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How to turn abstract Maths concepts like chance and probability into an inquiry learning task? Just ask Year 6, who created their very own amusement arcade, followed by a Carnival Day for Year 5!
It all began when the Year 6 teachers were workshopping ideas about how to teach chance and probability in an engaging and interactive way. They challenged Year 6 to create a free arcade game for their younger peers in Year 5 to play at special Carnival Day. The idea was to give Year 5 a more concrete grasp of the mathematical concepts of chance and probability - while really extending Year 6’s learning – and also provide lots of opportunities for both year groups to engage and have fun together.
The Year 6 teachers asked their students to come up with a vision for a game, including detailed guidelines on how to play it and a clear outline of the rules. They had to draw a diagram of their proposed game (or take a photograph of the finished product), clearly labelling each of the different elements. They had to calculate the theoretical probability of Year 5 students winning the game and outline all the possible outcomes, making predictions about how their game would unfold and why. Another proviso was that their game had to be sturdy, so that it didn’t fall apart when Year 5 students started playing it. And it also had to be attractively presented, so that they were persuaded to give it a try.
After mocking up their games, Year 6 had a chance to test out their theories at a trial Carnival Day. This presented them with an opportunity to troubleshoot any issues or teething problems, and make the necessary adjustments, recalculations and predictions.
On Carnival Day itself, the students had to record all their data on a data collection sheet that they had drawn up, so that they could then calculate the experimental probability. After the Carnival was over, they had to document the outcomes of their game and include a reflection on their learning and any other observations.
With ‘carte blanche’ to create their own game, the students were excited to unleash their creativity, harnessing their mathematical skills, design skills and conceptual thinking to come up with a variety of different options. It was amazing to see the different possibilities they produced.
Jessica created a game of chance called The Ring of Fire. Players had to throw a juggling ball through six differently sized hoops, which were all worth different points. Each player was allowed three goes, with the winner scoring the maximum number of points.
Jessica said, “I could make a lot of profit from this game in real life. I think people are willing to spend money on a game that looks easy, even though it isn’t. I think they’d be interested in playing it more times to get a better score, which would mean more income. Many carnival games are rigged like this. They look easy but are tricky. Another aspect that would make my game more profitable is the optical illusion you gain from looking at it. Many games, tricks and items are designed, so people believe things they see and are more attracted to them. In my game, the black border around it gives the impression that the board is smaller than it really is. This is called optical reduction. In many famous tricks - like the cutting a person in half trick - they use special paint jobs to make things appear smaller.”
At the start of the project, Jessica thought that her probability outcome would be a 19.1% chance of getting a ball inside a hoop. Before Carnival Day she said, “I am feeling very confident that it will work as I have tested it multiple times and even though my probability outcomes of winning aren’t skyrocketing high, I think there will be ways I can make it easier for people if I have to.”
After Carnival Day she said, “Overall, I found that my original probability outcomes matched my experimental probability outcomes. Only 3.8% of people didn’t miss on any of their throws, whilst 76.2% missed at least once. Overall, The Ring of Fire was a fun and interesting game. I didn’t think the overall percentages were going to influence the entire game as much as they did, but when I realised that only one person scored the top score of 300, I was a little rattled. I think if I had made the hoops a little larger and used lighter balls, I could have had a larger success rate. If I were to run my game again, I would change my data collecting system and make it a tally system. It was a good experience learning the maths behind it and seeing how the results panned out. I found it really fun and hope that I to do similar things in the future.”
Bronte created a game of probability called Fishin' Hole. Players had to use a fishing rod (made using a chopstick and string) with a magnet to ‘catch’ ping pong balls inside a box. There were 20 ping pong balls in total, numbered from 1 to 20. There were two lucky numbers: 2 and 12. If players caught these balls, they would receive 5 tickets and win the game. Each player was allowed three turns, leaving any of the ‘catches’ outside the box each time.
Bronte then created a tree diagram to illustrate the possible outcomes and the probability of winning each round, depending on what occurred in the earlier rounds. “My diagram also shows the overall probability of winning, which is 28.4%, and the probability of losing, which is 71.6%. Overall, my prediction is that my game will be won 28 times if it was played 100 times.”
On Carnival Day, Bronte’s game was played 100 times. Players won 26 times and lost 74 times. Bronte said, “My experimental probability shows the chance of winning my game is 26%, which is extremely close to my expected probability, with a difference of 2%. I think the reason for this is because of the location of the balls inside the box. Every time someone played, I shook the box. If balls had remained in the corner, where it was harder to catch them, it would have affected the accessibility of the lucky number balls. Although, it’s down to chance which balls end up in the corners, this could have been the reason that the experimental probability I collected and the theoretical probability I calculated were different.”
Bronte also created a pie graph using an app to represent the difference and illustrate the percentages between winning and losing in both her experimental research and theoretical research. Overall, Bronte was happy with the outcome of Carnival Day, but felt she could have improved on her time management skills. “I feel that I calculated the probabilities of winning and losing my game well, backing it up with evidence and a diagram. I believe that my game was well made and appealing and drew the attention of many Year 5 students. However, it took quite a long time for people to have three goes, which made the line build up. This caused people to become quite frustrated. A way to improve this in future, is to reduce the number of goes to two or make a time restriction.”
All in all, this project was a great ‘chance’ for Year 6 to work out all ‘probabilities’, helping them to polish up their mathematical reasoning and conceptual thinking. Furthermore, Carnival Day earned a big thumbs up from Year 5, who had fun and learnt a lot in the process. Bravo Year 6!