More problems to solve

I have spent the last hour tweaking what I intend to do in Monday’s course, “Using resources to develop problem solving skills in secondary mathematics” The problem I have is not what to do, but what to leave out. We have so many resources from on the eLibrary alone before adding resources from elsewhere into my list of good resources to be used to develop problem solving skills.

I was asked earlier I the week whether I had a scheme of work for problem solving as their school had a problem solving lesson. The short answer was “no”, for more reasons than I have space here to list. The intention of the new curriculum is that problem solving and mathematical thinking be integral to the way mathematics is taught and leant throughout the curriculum. I wanted to be helpful so the only advice I could give was to concentrate upon the problem solving skill you wish students to develop when selecting the problems chosen, rather than any particular mathematical topic.

The question attached, is taken from the UKMT 2013 intermediate mathematics challenge paper. I have adapted the question and I ask students: “What is the shortest possible perimeter of the shape produced when four identical isosceles right-angled triangles are joined together such that sides match exactly?” I give out appropriate triangle shapes for students to manipulate whilst considering how to approach the problem and only suggest the shapes given in this question as scaffolding where needed. Have a go at the problem and post your answers below, thinking about what problem solving skills students would use in solving the problem. The solution is attached together with some great extension ideas.

More maths challenge questions can be found in the UKMT collection and in a collection called Mathematical Education on Merseyside (Challenges)

More details can be found about upcoming courses on problem solving and using manipulatives by clicking on the links.


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Interesting problem. In your solution D should be 6x not just 6 to be consistent with the rest of the solutions.


Does anyone know a good source for plastic pattern blocks -rectangular ones and isosceles right-angles triangles + other shapes/triangles - I can get the standard ones.

kind regards


Colin P Yorkshi...



This is a nice problem for students who have not come across Pythagoras's theorem.

Suggest that problems can be solved in a number of ways and challenge all students to come up with a solution then another and another etc. with at least one that does not use the theorem.

 If d is the length of the diadonal of a unit square then the students need to justify this lies between 1 and 2. Furthermore d needs to be less than 1.5. The reasoning involved with these should be revealing and illustrate the students ability to reason within a problem.

I wonder if any students use B and draw a square on the diagonal with an area of 8 to justify that d<1.5?

The use of the "bar" method to compare A&B,C,E might also be in evidence?

YR Maths Hub.