zone 3: magician’s costume problem statement: for sam the magician’s next show, there will be a...
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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?
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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
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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.
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• 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!
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How many costume changes can Sam have?
Cartesian Product:
€
2 × 2 × 2 = 8
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How can the problem be extended?• Sam buys a purple cape.
Cartesian Product:
€
3 × 2 × 2 =12
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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
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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?