What it means
In maths, comparison involves understanding and identifying relationships between numbers, lengths, quantities or objects. These build the foundations of complex maths concepts, including understanding number operations (addition, subtraction, etc.) and encouraging logical thinking. Through play and repetition, we can prepare children for the application of maths in the real world, such as accurately sharing out resources, recognising symmetry, identifying similarities and differences, talking confidently about time or distance and so much more.
Everyday comparison play
Support developing mathematicians by encouraging embodied, hands-on learning and using clear and consistent mathematical language – download our ‘maths sparky words’ at https://bit.ly/3WLqKaU and use them as prompts or reminders. It's important to offer open-ended questions, especially during child-led play, to gauge whether children are using and understanding comparative adjectives and phrases such as greater than/more/fewer/less/same/similar/faster/slower.
At snack time, compare the number of grapes or crackers on plates: ‘Who has more? Who has fewer? How many more does this plate need to be the same/equal?’ Compare the number of spoons and forks needed for setting the table: ‘Do we need more spoons or more forks?’- At home, there are plenty of opportunities for comparison play, such as sorting laundry into matching socks or colours, deciding on which fruit or vegetables to choose at the shops and talking about portion sizes at mealtimes (Goldilocks!). At the park, consider which play equipment is the most popular – thinking about how many children are using it, or how long they play on it for.
- In the mud lab, use containers, scoops and utensils to work with quantities (think about weight as well as volume); use water from the water butt to compare weights – does a full bucket weigh more than a half full one?
- Use heuristic baskets of natural objects to give babies the chance to explore and compare – two or three of each object will encourage them to look, feel and choose objects.
- Chalk around the outline of puddles (jumping in them first, of course). Measure their depth using a stick or ruler and compare the surface area – a ‘big’ puddle isn't necessarily the deepest; why? As they evaporate, inspect the chalk line, marking a new one to show the shrinkage.
Outdoors and active
The nature of the human instinct to investigate and experiment means much of young children's play outdoors is rooted in STEM concepts (science, technology, engineering and maths); whatever they are up to outdoors, celebrate children's attempts to compare numbers, lengths and quantities, and promote exploration as well as accuracy. The more comfortable children are with maths, the less they will ‘fear’ it as it becomes more complex as they move up through school. We know that a moving child is a learning child and outdoors is the perfect location to get children physically active, noisy and collaborative with maths, so that the thinking around it fuses. Jan White's book Every Child a Mover has excellent suggestions for how this works in practice.
- Leaf collection: Gather leaves during a walk – encourage children to leap and scoop, using their whole bodies to create their own collection. These can be used for comparisons, from biggest and smallest or darkest to lightest through to number of leaflets/points, quantities found from different species of tree or who collected the most – whose pile is the biggest?
- Step by step: Choose a start and finish point outdoors – ideally with two permanent features such as a doorway and a tree. Each child and adult should walk normally between the two points, counting the number of steps required. Compare the number of steps each person took and ask children to account for the differences (e.g., adult legs are longer so they don't take as many steps). Record each child's total steps and repeat with long strides and then heel-to-toe steps. Repeat again every few months; can children explain why they might use fewer heel-to-toe steps as time passes?
- Scavenge and sort: Give children a basket or tub to collect interesting objects in – they could be natural or man-made – while scavenging outdoors. Children should lay their treasure out on the ground and discuss similarities and differences they observe – not just mathematical ones.
Maths in the garden: growing broad beans
Following on from last month's article where we planted some broad beans in yoghurt pots: have your beans germinated yet? If they have started to grow, count the number that have germinated and compare with the number that have not. Start a chart to count again each week until all have sprouted. Remember to keep the seedlings moist and not too warm – when they have all started to grow, they can be moved to a light but cool position or a greenhouse. Observe the seedlings with a magnifier, looking the delicate shoots and roots. Later on, when they are a little stronger, children can do a gentle tactile exploration of the beans as well.
It's not too late to get started on the bean maths project: you can also germinate the seeds on damp kitchen paper or inside a jar so the children can see what is happening with the roots and shoots.
Case study: Holmsdale Manor Nursery
Holmsdale Manor Nursery's extensive, multi-level gardens are stuffed with provocations for creative and active play. A rich seam of outdoor learning runs through the whole setting and bagged it a Nursery World Enabling Environment award in 2019. The setting's Katie Ward says, ‘Our environment is our “third teacher” and we use nature to help us explore mathematical concepts, such as the shape of broken ice, how heavy the pumpkin is to lift, and “can I squeeze into this small space?”’ She adds, ‘Counting is a part of our daily routine, from counting children in a line to counting and placing chairs at the table for mealtimes. The children love to play games of Hide and Seek and What's the time, Mr Wolf?.’
STEM is a strong focus for the team at Holmsdale. On an autumnal day I observed two groups of children experimenting with tyres and wheels on slopes, choosing sizes and, with support from the practitioners, considering weight and tread as factors that might influence speed. A group of boys found a set of small rubber tyres and organised themselves in a neat line as far up the hill as they could, recognising (although they couldn't necessarily articulate it) that the longer the hill, the faster the tyres would go. Counting up to three, they released them and chased them down the hill, full of glee as the tyres bounced off the gate and fence at the bottom – with lots of debate using super maths words such as ‘fastest’, ‘slowest’, ‘heavy’ and ‘speed’.
Higher up, a practitioner had set up a launch slope using a plank and crates. The children made excellent attempts to aim the slope so that the tyres would roll down the path and, like the boys lower down in the garden, used their whole bodies to roll the tyres back up the hill.
