WEEK 7 DISCUSSION 

The “What – If – Not” Strategy in action. By Brown and Walter

This is an interesting strategy to extend questions to a problem or going further to engage the students. Brown and Walter carefully explained the ‘What – If -Not’ Technique using four levels: Breaking up attributes, What – If – Not for the attribute, Asking Questions, and Analyzing questions.

Example: Ivan and Maria are playing cards using a special deck containing only 1,2,3,4,5,6,7, 8 and 9 each appearing once. Maria dealt Ivan a hand of three cards. He said that the three cards had a sum of fifteen. What are all the possible hands Ivan could have?

Level 1 Breaking up attributes. Cards contains numbers I,2,3,4,5,6,7,8 and 9 each appearing once

Level 2 What- if-Not for the attribute. What if the deck has numbers 1,2,3,4,5,6,7,8 and 9 each appearing twice? (Answer: 9,3,3; 7,4,4; 6,6,3; 7,7,1)

 Level 3 Asking questions. What hands are possible, each appearing twice, and Ivan has four cards that add to fifteen? (Answer: 9,4,1,1; 9,3,2,1; 8,3,3,1; 8,4,2,1; 8,5,1,1; 8,3,2,2; 7,6,1,1; 7,5,2,1; 7,4,3,1; 7,4,2,2; 7,3,3,2; 6,4,4,1; 6,5,3,1; 6,6,2,1; 6,5,2,2; 6,4,3,2; 5,5,3,2; 5,4,4,2; 5,4,3,3; 5,5,4,1; 5,4,3,3)

Level 4 Analyzing questions. The exercise deals with the decomposition of numbers for grades 1-2. What if the cards contained numbers up to only 7, could we still have summed up to fifteen? What highest possible number could have been formed? What if each number had appeared thrice, could we still have formed up to fifteen?