Promoting Problem-Solving and Skill Development in the Intermediate Classroom (Grades 7–9)

Area(s) of Focus: math
Division(s): Intermediate
Level(s): Grade 7, Grade 8, Grade 9

Skill development and problem-solving were investigated with respect to the topic of fractions in grades 7 through 9.

The essence of mathematics is problem-solving. When students leave the school system, we hope to have imparted on them the cognitive skills needed to deal with new situations, analyze, make connections, reflect and refine, and to communicate effectively. All of these skills are contained in good problem-solving. Yet, to be an effective problem solver, there are always some base knowledge and skills that will be important for the task at hand. Traditional mathematics teaching, for the most part, focuses on mathematical skills with little time devoted to using those skills to solve interesting problems. These students have the mathematical tools, but don’t get the chance to use them. On the other hand, current trends in mathematics reform can lead to problem-rich classroom environments, without a lot of time dedicated to skill development and practice. These students get the chance to develop the cognitive skills, but lack the proficiency with the mathematical tools for the problems. In our project, we engaged students in rich problems, but we also identified essential mathematical skills and their level of proficiency. We had plans to allow students to identify their weaknesses and work on improving them.

Team Members

  • Shawn Godin

    Ottawa Carleton District School Board

  • Lynn Miller

    Ottawa Carleton District School Board

  • Jennifer Rogers-Kelly

    Ottawa Carleton District School Board

  • Joanne Bothwell

    Ottawa Carleton District School Board

Professional Learning Goals

As teachers, we were able to research and think deeply about one topic (fractions) across several grades (grades 7 through 9). As such, we were each forced to think about the topic outside of the grades we usually teach.

We also got to collaborate with teachers from another division and school. As such, we got valuable insight into “another world.”

We got to develop and modify tasks that could be used across multiple grades.

Activities and Resources

We spent our time researching, discussing and developing materials for parents, teachers and students. We used materials from the ministry, websites and several books (purchased by our schools).

Unexpected Challenges

When it came time to discuss and modify some of the problem-solving material, we didn’t make as much headway as we hoped. This is probably due to us underestimating the time it would take to develop the diagnostic material, and prepare the presentation for parents.

We also were disappointed with the time frame behind the project. When we applied in September, we were hoping to start in October, but it was late December before we got all the details.

Enhancing Student Learning and Development

As we started working, we saw that the size of our goal was larger than we thought, and it kept growing as we discussed things and gathered materials. Using the adapted gap-closing materials, we could help identify any areas that students are struggling with, and use the gap-closing materials to address the problems.

Thinking about parents, and looking at ways to help parents learn how their children are learning, will pay dividends down the road.

Developing rich problems will help students strengthen their understanding of the concepts.

One of us has just started the fractions unit and plans to use the material with her students.


We have already shared some with parents at Heritage PS. We had an information night and presented some of the ideas and give parents time to work with manipulatives. In the future, we plan to have other “family math” nights, to help get parents more comfortable with the teaching/learning methods their students are exposed to.

We hope to do a presentation at a PD day next year at the OCDSB.

Project Evaluation

I think the project was a successful start to a long-term collaboration between two schools. We came to an understanding of the importance of having good material for students to work at school, at home and with their parents. We see our next steps as continuing to develop materials for teachers, students and parents.

Resources Used

Van De Walle, John. Elementary and Middle School Mathematics: Teaching Developmentally, ISBN: 9780801332531

Small, Marian. Uncomplicating Fractions K-7, 9780807754856

Gap-closing material from Edugains website (specifically the fractions materials from both the junior and intermediate sections).

The Math Edugains site in general.

The Leading Math Success website (in particular the TIPS4RM fraction continuum).

The CLIPS website (in particular the fractions lessons and e-practice).

Ontario Ministry of Education. The Ontario Curriculum Grades 1-8: Mathematics.

Ontario Ministry of Education. The Ontario Curriculum Grades 9 and 10: Mathematics.

We ordered a number of materials (free) from Service Ontario Publications. We got all the gap-closing materials for all the members of the team as well as a number of other mathematics resources.