Rich tasks - resource ideas
What exactly are ‘rich’ tasks and why are these relevant for high attaining pupils?
Where can I find good examples of rich tasks?
Things to think about
‘Mastery of core skills and knowledge is necessary for good mathematical progression and should not be undervalued, but developed in conjunction with the range of valued mathematical behaviours in a progressively deep and rigorous way.’
Raising the bar: developing able young mathematicians, (ACME, 2012, p. 3)
What is at the heart of mathematics? While it is of course critically important that young people develop fluency in counting and arithmetic, mathematical enquiry is about conjecturing, considering alternatives, being systematic, making generalisations, justifying, proving, communicating – in other words it’s about the use of higher order thinking skills. This does not have to be complicated - a Year 1 child who is thinking about different possible addition sums which have an answer of 10 is a child who is acting as a mathematician.
High attaining children tend to become fluent in arithmetic skills relatively quickly, and the use of rich tasks is a powerful way of challenging such children, of helping them experience the pleasure of thinking something through logically. If such children are mostly given ‘harder sums’ in mathematics lessons then they are likely to end up with a limited understanding of what it means to be a mathematician, and there is a danger that they will lose their enthusiasm for the subject. Such children need more opportunities for deeper mathematical thinking.
Excellent mathematics teachers do not see rich tasks as being separate in any way from the core mathematics curriculum. They seek ways to incorporate rich tasks into everyday mathematics lessons.
What does research tell us?
The concept of ‘rich tasks’ has been explored by many researchers. Afzhal Ahmed has suggested that a rich task:
must be accessible to everyone at the start;
needs to allow further challenges and be extendable;
should invite learners to make decisions;
should involve learners in speculating, hypothesis making and testing, proving or explaining, reflecting and interpreting;
should not restrict learners from searching in other directions;
should promote discussion and communication;
should encourage originality and invention;
should encourage "what if?" and "what if not?" questions;
should have an element of surprise;
should be enjoyable.
Jennifer Piggott in her article Rich tasks and contexts develops a similar list, and importantly adds that ‘On its own a rich task is not rich - it is only what is made of it that allows it to fulfil its potential’. A similar point was made in Mathematics: made to measure: ‘Pupils [in primary schools] were rarely given open-ended investigative activities. When they were used, the skills of using and applying mathematics were not generally specified’ (Ofsted, 2012, p. 47) and hence the potential for rich learning in such activities was not fully realised.
A teacher who makes consistent use of rich tasks is giving pupils the chance to make connections between different aspects of mathematics. Research carried out by Askew, Brown, Rhodes, Wiliam and Johnson (Effective teachers of numeracy, Askew et al 1997) suggested that a key characteristic of more effective mathematics teachers was the way they encouraged pupils to develop their understanding of the connections between different topics, for example helping pupils see that fractions, decimals, ratio and proportion are conceptually related to each other. Rich tasks can create excellent opportunities for discussion about such relationships.
Rich tasks also create excellent opportunities for pupil discussion and collaboration and so can help pupils develop communication skills. Mathematics: made to measure shares concerns that secondary pupils too often accept that learning mathematics is ‘important but dull. They frequently told inspectors that in other subjects they enjoyed regular collaboration on tasks in pairs or groups and discussion of their ideas, yet they often did not do so in their mathematics lessons, or even expect to do so.’(Ofsted, 2012, p. 14).
To read more about rich tasks go to Exploring rich mathematical tasks.
There is a useful discussion paper by Lynne McClure on the NRICH website entitled Using low threshold high ceiling tasks in ordinary classrooms, which explores these ideas from a different perspective.
Implications for the use of the Year 6 Level 6 tests
The case study schools in Investigation of Key Stage 2 Level 6 Tests (Coldwell et al, 2013) used a range of strategies to prepare children for the L6 test. Some schools focused strongly on test-specific preparation, while others did very little test-specific preparation and continued with normal teaching programmes. But the most successful strategy was to combine both approaches – to maintain a clear focus on wider learning, alongside an appropriate amount of test-specific preparation. Secondary schools expressed concern that an over-emphasis on ‘teaching to the test’ would mean that children would only have a shallow understanding of Level 6 mathematics.
