Some puzzles requiring no knowledge of knot theory, just a careful
inspection of the patterns. A glimpse of the classification of
knots and a little about prime knots, crossing numbers and knot
Investigations based on an Indian game.
All you need for this game is a pack of cards. While you play the
game, think about strategies that will increase your chances of
In the context of a game, this problem invites students to identify straight lines and state their equations. Many students can identify some of the lines easily (e.g. horizontal), but there is incentive to learn about 'harder' lines.
Move the group on to the next level by playing a demonstration game with the group, only using lines with gradients 2, -2, 1/2, -1/2. Allow time for students to explain to their neighbour/to the group how to establish the equations of these lines. When the group go back to working in pairs, they must only use the new family of lines for the first two games, and after that, they can use easier
or harder lines if they wish.
Repeat with each new level.
You may like to finish with a class (or class champion) vs teacher game.
If you wish to play this game without a computer, a set of twelve worksheets is available here.
One teacher has blogged about using this problem in the classroom. She created a PowerPoint with different boards to be used away from the computer.
Which lines pick up most diamonds?
Describe how you move from one diamond to the next in the line you're looking at.
Where would that line meet the y-axis?
Is the slope a positive or a negative gradient? Is it steep or shallow?
Ask students to work together playing against the computer on the single player version of the game. They could keep a running total of how many diamonds they get, as a percentage of the total number the computer gets.