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
- What questions emerge for the solvers as they consider the
- 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
- What areas of mathematics does the question seem to make use
- 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?
Possible extensions to rich tasks
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.
- Try reading
Student guide to getting started with rich tasks.
- Try warming up with a similar problem which is perhaps a little
easier. Use the Search by
topic link to search for questions on the same topic with
fewer stars or a lower stage.