Craig Barton’s “How I Wish I’d Taught Maths”

There is an awful lot in here.  A great book, I now need to reflect on what to do with it.  There are some things I want to try but it’s important that change is incremental.  In the meantime, so I don’t lose them, here are my notes.

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Revision questions for top-end GCSE

I have a top set Year 11 class this year. There is quite a range in the class and although there are definitely still gaps to be filled, I am always on the lookout for questions that will challenge them.  What worries me most about the mock papers they have done is that they panic when the context is unfamiliar. In the words of this fantastic resource which Danny talks about here, it is about making something that is unfamiliar more familiar.

So I thought I would scour some old O level exam papers.  It was an interesting exercise and I have pulled together a selection of questions here which I have categorised into Calc and Non-calc. Originally, of course these would all have been tackled with nothing more than a pencil and a book of tables!

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I have attempted to modernise some of them using metric units and trying to make the language more straightforward for today’s students.  I have also added some diagrams as there seemed to be a lot of reliance in those days on interpreting a dense description of a geometric situation and drawing it.

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I haven’t attempted to assign a number of marks to each question, I think they range from 3 to about 6 in today’s money, but I’ll leave you to decide that.

They haven’t been used in anger with my class yet, but please get in touch if you have any thoughts on these.

Getting confident with place value

I thought I would share a bunch of questions I have been using with my low attaining Year 7 class. These guys are pretty good at the process of column addition and subtraction but were not confident with place value such that they could immediately answer a question like this one:

What number is a thousand more than 17407?

I have been dropping one of these into our starters every lesson for the last couple of weeks and they now “get it”.  The next step is to carry over to the next place value, for example:

What number is eighty more than 1843?

We have also tried subtraction, for example:

What number is 500 less than 1935?

Moving on from this I have been using questions like these:

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These step up in difficulty quite considerably I think.  I will be using ones like the first few and see how they get on before looking at Qu 7 onwards.

You can access these on this Powerpoint slide. Clicking on the boxes reveals the answer beneath.

A decimal investigation

Inspired by playing the excellent Sumaze! 2 game from MEI, here is an investigation that aims to provide some purposeful practice on decimals. The aim is to provide an accessible entry point for all learners with opportunities for depth through generalisation. This slide presentation steps through it although exactly how you move from one part to the next will, of course, depend on the class.

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I have included solutions in this spreadsheet although I would be hesitant to display them in this form, as I would prefer that the results are found and discussed as we go along rather than just revealing them at the end.

Area of a triangle

I made these questions to hopefully reinforce the idea of area as the space inside a shape, rather than just the answer you get when you multiply numbers together.  Also I want them to see why the area of the triangle is half the area of the rectangle which it is enclosed within.  I made them using this Geogebra file but then pasted a few to make this worksheet, some with grids then some with just lengths.

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A colleague of mine @DrPMaths made this impressive collection of triangles with 3 integer side lengths and an integer height.  Again, they are a great way to check that students are identifying the perpendicular height and multiplying that by the base rather than just multiplying the numbers they are presented with.  There are literally hundreds of them, this is a snapshot from somewhere near the beginning!

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Ideas for better maths teaching