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.
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:
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?
Which methods leads most seamlessly to area scale factors and volume scale factors?
Is there an argument for method 2 being helpful to practice algebraic manipulation?
Imagine you had a scenario in which there was a missing length on both similar shapes. Which method might be least confusing in this case?
Which method connects most effectively to scientific concepts learnt in school regarding scaling things up or down – i.e. Antman is made 100 times smaller in length. How will this affect the strength of his muscles?