This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
Place four pebbles on the sand in the form of a square. Keep adding
as few pebbles as necessary to double the area. How many extra
pebbles are added each time?
Thomas and Ken-Ree thought the smallest
rectangle can be found by drawing around the net of the box. Here
are Ken-Ree's diagrams.
Camille tried something similar but
moved parts of the net around to get a smaller
I chose a box with 7.8cm
length, 5.6 cm width and 3 cm height. Firstly, I started by turning
the box on a sheet of white paper drawing around it every time to
get a net. Next I cut it out. Then on another piece of paper, using
what I cut out, I drew the rectangle just around its borders. On
this rectangle I turned the piece of paper to see what I could move
to another place to make the rectangle smaller. The final rectangle
measured 14.3 cm by 14.5 cm.
Well done to John from Nagoya
International School who used algebra to work out this