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.
Problem Solving with the
Mathematical Processes in Mind
Deck Problem
Will different decks require the same
amount of railing? Explain.
І
DECK
=
І
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.
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.
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 Strategies
Graphical Representation
Numerical Representation
Short
Edge
Long
Edge
1
2
3
4
6
8
24.5
13
9.5
8
7
7
Concrete Representation
Algebraic Representation
2xy – x2 = 48
y
48  x 2
2x
Cottage
Deck Problem: Tiles
Even Number of
Tiles Remaining
Perfect Square
Number
Cottage
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 = 180
240 m2
A2 = 60 m2
Problem Solving Across the Grades
A = 180 m2
A1=
120 m2
A = 240 m2
x = 12Am2= 2
60 m
A = 180 m2
x=6m
Problem Solving Strategies:

Use concrete manipulation
(cut and paste)
 Use logic
Note
Students cut the shape into 2 pieces along ML line and verify by finding congruent areas on each side
(as shown by the checked, striped, and dotted shapes). They check remaining areas by counting squares
(approximately 8 12 grid squares remaining in each section).
<<Click to next slide>>
H
12 cm
(6  x )(20) <<Click to next slide>>

2

x + y = 30
20y
2
A1 = A2
...
y=x+6
Problem Solving Across
the Grades
y=x+6
( 12, 18)
y = 30 - x
x = 12
and y = 18
Problem Solving Across the Grades
3
3
15 m
15 m
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.