rectangle perimeter

perimeter change with area the same
cutting a shape in half - in two different ways

this task is based on a SAT question
(KS3, L4 to L6, year 2000, paper 1, question 14)

congruent rectangles making up a larger rectangle

in two different ways

'P' is the perimeter

find the length and width of the smaller rectangles

square loops

quite a big square loop

some more modestly sized ones

 some rules:

it's probably better that students choose their own shapes to explore but in case they don't find enough...

explore the relationships between the three variables

students could explore a growing 'family' sequence

maybe an obvious 'family' to explore

"what growing families could be explored?"

some that might be suggested...

what are the general terms for the:
number of tiles
interior perimeter (free edges)
outside perimeter (free edges)

a powerpoint is here

see also 'octagon loops'

and 'hexagon loops'

regular octagon loops

in England this task was devised by a group called SEAC (a national assessment agency), many moons ago (1992) to assess students on an investigative task
green plastic octagon templates were distributed to all England schools
they might be lurking, dustily, in cupboards

be aware that octagons drawn on squared paper are not regular and lead to erroneous data

you can buy regular octagon paper plates for a group to work with
but accurate recording is still difficult...

the 'growing in a line' case can be explored using a semi-regular tessellation of regular octagons and squares

regular hexagon loops

this task could be initiated with the simpler, 'square loops'

there are various physical regular hexagons available (e.g. ATM mats and Pattern Block shapes) that can be helpful for some students

regular hexagon sheets ensure that recording is relatively easy

regular octagon loops are also interesting but much harder to record (square based octagons being slightly misleading)

a task sheet, for students

it's better for students to select this option themselves rather than be advised to take it...

some students might find some ready-prepared loops to be helpful
















a powerpoint is here

teacher's notes here

obloidal perimeters

L-shaped perimeters

these (compound) shapes are made with rectangles
what are their perimeters
as an expression?