The new primary maths curriculum has been criticised for its focus on fact fluency and traditional written methods. However, of the three key aims at the beginning of the document, only one focuses on fluency. The other two are that we should ensure that all pupils:
“reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language.”
“ can solve problems by applying their mathematic to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.”
It’s very important that we don’t lose sight of these very important aims in the new drive for increased fluency in recall and calculation. Regular use of rich mathematical tasks in our maths classes can really contribute to both of these.
So what is a rich task? In her very helpful Nrich article, Jennifer Piggott describes the characteristics in some detail and some of these are:
- accessibility – they should offer different levels of challenge to learners of different ability, giving opportunities for early success but also scope to extend learning for the more able (low threshold, high ceiling)
- encouraging growing confidence and independence, often by working collaboratively
- potential to link with other areas of maths or to introduce entirely new areas of maths
- encouraging different approaches and creative solutions to problems
- allow learners to pose their own problems and ask questions
Jennifer Piggott also makes the important point that a mathematical task, although it may have the potential to do many of these things, does not become rich unless it is well led by the teacher, asking timely questions and supporting the children just enough to start to construct their own mathematical understanding whilst avoiding ‘spoon-feeding’ them. In practice, this can be difficult to do. In a busy classroom, it can be very tempting to wade in when a child is stuck and show them how to do it, but if we can restrain ourselves and instead offer a hint or a question that might open up a new avenue to explore, the experience will ultimately be much more satisfying and beneficial to our learners.
One good example of the sort of activity that could be used in this way is the ‘Sticky Triangles’ activity from Nrich. Children are presented with a growing pattern of triangles as above. These can be made from lolly sticks or pencils or similar or just sketched. You might like to present just the first two steps to start with and see if the children can suggest how to extend the pattern. Then get them to work on their own or in pairs or groups to explore the patterns. It’s probably best not to ask too many questions to start with. Children often naturally start to notice things about eg. how many triangles are in each row, how many lolly sticks are needed to make each pattern. It can be very interesting to watch the children and see how they approach things. Do they work systematically? Do they record anything? After a while, you might want to suggest some possible avenues for exploration. Can you see any patterns in the way the number of lolly sticks increases with each new row? Can you predict how many triangles will be in the next row? How many triangles would be in the tenth row? How many lolly sticks would be needed by this stage? What about the 100th row? Can you suggest any good ways of recording your findings? Encourage children to explain the patterns they see to each other and to you, and encourage the use of accurate mathematical vocabulary as they do this. The notes on the activity on the Nrich site also offers some other possible ways of extending the task even further.
The Nrich site offers lots of these sorts of activities at all sorts of different levels. As a teacher, I’ve found their curriculum mapping documents for KS1 and KS2 very helpful in identifying activities which might be linked to our other current work. Another source of helpful activities is the BEAM resources which can now be found in the elibrary of the National STEM Centre. You do need to register to access these resources, but registration is free and well worth while as there are a great wealth of resources in the elibrary.
For other suggestions for mathematical investigations, puzzles and challenges, have a look at my Pinterest board.