Teachers' Guide to Getting Started

Stage: 3, 4 and 5

Published February 2011.

NRICH tasks are specially designed to encourage rich mathematical thinking and problem solving, and there are usually many different ways in which our rich tasks can be used in the classroom.

Our Teachers' Notes pages will outline a set of possible approaches and outcomes, but it is important to understand that a problem might evolve in many different ways and be subject to analysis by many different methods at a range of levels of sophistication. Our Teachers' notes should therefore be considered as 'a' way to consider the task, rather than 'the' way.

Leading a class in a rich mathematical task might call for a more open, reactive style than is traditionally seen in some mathematics classrooms. Luckily, there are several general ways in which rich thinking can be encouraged.

Possible approach to a rich task

How the problem is used will depend on the needs of the class or individual. You might try these approaches:
• It could be solved individually or discussed as a group.
• There is no need to stop once an answer is found: Students could discuss their methods of solution with others. Can the listeners spot flaws or gaps in the argument? Does a sense of a most efficient or elegant solution emerge? Are there many different approaches which have been used?
• There is no need to rush: the problem could be introduced to the students and then left for a period of time, for students to return to, giving them a chance to think things through at their own pace.
• What questions emerge for the solvers as they consider the problem?
• Perhaps you could provide the context and ask the students to suggest the questions they would like to ask or pursue.

Key questions to open up rich thinking

It is always good to ask the following sorts of question, especially if the solver is unsure as to where to start:
• Have you read the problem carefully?
• What information in the problem seems particularly important?
• What areas of mathematics does the question seem to make use of?
• How will you represent the information? Using numbers, diagrams, algebra .... ?
• Can you try out any special cases of the numbers and variables to get a feel for the structure of the problem?

Students, for any problem, can always:
• Consider variants of the problem with changed values of the numbers. Where do these explorations lead?
• Try to find alternative ways to do the problem. Study the contents of the Solution tab to see if any solutions have been done in another way. If there is no solution present, then the student can describe their own problem solving process and submit their own solution, which we will show on the website.
• Try to invent a similar problem on the same theme.
• Use the Search by Topic link to find similar problem on the same topic, perhaps with more stars or a higher stage?
• Explore the ideas discovered on the internet or through NRICH articles .

Possible support for learners in rich tasks

Students struggling to get started could:
• Try to explain as clearly and precisely in words exactly what it is that they do not understand. Often this simple device will help students to see a way forward.