This indicates that there is a valuable place for the use of rich tasks in the run up to the L6 tests, while specific test preparation is also important.
Working with colleagues
Colleagues who are less confident about mathematics are likely to need support in order to develop their own understanding of the essential features of rich tasks and through this to develop a better understanding of what it means to ‘think mathematically’. Doing mathematics together and discussing the experience is likely to be productive. The NRICH website has a wide range of rich tasks that you could use with colleagues.
Ideas for staff meetings
A simple entry point is to explore the idea of what happens if you start with an answer and work back to what the question might have been. If the answer is 100, what might the question have been? What if you were only allowed to use multiplication? See Going backwards – from answers to questions. Ask colleagues to think about the types of mathematical thinking they use when working in this way.
How can I devise rich mathematical tasks for the primary classroom? has ideas and links to other resources which you could use as the basis of CPD sessions with colleagues.
Integrating rich tasks is an extensive CPD resource from the NRICH website that gives colleagues opportunities to develop understanding about the nature of rich tasks, how these relate to higher order thinking, and how to integrate such tasks into the curriculum.
Encouraging children to work systematically explores what ‘being systematic’ actually means in mathematics. This would be useful to help teachers identify relevant learning objectives within rich tasks.
Rich mathematical tasks and Using rich tasks for the first time both describe work done by groups of teachers on developing the use of rich tasks. They may prompt ideas for your own work with colleagues.
You could use Lynne McClure’s discussion paper Using low threshold high ceiling tasks in ordinary classrooms as the basis of discussion with colleagues.
If you want to explore the use of ICT to encourage mathematical reasoning, look at the resources in Leading and supporting the development of digital technologies in mathematics. It covers topics such as the use of digital cameras and flip video, Logo, data loggers. Each section has details of how to run a CPD session with resources
Resources to use
Learning mathematics outside the classroom offers a range of ideas for creating rich, challenging learning contexts.
ICT in the classroom - Using the internet for real data handling has suggestions for sources of real data that you could incorporate into cross-curricular topics.
The NRICH website has a huge range of resource ideas with notes for teachers to accompany each activity. The Curriculum Topics page includes useful curriculum mapping documents
To help with resources for Level 6 topics look at NRICH’s Stage 3 and 4 Curriculum page and download the Secondary Mathematics Curriculum Mapping Document.
Malcolm Swan in Improving learning in mathematics: challenges and strategies (Swan, 2005) provides many examples of rich tasks, looking at five different types of activity:
classifying mathematical objects
interpreting multiple representations
evaluating mathematical statements
analysing reasoning and solutions
While many of the examples are more appropriate to secondary school pupils, you could easily adapt them for Key Stage 1 or 2 content.
The BEAM (Be A Mathematician) resources have some excellent activities and games to develop mathematical thinking.
There are several old DfEE/DfES publications that have some excellent resource ideas:
Mathematical challenges for able pupils in Key Stages 1 and 2
Problem solving with EYFS, Key Stage One and Key Stage Two Children - these resources include ideas for ways to use the activities in lessons.
Reasoning about numbers with challenges and simplifications - this resource pack has helpful suggestions for ways that puzzles and investigations can be made more challenging.
Brainbashers is a collection of brain teasers and puzzles – these could be used independently by high attaining children, for example as homework tasks or in a Mathematics Club.
ACME (2012) Raising the bar: developing able young mathematicians.
Ahmed, A. (1987) Better Mathematics: A Curriculum Development Study Based on the Low Attainers in Mathematics Project. London: HMSO.
Askew, M., Brown, M., Rhodes, V., Johnson, D. and Wiliam, D. (1997) Effective Teachers of Numeracy: Report of a study carried out for the Teacher Training Agency. London: School of Education, King’s College.
Coldwell, M., Willis, B. & McCaig, C. (2013) Investigation of Key Stage 2 Level 6 Tests. Centre for Education and Inclusion Research & Sheffield Hallam University.
Ofsted (2012) Mathematics: made to measure.
Swan, M. (2005) Improving Learning in Mathematics: Challenges and Strategies. Department for Education and Skills Standards Unit.