don steward
mathematics teaching 10 ~ 16

Tuesday, 17 April 2018

downloading images

I am aware that some of the (png) images have a white background and others are transparent when you click on them

this used not to be the case and I don't know what I'm doing differently, or what has changed...

I think the images can still be saved and put into e.g. powerpoint even though they appear blank

I can change them manually so that they are viewable but that will take a while...

I'll try to sort this out - any advice is welcome!

Wednesday, 11 April 2018

ancient Chinese maths in right angled triangles

the 'Jiuzhang Suanshu' ('the nine chapters on the mathematical art') appears to be problems illustrating general techniques that were collected together over time

much light is shed on the processes and justification for the methods used in this important document by Liu Hui (around 260 CE) but he indicates that the ideas date back to before 210 BCE

the ninth (final) chapter is devoted to the 'Gougu rule' (otherwise known as Pythagoras' rule) and to problems involving similar triangles, connected to surveying

the 'gou' is the shortest side, 'gu' the middle side and 'xian' the longest side in a right angled triangle

most of the 24 problems in this chapter have a practical origin

measures are a simple decimal structure

a powerpoint suggests approaches to each problem
diagrams are included from some translations but were lost in the original

Thursday, 15 March 2018

growing squares under the stairs

these resources are based upon an article by Daniel Pearcy in Maths Teaching 247 (July 2015)

starting from a coordinate sequence
to powers (the y coordinates)
to sums of powers (the x coordinates)

the powerpoint looks at squares drawn underneath e.g. y = 2x + 1

what would the next coordinates be?
and the next?

coordinate sequences

what are the coordinates of e.g. the lowest left hand points of the Ms
what would the next ones be?

try some with your initials

coordinate practice

checking that students can plot coordinates in all four quadrants

the powerpoint begins by involving negative coordinates to plot squares

and goes on to involve points on straight line graphs

probably you can let us know some other points that will lie on this line

maybe there's a rule that says whether or not a point lies on this line

coordinates CBSE questions

it is interesting to see how an approach that can involve vectors and properties of quadrilaterals develops from the KS2 based SAT questions (here) to these from the CBSE exam (India) for Y10 students

the powerpoint goes through some of the ways to solve question 5(b)

printable version

quadrilaterals and coordinates

problems based on the KS2 SAT questions
the ppt is here

same questions, printable:

Sunday, 11 March 2018

smaller radiating directed numbers

still not easy - but simpler
there should be no duplicates of numbers in the loops for each task

Friday, 2 March 2018

Thursday, 1 March 2018

from one fraction to another

@pbruce maths and @misswillismaths indicated a wish for such a resource
it seemed like a good idea
with some generalities unearthed

a proof involves expanding brackets to form a quadratic expression
a proof is reasonably straightforward

how are these two general forms related?

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