P ROBLEM S OLVING – T HE H EART AND S OUL OF M ATHEMATICS David McKillop, Consultant Pearson Education Canada

M ATHEMATICAL P ROFICIENCY

W HAT IS MEANT BY T EACHING A BOUT P ROBLEM S OLVING ?

P OLYA ’ S P ROBLEM - SOLVING P ROCESS

U NDERSTANDING THE P ROBLEM What information are you given? What are you asked to find or show? Can you restate the problem in your own words? Can you think of a picture or a diagram that might help you understand the problem?

U NDERSTANDING THE P ROBLEM : T HE T HREE -R EAD S TRATEGY At your tables, read and discuss the Three-Read Strategy handout.

U NDERSTANDING THE P ROBLEM : K-W-C K: What do I K now for sure? W: What do I Want to do, figure out, find out? C: Are there any special Conditions, rules, or tricks I have to watch out for?

Five hundred people are lined up outside the Apple Store by 7 am. Since the store doesn’t open for an hour, three of the staff at the store decide to distribute an iPhone brochure to every 2 nd person in line, an iPad brochure to every 5 th person in line, and a gift certificate to every 7 th person in line. If they all start distributing at the head of the line, how many people in line get all three things?

Braid Model of Problem Solving

P OLYA ’ S Devising a Strategy  How will each piece of information contribute to finding what I am looking for?  Is some information not relevant?  What should I do first? Second?