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Diamond Collector

Stage: 3 Challenge Level: Challenge Level:1

Why do this problem?

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.

Possible approach

You may want to take a look at Parallel Lines and Perpendicular Lines before introducing students to this game.

Depending on the group's experience of equations of straight lines, the following 'levels of difficulty' could be adapted as appropriate.
  • horizontal lines
  • gradient 1 and -1
  • gradient 2, -2, 1/2, -1/2
  • integers and their reciprocals
  • non-integers and their reciprocals
If you have access to a big screen computer, put the game into 2 player mode, (click the yellow/orange icon). Demonstrate the game with half the class against the other half or with a small group against the teacher, using an appropriate level of difficulty in choice of lines and line equations.

Explain that the class is going to 'get in training', focussing on one skill at a time. Play another demonstration game with all lines strictly limited to horizontal (or grads 1, 0, -1). If appropriate play it as a teaching game first, discussing the lines chosen, and letting students explain how they established the equations.

Set the class working in pairs at computers, playing against each other. The first TWO games each are to be strictly limited to the stated family of lines, if pairs have time for more than two games each, they are free to include any lines they want to try.

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.

 

Key questions

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?

Possible extension

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.

Possible support

Ensure that students have sufficient time to become really confident with the early levels described above. Some students may like to hold a ruler up to the computer screen to clarify the lines that they are trying to get.

Students may need help interpreting the equation entry interface.