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Raising achievement in GCSE mathematics - ILIM - Stem-and-Leaf Diagrams

Created on 26 July 2011 by ncetm_administrator
Updated on 30 October 2015 by ncetm_administrator


Raising achievement in GCSE mathematics

Resource: Improving Learning in Mathematics
School: Cramlington Learning Village
Teacher: Graham Macphail,


Improving Learning in Mathematics,  LSIS STEM Programme, Mathematical Moments, Stem-and-Leaf Diagrams (Using rich collaborative tasks)

What we did – the use of the resource and the impact on learning

I was searching for a different way to teach stem-and-leaf diagrams and came across this link in the resource section of the NCETM. It is to the Excellence Gateway of LSIS (Learning and Skills Improvement Service), in the Mathematical Moments section of which there are many resources. These resources are a selection of lesson plans that describe how you could implement rich collaborative tasks into the classroom. There are four topic areas: Mostly algebra, Mostly number, Mostly shape and space, Mostly statistics. I really like a lot of the ideas and have embedded them into the GCSE Scheme of Work.

Taking the Stem-and-Leaf activity into the classroom is straight forward. All you need to do is clear a space in the middle of the room. Instructions in the lesson plan are clear and break the activity into easy-to-follow steps. Other resources needed are listed, along with a suggested teaching approach and explicit questions to ask. A questioning approach is used to build the understanding of pupils.

The impact on learning is immediate. Asking the class to hold their breath and record their time on a whiteboard hooks them into the lesson. It is also a good way to generate primary data that can then be sorted. Rather than telling pupils to sort themselves in a particular way, I ask them how they could sort themselves. They usually suggest in time order then by gender.

Asking boys to stand on one side of the room and girls on the other makes space to put two parallel pieces of string on the floor to act as the framework for the stem-and-leaf diagram.  After that, follow the lesson plan.

Using a kinaesthetic approach engages learners.  Encouraging pupils to ‘act out’ the maths provides an opportunity for them to ask and answer their own questions as the activity unfolds. When pupils return to their seats, they leave behind a back-to-back, sorted stem-and-leaf diagram. All you need is a key to unpack the diagram.

Next steps

There is a selection of similar lesson plans available on the Excellence Gateway, including Mostly algebra, Mostly number, Mostly shape and space, Mostly statistics. Each link contains kinaesthetic approaches and collaborative ideas that work in the classroom.

To support this approach I have created a learning mat to make mathematical learner behaviour explicit, based on Howard Gardner’s Five Minds, focusing on the disciplined mind. 

Top tips

Make time to unpack not only what was learnt but how it is was learnt. Make it clear that the processes used included ‘acting it out’ and ‘drawing a diagram’.

Make sure that pupils can find the median and quartiles before they make the stem-and-leaf diagram, so you can also ask extra questions to include comparisons of the back-to-back stem-and-leaf diagram, thereby facilitating higher order thinking in the classroom

Potential barriers and possible solutions

You need space to ‘act out’ the mathematics. Ensure there is enough available before you begin. If space is limited, use a subset of the class to act it out.

Personal Learning

Key action points

Look for opportunities to embed rich collaborative tasks throughout the Scheme of Work and write them into lesson plans to make the mathematics more accessible, engaging and fun.

Reflective thoughts

Breaking the new learning into smaller, more manageable chunks and asking questions throughout the learning is very powerful and provides the opportunity to unpack misconceptions and hold a mathematical dialogue.

The lesson plans from the LSIS site are easy to follow, but you will need to think ahead about the questions you ask and the resources you need.

Doing this activity allows pupils time to construct the learning, but they will also need an opportunity to demonstrate what they can now do.  This could be a pairs’ task, involving drawing a stem-and-leaf diagram on sugar paper.


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02 December 2011 13:38
The Mathematical Moments resource sheets 'Mostly Shape and Space, 14 to 18' were first published as the resource sheets of the 'Loci' topic in the NCETM Mathematics Department Workshops, where there is much other very useful material.
By mary_pardoe
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