For the first time that I can remember, I am in an appraisal process that is aimed at both my development as a teacher and as part of a department. Three specific appraisal targets which I’m really excited to get my teeth into. The plan is to blog about all of these, but one target at a time…

So firstly, my second target is to develop the use of manipulatives in my teaching and to share these strategies with the department. There is a particular focus with my lower prior attaining year 8 group, but not restricted to just this group.

Prior to this year, I’ve started introducing myself to the use of manipulatives with the following:

- Attending a workshop from Johnny Hall @studymaths on the use of double sided counters, including his amazing mathsbot.com website
- Attending a workshop from Bernie Westacott @berniewestacott on the use of double sided counters
- Attending a workshop from Peter Mattock @MrMattock about division, and the use of cuisinere rods
- Dipping into Pete’s book Visible Maths (the negative numbers part so far)
- Attending a workshop on manipulatives and their representations exploring algebra tiles
- Reading Mark McCourt’s @emathsuk book Teaching for Mastery – a huge influence on how I approached and presented
- Attending a workshop from Dr Liz Henning on the use of manipulatives to deepen conceptual understanding (see notes here)

## Double Sided Counters

From these, I have made use of double sided counters when teaching negative numbers. To begin with, I printed out some squares, with a yellow 1 on one side and and red -1 on the other side. A bit fiddly, but did the job as I introduced negative pairs and adding and subtracting with negative numbers. I’ve since upgraded to actual double sided counters (Amazon – 2 packs of 120, so 16 sets of 15 for classroom use).

So to the actual lessons and use of the double sided counters. The learning plan goes like this:

- Use of number line with negatives as starting points or ending points
- Context questions
- Introduce double sided counters
- Zero pair
- Playing with counters
- Adding a negative and seeing result
- Quick questions
- Subtracting a negative and seeing result
- Quick questions
- Mixture of adding and subtracting negative numbers (for some groups I used these questions from variationtheory.com

The powerpoint I made is here: Add and subtract negative numbers. You’ll have noticed the mathsbot.com links – there was lots of talk and playing, with demonstrations using Johnny’s site.

I am still looking to improve and refine, but so far the students appeared to make sense of what was happening. Ideally, I would have liked more time, as always! My year 8 group used the counters to help with the questions, whilst there was a mixture from my year 7 groups. The higher attaining students, who had learned shortcut rules previously, wanted to just use “the rules”. For other students, some fell back on these rules, whilst others were writing out the R and Y to help them.

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