Guessing Colours GameTask 218 ... Years 2  7SummaryGuessing Colours Game involves placing a known number of discs of five different colours into an opaque bag and also knowing how many of each colour there are to start with. Students then take turns to select a disc from the bag, but first they each have to guess which colour will come out. A points scoring system is involved and a running total of points is kept for each player until all the discs are removed. The game involves simple addition and subtraction which may include negative numbers and is an excellent experience of chance events which may be at an intuitive level or measured by a probability score. 
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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. 
At the first level, Guessing Colours Game is a bit of fun involving addition and subtraction. An additional feature is the need to record in a way that keeps track of the guesses, whether or not they are correct, and the changing score. It is also helpful to keep a record of the changing number of each colour in the bag. Even if the game is nothing more than this, it can potentially throw up the need for negative numbers. The players start with 15 points each (one for each disc) and on each move gain or lose 2 points depending on their guess. So it only takes 8 incorrect guesses in a row to reach a score of ^{}1 and there are still 7 more discs to draw. One Year 1 teacher, who wasn't using this task at the time, was involved in a discussion with a colleague about negative numbers in the context of using a calculator and commented: Oh, negative numbers, they're no problem to my class. They just call them underground numbers.To add a little more to the arithmetic of the game expect the students to record not just who won, but the winning margin, or difference between the two scores.
Another way to add a little to the arithmetic is to declare that the winner is the person with the higher total score after 3, or perhaps 5 rounds. What is the winning margin in each round and for the grand totals? Beyond this, without requesting it, the game almost forces consideration of probability. For example, knowing that on the first move there are 7 Red discs in the bag of 15 discs, clearly the best chance of success is to guess Red ( 7 chances out of 15 = ^{7}/_{15}). The chances then change for all colours on every draw until the last draw which is a momentary experience of certainty, with a probability of 1 (1 chance out of 1 = ^{1}/_{1}). It is worthwhile encouraging the students to keep a record of these changing fortunes. ExtensionsThe challenge on the card suggests the first extension.
Perhaps each pair playing each version 5 times doesn't give a clear indication. Perhaps they should record their outcomes on a poster in the 'mathematics corner' which is a cumulative record contributed to by each pair that uses this task. Using Guessing Colours Game in its whole class investigation form (see below) would collect a lot of data about this hypothesis very quickly. Also, there is an opening here from designing software that would play many games with a chosen colour combination very quickly. Further, if we can change the number of discs of each colour in a bag, then what else could be changed and what would that change do to the game? What happens if...

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. 
It is quite easy to set up Guessing Colours Game as a whole class investigation. You need need something to substitute for the black bag in the task, perhaps brown paper lunch bags will do the job, and coloured squares, discs or blocks. Write the combination of colours on the board first, then set up the first game in a fish bowl situation with one pair at a table in the middle of the room. Spend time  perhaps the whole first lesson  exploring the game for its suite of arithmetic connections described above. Then, using a question like:
At this stage, Guessing Colours Game does not have a matching lesson on Maths300. However, this task is related to Task 47, Red & Black Card Game, and Task 131, Walk The Plank, both of which have a Maths300 matching lesson. The Walk The Plank lesson also includes software. 
Is it in Maths With Attitude?Maths With Attitude is a set of handson learning kits available from Years 310 which structure the use of tasks and whole class investigations into a week by week planner. 
The Guessing Colours Game task is an integral part of:
