don steward
mathematics teaching 10 ~ 16

Wednesday, 29 June 2016

directed number target

directed number addition and multiplication
deliberately designed so that there at least two possible solutions

the powerpoint goes into ( fairly ridiculous) detail about possible generalisations

find the linear rule

given 7 points that fit a (linear) rule
but 2 of them are incorrect
from an idea by David Wells

plotting them seems to be cheating...
putting them in order eminently sensible

the powerpoint goes through a couple of examples

a quadratic meets a linear family

practice in factorising a quadratic when 'a' is not 1

a generalisation can be explored
and proved
('put a pattern in and you'll get a pattern out' David Wells)

slopes of hills

an introduction to gradients

the powerpoint has some pics of steep hills, mostly in the UK
and contains some links (first, hidden slide) to youtube clips

the Gloucestershire cheese rolling annual event was introduced to me by Darren (thanks to him)

tackling, a bit anyway, a difference between sinA (usual on signs) and tanA measures

circular perimeter

this problem is from David Wells' collection in 'curious and interesting geometry'
does the line always bisect the perimeter?

the powerpoint goes through a special case and the general case

is presented with animation on the slide

dividing by 7

the powerpoint shows some of the divisions
and makes links to the recurring decimal form of 1/7th
(including some at an advanced level - using the sum to infinity of a geometric series)

plenty of practice with the 7 times table

that's curious

the powerpoint involves
  • decimals
  • directed numbers
  • fractions
sometimes the relationship does hold even though it usually doesn't

Tuesday, 28 June 2016

polyhedra: total angle sum

Euler's relationship connecting the numbers of faces, edges and vertices (F + V is close to E) for polyhedra is fairly well known

another (very neat) relationship for the 'total angle sum' was brought to my attention by Gordon Haigh, when he worked at Wolverhampton University

a powerpoint for this task gives the steps for proofs for a general prism and general pyramid, establishing Euler's  relationship for these polyhedra

animated platonic solids from Wikipedia:

sum product

a curious relationship that works for a restricted set of numbers

intended to practice many number skills

thanks to David Wells


work out the rule
find as many solutions as you can
find the missing number
what relationships can be found connecting the three outside numbers to th middle one?

number links

the powerpoint for this task (needs downloading for the animations to work)

Wednesday, 15 June 2016


a second attempt, grouping aspects together