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?

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

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.

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!

How many costume changes can Sam have? Cartesian Product:

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

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

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?