Board Block Challenge

'Board Block Challenge' printed from https://nrich.maths.org/

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Board Block Challenge

Before playing this game, you might like to have a go at the simpler version, Board Block.

This version is also for two players and can be played on the interactive version of the pegboard, or a real circular pegboard if you have one.

Firstly, choose the number of pegs on your board.
Decide what shapes you will be allowed to make.
You could allow:

triangles and quadrilaterals

triangles, quadrilaterals and pentagons

triangles, quadrilaterals, pentagons and hexagons

triangles, quadrilaterals, pentagons, hexagons and...

Take it in turns to add a band to the board to make any of the shapes you are allowing.
A band can share a peg with other bands, but the shapes must not overlap (except along the edges and pegs).
A player loses when they cannot make a shape on their turn.

For your choice of shapes, how does the winning strategy change as you increase the number of pegs on the board?

If you keep the number of pegs fixed, how does the winning strategy alter as you change the shapes you are permitted to make?

How is the game affected if you play to lose?

Perhaps you can invent some of your own games using the pegboard? Email us if you'd like to share your ideas.

Why play this game?

This game reinforces properties of 2D shapes but, at the same time, the strategic element demands higher-order mathematical thinking. It is a great context in which to encourage learners to pose, and try to answer, their own questions.

Possible approach

It would be good to introduce pupils to Board Block first, which is a simpler version of the game just involving triangles.

Once they are familiar with the Board Block game, open up the challenge so that pairs can choose the shapes they use and the size of the circular geoboard. Give learners time to decide on the rules of their own game before giving them plenty of time to try it out several times.

At a suitable point, bring everyone together for a mini-plenary and focus their attention on strategy. Has anyone found something out that might be important? How will they go about finding out if there is a strategy for the game they have created? It may be that some of the learners' games are rather complicated so that analysing strategy is rather unwieldy. This could be a good opportunity to discuss the usefulness of simplification.

If time allows, you could invite pairs to write up the instructions for their game (writing for a purpose) and the different versions could be tried out by others.

Key questions

How do you play your game?
How do you win?
Have you found any good ways of winning?
How could we find out whether there are any good ways of winning?
Can you guarantee a win? Why or why not?

Possible extension

Challenge pairs to tweak their game somehow and see how this affects the strategy. This could involve, for example, using more/fewer pegs on the geoboard or perhaps allowing a greater/narrower range of shapes. In addition, you may like to introduce the class to more of our strategy games.

Possible support

Playing the game on a print-out of the geoboard might help children as they will then have a record of the moves they made (see this page). They could then refer back to previous games more easily and refine their strategies.