The 20 Matchstick Triangle Challenge; an Activity to Foster Reasoning and Problem Solving

In this article we look at a simple geometry problem that also involves some reasoning about number combinations, and show how it was used in a Year 7 classroom. The problem is accessible to students with a wide range of abilities, and provides scope for stimulating extensive discussion and reasoning in the classroom, as well as an opportunity for students to think about how to work systematically. Pat, the first author and a classroom teacher, used the problem with her students and we will present some of the strategies, solutions, and issues that they encountered and discussed. Helen, the second author who works with pre-service and inservice teachers, has used this problem with teachers and likes thinking about tasks that are good for fostering reasoning and problem solving.