We spend a lot of time teaching students how to do mathematics.

We teach them how to solve systems of equations, graph functions, calculate statistics, and apply formulas. We give them opportunities to practice those skills and check whether they can get the correct answer.

But there’s another part of mathematical thinking that I think we sometimes overlook.

Do students know when to use the mathematics they’ve learned?

Think about the last math assignment you gave your students. How many mathematical decisions did they actually have to make?

And I don’t mean deciding whether to add or subtract a negative number correctly. I mean, did they have to decide what mathematics might help them solve the problem?

We accidentally make a lot of those decisions for students.

We title the worksheet “Systems of Equations.” We put it in the systems section of their notebook. We spend the lesson solving systems by elimination, and then we hand them a set of problems asking them to solve systems.

There’s not much mystery about which math they’re supposed to use.

And to be clear, students need that kind of practice. When they’re learning a new skill, I want them focused on understanding the mathematics and becoming comfortable using it.

But eventually, I want to remove some of those signposts.

I want students to encounter a situation and think, “What mathematics would actually help me figure this out?”

That’s a completely different skill. It’s also an important part of learning how to choose math strategies independently.

Stop Telling Students Which Math to Use

Think about how often we give students the mathematical strategy before they even begin solving a problem.

Sometimes it’s obvious. The worksheet title tells them exactly what to do. Other times, it’s a little more subtle. We’ve just finished a lesson on a particular concept, so students know the next assignment will probably involve that same skill.

Even when we’re using word problems, we’re often still giving students plenty of clues about which mathematics to use.

And again, that’s not necessarily a bad thing. Students need opportunities to practice specific skills before they can confidently apply them independently.

But if we want students to become stronger mathematical thinkers, we eventually need to give them opportunities to make those decisions themselves.

Choosing math strategies means recognizing what a situation is asking, identifying what information matters, and deciding which mathematical tools could help.

That’s different from simply following a procedure.

Outside of math class, problems don’t arrive with unit labels. Students need opportunities to practice recognizing when and why a particular mathematical strategy might be useful.

Give the Mathematics a Job

One of my favorite things about using projects in math is the opportunity to give mathematics a job.

Students aren’t solving something simply because I told them to solve it. They’re trying to figure something out.

They’re comparing, predicting, optimizing, designing, defending, or making a decision.

Think about systems of equations.

When we introduce systems, students often see two equations and are asked to find the point where they intersect. Mathematically, we know why that intersection matters. But students don’t necessarily have a reason to care about it yet.

Now imagine a different starting point.

You’re starting a business. You have expenses, costs, and revenue. You want to know how much you need to sell before you actually start making money.

Suddenly, that intersection has a job.

It’s your break-even point.

The mathematics hasn’t changed, but the reason for using it has.

Instead of finding an intersection because it’s the skill on today’s worksheet, students are using a system of equations to answer a question about a business.

That’s one of the things I love about meaningful math problems. They give students a reason to think about which strategies will help them reach a goal.

From Finding an Answer to Making a Decision

This is a distinction I want more math teachers to think about.

A lot of traditional math problems ask students to find an answer. But a really interesting mathematical experience often asks students to use an answer to make a decision.

Those are two different things.

If I ask students to calculate two values and tell me which is larger, there’s an answer.

But if I ask them to decide which option is better, they have to think about what “better” actually means.

Is it cheaper? Faster? More efficient? More profitable?

Better under which conditions?

Now there may be constraints, trade-offs, and multiple reasonable approaches.

Two students might even make different decisions using completely valid mathematics.

And I love when that happens.

The conversation moves beyond “What’s the answer?” and becomes “What evidence supports your decision?”

That’s where mathematical reasoning becomes so important.

Students aren’t just demonstrating that they can complete a calculation. They’re interpreting their results, evaluating their options, and using mathematics to explain and defend their thinking.

The answer is still important. But now students have to decide what to do with it.

What This Looks Like in the Classroom

One example I love is my Pitch Profit Systems of Equations Project.

Students create their own business, think through costs and revenue, build mathematical models, and use a system of equations to determine their break-even point.

But here’s what makes the experience interesting.

The system of equations isn’t the destination. It’s the tool students use to answer a question about their business.

Once they find their break-even point, they have to think about what that information actually means.

Let’s say their calculations show that they need to sell an absolutely ridiculous number of products before making a profit.

Their algebra might be completely correct.

But is their business model any good?

Should they change their price? Reduce a cost? Rethink their product?

Now students have an opportunity to use their mathematical results to make another decision.

They’re not just demonstrating that they can solve a system. They’re interpreting the solution, evaluating what it tells them, and deciding what to do next.

That’s a much richer experience than finding an intersection and moving on to the next problem.

It’s also a great example of how a real-world math project can help students connect mathematical procedures to actual problem-solving and decision-making.

We Don’t Need to Do This Every Day

Now, you know me well enough to know what I’m about to say.

Please don’t turn every math problem into an elaborate decision-making scenario.

Sometimes students need to solve the system. Sometimes they need to practice elimination ten times so the procedure becomes more comfortable and doesn’t take up all of their brain space.

Sometimes I need to know whether they can independently perform the skill.

That’s important too.

I’m not suggesting we stop teaching procedures or eliminate straightforward practice. Students need mathematical tools before they can make meaningful decisions with them.

But once those tools are available, I want to create opportunities where I stop telling students exactly which one to pick up.

Think about problems outside of math class.

Your bank account doesn’t announce that today’s problem requires an exponential function. A business doesn’t hand you a worksheet labeled “Systems of Equations” and ask you to use elimination.

Real-world problems give us information, constraints, and questions.

Then we decide what mathematics might help.

That process of choosing math strategies, applying them, and interpreting the results is a skill worth practicing too.

Start With One Question

You don’t need an elaborate project to start giving students more mathematical decisions.

Take something you’re already teaching and ask yourself:

What decision could someone make using this mathematics?

Here are a few ways to think about it:

• Linear equations: Which pricing plan makes the most sense under different conditions?
• Statistics: What conclusion is actually supported by the data?
• Geometry: Which design uses space or materials most efficiently?
• Quadratics: Which model best represents what happened, and what can we predict from it?
• Systems of equations: At what point does one option become better than another?

You don’t have to build an entire project around the question.

You can start with one decision.

And when students calculate something, don’t immediately move on to the next problem. Pause and ask:

• What does that number tell you?
• What would you do now?
• What would you recommend?
• What evidence supports that decision?

Those small questions can change what students are doing with the mathematics.

They’re no longer just completing a calculation. They’re interpreting the result and figuring out what it means.

And that’s one way we can build more mathematical reasoning and independent problem-solving into the lessons we’re already teaching.

If You’re Teaching Systems of Equations

If systems of equations are coming up in your pacing guide, my Pitch Profit Systems of Equations Project is built around exactly this idea.

Students create a business, develop cost and revenue models, determine their break-even point, and ultimately pitch their business.

The project gives students a reason to use systems of equations and an opportunity to do something with the answer they find.

I’ve already created the project structure and materials, so you don’t have to spend your weekend building the entire experience from scratch.

You can find the Pitch Profit Systems of Equations Project in my Teachers Pay Teachers store.

But whether you use Pitch Profit or create your own experience, I want you to look at your next unit through this lens.

We’re really good at teaching students how to do mathematics.

We also need to give them opportunities to decide when and why to use it.

So here’s something to think about as you plan your next lesson:

Where are you currently giving students an answer to find, and could you instead give them a decision to make?

Because when students have something worth deciding, mathematics becomes more than the thing they’re being asked to do.

It becomes the tool that helps them figure out what to do next.

Until next time, keep it real.

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