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Situation: Match Stick Stairs

Situation: Match Stick Stairs. By  (Cor) 2 an. A Square Match Stick Unit. Suppose a square match stick unit is defined to be a square with one match stick per side. A Track of Square Match Stick Units. A track of two square match stick units would look like this.

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Situation: Match Stick Stairs

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  1. Situation: Match Stick Stairs By (Cor)2an

  2. A Square Match Stick Unit • Suppose a square match stick unit is defined to be a square with one match stick per side.

  3. A Track of Square Match Stick Units • A track of two square match stick units would look like this. • A track of three square match stick units would look like this.

  4. Problem • How many match sticks would you need to create a track of 500 square match stick units?

  5. What Problem Solving Strategies Can You Try? • Simplify the problem. • Make a table. • Look for a pattern. • Make a generalization. • Describe a function.

  6. Simplify the Problem • How many match sticks does it take to make 1 square? • How many match sticks does it take to make 2 squares? • How many match sticks does it take to make 3 squares? • How many match sticks does it take to make 4 squares?

  7. Make a Chart

  8. Look for a Pattern: Deconstruct the Information in the Chart

  9. Make a Generalization

  10. Create a Function • f(n)=4+3(n-1) or f(n)=3n+1 where n represents the number of squares and f(n) represents the number of match sticks.

  11. Solution to Problem • It would take 1501 match sticks to create a track of 500 squares. f(n) = 3n+1  f(500) = 3x500+1 = 1501

  12. Steps in Investigating • Understanding. What is the investigation asking? • Strategies that lead to mathematical conjecture. How? • Generalisations. What I have discovered? • Justification. Prove it! • Communication. Tell the world.

  13. Situation • Stairs made with matches:

  14. Steps to follow: ONE • Understanding. What things could we consider? • Number of matches.Length of stair case.Height of stair case.Number of squares.Etc.

  15. Steps to follow: TWO • Explore and begin to develop strategy. • Let’s examine more closely links or patterns with numbers of matches.length of stair case,height of stair case,number of squares,Etc. • Conjecture ?

  16. Maybe Draw a Table:

  17. Look for patterns:

  18. Steps to follow: THREEConjecture/Generalisation

  19. Steps to follow: FOURJustify or Prove for all cases.

  20. Steps to follow: FOURJustify or Prove for all cases.

  21. Another Table:

  22. Look for patterns:

  23. Steps to follow: THREEConjecture/Generalisation

  24. Steps to follow: FOURJustify or Prove for all cases.

  25. Steps to follow: FOURJustify or Prove for all cases.

  26. Match Stick Triangles ? • Here is a triangle made of 3 match sticks. • A track of two triangles looks like this. • A track of three triangles looks like this.

  27. Steps to follow: FIVEWritten Report • Strategies explored. • Data representation. Tables, graphs, diagrams. • Generalisations and/or mathematical formulae. • Justification. • Logical, Neat, Clear & Concise.

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