teaching through the mathematical processes session 2: problem solving with the mathematical...

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

=

=

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.