Research-based guidance and classroom activities for teachers of mathematics

Equivalence

This link takes you to Algebra Makes Sense, a SMILE mathematics pack on the National STEM Centre eLibrary. The relevant task is on pages 36-37.

Traditionally, most of the algebra curriculum used to be about learning to manipulate expressions by collecting like terms, factorising, multiplying brackets and so on. This achieves alternative forms of expressing the same relations between unknowns and variables.

For algebra to be meaningful, students can see that these manipulations (which can now be done by software) produce equivalent expressions to describe situations that the students will understand. Embedded in this kind of work, but usually left implicit, is the use of = to mean 'is equivalent to', i.e. whatever the value of the variables. This is in contrast to equations where non-equivalent expressions are temporarily equal for particular values of the variables.

Go to Algebra Makes Sense on the National STEM Centre eLibrary >>