I forgot how much I love Scratch, I have been running an after school ASA for grade 4 students using Scratch. Scratch is a drag and drop block coding app that is low entry high ceiling, meaning it is easy to get started but you can program some pretty complex stuff.
I was working with a grade 7 Math teacher helping her to plan a MYP Criterion C,D probability assessment. The current probability assessment had students creating their own "win at the fair" game to make money. They explored some common fair games and then made a game where the owner would make a profit. While this task is open ended, it took a lot of time and there wasn't very much higher level thinking or Maths involved.
It reminded me of a really cool Math300 assessment from years ago where students were given a win at the fair type game. The students had to identify who won or lost (the person playing or the fair owner). It turns out the game is set up so the fair owner loses quite a bit of money. Students then have to adjust the game so the fair owner wins. It included an app to run simulations where students could change different variables, explore theoretical probability vs real life results and run the game thousands of times in the blink of an eye. The simulation and the ability for students to change variables to explore real life probability was the greatest strength of the activity.
So with this in mind, we created our own win at the fair game and simulation.
I created a game board in Google Slides
- From your results who makes money - remember it costs $1 to play each time? You or the fair owner? Explain.
- Run the (online) simulation 100 times. Describe any pattern or trend.
- Explain and describe any differences between your data and the 100 simulation.
- If you ran the simulation again would you get the same results? Explain and justify your answer.
- Who makes money after 100 plays? You or the fair owner? Explain. What would you expect for 1000 times?
- Would you like to play the game? Think in terms of do you make money? Justify your answer using mathematics.
- Which number comes up the most and the least from rolling the dice and adding the outcomes?
- Draw a sample space of the outcomes of the sum of rolling 2 dice to illustrate your answer above. Explain how you know.
- Discuss which direction is the counter most likely to travel and why.
- What is the theoretical probability of getting a $5 prize? Use a tree diagram to demonstrate this outcome, and then explain the probability.
- Mr Derry created this simulation - the fair owner doubts his programming skills. Do you think the simulation is accurate, how can you prove your point using mathematics? (Level 7/8)
Redesigning the game.
- choose the number of trials
- change the prizes
- change the numbers that decide the direction of the counter