median
don steward
mathematics teaching 10 ~ 16

Saturday, 17 February 2018

directed number arithmogons

the word 'arithmogons' (rather than 'arithmagons') seems to stem from an article by Alistair McIntosh and Douglas Quadling in Maths Teaching number 70 (in 1975)

amongst many other things Leo Moser (1921 to 1970) studied pairs of numbers adding up to totals, including the work in the third resource: pairs of numbers always summing to a square number

the powerpoint goes through various algebraic solution steps - one good reason for studying arithmogons, as well as (in this case) practice with directed numbers

Craig Barton details the reasons he enjoys working with arithmogons and has various tasks based on their structure here





Monday, 5 February 2018

tangents to circles

these are based on problems from the CBSE exams (India) Y10






simultaneous equations generalising

these resources follow a theme of providing practice questions with some pattern built in

that way the 'depth' to a task can involve generalisation and proof

some of the proofs are demanding
you might go through steps with students with them trying to explain what is happening
the powerpoint goes through the proof steps (but it might be better to go through this on the board)



Saturday, 3 February 2018

similar triangles

these questions are from or are similar to CBSE (India) Y10 papers


(5) and (6) also need circle theorems

Tuesday, 30 January 2018

radiating equations

maybe curiously, maybe not, a single operation changes both sides of an equation

the powerpoint introduces this notion (with animations if downloaded)


introducing the idea of the transformation




Sunday, 28 January 2018

pythagorean triples

studying square numbers with two of them summing to a third (for integers) has interested various ancient and hopefully modern civilisations

this work develops some of the extensive ideas provided by Dr Ron Knott at Surrey University (many thanks to him)
Hannah Jones used these and other resources to devise classroom tasks for an EPQ project

pythagorean triple introduction ppt





















various patterns can be used to find pythagorean triples, those starting with an odd number being more commonly known

finding pythagorean triples ppt



















seeking pythagorean triples with a selected shortest side uses the difference of two squares and factor pairs

triples for a shortest side ppt






















a longer list of pythagorean triples is available at TSM resources

there are various formulae for finding pythagorean triples from a parameter (or two)
these provide primitive triples (without common factors) but not usually multiples of these

triple generators ppt



















the graphical work of Adam Cunningham and John Ringland (in the Wikipedia entry) on primitive pythagorean triples is interesting

graphing primitive triples ppt





















there are also some novel methods for generating triples from fractions, identified in Dr Ron Knott's work

fraction generators ppt




















some problems with lengths in triangles and rectangles, involving pythagorean triples

triangle lengths ppt



















a variety of problems, all involving the 3, 4, 5 triangle

3, 4, 5, problems ppt





















some problems on quadratic equations set up as pythagorean triples with various expressions for their lengths

expressions triples ppt


















the perimeters of pythagorean triple triangles have some interesting patterns

perimeters of triple triangles ppt