median
don steward
mathematics teaching 10 ~ 16

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








grid geometry perpendiculars

it seems helpful to consider (and then define) perpendicularity in terms of a 'rotated' vector (through 90)

equal lengths can be established from the diagonals of rectangles (or pythagoras)

the powerpoint is here
 





grid geometry parallels

Pierre van Hiele maintained that geometry should be started off using a square grid

it might be advantageous to describe (and define) parallel lines as having the same gradient/slope/journey/vector on a grid

dwelling on the properties of shapes:
  • parallel sides
  • right angles (perpendiculars)
  • equal sides
  • convex/concave
  • mirror symmetry and rotational symmetry
should probably precede the naming of shapes and classifying them

the powerpoint is here






Wednesday, 19 July 2017

maths jigsaw

the shapes fit together to make a square (on the 5 by 5 dotty grid)
I'm fairly sure that you just need to rotate some of the shapes (mentally or otherwise) to fit them together i.e. not reflect/flip them







Friday, 14 July 2017

equivalent fractions shaded


 pair off the equivalent fractions
and here

Thursday, 13 July 2017

radiating numbers

you are only allowed to do one of the allowed steps indicated for each connecting line
try to work from the outside to the inside
there should be no repeated numbers in the solution

[ there's a 'radiating' tag now - if you want to find the rest ]





Wednesday, 12 July 2017

Saturday, 8 July 2017

a shape problem

this is a problem used by Einav Aizikovitch-Udi, School of Education in Israel to analyse the responses of high attaining 14 year old students



a number puzzle

some developments of a number puzzle






Sunday, 2 July 2017

corner coordinates

these are questions from or similar to the KS2 SAT test questions (for 10 to 11 year olds)

(they are on the  problem solving and reasoning presentation of 27th June 2017)