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.

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

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

generalising reflections in x = 3

find the ostrich

this game was one of the SMILE software programmes (as 'Elephant' I think - on 'Microsmile, first 30')

NRICH have a ('find the giraffe') software version (that needs Flash enabled)

it seems better, initially at least, for students to call out coordinates to each other

the game can lead to some work on 'Manhattan metric' geometry:

• which points are 3 away from (4, 4)?
• which are equidistant from (1, 5) and (5, 1)?
• find points (P) so that the distance away from (2, 3) add the distance away from (6, 3) is 8

the game can also be played with negative coordinates

dividing line segments in a ratio

each of the shorter line segments is one third of the way along the line segment

also thirds
find the missing coordinates















this work links with the task 'jumping' where the triangle is at the mid-points of each side

rectangles on a grid

[based on an idea in the AQA GCSE additional maths Problem Solving set of resources]

regular octagon?

from an MEI question