How Kids Benefit from Exploring Multiple Strategies to Solve the Same Math Problem

Too often, kids rely on a single, memorized strategy to solve a math problem. 

If it doesn’t work, they get stuck or frustrated. But when they explore different approaches, like drawing a model, breaking numbers apart, or using a number line, they begin to break out of memorization into true understanding. 

Along the way, they become flexible thinkers who can adapt, reason, and problem-solve with confidence—skills that will serve them well in the elementary and middle school years and far beyond the classroom!

We’ve created a parent-friendly overview of what multiple strategies look like, why they matter, and how parents can support this mindset at home. We’ll also show how Mathnasium helps students not just learn math but truly understand it.

What Do We Mean by Multiple Math Strategies?

When we talk about multiple math strategies, we don’t mean giving kids a list of steps to memorize. We’re talking about empowering them to approach the same problem from different angles, perhaps using a number line, drawing a model, breaking apart numbers, or even inventing their own method.

For example, let’s take a simple problem: 18 × 4. 

• One student might use repeated addition (18 + 18 + 18 + 18). 

• Another might break it apart into (10 × 4) + (8 × 4). 

• A third might draw an area model to visualize the problem. 

Each strategy works, and each reveals something different about how that student understands multiplication.

Students who can solve problems in more than one way demonstrate flexible math thinking—the ability to choose, adapt, or even invent strategies based on what makes sense in the moment. This is at the heart of problem-solving, not just in math class but in life.

We know that when children explore multiple strategies, they become better at identifying errors, selecting efficient methods, and understanding how math ideas connect. 

For instance, a classroom-based study found that students who compared different approaches developed a better grasp of underlying concepts and were more flexible and efficient in their problem solving.

In short, multiple strategies help kids think more mathematically.

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The Catch: Why Multiple Math Strategies Need Comparison and Discussion

Teaching kids multiple strategies is a great start. But the real learning happens when they compare those strategies and talk about what makes them work.

Let’s say two students solve the same subtraction problem:

• One uses a number line and counts up from the smaller number.

• Another subtracts by place value, breaking the problem into easier parts.

Each strategy is valid. But what happens when we ask, “Which one is faster?” or “Which one helped you understand the problem better?” That’s when students begin to think critically, focusing on how they do math.

This process of comparison builds something powerful: mathematical reasoning. As students begin to reflect on different approaches, they start to see patterns, relationships, and efficiencies. Gradually, they begin to choose strategies purposefully instead of randomly.

Of course, developing this skill requires guidance. 

Without structure, comparing strategies can feel scattered or even confusing, particularly for students who are struggling with math. That’s where thoughtful instruction comes in. 

At Mathnasium, for instance, tutors guide students through strategy comparisons using targeted questions and interactive examples. We anticipate which approaches are likely to surface, sequence them intentionally, and help students make the connections that lead to real understanding.

So while it’s tempting to celebrate variety for its own sake, the real goal is connection. 

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Mathnasium tutors use everyday examples to bring math concepts to life and explore them from different angles.

Flexible Math Thinking in Action

So what does this look like in real life?

Let’s say a 3rd grader is solving 18 × 4. They might:

• Use repeated addition: 18 + 18 + 18 + 18

• Break apart the problem: (10 × 4) + (8 × 4)

• Draw an area model to visualize two rectangles side by side

Each method works. But when the student explains their thinking or compares their strategy to a classmate’s, they begin to understand why they work. As we’ve seen earlier, that’s where flexible math thinking really starts to grow.

Or take a 5th grader adding \(\Large\frac{3}{4}\) +\(\Large\frac{2}{5}\) .

They might:

• Convert both to common denominators

• Use a visual model like a bar or circle diagram

• Estimate both to get a ballpark answer first, then calculate precisely

When students learn multiple strategies like these, they’re making choices, evaluating their own understanding, and adjusting their approach as needed. As you can imagine, these skills will serve them in the classroom and everyday life!

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How Parents Can Encourage Multiple Strategies at Home

You don’t need to be a math teacher to support flexible thinking. In fact, the most meaningful thing parents can do is normalize the idea that there’s more than one way to solve a problem.

Here are a few simple ways to make that happen at home:

• Ask open-ended questions: Try: “Is there another way you could solve this?” or “Can you show me how you thought about it?” Questions like these invite kids to reflect, experiment, and explain, rather than fixate on the answer.

• Celebrate math conversations: Even if your child gets the wrong answer at first, focus on the thinking behind it. “That’s an interesting way to solve it; can we try a different strategy and compare?” These moments help build confidence and curiosity.

• Use visual tools and real-life objects: A number line, a pizza, a pile of coins—these can all be jumping-off points for talking through different approaches. Visuals support kids who may struggle to follow symbolic or abstract methods right away.

Most importantly, avoid rushing to the “fastest” method. Sometimes students feel pressured to pick the one right way, especially if they’re used to timed tests or worksheets. But in the long run, the ability to explore and compare strategies leads to stronger, more independent problem solvers.

Flexible math thinking grows over time, and your encouragement plays a big role. When kids see that math isn’t about speed but about sense-making, they start to feel more ownership of their learning.

Mathnasium is a math-only learning center committed to helping students truly understand and even enjoy math.

How Mathnasium Builds Flexible Problem Solvers

At Mathnasium, we believe math should make sense. We help students discover strategies that feel intuitive to them and guide them to understand how and why those strategies work.

Using our proprietary teaching approach, the Mathnasium Method™, tutors create personalized learning plans based on each student’s assessment results. 

From there, we introduce new concepts through a mix of mental, visual, verbal, tactile, and written strategies, adjusting our instruction to each student’s learning style to help concepts click.

In a typical Mathnasium session, a student might solve a problem using a familiar method, then be encouraged to try a different strategy. 

Tutors lead these moments with care, asking thoughtful questions, prompting comparisons, and guiding students to explain their thinking. As a result, students begin to recognize which strategies work best for them and why.

Whether in person or online, all Mathnasium students receive live, face-to-face instruction in a caring and fun group environment. Our goal isn’t just to help kids get the right answers but to help them develop confidence, curiosity, and flexible math thinking.

Mathnasium operates over 1,100 centers nationwide, serving families across the country. For families in Frisco and Plano, TX, Mathnasium of Frisco East has become a trusted local resource, known for its excellent results and strong community reputation. With over 100 five-star Google reviews and multiple Reader’s Choice Awards from Living Magazine, it’s been recognized for:

• Best Tutoring (2022)

• Best Early Education (2023)

• Best Tutoring and Best Summer Camp (2024)

Book a free assessment at Mathnasium of Frisco East today.

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