Is it helpful for the department to all use the same approach, or can different approaches be utilised depending on whether it is being introduced or consolidated?

Cell 1: Why don’t we teach partial factorisations with the same importance? In proofs partial factorisations are often required.

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 an obvious concept to me now, but I’m not sure that it was wholly obvious to me when I first started teaching. Finding common units is a necessary element to adding and subtracting all things.

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:

Questions:

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?

Some of these are amended from the work of others – but unfortunately I don’t know which ones I made up, which I amended and which I found. It’s likely that one of them comes from Don Stewards blog.

Even if simple interest does not appear in the curriculum, would you still utilize it in order to make a direct comparison between linear and exponential growth?

Do you show the entire curve to begin with, or would you build up as in the 3 pictures given in the prompt?

b. Nrich Task – Modelling an Epidemic (Nice kinaesthetic starter). You could also have an interesting discussion about how gossip could be modelled very simply with exponential growth.

In regards to Cell 1, students require Pythagoras’ Theorem to find the area of the inscribed triangle. Would you ever set this as a question after a unit on Pythagoras?

Cell 2, 3 and 4: The parallelogram method may be the most common way of understanding the formula. However, the triangle method may lead more seamlessly into deriving the formula with calculus. Does this affect your decision of which method you show earlier on in school?

The How-before-Why debate is a popular one right now. Would you ensure students knew how to use the formula before promoting understanding or vice-versa? How about if you go backwards from a parallelogram or a triangle into a circle – does drawing on what students already know about areas of shapes change your response to this question?