don steward
mathematics teaching 10 ~ 16

Sunday, 18 June 2017

exam questions generalised (ii)

the second powerpoint from the Salop and Herefordshre Maths Hub sessions

aimed at higher tier questions

thanks to the exam boards for their questions

exam questions generalised (i)

the first powerpoint from a session for the Salop and Herefordshire Maths Hub on Friday 16th June 2017
thanks to Graham Charles

thanks to the exam boards for their questions
(an Eduqas/Welsh GCSE version to follow)

a development of a similar session held (thanks to Jo Morgan) at Glyn School, Epsom last year

these questions aim to provide more extensive practice at GCSE style questions in the novel manner of attempting to form and possibly prove generalisations

exploring ideas more fully, playing around with a purpose

I suggested that participants might trial some of the ideas with Y10 towards the end of term

this first ppt is aimed at foundation tier questions

Wednesday, 14 June 2017

decimal sequences

the powerpoint has some examples of counting up and down in constant decimal steps

these are intended to be done orally - class chanting

 (fairly easily checked)

Monday, 12 June 2017

fdp scales

thanks to Mathspad (and to Jo)

times tables puzzles

practice in identifying digit products

note that the multipliers are all the digits 2 to 9 (inclusive)

Thursday, 25 May 2017

fraction sequences

starts by counting on
fraction sequences with their 'simplest' (cancelled) form on the powerpoint
this could be done orally, with some explanations sought

then finding three missing terms and a general rule (nth term) for a fraction sequence
with (assumed) regular increases on the first resource
and a regular pattern (nth term) for the numerators and the denominators on the second resource

students might need nudging to consider equivalent fractions - hopefully not...

Tuesday, 23 May 2017

intervals of 10

variations on a theme

what is a general rule for the end numbers?


Monday, 22 May 2017


  • place value, zooming in
  • reversing the question
  • generalising
  • harder generalising
a powerpoint, kind of illustrating the zooming in

Friday, 12 May 2017

half is in the middle

what do students notice about the results?

why is that?

fraction addition denominators multiples

to start adding fractions it can be helpful if one denominator is a multiple of the other
so that only one denominator needs to be changed

in England such work is offered to 9 to 10 year olds (Y5)

fraction cancelling

powerpoint here

sometimes, as in question (7), you only part-cancel a fraction in order to find the nth term rule
sometimes, for other fraction sequences, there is a stray fraction that cancels - not part of the general cancelling rule
some features of an overall generalisation are relatively easy to discern
and others aren't (for me anyway)

Wednesday, 3 May 2017