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 PictureTrial & ErrorGuess & CheckMake a ModelMake a TableMake a ListCreate a RuleMake a Chart or

GraphReduce the

ProblemWork BackwardsUse LogicRe-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:

€

2 × 2 × 2 = 8

How can the problem be extended?• Sam buys a purple cape.

Cartesian Product:

€

3 × 2 × 2 =12

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

etc

etc

Cartesian Product:

€

3 × 2 × 2 × 2 = 24

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?