1. Zone 3: Magician’s Costume Problem Statement: For Sam the Magician’s next show, there will be a number of costume changes. Sam always wears a hat, a cape and a magic wand. He can choose from either a Black velvet or Red satin cape, a Top Hat or Beret, and a Silver or Gold wand. How many costume changes can Sam have?

2. Explicit teaching concepts Within a problem and through team planning consider –What strategies can be explicitly taught? –What are you looking for as students work through a problem? –How can the problem be modified or extended to provide for consolidation of key concepts? –Are there any similar problems? Problem Solving Strategies Act it out (role play) Draw a Picture Trial & Error Guess & Check Make a Model Make a Table Make a List Create a Rule Make a Chart or Graph Reduce the Problem Work Backwards Use Logic Re-write the problem

3. What strategies can be explicitly taught? Re-wording and looking for key information in mathematical text. Mathematical text is often compact – most words lend meaning to the problem. Visualisation: Changing words to pictures and symbols. Helps students through visual learning. Mathematics itself is a symbolic language. Concrete materials: Using objects, props etc and have students demonstrate or act out parts of a solution. Using tables and lists: The emphasis needs to be on systematically or logically developing a solution. Look for students who randomly arrive at answers.

4. Sam can choose from either a Black velvet or Red satin cape, a Top Hat or Beret, and a Silver or Gold wand. Use the pictures to make a list of all the different costumes This can be set-up on an interactive whiteboard, and using the ‘infinite cloner’ tool allows for duplication of objects. Very handy for grouping objects and compiling lists!

5. How many costume changes can Sam have? Cartesian Product:

6. How can the problem be extended? Sam buys a purple cape. Cartesian Product:

7. How can else can the problem be extended? Sam buys some black leather shoes and some red shoes. etc Cartesian Product:

8. Are there any similar problems? Checker Boards –You can choose any two colours from black, white and red. What’s possible? Coin Toss –A coin is flipped 3 times. What’s possible? Ham & Cheese –You can choose either white or brown bread, ham or chicken, and cheddar or cream cheese. What’s possible?