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?
This is a task I gave to a Year 8 mixed attainment class which I think would be a nice pedagogy prompt given the question set below:
How do you show balance operations between steps? Is this consistent between department members? Should all department members use a consistent approach?
Do you explicitly reference all variants of linear equations in curriculum documentation? i.e. I can solve a linear equation with unknowns on both sides when one or both unknown terms are negative, or, I can create a linear equation given the solution.
Do you teach only one method for an equation like this? How do you approach different methods? Is this student led or do you explicitly instruct on a range of methods?