Problem Solving and the Ontario Curriculum
The set of skills our children need today extends beyond the traditional paper and pencil calculation
skills that dominated mathematics instruction that most parents remember. In addition to having a good
understanding of number facts and the ability to work with numbers, there are other important skills
such as reasoning, problem solving and the communication of mathematical ideas that are also essential
in the twenty-first century. For example, students need experience with making estimates, deciding on
and adjusting their strategies, persevering through to a solution, and justifying their thinking. The
Ontario Curriculum; Mathematics, Grades 1-8 (2005) supports the development of this mathematical
thinking in a way that is meaningful and relevant to students.
You can help your child to become a confident math problem solver by demonstrating persistence and a
willingness to try multiple strategies or ideas. Also, talking through these challenges will help your child
to develop his/her ability to improve communication skills and the development of math vocabulary. Be
sure to encourage the use of concrete materials (e.g., coins, counters, shapes) as well as visuals (e.g.,
making a chart, drawing a diagram) when working through these math tasks.
There are five strands in the Ontario Curriculum:
Number Sense and Numeration
Geometry
Data Management and Probability
Measurement
Patterning and Algebra
In addition, there are 7 Mathematical Process Expectations which permeate the curriculum:
Problem Solving
Reasoning and Proving
Reflecting
Selecting Tools and Computational Strategies
Connecting
Representing
Communicating
For more information on the Ontario Mathematics Curriculum visit:
http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf
The challenges for this week are focused on skills found within the Patterning and Algebra
Strand. Specifically, the junior expectations include:
Grade Four:
 Connect each term in a growing or shrinking pattern with its term number and record
the patterns in a table of values that shows the term number and and the term
Grade Five:
 Build a model to represent a number pattern represented in a table of value that shows
the term number and term value
Grade Six:
 Determine a term, given its term number, by extending growing and shrinking patterns
that are generated by adding or subtracting a constant, or multiplying or dividing by a
constant, to get the next term
Here are the junior math problem solving challenges for this week:
Grade Four
*Create a table of values to represent the above pattern. Describe the pattern using numbers and
words. What is the 7th term? How do you know?
Represent this same pattern in a different way.
Think about:
What language can I use to describe the pattern (e.g., shrinking, growing, repeating)?
How can I show this same pattern in a different way?
*Note to Parents – A Table of Values is a chart which shows the pattern data in a manner which
helps students to see relationships between the Term Number (e.g., first pattern example
shown above) and the Term Value (e.g., the number of corresponding blocks related to a term
number).
Grade Five
Use manipulatives (e.g., items such as toothpicks, coloured blocks) to build models which represent the
number pattern below:
Term Number
1
2
3
4
5
Term Value
1
4
7
10
?
If the pattern is extended, what is the value of the 20th term? How do you know?
Think about:
How can I describe the relationship between the term number and term value?
*Grade Six
Two patterns are shown below:
If both patterns continue in the same way, which pattern will reach a term with a value of
23 first?
Justify your answer.
Think about:
How can I organize my work effectively to communicate my answer?
How can I prove that my answer is correct?
This grade six question is taken from the released 2013 – 2014 EQAO Assessment questions and
is an example of the problem solving questions our grade six students will be asked to solve
during EQAO.
Try this problem with your child and afterwards take a look at the two sample responses below.
These do not represent the only way to show the answer, but do provide examples of student
responses at level three and level four.
Level 3 Response
Level 4 Response