Big Toe Noughts & CrossesYears 2 - 8SummaryNoughts & Crosses, or Tic-Tac-Toe as it is sometimes known, is a game every child knows. The aim of the game is to be first with three counters in a row - horizontally, vertically or diagonally - to win. The attraction seems to be that you can sometimes win - of course you can sometimes loses to, but at other times you can draw and that is almost as good as winning. However when the question 'Is there a winning strategy?' is investigated is turns out that the game should also be a draw. That's very fair, but not very interesting. So, what happens if we add an extra place to the game and create Big Toe Noughts & Crosses? |
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IcebergA task is the tip of a learning iceberg. There is always more to a task than is recorded on the card. |
When analysing a game it must be assumed it is being played by the two best possible players. It's one thing to win a game by chance, or against a week player, but another thing entirely to win against the best possible opponent. With this approach it can be seen that standard Os & Xs should be a draw every time.
So, this game is not fair. But it does produce a win. Is it an improvement on Os & Xs? |
Whole Class InvestigationTasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works. |
If you are using Menu Maths Packs one between two in your class, you have sufficient material to use this menu item as a whole class investigation. Today we are all going to choose Big Toe Os & Xs from the menu.The purpose in doing so would be to model Working Mathematically. Structure the lesson in a similar way to the outline above, and encourage students to record and perhaps publish their analysis. PowerPoint, or a sequence of photos, might be useful publishing tools. Extension
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Is it in Maths With Attitude?Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner. |
Big Toe Os & Xs is not in any Maths With Attitude kit, but it is part of Poly Plug Game Pack resource book. This publication focuses on content-free reasoning based on four families of games, each of which has four variations. The Noughts & Crosses family is one of those families. |