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Critical Thinking Lessons in Maths Trek

Maths Trek 17/2/25

Critical thinking is an invaluable skill and one that’s fostered throughout the Maths Trek program. Students will find plenty of opportunities to apply critical thinking skills to problem-solving tasks and investigations, but did you know Maths Trek also includes dedicated lessons to help you explicitly teach critical thinking? Let’s take a look at what the lessons are, when you’ll use them and where to find them.

What are the critical thinking lessons?

The critical thinking lessons are short and sharp lessons that focus a particular cognitive verb such as explain, prove, compare or justify. Cognitive verbs are common in extended maths problems and require students to provide an extra layer of reasoning to their worked solution. Essentially, cognitive verbs are an ideal prompt to help students draw out their critical thinking skills.

Each critical thinking lesson includes three key steps:

1. Define the cognitive verb
2. Discuss a real-life example
3. Model a maths example

Let’s see these steps in action using the Year 3 critical thinking lesson for the verb prove.

1. Define prove

Each cognitive verb is accompanied by a student-friendly definition and at least one accompanying hint to prompt the student.

Read and discuss the definition of prove to check for understanding.

to give evidence to show whether something is correct

Discuss the hint.

What evidence can you find?

2. Discuss a real-life example

Use the ready-made example* that uses the cognitive verb in a real-life context. For this step, it’s important to strip out the cognitive overload of any specific mathematical application and just focus on the word in a general and relatable scenario.

In this example you would discuss how we can prove that the duck left the footprints. Use the definition to help students prove their answer. Explain that a proof can sometimes involve eliminating all other options.

Once you’ve finished your class discussion (or if students are a little stuck) you can show the example answer provided.

Note: Examples in the lessons differ depending on the year level.

3. Model a maths example

Now it’s time to demonstrate the verb in the context of a maths problem.

In this maths example you would discuss what evidence we need to prove the coin is a 20c piece, and how we can show our proof. Explain that we need to show the 20c coin is the only coin that fits all conditions.

Again, once you’ve had your class discussion you can show the example answer to confirm your discussions and demonstrate a well-reasoned response.

When will I use the critical thinking lessons?

Investigations provide the perfect opportunity for students to reflect, reason and communicate their understanding of what they have discovered. For this reason, you will find the relevant critical thinking lesson embedded into the final step of the teaching sequence in every investigation for Years 1–6.

These succinct and relatable lessons can also be revisited anytime students need to revise and consolidate their understanding of cognitive verbs.

Where do I find the lessons?

Teachers can access these lessons in two ways: in the investigation unit using the embedded links, or from the Resource Links section on the year level home page.

While students do not have access to the complete lesson, they do have access to the critical thinking definitions as a helpful reminder of what common cognitive verbs mean and hints on how to use them when providing a well-reasoned solution.

So there you have it! The Maths Trek critical thinking lessons in a nutshell.

If you’re not yet using Maths Trek, sign up for a free trial so you can explore more of these critical thinking lessons firsthand. Or for a more in-depth look at how Maths Trek incorporates critical thinking contact your local Education Consultant to request one of our new Critical Thinking professional learning workshops.

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