One Question, Many Paths

In math, there’s often more than one way to reach the answer, but the magic happens when students realize it for themselves.

It was a Grade 8 algebra lesson on solving linear equations.

The question on the board was simple enough:
Solve 3x + 5 = 14.

I expected everyone to work quickly and take neat steps. But as I walked around the room, I saw something unexpected: three completely different solution methods.

One student subtracted 5 from both sides first, the classic approach.😀

Another divided through by 3 first, a less common but still correct method.😇

And one quietly guessed and checked numbers until she landed on the right one.😎

Usually, I might have stepped in to “standardize” the process, but that day I paused. Instead, I invited all three students to the board and asked them to explain their thinking.

It was eye-opening. 👀

Students began to see that math is less about memorizing “the right way” and more about understanding the relationships between numbers.

We discussed efficiency, clarity, and the methods that might work best in more complex problems.

I realized that giving space for multiple methods not only boosted confidence but also reduced the fear of making mistakes because students saw that there isn’t always just one narrow path to success.

Encouraging multiple solution paths builds flexible thinkers. It lets students approach problems with their own strengths, and it validates the idea that creativity exists in math, too.

In math, the destination matters, but sometimes, the journey is the lesson.

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