Crackers
See also: teaching, teaching-digital-technologies, teaching-mathematics
As described by Cathy Williams on YouCubed's cracker's page, Crackers is the name of a low-floor-high-ceiling-wide-walls mathematics learning task which is based on a prize from a Cracker Jack box.
The game#
Given 6 specifically designed cards all full of numbers (between 1 and 63) you
- Find a partner
- Ask them to pick a number between 1 and 63 and not tell you.
- For each of the six cards
- Ask them if there number is on the card.
- If they say yes, record the first number in the table on the card
- Add up all the numbers you recorded and the total will be the number they picked.
Mathematics task#
The YouCubed task has students working toward doing this without writing down the numbers selected and then scaffolded with questions
- What do you notice & wonder?
- Create a convincing argument showing why this works. Can you make a visual proof?
- Make a presentation showing how this puzzle might have been created.
- If you were going to continue this pattern, what would the 7th card look like? What would be the greatest number your partner could choose if you had 7 cards? Would the puzzle still work?
Re-purposing as an activity for teaching-digital-technologies#
Aim here is to link with some data representation content descriptions (AC9TDI8K03 and AC9TDI8K04) but also give an example of generally solving a problem with digital technologies, computer programming etc. The program would allow an individual to play the game without a partner with the computer doing the addition.
Design#
Task required
- Allow the user to select an upper bound for the game (i.e. from 1 to x - where x by default is 63)
- calculate the numbers to appear on each card
- display the cards to the user
- allow them to indicate yes/no their number is there
- represent the cumulative total
- inform them of the total