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

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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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Mathematical Processes

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

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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

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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.

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DECK = = І І Problem Solving with the Mathematical Processes in Mind COTTAGE 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. Deck Problem

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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.

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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.

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Deck Problem: Multiple Strategies Graphical Representation Short Edge Long Edge Numerical Representation Algebraic Representation Concrete Representation 2xy – x 2 = 48 Cottage

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Deck Problem: Tiles Cottage Perfect Square Number Even Number of Tiles Remaining 48 – 1 2 = – 2 2 = – 3 2 = – 4 2 = – 5 2 = – 6 2 = 12

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Problem Solving Across the Grades A 1 = 120 m 2 A = 240 m 2 A 2 = 60 m 2 A = 180 m 2

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Problem Solving Across the Grades A 2 = 60 m 2 A = 240 m 2 A = 180 m 2 x = 12 mx = 6 m A 1 = 120 m 2

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12 cm H >

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x + y = 30A 1 = A 2... y = x + 6 >

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

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Problem Solving Across the Grades 15 m 3 3

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Problem Solving Across the Grades 18 cm

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Problem Solving Across the Grades

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

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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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