Here is a small subset, not all, of the examples I recently used for simultaneous equations. My other examples relied heavily on bar modelling along side the abstract, and now I was transitioning to just the abstract.
I wanted to share these example for two reasons, firstly they use example fading, which can be a really powerful way to use examples. There is research to suggest it will improve far transfer and problem solving. Secondly, because of how I have set out and labelled the steps. Whilst we may not expect pupils to continue to set it out exactly like this because of the repetition of some lines etc, I believe it can be beneficial on initial instruction. When pupils are looking back over a complete worked example, steps may blur into one, and identifying where their understanding breaks down or an aspect they are unsure about may become challenging. I believe it allows pupils to articulate clearly which step they didn't understand, it highlights the intention of each step, and could help create a framework for pupils thinking.
I would like to emphasise that on its own this can be extremely procedural, and that this was after we had built up lots of conceptual understanding, I also found it worthwhile getting students to link each step with the pictorial retrospectively.
I would love to hear your thoughts on setting out examples like this.
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