median
don steward
mathematics teaching 10 ~ 16

Sunday, 21 January 2018

generalising statistics GCSE questions

one or two additions to previous resources

powerpoint

thanks to the exam boards





generalising algebra GCSE questions

some further material added and previous slides revamped

using past paper and practice GCSE questions to provide deeper tasks

powerpoint

thanks to the exam boards




generalising geometry GCSE question

powerpoint

based on exam board questions but rewritten and adapted to provide tasks that can be more fully explored and, usually, generalised

thanks to the exam boards




generalising number GCSE questions

revamped and larger collection
questions based on some recent GCSE exams or practice papers but adapted so that they can be explored more playfully, often with a view to generalising and possibly proving statements

thanks to the exam boards

powerpoint 




Tuesday, 9 January 2018

products of primes

the powerpoint is here
[ it needs to be downloaded for the animations to work ]




what is the common form of these pairs of numbers?

what, in general, will the hcf be?

the lcm?

Monday, 8 January 2018

pythagoras questions

these questions are from CBSE (India) Y10 papers


the top left question leads to the cosine rule

cos(180 - B) =
 - cos B




Tuesday, 2 January 2018

straight line graphs with ratio

Martin Wilson, of Harrogate, UK developed this idea to intermingle straight line graphs with ratios

it might be interesting to compare student's approaches to these problems

later questions have non-integer solutions



quadratic formula

the powerpoint is here






biggest square inside a right angled triangle

a good, if demanding, application of similar triangles





 general cases
proving a general result

what are the steps?


















unsurprisingly, I subsequently found that this has been explored by (amongst others) Marion Walter in FLM 21 in 2001 and MT 53 in 1970

her general results agree with those above (although there is a small numerical error on p.29 of her article)

she points out that 1/y^2 = 1/x^2 + 1/c^2 where 'c' is the hypotenuse

Monday, 18 December 2017

equable triangles

the proof that there are only five equable triangles (integer sided) was done in 1904

this version of a proof is largely due to David Wells with small bits of help from me
it is complex but involves only GCSE tools















equable right angled triangles

not using pythagoras
working out the radius of the incircle

three little triangles sum to the large one
an alternative method, using pythagoras, to find the radius of the incircle
proving that there are just two right angled equable triangles with integer lengths








two of the possible values duplicate the other two