An Inside Look at How One Math Lesson Builds Strategy and Confidence

“I don’t know what to do.”

It’s a phrase you’ll hear many students say at the kitchen table while doing homework, or while staring at a test question. Not because they weren’t listening. Not even because they don’t know how to solve the problem. But because they don’t know which strategy to use.

Many students experience math as a collection of disconnected pieces: a formula here, a process there, each introduced one lesson at a time. Every idea may make sense in isolation, but students aren’t always shown how those ideas connect or when each one applies. Without that structure, every new problem can feel overwhelming. They’re left scrambling to determine which of the many things they’ve learned fits the question.

However, if students are given a clear method for approaching a problem, a way to sort what they see and choose a direction, that initial barrier begins to disappear. They’re no longer guessing which idea might work; they’re using a repeatable framework to determine the best approach.

In our sessions at Inquisia, we make that structure visible through a simple metaphor: math is a toolbox. Over time, students collect tools — formulas, strategies, and processes — and learn how those tools relate to one another. To show you how this looks in action, let me share an example from a Grade 10 trigonometry lesson.

Step 1: Make the Toolbox Visible

Students often don’t realize how much they already know, so before solving problems, we make that knowledge visible.

At the start of this lesson, we gave this student a table and asked them to fill in as much as they could remember about sine law, cosine law, and trigonometric ratios. The goal wasn’t perfection. It was to put their thinking on paper, however incomplete it might be.

	Sine Law	Cosine Law	Trigonometric Ratios
Formula
When do you use it?

This recall activity does two important things. It forces retrieval, strengthening long-term memory, and it organizes knowledge into categories, giving their thinking structure. Instead of isolated formulas, students see a defined set of tools.

Just as importantly, they recognize they are not starting from zero. The knowledge was already there; it simply needed organization. Once that foundation is visible, the next set of problems feels less like guesswork and more like building on something they already understand.

Step 2: Let Them Test Their Tools

Once the tools are visible, they’re ready to use them.

We gave this student three triangle problems that looked similar but required different strategies. Rather than telling them which formula to apply, I asked them to decide.

They chose a method and began substituting values. If the strategy fits, the solution progresses. If it doesn’t, it stalls. When that happens, we pause to examine why. We ask questions such as: What information is missing? What assumptions were made? What does this reveal about when this tool applies?

Here is where the lesson shifts from explanation to evaluation. Instead of memorizing rules about when to use sine law or cosine law, students see the conditions under which each method works. They also practice adjusting as they go. If a strategy fails, they reassess and select another. Learning to diagnose and correct in this way prevents them from feeling stuck when they’re working independently.

Step 3: Put The Model Together

After working through both problems, we returned to the original table. This time, we weren’t filling it in from memory; we were revising it based on what we had just discovered. What information was given in each problem? How did that determine which tool we used?

As we clarified those patterns, the chart shifted from a list of formulas to a guide for choosing a strategy.

This step makes the learning explicit. Students can see, in writing, how their understanding has changed over the course of a single lesson. The next time they face a similar problem, they think “Which tool fits?” instead of “I don’t know what to do.”

Step 4: Test the Understanding

To close the lesson, I gave a few more triangle problems. However, we didn’t ask them to solve them. Instead, we asked them to identify which tool they would use and why.

By removing the calculations, the focus shifts entirely to strategy selection. Students examine the information given and apply the decision-making framework we built to choose the appropriate method. If they can clearly justify their choice, it shows the structure is in place. And, they leave confident they will know what to do next time, not because the problems are easier, but because they have a repeatable way to approach them.

Moving Beyond Explanations

This single lesson isn’t just about using sine law, cosine law and trigonometric ratios. Students are usually familiar with those from class. Instead, it’s about elevating what they already know and clarifying when and why each strategy is appropriate.

That’s why traditional tutoring doesn’t always create the result we’re looking for. Students simply don’t need another explanation; they need a clear way to think about a problem.

When students understand what tools they have, how to evaluate a problem, and how to match it with the right tool, they no longer get stuck at the beginning thinking, “I don’t know what to do?” Instead, they begin with a different question: “Which of my tools fits best?”

And when students have a repeatable system to rely on, the math feels easier and they feel more confident they can do it on their own.