median
don steward
maths teaching 10 ~ 16

Thursday, 23 April 2015

ratio Venn diagrams

the idea for this task is from one of John Mason's presentations e.g. in Vancouver 2014
(see the workshop resources on his website)


prove that 1 : 5 is impossible
prove that there is only one way for 4 : 5
prove that 1 : 6 is impossible
John Mason's extension task

Wednesday, 15 April 2015

pythagoras and surd forms

students find the missing length in simplified surd form
and find patterns
to extend
and maybe prove

this work arose from James Pearce (@Maths Pad James) finding some interesting surd forms (question (3) on sheet (i) and question (1) on sheet (ii))


Friday, 10 April 2015

spider on a cuboid
























Henry Dudeney posed a slightly more complex version of this problem ('Spider and Fly') in an English newspaper (Weekly Dispatch) on 14th June 1903

“Inside a rectangular room, measuring 30 feet in length and 12 feet in width and height, a spider is at a point on the middle of one of the end walls, 1 foot from the ceiling, at A, and a fly is on the opposite wall, 1 foot from the floor in the centre at B. What is the shortest distance that the spider must crawl in order to reach the fly, which remains stationary? ”

it later appeared in his collection, 'Canterbury Puzzles' in 1908

exact trigonometric values




find a quick(er) way to do this question






Thursday, 9 April 2015

3D trigonometry and pythagoras


















first step in finding the length of the space diagonal
second step
unusually, the length of this space diagonal is an integer











exam-style questions
thanks to Ashlawn School

Tuesday, 7 April 2015

ratio and polygon angles

the idea for this task (and one of the questions) comes from the AQA 8360 course

















students may or may not be provided with some information:

thanks to Wikipedia and László Németh for the sequence of regular polygons


fraction that is a triangle

this task is adapted from one by Tony Gardiner
a rectangle grid doesn't actually alter the problem but can make it a bit different...
it is similar to the triangles in a 5 by 5 square post



all 30ths from 7 to 14 inclusive can be drawn for this grid size

apart from the two indicated

Friday, 3 April 2015

third of the way along

each of the shorter line segments is one third of the way along the line


















this work links with the task 'jumping' where the triangle is at the mid-points of each side

Thursday, 2 April 2015

harder ratio questions

these could involve algebra
the course AQA 8360 has involved questions like ratio (ii) 





Sunday, 29 March 2015

squares nth term

for Fawn



















students form a growing sequence for each question and maybe describe it
(what will e.g. the 11th or 23rd shape in the pattern look like?)

they can then find an nth term rule
and hopefully justify this in relation to the diagram

can they make a rectangle out of the squares for each question?
and form an alternative generalisation?

how are the two generalisations the same?

Monday, 23 March 2015