Diamond Collector
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
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.
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.