Problem Solving Blog

Welcome back to the Problem Solving Club! If you've ever seen your students blaze through worksheet problems but freeze up the moment they don't know exactly what to do… this post is for you.
Let's talk about two kinds of maths problems: routine and non-routine. The names sound simple, but the difference they make in your classroom is anything but.

🚚 Let's Start with a Food Truck

Introducing our very first Problem of the Week at Problem Solving Club:

The Problem:
Two food trucks are catering at a festival.
Truck A can serve lunch to 160 people in 4 hours.
Truck B can serve the same number in 2.5 hours.
If they work together at full speed, how long will it take to serve 160 people?
Have you tried it yet? Have your students? Shared your strategy?
This is a non-routine problem, it's unfamiliar, a bit puzzling, and most students won't instantly know what to do. That's the point.
Let's see what a routine version of the same context might look like:

Routine version:
Truck A serves 40 people per hour. How many people will it serve in 3 hours?
Truck B serves 64 people per hour. How many does it serve in 5 hours?

Here, students apply known procedures, multiplication, division, interpreting rates. These are still important skills, and we definitely want students to be fluent in them.

But in the non-routine version, those same skills are still needed, but students now need to:
• Decide how to begin
• Combine rates
• Model and test ideas
• Make sense of context
• Justify solutions
And if you take the thinking further…

Stretch it:
What if there are 200 people? What about 500? What's the cheapest way to do it if Truck A costs less per hour?

Now we need to find generalisations. Does our strategy for work for every situation? This is mathematical thinking!

As one of my favourite papers, Adding it up (2001) puts it…

""Routine problems are problems that the learner knows how to solve based on past experience. When confronted with a routine problem, the learner knows a correct solution method and is able to apply it. Routine problems require reproductive thinking; the learner needs only to reproduce and apply a known solution procedure. For example, finding the product of 567 and 46 is a routine problem for most adults because they know what to do and how to do it.

In contrast, nonroutine problems are problems for which the learner does not immediately know a usable solution method. Nonroutine problems require productive thinking because the learner needs to invent a way to understand and solve the problem.""

It's Not Just About the Answer
Here's what makes non-routine problems so powerful:
• They build flexibility – there's no single path to the solution, so students try things, revise, and learn from what doesn't work.
• They foster collaboration – students compare strategies and reasoning, see multiple ways of thinking, and learn to communicate ideas clearly.
• They spark curiosity – there's a bit of mystery and experimentation involved. The challenge becomes something to figure out, not just a question to answer.

And yes, students still need their routine skills to attempt these problems: unit rates, multiplication, division, proportional reasoning, time, etc. But the thinking they do with them is what makes the learning powerful.

Strategies students might use
When solving non-routine problems, you might see students:
• Draw a diagram
• Use guess and check
• Make a table
• Work backwards
• Look for patterns
• Simplify the numbers
• Act it out

There are many more. And often, students invent new ones and that's what makes non-routine problem solving so rich. At times you might see that one of these strategies are not used and need to do some explicit teaching after the problem to support them with a way forward.

So, next time you're designing a task, try giving it a little twist. Keep the skills but open up the thinking. You might be amazed what your students come up with!


Problem Solving Club ✨

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References
National Research Council. (2001). Adding It Up: Helping Children Learn Mathematics. Washington, DC: The National Academies Press. https://doi.org/10.17226/9822.

Where curiosity meets challenge and every learner can think and work like a Mathematician.

Hi, I'm glad you're here.

I'm an Australian educator, working with Teachers to improve outcomes in mathematics across my state. However, this improvement moves beyond simply acquiring knowledge, but also to building the capabilities to think and work like a mathematician, and develop a productive disposition towards mathematics.

In my work with teachers, I've seen a common challenge: we all want students to think deeply, to get curious, to problem-solve, but when it comes to designing non-routine tasks, the kind that truly stretch thinking, it's hard to know where to start.

Too often, classroom problems are either too scaffolded or too familiar. What's missing is that messy, uncertain space where students don't immediately know what to do, where they're forced to try a strategy, test an idea, backtrack, talk it through and try again. That's the space where they start thinking and working like mathematicians.

That's why this site exists.

What is the Problem Solving Club?

is a place to explore problems that put us in that uncertain space, where we need to think of a way forward when the path isn't obvious. Every week, we post a new non-routine mathematics challenge. These aren't about speed or procedures, they're about reasoning, flexibility, perseverance and creativity. Each week, we will explore the nature of problem solving a little further and the pedagogical strategies that support it.

On this site, people can:

• Submit their solutions with a photo of their thinking
• See how others approached the same problem differently
• Be part of a growing community of thinkers

We'll also share regular blog posts and updates on the upcoming Problem Solving Cards, designed to help students reflect, seek support, challenge themselves and try new strategies, right in the moment they need it. These will be an excellent student and teacher resource, with tips for teachers on how they can be used to support the development of metacognition and problem-solving strategies.

Why now?

According to the OECD, "in a rapidly changing world, students need more than just the reproduction of routine knowledge, they need the ability to think creatively, collaborate and solve problems in unfamiliar situations."

Mathematics should be a space to practise exactly that, not just learning about mathematics, but learning how to think and work mathematically. Problem solving is not a gift some have and others don't. It's a habit. It's something we build by doing. It's something we develop the dispositions for and from. And it's for everyone.

This is your invitation to think, to try, to get it wrong and try again. can be accessed by teachers, students and parents and we welcome all stages of thinking.

Thanks for being here, I look forward to seeing your thinking come to life.



Problem Solving Club ✨

References:
OECD (2018) The Future of Education and Skills: Education 2030 – The OECD Learning Compass 2030. Paris: Organisation for Economic Co-operation and Development. Available at: https://www.oecd.org/education/2030-project/ (Accessed: 1 June 2025).