teaching through the mathematical processes session 2: problem solving with the mathematical...
TRANSCRIPT
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
Mathematical Processes
Mathematical Processes
Mathematical Processes
Exploring Mathematical Processes
Individually, explore the Mathematical Processes package with particular attention to a “different” process from what you studied earlier.
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
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.
DECK
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=
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
Problem Solving with the Mathematical Processes in Mind
Trapezoid ProblemThree 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.
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.
Deck Problem: Multiple StrategiesGraphical Representation
ShortEdge
Long Edge
1
2
3
4
6
8
24.5
13
9.5
8
7
7
Numerical Representation
Algebraic Representation
Concrete Representation
2xy – x2 = 48x
xy
2
48 2
Cottage
Deck Problem: Tiles
Cottage
Perfect SquareNumber
Even Number of Tiles Remaining
48 – 12 = 47
48 – 22 = 44
48 – 32 = 37
48 – 42 = 32
48 – 52 = 23
48 – 62 = 12
Problem Solving Across the Grades
A1=120 m2
A = 240 m2
A2 = 60 m2
A = 180 m2
Problem Solving Across the Grades
A2=60 m2
A = 240 m2
A = 180 m2
A = 180 m2
x = 12 m x = 6 m
A1=120 m2
12 cmH
<<Click to next slide>>
x + y = 30
2
)20)(x6(
2
y20
A1 = A2
. . .
y = x + 6
<<Click to next slide>>
y = 30 - x
y = x + 6
( 12, 18)
Problem Solving Across the Grades
x = 12 and y = 18
Problem Solving Across the Grades
15 m 15 m
3 3
Problem Solving Across the Grades
18 cm
Problem Solving Across the Grades
Problem Solving Across the Grades
Discuss
How did solving this problem in more than one way encourage and promote the use of different Mathematical Processes?
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.