# Ramblings from the Classroom – Week 11

I feel like I have finally taken the manipulatives leap this week and delivered my first set of lessons introducing equations. Using the excellent Mathbot.com Equation Solver. I took the first stage of the lesson explaining how my education involved being taught a lot of processes and methods and I had the nack of retaining these and then applying them when requested. After reading the excellent book below I understood that the concrete and pictorial stage in my understanding had repeatedly been jumped into the abstract world of maths.

I am teaching a group in Year 8 who have always generally ‘got maths’ and felt these were a good test bed for testing out these new principles. So I started with

Used the copy arrows at the top left (have got much quicker now at producing the questions because of this feature) and then asked them what we then do. All to a student said “take 3 off both sides, sir” to which I then followed up with “Why?”. Stunned silence in the room – after a few minutes a student articulated that we are aiming to find the value of the x so need to make the left hand side as ‘simple’ as possible. So I dragged out three red -1 blocks on one side.

We then had a good discussion about the equals sign then I placed three red -1 blocks on the other side.

Quite a few students were still staring at the board trying to understand why the equation in the middle looked simplier but the blocks around it had become more complex. I then had a discussion around zero pairs and dragged the red -1 blocks over a yellow 1 block and…

Then there was a audible noise in the room as I was doing this. The modelling took me probably twice the time compared to the standard modelling I would have previously done but then students were a lot more resilient on some non-standard questions like:

8 + 2x = 16

19 = 3x + 7

Manipulating them with ease as I could see them visualising these mental models in their heads and then realising the power of the equals sign.

Then I moved onto the following board slide (I’ll be honest I’d not planned to use manipulatives in the lesson part but the students were now keen to understand through these visual models).

We discussed that 5/2 can be expressed at a mixed number and then I drew the visual model this showed. Was this the way to introduce it? Or should I have modelled it on the right hand side (which I did as well) and then go visual at the 5x = 26 part?

Still on very much a learning curve with this but feel like i’m actually teaching the students to fully understand and not just apply methods.

Have a good week everybody!