Do you want your older children to learn problem solving skills? While most homeschooling moms do, quality problem solving resources can be difficult to find beyond the elementary level. After all, very few math curricula spend a huge amount of time on problem solving, and not many helpful books are available.
However, there is an incredible resource, tucked away in the website of the University of Waterloo’s Center for Education in Mathematics and Computing (CEMC). For the past 50 years the CEMC has worked to promote students’ enjoyment of mathematics and to develop their problem solving skills. It is Canada’s largest math and computing outreach organization, reaching well over 100,000 students each year with its annual math competitions for grades 7-12. Since the late 90’s, it has posted both the tests and detailed solutions online.
These CEMC tests and solutions are a treasure trove of math problems at all levels of difficulty. Using only concepts common to all Canadian math curricula, most of the contest problems test logical thinking and mathematical problem solving rather than content. These tests are well-organized, error-free and have complete and thorough solutions. We have been using them for 8 years to give our children valuable math practice. Although our family uses them to prepare for the actual contests, they can also be used as a problem solving unit in math or for math-fun days.
One series of tests, the Gauss (grades 7 and 8), Pascal (grade 9), Cayley (grade 10), and Fermat (grade 11) tests, each feature 25 multiple choice questions worth 150 points, and are meant to be written in one hour. Each test is divided into an easy, a moderate, and a difficult section. All students should be able to do the easy questions but very few students can do all the difficult ones. In the actual competitions, almost no one achieves a perfect score.
The other series of tests our children have used are the Fryer (grade 9), Galois (grade 10), and Hypatia (grade 11) tests which include both long and short answer segments. Each 75-minute test is composed of four questions, worth 10 marks each, that have both simple and challenging aspects.
How do we use these great resources? Very simple. I just give our children an old test and ask them to see what they can do in the allotted time. Then we mark it and go over the solutions until we understand them. The solutions are written up so clearly that my children often do not need my help. The next day we do another test. Obviously, we do this at least once a year, twice if we’re doing the long answer tests as well as the multiple choice tests.
Usually our children encounter their lowest marks ever when they first try these tests, and this can be discouraging. It helps them to see that, world-wide, average scores hover around 60%. After a few weeks of intensive problem solving work, however, my children have typically learned how to think more logically and have greatly improved their scores as well as their confidence and math ability.
These free tests with their clear solutions and explanations are the best problem solving resource I’ve ever come across for teens. If you want your teens to learn problem solving, do check out the past CEMC Contests. If your teen is mathematically inclined, it may even be worth your while to organize a homeschool group to take these tests, especially if you live in Canada.
Note: The CEMC also hosts other math and computing competitions that we have not been involved in, and these contests and solutions are also posted online.
Disclosure: As usual, I am in no way compensated for telling you about this resource.
This post is linked to Trivium Tuesdays.