don steward
mathematics teaching 10 ~ 16

Saturday, 15 December 2018

four numbers

the powerpoint is here

thanks to Mike Askew for this question

it explores oddness and evenness
and divisibility by 4, including - possibly - a divisibility test for 4

and it can be set in the context of probability
finding all the outcomes, theoretically
maybe checking these by experiment

isosceles triangles and Penrose tilings

the powerpoint is here

the relationship between the Penrose tiles and a 'golden' triangle, involving phi is explored here

two isosceles triangles stuck together

the powerpoint is here

exploring how two isosceles triangles can be put together to create a triangle
or, how some triangles can be dissected into two isosceles triangles
exploring the angle relationships for the various options

generalising isosceles triangles

exploring the function/relationship:

  • simple numbers (and maybe harder numbers)
  • algebraic treatment
  • graph 

the powerpoint is here

isosceles triangle angles

the powerpoint is here

it contains a range of questions that are intended for students to answer orally

see WR Somsky's dissections here

isosceles triangle proofs

updated version

powerpoint is here

Thursday, 6 December 2018

trapezium area and quadratic

based on
'exercises in algebra'
part three

surface area and factorisable quadratrics

set up a quadratic equation
and solve it

trial and improvement may well be speedier...
(students shouldn't do that
because they might neglect to find further solutions,
- even though there aren't any)

Wednesday, 5 December 2018

percentage increase/decrease questions

a powerpoint for this is here

relating % increase and decrease to a picture

a number, increased by N% is N

a number, decreased by N% is N

Monday, 3 December 2018

search for unusual cuboids

this involves work on the surface area and volume of a cuboid
the powerpoint is here

there are three tasks
  • adding 1 to each of the (integer) dimensions, doubles the volume
  • different cuboids with the same surface area and volume
  • cuboids with the same value for the surface area and the volume (see lovely cuboids for a slightly different approach)

task 1

this task was offered by James Tanton

cuboids that double in volume when 1 is added to each of the (three) integer dimensions

task 2

different cuboids with the same surface area and volume

factors of the volume can be used to narrow the search

task 3

same value for surface area as volume

there are 10 altogether

see also lovely cuboids for a different approach to task 3