Maths Meets Design: Students Craft Digital Flags in Desmos

Our Year 10 Newman Mathematics students recently embarked on a unique challenge that bridged the gap between textbook algebra and digital graphic design. As part of our Linear Relationships topic and using Desmos, an advanced online graphing tool, students designed custom flags—built entirely out of mathematical equations.

At first glance, a flag looks like a collection of simple geometric shapes. However, behind the facade is a complex web of Coordinate Geometry and Linear Relationships. Students were restricted to using straight line segments, meaning every single border and line needed to be precisely calculated and coded into the software.

To successfully construct their designs, students successfully applied four core algebraic concepts to every line they drew:

●     Gradients: Determining the exact "steepness" or slope of each line so they tilt at the perfect angle.

●     Y-Intercepts: Calculating exactly where each line crosses the vertical axis to ensure accurate placement on the grid.

●     Linear Equations: Combining the slope and intercept together to formulate a functional mathematical equation (in the form y = mx + c).

●     Boundaries (Domain & Range): Writing mathematical restrictions to "cut" infinite lines into perfect segments. This ensures corners meet flawlessly without overlapping or leaving gaps.

This task went far beyond black-and-white outlines. To add colour and shading, students utilised linear inequalities (using less-than and greater-than symbols) and made use of all of the functions available to them in the graphing software.

Why This Matters: This task shifted mathematics from a passive pen-and-paper exercise into an active, problem-solving experience. When a line didn't connect properly, students needed to troubleshoot their equations to find the error—developing the exact same logical thinking skills used by modern computer programmers and engineers.

Congratulations year 10 on some amazingly creative and mathematically in-depth designs!