median
don steward
mathematics teaching 10 ~ 16

Saturday, 22 April 2017

geometric sequences

a revamped version of a previous posting, this one without surds







quadratic nth term







Friday, 7 April 2017

solving cubic equations iteratively

a method that is fairly fraught with difficulties (smoothed out in trial GCSE questions)
bring back trial and improvement...

there are much better ways to solve a quadratic equation

perhaps we could teach the general cubic solution (and quartic)??






quadratic points

intercepts and turning points



proving last digit facts about square numbers

work based on an article by David Wells, Maths in School, January 2017
practice in proving statements by multiplying out brackets
and involving some diagrams



multiplying three brackets

practice in multiplying out three brackets
also considering how to factorise some cubic functions (which is beyond GCSE)
the powerpoint is here









Thursday, 30 March 2017

cleverly calculating

upgraded...



students say how the original sum has been transformed and consider which transformation is most helpful (in finding the result of the calculation) :






Friday, 10 March 2017

in the limit

puntmat posted an interesting idea (7th August 2014) involving various functions and exploring their limit as n gets very large indeed (tends to infinity)

these resources involve two of their functions plus another one

what fractions are shaded with a colour (out of the whole rectangle) at each stage?
what happens to this fraction as the shape (n) grows bigger and bigger?

all give rise to a common set (or subset) of fractions
with the same limit...
why?



















the puntmat post helpfully included some animated gifs for two of these sequences:




cuboidal parts

this problem varies one posed by Suman Saraf (found here) involving areas

this task considers cuboid volumes (and factors)
a cuboid is cut into 8 cuboids (with 3 cuts, parallel to the original faces)
their volumes (apart from one) are as shown
dimensions are integers
choose a solution that looks about right...


fractions of rectangles

this is practice in areas of shapes
with the question reversed - given the area, what could the shape look like?

students will hopefully seek suitable base and height dimensions
(possibly forgetting that in a triangle the area involves halving)

some questions have two solutions
this can create opportunities to discuss why e.g. triangles with the same base and between two parallels have the same area


it's been suggested (thanks Tom) that you need blank grids on the back of each sheet




these could involve finding areas by dissecting a rectangle

the bottom left two can be justified visually

or you could involve surds

Sunday, 5 March 2017

getting the same number (ii)

extending 'getting a positive whole number' (here) to two expressions

could be a start to solving simultaneous equations