# Substitution

## How does Rachel show her students substitution is everywhere?

I have noticed that the skill of substitution turns up in many topics; anywhere there is a formula. Here are a few examples from my students’ workbooks showing their use of substitution in the topics of area, straight lines, and trigonometry.

• Examples of how Rachel shows her students substitution is everywhere

4.061 Substitution 1

4.061 Substitution 2

## What are Rachel’s important messages?

In no particular order, the team from our school has learned:

• What we have done is not new but it brings together a lot of ideas we’ve had for a while about how we can teach algebra.
• We feel that the New Zealand Curriculum (2007) has gone the right direction with the number and algebra strand being an umbrella over the other ones (i.e. geometry, measurement, and statistics).
• We realised that we need to introduce algebra through context (e.g., geometry, measurement, fractions) and we have achieved this with our new Year 9/10 programme.
• We come back to the skills on a regular basis and this need for revisiting skills can be seen in our new Year 9/10 programme).
• We use the correct terminology right from the beginning.
• We demonstrate rigour in setting out our working because mathematics is the language of numbers and just like English, mathematics has rules. We show our students how to set out their work vertically and this means they can only use one equals sign per line.
• We realised that we need to scaffold our students with differentiated levels of work by:

– Adding skills and knowledge to the toolbox

– Building on what students already know and revisiting those skills and concepts

– Reviewing important skills and ideas

– And extending skills and ideas

• We’ve noticed that there is no replacement for enthusiasm. If we show passion and excitement for mathematics our students can’t help but become interested too.

Any views or opinion represented in this site belong solely to the authors and do not necessarily represent those of the University of Otago. Any view or opinion represented in the comments are personal and are those of the respective commentator/contributor to this site.