don steward
mathematics teaching 10 ~ 16

Monday, 20 May 2019


this is based on a picture by Michael Kidner 1917 ~ 2009
an intention is to show the picture and to ask students to analyse how the picture is constructed, mentioning fractions, angles and rotations

what fractions can students see here and what are the associated angles?

colouring in

Monday, 29 April 2019

AQA problem solving questions

these (90) problems cover a range of topics and have been made available by the AQA exam board in England


the questions are mainly unaltered but I have slightly altered the wording in places, changed some of the numbers and added some suggestions for extending some of the questions

there are links to the questions in pdf form and a powerpoint via Jo Morgan's blog
the powerpoint there includes an identification of tasks with topics and pitch (higher, foundation or easier foundation)

Friday, 19 April 2019

probability history (2)

the 'problem of points' is usually identified as the birth of a proper study of probability
this is a little harsh on Cardano, who had several impressive insights

developments were largely prompted by an interest in winning at gambling

some of the (translated to English) letter correspondence between Fermat and Pascal can be read

powerpoint: history 2

probability history (1)

the history of probability presents insights into the (genuine) problems that were faced and how they were overcome

it shows people collaborating, making and correcting errors and persevering

ideas that students can engage with and maybe find interesting

powerpoint: history 1


the first part of the presentation at the ATM/MA conference 2019
download the powerpoint for the animations to work

my thanks to those who attended

Thursday, 4 April 2019

dividing a number of coins in pairs of ratios

this idea is from Martin Wilson in Harrogate
and is intended to be a variation of dividing in a ratio

(sorry about the names, mine rather than Martin's)

Saturday, 23 February 2019

given the lcm and hcf

reversing the question
given the lcm and hcf of a pair of numbers
what could they be?

the powerpoint is here

from an idea by David Wells (question 1)

lcm and hcf generalising

deducing the hcf and lcm of two numbers from their prime factorisations
the powerpoint is here

type 1

type 2

Wednesday, 20 February 2019

directed number addition and subtraction 2 (of 2)

the powerpoint is here

with subtraction, viewed as a 'gap', you can always shift it along to a more convenient location on a number line

add (or subtract) the same amount to both keeps the sum the same

looking at sequences/patterns  to decide what the results should be

directed number addition and subtraction 1 (of 2)

the powerpoint is here

uses directed numbers as vectors
involving the start and end (like stations) and the journey
these journeys can be described in two different (but the same) ways

Simon Razvi, in Birmingham (England) suggested that the positions on a number line are like nouns (e.g. 'negative 4')
and the journeys are like verbs (e.g. 'subtract 4')
usually these get muddled up
and usually I think there's value in muddling them up
[technically I guess you can't add a position on a number line to anything!]
it seems to me that it's (one dimensional) vectors that can be added and subtracted

thanks to Worcester Uni (PGCE) students and Jane Moreton for their comments (in Jan 2018)

directed number teaching four articles

four articles on the teaching of directed number

(1) some history
(2) three effective models
(3) a 'vector'approach
(4) further considerations

simultaneous equation generalising 6 (out of 6)

some reasonable ones..
involving a linear nth term

powerpoint is here

simultaneous equations generalising 5 (out of 6)

three patterns

powerpoint is here