This week, students were introduced to this number sense task that can be solved in different ways. First, students were asked: How many unique 2-scoop ice cream cones could be made with only 1 flavour of ice cream? The answer is 1 (for example, chocolate for the bottom scoop and chocolate for the top scoop). Next students were asked: How many unique 2-scoop ice cream cones could be made if there were 3 flavours of ice cream available at the store? The answer is 3. -chocolate, chocolate -vanilla, vanilla -vanilla and chocolate (which is the same as chocolate and vanilla since order of the scoops does not matter). Next students were given the below task: When students were done, we displayed their work on our math Bansho wall to discuss student's math strategies. Some groups used a strategy. They tried different ways to make 2-scoop ice cream cones without repeating cones.guess and check Other groups used an idea of an . Starting with one flavour, they added other flavours to make 2-scoop ice cream cones until there were no more cones to make with that flavour.organized listThis group used an organized list. They also made sure not to repeat 2-scoop ice cream cones. They started with peach ice cream in the first column. In the next column they used blueberry ice cream (note they did not repeat the peach-blueberry combination). They also noticed that the number of cones decreased by 1. This group assigned a number to each of the ice cream flavours and proceeded to make the 2-scoop ice cream cones by combining the numbers in a list. Finally we worked through a solution together. We simplified the problem by assigning numbers to the flavour (like the group above). Students noticed patterns very quickly. We found out: 5 flavours of ice cream produces 15 unique 2-scoop ice cream cones: 5+4+3+2+1 10 flavours of ice cream produces 55 unique cones: 10+9+8+7+6+5+4+3+2+1 We also applied this solution to Baskin Robbins and found out that with 31 flavours of ice cream, we predict there would be 465 unique 2-scoop ice cream cones. |