Initial state of the game

The link to the game be found here.

Description

The game in progress

Building Critical Thinking through Square Town

How can a simple activity involving squares encourage students to think more deeply about numbers?

Square Town is a two-player mathematics game that helps students explore how numbers can be composed and decomposed. One player selects a target number of squares, while the other uses the split and merge functions to construct the required number before submitting the answer.

Although the task may appear straightforward, students engage in several important critical-thinking processes as they play.

Analysing the Problem

Students must first understand the target and examine the arrangement of squares available. Instead of immediately clicking the controls, they need to consider:

• How many squares are required?

• How many squares are currently shown?

• Which groups should be split or merged?

This encourages students to identify relevant information and understand the relationship between the current arrangement and the intended outcome.

Breaking Numbers into Parts

The split function allows students to see that a number can be broken into smaller parts, while the merge function shows how smaller quantities can be combined to form a whole.

For example, students may recognise that eight squares can be represented as:

• 4 and 4

• 5 and 3

• 6 and 2

• 4, 2 and 2

Students are therefore not merely counting individual squares. They are considering different number combinations and strengthening their understanding of part–whole relationships.

Planning a Strategy

Before making a move, students can consider which sequence of splits and merges will help them reach the target efficiently. They may ask themselves:

• Should I split a large group first?

• Can I merge two smaller groups?

• Is there a shorter way to create the required number?

This involves planning ahead, comparing possible approaches and choosing a strategy rather than relying only on trial and error.

Monitoring and Revising

As students manipulate the squares, they receive a visual representation of the result of each decision. They must continually check whether their actions are bringing them closer to the target.

When a strategy does not work, students can reconsider their approach, undo their assumptions and try a different combination. This process of testing, checking and revising is central to both critical thinking and mathematical problem-solving.

Explaining Mathematical Reasoning

The two-player format also creates opportunities for mathematical dialogue. Students can be encouraged to explain:

• why they chose a particular split or merge;

• how they knew that the arrangement represented the target number;

• whether another method could also work; and

• which strategy was the most efficient.

The focus shifts from simply obtaining the correct answer to making students’ thinking visible.

From Playing to Thinking

Square Town demonstrates how an interactive mathematics game can support more than procedural practice. As students analyse the target, decompose numbers, plan their moves, monitor their progress and justify their decisions, they develop stronger number sense alongside critical-thinking skills.

Teachers can deepen the learning by asking questions such as:

How did you decide which group to split?

Can you create the same number in a different way?

Which method uses the fewest moves?

What would you do differently in the next round?

Through purposeful questioning and peer discussion, a simple activity involving squares becomes an opportunity for students to reason, make decisions and reflect on their mathematical strategies.