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• PixiMaths

I’m starting to use more and more rich tasks in my lessons. I’m finding that it’s developing my subject knowledge (particularly at A Level) and my students’ understanding of the topic we’re covering.

A rich task is usually a task that doesn’t have an obvious answer when it’s first looked at. It doesn’t have to be open-ended, but should have multiple different routes that students could take to get to an answer. It should stretch and challenge all your students, but still have an accessible “way in” so that all your students can access it too. Rich tasks encourage exploration of topics and also inspire students to play around with the maths that they know. They are often posed as a problem that needs solving.

Nrich says, “The resulting learning process is far more interesting, engaging and powerful; it is also far more likely to lead to a lasting assimilation of the material for use in both further mathematical study and the wider context of applications.”

The more I use these rich tasks, the more I see the impact on my teaching and my students’ comprehension. I’ve started to write my own rich tasks too – something which is definitely not easy! Writing rich tasks is not something that you can decide you’re going to do and just pull it out the bag. The few I have written have come to me whilst teaching a given topic or in that stage of sleep where you’re only a little bit conscious.

My most recent task, however, was created collaboratively with another maths teacher, @vicky_maths. Not only was it fantastic to spend some time together just making resources and talking maths, but I’m also really impressed with what we produced. With our A Level classes in mind, we designed a task on logarithms and exponentials to help our students consolidate their learning. Students were to be given eight exam questions to sort into either a two-way or three-way Venn diagram. And that was all the instruction they were to receive! We had a good range of exam questions, including the basics of exponentials and laws of logarithms, up to differentiation of exponentials and applied questions.

I tried this task with my A Level group yesterday, and I am really happy with the result. All pairs started by solving the exam questions. I was quite happy with this as I knew they needed further practice anyway. Some struggled as they had different exercise books since we covered logs, so they didn’t have access to their notes. However, this prompted some brilliant peer-to-peer support. I heard phrases like, “teach me”, “show me” and “explain why”, which were not directed at me for a change. I didn’t even use my question cards!

With the end task in mind, throughout working on the questions, my class were making observations and relationships: “that one is similar to that one but with a sharper gradient” for example. Conversations were definitely more useful and focused with stronger vocabulary. I’ve included some pictures below on how the questions were eventually sorted.

The more of these tasks I do, the more observations I make too. Points that need addressing before the next rich task for this task are:

• Basics! Rearranging skills, use of fractions and laws of indices let some students down. They had forgotten that the space outside the Venn diagram could also be used.

• The need for reassurance – how do I make them a more resilient bunch?

• Listening skills – each student thought their idea was best, and whoever had the loudest voice ‘won’ each discussion/debate.

I’m looking forward to writing and using more rich tasks with my classes. There are loads already available online too: