median
don steward
mathematics teaching 10 ~ 16

Monday, 20 November 2017

equable shapes

we looked at equable shapes (where the value for the perimeter = the value for the area) in the Leeds session

this is an updated version, to include the area and perimeter of more shapes

the powerpoint is here

for rectangles, it can be beneficial to appreciate the function/relationship by looking at a full range of values (not just integer values, as is usually a restriction for equable shapes)
the values for 'a' are selected so that the corresponding values for 'b' can be calculated, maybe without a calculator
and a graph of (a, b) values plotted - or at least considered



students can check that the area and perimeter values are the same



Thursday, 16 November 2017

arithmetic sequences meets equations

this task was devised by Martin Wilson, of Harrogate

students could substitute numbers (trial and improvement)
or, if they appreciate that there are equal 'steps' between adjacent (and other) pairs of terms,
they can set up and solve an equation

for the quadratic version there may appear to be two solutions
but checking will show that only one of these works





Wednesday, 15 November 2017

quadratic nth term using factors

this is an idea for working on quadratic sequences, developed with Martin Wilson in Harrogate

we hope that students will be able to make a link between factorising numbers and factorising a quadratic expression

the powerpoint is here

the technique involves
  • transforming a given sequence by adding or subtracting a number to/from all of the terms, this number chosen so that all of the resulting terms have factor pairs
  • seeing if this provides a regular growing (or decreasing) pattern
  • if not, looking at another option
this approach might precede an algebraic one (outlined here)

three GCSE exam board questions set this summer (2017) are explored, one that can be factored without transformation




the transformation can have various forms

 factorises straight away

Sunday, 12 November 2017

'cultivating curiosity' presentation

here are the two powerpoints from my presentation 'cultivating curiosity' on Friday 10th November 2017 in Leeds
the first was pitched mainly at KS3 (around 11 to 13 year olds)
the second continues (with some repeats) my interest in generalising or at least opening out some of the new GCSE questions

Leeds 1
Leeds 2

here is an example of a long multiplication sum presented in a loop
(it needs to be downloaded for the animations to work)
start it off and it should continue playing, until you press escape

I very much enjoyed the session and hope that some of it is useful
apologies for trying to jam in quite a lot of examples on a Friday afternoon...
thanks to Liz Smith and the Leeds team for inviting me



Sunday, 29 October 2017

cancelling fractions

maybe slightly too many questions....
(not using a calculator, especially a scientific one)

















the equivalent fractions below each involve all of the digits, 1 to 9
there are several more of these for some of the fractions
reference: ben vitalis at fun with num3ers
many thanks

practice at multiplying and dividing



there is another one for a third

Tuesday, 24 October 2017

from one percentage to another

this is my version of a very fine idea by Miss Konstantine (@GiftedBA)
clearly linking (as she says) percentages to ratio 
it will be interesting to see (and hear) how various students tackle these problems

she gives a description of her lesson sequence and her sheet here




Monday, 16 October 2017

algebra problems


equation of a circle

an introduction to the equation of a circle
which can later be generalised, using pythagoras





Saturday, 26 August 2017

rounding to different amounts

usually rounding to a finer amount (5p or 5c) will provide a more accurate estimate to the true cost than rounding to e.g. the nearest 10p or 10c
but not always...





for three addends:
rounding to the nearest 5p is more accurate in 123 cases
rounding to the nearest 10p is more accurate in 28 cases
and for the remaining 69 cases, both methods of rounding are equally accurate

for four addends:
nearest 5p = 417 cases
nearest 10p = 105 cases
equally accurate = 193 cases

for five addends:
nearest 5p = 1210 cases
nearest 10p = 321 cases
equally accurate = 471 cases

[thanks to the National Mathematics Project team (published in the UK in 1989, Eon Harper et al) for these solutions and the suggestion for this task]