median
don steward
mathematics teaching 10 ~ 16
don steward
mathematics teaching 10 ~ 16
Tuesday 30 November 2010
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?
[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?
Thursday 25 November 2010
Monday 15 November 2010
Saturday 13 November 2010
Tuesday 9 November 2010
pitches
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgNi2gIH7hiaV_mcbG2N6KdGpxufPoFnIDPItDye2ntZ-jbdeiZUPrseAAl49cNe8euznuNm6LuLDAxxU1TFWmDukDKanggRfp67jF2DXAUL9ylFKi3ah8mdzEPW6GbD83SJtbZqnJkOyA/s320/blayout.jpg)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjDt37MRPCrlxqja_zJFZtgWDr9xbGkHL-DHCj8HMEQo5bbGSbZC0A0Qq9b8iXxAGA84l1QPO4vvxSW6i7p8sVnr_flTkmROWIgq-PpKmcxhJp6SXEQar2ow4gnEgdKydxa0nbS0MFhosU/s320/01-Pitch.jpg)
there are various diagrams of basketball courts available e.g. here
football pitch dimensions or here
tentative
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgSxftt5XAa6oOIgD_q-63-67joViKZcABxN9moUXe5RHCA19QzRX0TudcxuiBpU-4y97Ss4oPtlgwKZNiFMAx5AtC_0jkTjPW7yNO0W3m10i7fmLDi4NNOpEPwKfl5J1WUve7Jx8ERINA/s200/grid.png)
put some numbers in the boxes so that each of the four blocks of four sum to 10
for example:
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
Sunday 7 November 2010
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
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