You may also like

Tangrams

Can you make five differently sized squares from the interactive tangram pieces?

Geoboards

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

Polydron

This activity investigates how you might make squares and pentominoes from Polydron.

Tiles on a Patio

Age 7 to 11
Challenge Level

These solutions are just some examples showing the work of four children.

First of all we have Izzy's examples:-

Tiling pattern
9  2 by 2
 

 

 

 
 2  4 by 4
 

 

 

 
32  1 by 1
 

 

 

 
43  Total

Tiling pattern
96  1 by 1
 

 

 

 
 1  2 by 2
 

 

 

 
97  Total

Izzy found that you could not get a solution using 98 or 99 tiles so the next highest after 100 was this one with just 1 2 by 2 replacing 4 1 by 1's.

Now we see Lizzy's:-

Tiling pattern
2  5 by 5
 

 

 

 
 1  3 by 3
 

 

 

 
 1  4 by 4
 

 

 

 
 4  2 by 2
 

 

 

 
 9  1 by 1
 

 

 

 
17  Total

Tiling pattern
16  2 by 2
 

 

 

 
20  1 by 1
 

 

 

 
 1  4 by 4
 

 

 

 
37  Total

I rather liked her 17 made up of 5 different sizes. The 37 was not symmetrical, many results were, that's neither good nor bad ... it's all O.K.

Then we have Ben:-

Tiling pattern
20  2 by 2
 

 

 

 
20  1 by 1
 

 

 

 
40  Total

Tiling pattern
8  2 by 2
 

 

 

 
 1  6 by 6
 

 

 

 
32  1 by 1
 

 

 

 
41  Total

His 41 would really look good if you wanted it to be very symmetrical. You could probably invent some games in going around the edge from 4 1 by 1's to a 2 by 2. The 40 is interesting because there is the same number of each tile size.

Tiling pattern
14  2 by 2
 

 

 

 
 2  3 by 3
 

 

 

 
26  1 by 1
 

 

 

 
42  Total

Tiling pattern
12  2 by 2
 

 

 

 
 1  3 by 3
 

 

 

 
 1  5 by 5
 

 

 

 
18  1 by 1
 

 

 

 
32  Total

I think Bo's 42 is rather like a robot! The 32 was very different.

Well done and thank you Izzy, Lizzy, Ben and Bo. Yes these are four real children from the South West of England who were in a group of 19 doing this activity.