider the following:

• The meaning of a fraction embedded in the representation.
• The language associated with the representation.
• The process of constructing and using the representation.
• The limitations or challenges of the representation.