don steward
mathematics teaching 10 ~ 16

Thursday, 17 August 2017

quadrilaterals on a 6 by 6 dotty grid

quadrilaterals on a 3 by 3 dotty grid

almost an antique
part of the South Nottinghamshire Project ('Journey into Maths')
by Alan Bell, David Rooke and Alan Wigley
published by Blackie in 1978
the teacher's guide (1) claims there are a total of 94 different positions
counting translations, reflections or rotations

an intention might be that students don't count transformations of each shape (initially anyway)

quadrilaterals on a 5 by 5 dotty grid

Wednesday, 16 August 2017

power sums

a reworked resource:

 a development of an idea suggested by Martin Wilson, Harrogate

Sunday, 6 August 2017

shape fitting

the intention of this task is that students progressively fit shapes together
to form a rectangle at each stage

a while ago, Edward de Bono devised similar shape puzzles to encourage a view that when problem solving, sometimes you need to dismantle what you have done already and start again

there is a powerpoint that reveals the shapes, one at a time

alternatively two students could work together, revealing each new shape (in a column) one at a time (after the first two)
holding another piece of paper over the rest

as this task is/was envisaged, it is important that the shapes are encountered one at a time

students will need some kind of squared paper

Monday, 31 July 2017

circle theorems meet 0.5absinC

an idea by Martin Wilson, in Harrogate, blending the circle theorems with area

you could use normal trigonometry (by bisecting chords) but Martin's intention is that students use the (more efficient) method of calculating 0.5 a b sinC

resources 2, 3 and 4 present an interesting relationship between sines
that is not easy to justify(?)
without involving the trig. formula sinA + sinB = 2sin(semi-sum).cos(semi-difference)
and noting that cosD = sin(90 - D)

Friday, 28 July 2017

directed number multiplication

the first resource is an idea from Martin Wilson, in Harrogate
and is intended to be practice with directed numbers rather than solving a quadratic equation

the other resource I have moved from elsewhere

square roots and cube roots

an idea from Martin Wilson, in Harrogate
(some of his questions slightly adapted, for ease of checking)

cuboid in a shell

Thursday, 20 July 2017

grid triangles and pythagoras

advanced level students (those who have covered the expansion of tan(A + B)) might like to think about reasons for it being impossible to draw an equilateral triangle on square grid paper

grid kites and rhombuses

Pierre van Hiele advocates constructing the special quadrilaterals by means of reflections and rotations
that way the properties are easily deduced (e.g. "because of the mirror line") from the constructions

this has been explored more fully by Michael Villiers in South Africa, using an interactive geometry package

the powerpoint goes through the constructions (but it's probably better demonstrated with an interactive package)

grid geometry angles

using the tangent of the angle (but not saying it's that) as a measure of the size of the angle
way better than a protractor!

the powerpoint is here