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What is it?
“Equivalence” is something I used assume my students understood. I would cover it when teaching equivalent fractions, equivalent expressions, or equivalent ratio. In fact “cover it” is a bit of an overstatement. It would usually be a matter of explaining to students that equivalent means “the same” and then cracking on.

But equivalent does not quite mean “the same” and if the key mathematical terms and concepts are not addressed carefully and thoroughly early on, then there is nothing solid to build upon and this will likely come back to haunt us as the maths gets more complex. This resource takes the concept of equivalence and looks at it in depth in the context of algebraic expressions.

How can it be used?
This resource is ideal to use with students right before a unit of work on collecting ‘like terms’. If we can get our students comfortable with the concept of equivalence, then they can dedicate all their energy and attention to thinking about the more complex algebraic skills that will be required as the unit of work progresses.

However, this resource doesn’t just brush over the concept of equivalence. Students are confronted with a wide range of expressions, some of which appear equivalent because they give the same total for certain values of a variable, but upon further investigation they are not. Hence students get an opportunity to practice substitution as well as algebraic manipulation.

This resource could be supported by using a graphing package such as Desmos, plotting each of the expressions, seeing which ones look exactly the same and discussing the significance of where different expressions cross.

Thanks for sharing!
Craig Barton

Download: The meaning of equivalence
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