This research focuses on enhancing critical thinking in secondary mathematics education using carefully constructed teaching materials. Utilizing socially open-ended framework, complemented by perspectives from critical mathematics education, the study aims to promote students' critical thinking skills. The developed materials were implemented in a unique lesson centred around the 60-second challenge, whereby students were tasked to propose rule modifications. The study also aimed to identify students' social values, considering these as interconnected with their capacity for critical thought. The assessments involved multiple teachers evaluating student reports using rubric and students participating in peer review activities within the class. The lesson's outcome illustrated students' ability to propose thoughtful improvements to the existing rules, reflecting their critical thinking abilities. Furthermore, this innovative series of evaluation activities via the rubric provides a foundation for future research in the assessment of critical thinking, serving as a potential model for future studies.