In Autahi, we love to get hands-on with our Maths learning. During the first years at school, students are securing vital foundation knowledge of how numbers work. This includes counting forwards and backwards, sequencing numbers, learning about place value (hundreds, tens and ones) and beginning to partition numbers (split them into parts, for example tens and ones). Over the course of years 0 to 3, children move from counting to calculating.
Our number-writing system of numerals (1, 2, 3, 4, 5 etc.) has developed as a means of representing concrete objects in an abstract form. The numeral 5 stands in for an idea. The idea is the quantity of five objects, for example five counters. Perhaps the most remarkable and abstract numeral is zero, since it represents nothing: an absence.
In order to make these abstract numerals meaningful, they have to be attached to objects in the real world. Many very young children can count to ten as a sequence of words without necessarily being able to attach these words to objects in the real world. Children have to have a mental image of what four or ten or zero looks like. To achieve this, we start with concrete objects (beads, teddies, jewels etc.), then extend to include pictorial representations and, finally, abstract numerals.
Numicon is one of the resources we’re using to help our students to make these vital connections between the concrete and the abstract. You may have seen these colourful pieces in our classroom.
Each numicon piece represents a number from 1 to 10. Each is a different colour and has a distinctive pattern of holes corresponding to its number. The picture above shows a number line from 0 to 10, created with Numicon. Our Autahi students love to grapple with the idea of zero so we always make sure to include it.
Arranging the shapes this way gives an immediate sense of how the numbers increase in size as they go along. This aids sequencing (what comes next/before). These pieces can be picked up and manipulated. A nice detail is that the bigger ones are also heavier than the small ones.
Numicon shapes go two by two, making them very handy for teaching skip counting in twos. They also give an immediate sense of odd and even numbers, as you'll see in the pattern above.
Learning to work with tens and ones is a vital skill. The biggest piece in Numicon is a ten. Children learn that tens can be put alongside other numbers to build teen numbers. The tens place value house is placed to the left, corresponding to how the 'houses' are written (e.g. 11, 12, 13).
Two 'tens' plus some 'ones' gives a number in the twenties. The beauty of Numicon is that, unlike with counters, the ten cannot be divided and there is no need to count it before using it: it can be manipulated and viewed as a unit (a 'ten').
Our students are also learning to partition numbers. Partitioning is breaking down numbers into smaller parts that are either more manageable or make a calculation easier.
During the first six months at school, they will learn that number less than ten can be made by putting together smaller numbers. Numicon provides a model to visualise this and also verify ideas. Here, you can see how three and two fit together to make five. We would call this trio a 'family of facts'.
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Fast recall of numbers that go together to make ten is a foundational numeracy skill. Numicon is a great way for children to explore this for themselves, using the tens piece to check their ideas.
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Visualising these relationships also helps with fast recall of these facts for calculations.
This student has filled up their peg board with different combinations that total ten, making one hundred altogether.
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Finally, here's an example of how the concrete becomes abstract as students begin to relate the familiar Numicon shapes to numerals, writing addition 'number sentences'.
By carefully building our students' foundational number sense and knowledge, we aim to set them up for a lifetime of using and enjoying numbers in a meaningful way.
