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 Number Sense and
Numeration Strand. Specifically, the intermediate expectations are as follows:
Grade Seven:
 Represent perfect squares and square roots using a variety of tools
Grade Eight:

Estimate, and verify, using a calculator, the positive square roots of whole numbers, and
distinguish between whole numbers that have whole-number square roots and those
that do not
Grade Seven (Use the chart provided)
A prime number is a whole number greater than 1 which that only has two factors, itself and 1 (e.g., 7
only has factors of 1 and 7).
A composite number is a number that has factors in addition to 1 and itself (e.g., 8 has four factors
including 1, 2, 4, and 8).
A perfect square is a number that can be expressed as the product of two identical natural number
(e.g., 9 = 3 X 3 and therefore 9 is a perfect square).
Use the chart provided to investigate patterns in prime numbers and perfect squares.
Think about:
What patterns do I see on the chart?
How can I describe these patterns?
Grade Eight
*A palindrome is a number which is the same when read from left to right and right to left. The
number 14 641 and its square root of 121 are palindromes. Find other examples of numbers which are
palindromes and also have square roots which are palindromes.
Think about:
How can I organize my answer to prove that my examples show palindromes?
*Based on problem from Nelson Mathematics 8
http://www.edugains.ca/resources/LearningMaterials/
TIPS/tips4rm/grade7/Unit1_Celebrating7.pdf