Creating models to understand reality is at the core of mathematics, as is the ability to solve problems through those models and communicate the solutions to others in a way that can be understood by anyone.

With the students in Grade 7, we explored the topic of systems of linear equations through modeling and problem-solving activities. The problem we used to trigger the process was this:

“Tom and Henry deliver newspapers for different companies. Tom gets a basic salary of $4 plus $0.5 for each newspaper delivered, and Henry gets a basic salary of $6 plus $0.4 for each newspaper delivered. Who has the better payment?”

Breaking the tradition of problems with straight forward answers, students realized that it depends on the number of newspapers delivered. Using Microsoft Excel, they modeled both pay systems and discovered the point of intersection, where both earn the same amount. They also observed how, before and after that point, the “best payment” changes depending on the company.

Later, students used the simulation at ophysics.com to explore car races, observing how velocity, acceleration, and initial position affect motion graphs.

These activities strengthened their problem-solving abilities and improved communication skills, as they explained their reasoning, compared results, and presented conclusions using mathematical language and visual representations.

Through these virtual simulations, students experimented with various racing conditions that led one car to overtake another. As they changed the acceleration and velocity values, they could identify when graphs remained linear and when they became non-linear—creating a perfect opportunity to explain the difference between linear and non-linear relationships.

Conclusion

Modeling real-life situations not only deepened students’ understanding of systems of equations but also built essential skills for lifelong learning. By connecting abstract mathematical concepts to authentic contexts, students saw math as a meaningful language for describing and explaining the world. They became more independent thinkers, better communicators, and more capable problem solvers—ready to face new challenges with logic and creativity.