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!
sorry,
Don
Tuesday, 17 April 2018
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
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?
etc.
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
and the next?
etc.
coordinate sequences
what are the coordinates of e.g. the lowest left hand points of the Ms
what would the next ones be?
up?
down?
etc.
try some with your initials
what would the next ones be?
up?
down?
etc.
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
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
the powerpoint goes through some of the ways to solve question 5(b)
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
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?
it seemed like a good idea
with some generalities unearthed
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
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
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)
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
the powerpoint introduces this notion (with animations if downloaded)
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