Problem Posing What If Not Glenn Waddell Jr
Problem Posing: What – If – Not? Glenn Waddell, Jr.
Why? : I have struggled to find a way to TEACH my teachers to create rich problems.
The Art of Problem Posing By Stephen I. Brown & Marion I. Walter
An example:
Level 1: Attributes 1. 2. 3. 4. 5. 6. Pot is a cylinder Pot has a diameter of 14 inches There is sauce in all but 2 inches of the pot Meatballs are spherical Meatballs are 2 inches in diameter Any others? Level 2: What-If-Not What if attribute 2 is not 14 but 18? What if attribute 4 is not spherical but square? Etc.
Now you try! 2 The problem: x + 6 x + 5 = 0 Level 1: Attributes 1. 2. 3. 4. 5. 6. 7. The exponent is an integer The degree is 2 There are 3 terms on left The solutions are integers The middle term > last term There is an equal sign There are two plus signs
The problem: 2 x + 6 x + 5 = 0 Level 2: What-If-Not What if attribute 4 is not known? 2 x + ? x + 5 = 0
2 x + ? x + 5 = 0 • Can you give 4 solutions that are integers? • Can you give 4 solutions that are NOT integers? • Can you give 4 solutions that are not real? • How does the graph reflect the different solutions? Can we generalize something about the different solutions?
The problem: 2 x + 6 x + 5 = 0 Level 2: What-If-Not What if attribute 2 is a 4? What else needs to change to keep the pattern? 4 x + 2 6 x +5=0
4 x + 2 6 x +5=0 Can we substitute something to simplify the problem? What if the exponents are not integers, but rational? (attribute 1) 1/4 x + 1/2 6 x +5=0
What – If – Not Substitution of values (what if it is not an x, but a 3? ) Exploring Conics (what if it is not a +, but a -? ) Exploring rational expressions / equations Truly creates a spirit of “this is a game” and wraps up with “What did you learn about ____? ”
- Slides: 12