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Teaching through the Mathematical Processes

Teaching through the Mathematical Processes. Session 2: Problem Solving with the Mathematical Processes in Mind. Find Someone Who. Find someone in the group who satisfies a criteria on the card. Each square must have a different name. First BINGO - diagonals Second BINGO – full card.

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Teaching through the Mathematical Processes

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  1. Teaching through the Mathematical Processes Session 2: Problem Solving with the Mathematical Processes in Mind

  2. Find Someone Who . . . • Find someone in the group who satisfies a criteria on the card. • Each square must have a different name. • First BINGO - diagonals • Second BINGO – full card

  3. Mathematical Processes

  4. Mathematical Processes

  5. Mathematical Processes

  6. Exploring Mathematical Processes Individually, explore the Mathematical Processes package with particular attention to a “different” process from what you studied earlier.

  7. Big Idea is Problem Solving Problem solving forms the basis of effective mathematics programs and should be the mainstay of mathematical instruction. The Ontario Curriculum Grades 1 – 8, Mathematics,Revised 2005

  8. Problem Solving with the Mathematical Processes in Mind • With your partner(s) select one of the given problems to solve. • Ask questions using the Mathematical Process package prompts. • Note when a Mathematical Process is being used.

  9. І DECK = І COTTAGE = Problem Solving with the Mathematical Processes in Mind Deck Problem You have been hired to build a deck attached the second floor of a cottage using 48 prefabricated 1m x 1m sections. Determine the dimensions of at least 2 decks that can be built in the configuration shown. Will different decks require the same amount of railing? Explain.

  10. Problem Solving with the Mathematical Processes in Mind Trapezoid Problem Three employees are hired to tar a rectangular parking lot of dimensions 20 m by 30 m. The first employee tars one piece and leaves the remaining shape, shown below, for the other 2 employees to tar equal shares. Show how they can share the job. Justify your answer.

  11. Problem Solving with the Mathematical Processes in Mind • Revisit the problem. • Solve the problem in two more different ways: - ask questions using the Mathematical Process package prompts - note when a Mathematical Process is being used.

  12. Cottage Deck Problem: Multiple Strategies Numerical Representation Graphical Representation Concrete Representation Algebraic Representation 2xy – x2 = 48

  13. Even Number of Tiles Remaining Perfect Square Number Cottage Deck Problem: Tiles 48 – 12 = 47 48 – 22 = 44 48 – 32 = 37 48 – 42 = 32 48 – 52 = 23 48 – 62 = 12

  14. Problem Solving Across the Grades A1=120 m2 A= 180 m2 A= 240 m2 A2 = 60 m2

  15. Problem Solving Across the Grades A= 180 m2 A1=120 m2 A= 240 m2 A= 180 m2 A2=60 m2 x = 12 m x = 6 m

  16. 12 cm <<Click to next slide>> H

  17. <<Click to next slide>> x + y = 30 A1 = A2 . . . y = x + 6

  18. ( 12, 18) Problem Solving Across the Grades y = x + 6 x = 12 and y = 18 y = 30 - x

  19. Problem Solving Across the Grades 3 3 15 m 15 m

  20. Problem Solving Across the Grades 18 cm

  21. Problem Solving Across the Grades

  22. Problem Solving Across the Grades

  23. Discuss How did solving this problem in more than one way encourage and promote the use of different Mathematical Processes?

  24. Home Activity • Reflection Journal: Write about the interconnectivity of the Mathematical Processes and problem solving. • Investigate other ways to solve the problem you were given.

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