Working Systematically at Stage 4 and 5

These resources can be used with older students to improve their skills of working systematically.

How Old Am I?

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

In this problem students create quadratic equations and solve them by factorisation or by using the quadratic formula. The follow-up questions offer the chance for some interesting generalisations and justifications.

Odds and Evens Made Fair

Stage: 4 and 5 Challenge Level: Challenge Level:1

To search for a fair game in this probability task, students will need to work systematically and record their findings appropriately.


Stage: 5 Challenge Level: Challenge Level:1

This problem uses playing cards and video to introduce students to some well-known sorting algorithms.

A Long Time at the Till

Stage: 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

This problem provides an introduction to advanced mathematical behaviour which might not typically be encountered until university. The content level is secondary, but the thinking is sophisticated and will benefit the mathematical development of school-aged mathematicians.