trapezium reptiles

what are the angles in the trapeziums (trapezoids) so that four of them (all identical) are similar to the original?

named quadrilaterals

"I'm thinking of one of these shapes"
[I've written it down, so that I will not be tempted to cheat...]

"you can ask me any questions
but I can only reply yes or no"















you can firmly identify a shape in at most three questions
what would your first question be?
are there alternatives?


can you string the eight special quadrilaterals in a line with just one difference between them?

kite angles

an equilateral triangle with two isosceles triangles

what are the angles inside the kite?

music is math

on Vimeo
film: Glenn Marshall
music: boards of Canada (a Scottish band)
music is math

leap years

shrink these

pitches

drawing scale diagrams of football and basketball pitches might be a useful task in using a compass and ruler - as a context where accuracy is clearly important


there are various diagrams of basketball courts available e.g. here

football pitch dimensions or here

tentative

 

put some numbers in the boxes so that each of the four blocks of four sum to 10

for example:

what happens when you add the four corner numbers of a resulting (3 by 3) square?

why must this total must always be even (for integer entries)?

in the last (incomplete) example why must the bottom right cell be the same as the top left cell?

fraction division simplification

explore, by substituting some numbers









obtain a general result by substituting some numbers

and maybe establish this result algebraically

five subtract negative three

(some) reasons why 5 - -3 = 8

(i) with subtraction you can add the same amount to both bits (the minuend and the subtrahend) and it doesn't change the result; so add 3 to both: 5 - -3 = 8 - 0

(ii) it's the gap from -3 up to 5 on a number line

(iii)  an equivalence class that can be adjusted by adding 'nothing':

(iv) extending a pattern:
5 - 3 = 2,
5 - 2 = 3,
5 - 1 = 4,
5 - 0 = 5
so 5 - -1 = 6,
5 - -2 = 7,
and so 5 - - 3 is 8

(v) using a straight line graph rule: continuing the graph of y = 5 - x into the negative quadrants you can see that when x = -3, y = 8

(vi) using inverses: 5 = 8 - 3 so 5 - -3 = 8

(vii) also using inverses: 8 + - 3 = 5 so 8 = 5 - -3