In January 2025 Tymoteusz Zdunek organised an Inquiry Maths workshop with Dr Andrew Blair at Akademeia High School in Warsaw (Poland). 

As part of the workshop, Andrew took a year 10 class through their first inquiry. He used the difference of two squares inquiry to model how an inquiry might develop and showed what the regulatory cards mean in the context of that inquiry (see picture).

The students then inquired into the difference of two cubes prompt following the same lines of inquiry - finding more examples, changing the prompt, and making and proving a generalisation. 

Mathematical structure

In another line of inquiry the students analysed the mathematical structure of the prompt through a diagram. The difference of 43 and 33 is presented as three cuboids in the pictures below.

Learning how to inquiry contains the slides that Andrew used in the lesson.

My first attempt at an inquiry lesson was with a year 9 class. We had just finished an algebra topic and I wanted to give them something to really challenge them. I started with the prompt and let them discuss it for around five minutes. We then shared ideas which I wrote up on the board. 

I gave each pair the six regulatory cards and asked them to pick where to go with the inquiry. Most wanted to Find more examples or Decide the aim of the inquiry. As a class we decided to try and prove the prompt algebraically.

During this first lesson some pupils were changing the prompt and looking at what happened when the difference between a and b was more than 1 (i.e. a2 - b2= a + b). Others, who were trying to prove algebraically for a difference of one, spent quite a while trying to write the prompt algebraically, which can be seen at the top of the image above. Other pupils were exploring what happens when square numbers are added and others wondered what would happen with cube numbers.