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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

  1. Find a partner
  2. Ask them to pick a number between 1 and 63 and not tell you.
  3. For each of the six cards
  4. Ask them if there number is on the card.
  5. If they say yes, record the first number in the table on the card
  6. 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