don steward
mathematics teaching 10 ~ 16

Friday, 21 October 2016

triangle areas, various ways

rather big numbers (use a calculator)
the intention, advocated by Ed Southall (solve my maths), is for students to decide which dimensions they need in order to work out the area of a triangle

then they can be asked to calculate it another way
(and possibly a third way)

the areas are:
(1) 150
(2) 5,070
(3) 302,580
(4) 1,227,930

circle theorems using parallels

normally the circle theorems are justified using isosceles triangles
but it's quite neat to use alternate and corresponding angles on parallel lines

this and other ideas are explored more substantially by Dietmar Kuchemann in this article

construct a parallel line

but A = B

the angle in a semicircle being 90 degrees can follow from the fact that an isosceles triangle is perpendicularly bisected by its line of symmetry

construct a parallel line


Thursday, 20 October 2016

triangles cut into triangles

the main purpose of this work is to focus on triangle areas
there are various possible spin-offs:
  • perpendicular lines
  • surds
  • length and area ratios of similar shapes

directions for the task below

questions for the triangles above

Saturday, 8 October 2016

quadratric sequences

intending to familiarise students with the properties of a growing quadratic sequence
rather than finding a quadratic rule from a (given) procedure

the second resource was suggested by David Wells
intending to explore the differences - possibly by students looking at a few quadratic rules to discover generalities for themselves

you might choose to just use the second resource
hopefully students will appreciate the symmetry of some sequences

possibly exploring when a growing quadratic sequence has symmetry and when it has not

Sunday, 31 July 2016

number puzzles

it may be helpful to have numbers to move around

there is an added dimension/extension of proving various statements, usually connected to the sum of the numbers used and those numbers that are in more than one line

Graeme Brown did some Excel versions of four of these puzzles (the first three and hollow triangle (i))
these can be found at nrich 5512

Wednesday, 13 July 2016

gradient contexts

slides about the gradients of
  • qanads (water channels)
  • wheelchair ramps
  • roof pitches
  • pyramid inclinations
  • stadium seating rake
mainly useful to introduce arc tan (rise / run) to obtain the angle of inclination

ratio presentation

the ratio slides
Prince's Trust (PTI) presentation
London 12/7/2016

Sunday, 3 July 2016

factors of numbers and number of factors

once the prime number decomposition of a number has been identified, there are reasonably straightforward rules for deciding how many factors a number has

using facts such as a prime cubed has four factors

the powerpoint for this

Thursday, 30 June 2016


these are based on the symmetrical arrangements for the Zygolex (word linking) puzzles

in these problems the centre expression can only be changed by one of the four allowable steps at each stage, to (eventually) reach the outer expressions

there should not be any repeated expressions in the solution

work out what the allowable steps must be first

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