Polydron

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

Fencing Lambs

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

Lawn Border

If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?

Dicey Perimeter, Dicey Area

Stage: 2 Challenge Level:
This is a game for two players.

You will need two dice, some sheets of centimetre squared paper and two pencils or pens.

The aim of the game is to be the first to reach the agreed score.

How to play:
1.  Decide on your target score.  10 might be a good number.
2.  Decide who will go first.
3.  Player 1 throws the two dice and finds their product.
4.  Player 1 must then draw as many rectilinear* shapes as possible which have either an area or a perimeter equal to the product of the dice.  Player 1 scores 1 point for each correct shape.
5.  Player 2 throws the dice, finds their product and draws as many shapes as possible in the same way.
6.  The winner of the game is the first to reach the agreed target score.

What are good numbers to throw?  Why?
What are not very good numbers to throw?  Why?
Is it better to go first or second or doesn't it matter?

*A rectilinear shape is one whose edges meet at right angles.  In other words, if you are drawing your shapes on centimetre squared paper, the sides of the shape will always be on the grid lines, not drawn diagonally.