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We had an interesting discussions about this in a department meeting…
This prompt is designed to get departments thinking about where in the curriculum students must create and solve linear equations. Can you think of any other concepts this connects to? Are you teaching creating linear equations explicitly? Do the department have a common approach to solving linear equations?
- For cell 3 and 5, are you explicitly teaching cross multiplication as a trick, or is it something students develop themselves? What the the issues with cross multiplication?
See this twitter thread started by @DrFrostMaths on cross multiplication.
- Further topics: Direct/Inverse Proportion, Simple Interest, Similar Shapes, Angles in Parallel Lines
This is less of a pedagogy prompt, and more of a prompt to help us discuss and explore approximations of pi with the maths enrichment club at school around pi day. Hope it’s useful.
An object moves away from a point, X. Describe what it is doing in each section of the graphs below.
After a first lesson on Distance-Time Graphs, I gave this as an independent starter. After 30 seconds, I said, “There may be parts of the graph that you are struggling to describe – keep thinking and you will have the opportunity to discuss this with your partner in 2 minutes.
Would you do anything differently?
- When do you choose to prove this? Do you begin intuitively and then only prove when students have knowledge of angles in parallel lines? Could you use the proof in cell 1 immediately?
- How do you choose to prove that the angles in a triangle sum to 180 degrees? One of the techniques above, all of them?
- Could you utilise the idea of goal free problems so that students identify all angles they can in the 4 cases above and then you reveal that they have just proven that the angles in a triangle add to 180 degrees in 4 ways?
To have students complete a proof, I developed one that provides multiple avenues in the final step, so as to increase the chances of a proof from more students:
- Do you have an agreed departmental structure?
- Which method is slowest? Which method is quickest?
- Should we teach more than one method? i.e. On first learning, teach cell 3, but then transfer to cell 2?
- Which method extends most naturally to three or more brackets?
- Should cell 2 and cell 4 come with a discussion of the distributive property, or an intermediate step showing this? i.e. (x + 3)(x – 5) = x(x – 5) + 3(x – 5)?
- Additional thinking:
- Are all of these misconceptions directly addressed through explicit curriculum objectives, or is it luck as to whether they are addressed whilst doing algebra? i.e. Is there a specific lesson or sequence of lessons about the difference between (a+b)/a, and a/(a+b)?
- For each of the prompts, how exactly would you set up a pedagogical sequence to address and teach students the correct manipulations?
- Are there any other common misconceptions you can think of?
Additional common misconceptions: