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

## Thursday, 23 April 2015

## 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))

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))

Labels:
pythagoras,
surds

## 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

Labels:
pythagoras in 3D

## 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

Labels:
pythagoras in 3D,
trigonometry in 3D

## 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

students may or may not be provided with some information:

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

Labels:
angles in polygons,
ratio

### 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

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

Labels:
area of a triangle,
fractions of

## 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

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

Labels:
coordinates,
mid-points,
vectors

## Thursday, 2 April 2015

## 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?

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

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