Using UKMT problems to develop problem solving skills
I like using problems like the one attached to this post, taken from the 2012 UKMT Intermediate Mathematical Challenge, in the classroom. If you haven’t seen it before, have a go at it now, but also think about how you might use it in the classroom.
I have used this question by just drawing the diagram on the board. I then carefully explain the problem in an attempt to ensure all students understand the problem. The important point to stress at this point is that I know the answer to the problem as I have the answer book. What I am interested in is how to get the answer.
Without writing anything down at this stage, I ask students, in groups, to discuss how they may begin the problem; what strategies would they use, but I do not want to know where any of the remaining numbers go. Hopefully students will suggest drawing the diagram for themselves, writing down the numbers 1 to 9 so we can tick them of when we have used them and looking for a place to start, a section in which only one number can go.
In groups I ask students to solve the problem but not to reveal to any other group what the answer is. I would then ask groups to explain to the class their process of solving the problem. Did all groups do the same? Is there only one solution, or variations?
Extensions include; in groups making up a similar problem for peers to solve.
The National STEM Centre has many resources that can be used to develop problem solving skills. The CIMT resource ‘Logic’ contains many examples of how to use tables and Venn diagrams in lessons and ‘The Problem Solving Pack’ from the Spode Group has many more useful examples.
For more information about the UKMT Mathematical Challenges see their website.