Building Blocks of Math: Teaching Pre-Number Concepts to Children

A child who can count to twenty without missing a beat can still struggle to hand out five pencils – one to each classmate. This disconnect is far more common than most people realize, and it sits at the heart of why pre-number concepts matter so much. Before children can truly count, add, or subtract, they need a set of foundational mathematical understandings that go far beyond reciting numbers in sequence. For children with intellectual disabilities, building these foundations in a deliberate and structured way is not optional – it is essential.

What are pre-number concepts? 🔗

Early numeracy encompasses skills like recognizing quantities, comparing magnitudes, and discerning patterns – all of which must develop before formal number operations. Pre-number concepts are the specific foundational understandings a child must have before formal counting becomes meaningful. They are about relationships: between objects, between quantities, between sizes and arrangements. A child who has not grasped these relationships will often learn to count by rote – reciting numbers fluently – but fail when asked to count real objects accurately.

Consider Pankaj, a six-year-old who can rattle off numbers from one to twenty without hesitation. His parents are understandably proud. But when a teacher places five blocks on the table and asks him to count them, Pankaj points to one block while saying “one, two,” skips another entirely, and confidently announces there are seven blocks. This is not a memory problem. It is a pre-number problem. Research consistently shows that children with intellectual disabilities are fully capable of acquiring mathematical skills, but they need more time, structured approaches, and concrete experiences to develop the abstract thinking that numbers actually require.

Core pre-number skills every child needs 🔗

There are five key pre-number skills that together prepare a child for meaningful counting and number work. Each one builds on the previous, and each can be taught through simple, hands-on activities.

Matching 🔗

Matching is the most basic skill: recognising that two things go together. Early childhood mathematics research identifies matching as the starting point from which all other pre-number skills grow. A child who can match a red circle to another red circle, or a cup to a saucer, is building the cognitive groundwork for understanding that numbers correspond to specific quantities. Matching activities can be as simple as pairing identical objects, matching pictures to real items, or connecting animals to their homes.

Comparing 🔗

Comparing involves looking at two or more things and identifying how they differ – bigger or smaller, more or fewer, heavier or lighter. According to Michigan State University Extension, “more” is one of the first mathematical concepts children naturally understand, and embedding comparison language into daily routines is one of the most effective ways to teach it. When a teacher says “this pile has more stones than that pile,” they are laying the groundwork for understanding quantity and eventually for addition and subtraction.

Ordering (seriation) 🔗

Seriation is the ability to arrange objects in a logical sequence – from smallest to largest, shortest to tallest, lightest to darkest. Children who understand seriation can grasp that numbers follow an ordered sequence and that 6 is larger than 5 in the same way that a tall tower is bigger than a short one. Simple classroom activities – arranging crayons from shortest to longest, or lining up students from tallest to shortest – make this concept accessible and concrete.

Sorting (classifying) 🔗

Sorting means grouping objects by a shared attribute: all the red beads together, all the round buttons in one pile. Classification skills develop in stages – first by a single attribute like colour, then by multiple attributes like colour and shape together. For children with intellectual disabilities, starting with very obvious differences (large vs. small, red vs. blue) and then gradually introducing finer distinctions works best. Sorting underpins a child’s ability to later group numbers into sets and understand what a “number” actually represents as a category of quantity.

Recognising patterns 🔗

Pattern recognition – understanding sequences like red-blue-red-blue or clap-clap-stomp – develops the logical thinking children will later use for skip counting, place value, and even basic algebra. When a child can predict what comes next in a pattern, they are demonstrating an understanding of order and predictability that is fundamental to number sense.

Teaching the concept of “more” and “less” 🔗

Once children can match and compare objects at a basic level, the next step is helping them understand the quantitative concepts of “more” and “less.” These concepts are best introduced through concrete, hands-on comparison activities using everyday objects.

A practical classroom activity: place two unequal piles of stones or pebbles in front of the child. Start with a very clear difference – perhaps three stones in one pile and eight in another. Ask the child to point to the pile with “more.” Once this is mastered with obvious differences, gradually reduce the gap – five stones versus seven, then six versus seven – to sharpen the child’s discrimination skills. The same activity works with pencils, juice cups, blocks, or any familiar objects. Using items from the child’s daily environment makes the concept feel relevant and meaningful rather than abstract.

It is important to consistently use the words “more” and “less” (or “fewer”) during these activities, and to vary the objects so the child understands these are relational concepts, not tied to any particular item. LD OnLine emphasises that connecting mathematical language to many different concrete examples is essential for children with learning disabilities to genuinely grasp what a term means.

Establishing one-to-one correspondence 🔗

One-to-one correspondence is the understanding that each object in a set is counted once, and only once. It is the single most critical pre-number skill, because without it, counting is nothing more than reciting a memorised sequence of sounds.

The clearest way to teach this is through matching activities that are embedded in real situations. A child can place one plate at each seat at a table – not two plates for one seat, not one plate for two seats, but one plate per person. They can hand one leaf to each classmate, or place one crayon in each box. Each of these activities builds the understanding of “as many as” – a concept that directly precedes accurate counting.

Begin with a small number of objects (two or three), where the relationship is easy to see, and gradually increase to larger sets as the child gains confidence. The physical act of moving objects – picking up one block and placing it, then picking up another – helps the child track what has been counted and what has not. Research published in the Mathematics Education Research Journal confirms that the acquisition of the quantity-number concept – especially the linking of quantities to numbers – is a significant predictor of further mathematical progress in children with intellectual disabilities.

Moving from concrete objects to pictorial representations 🔗

Once a child has practised pre-number skills with physical objects, the next important step is bridging that understanding to pictures. This transition is a significant developmental leap – from handling real things to working with their visual representations – and it should be introduced gradually.

The Concrete-Representational-Abstract (CRA) approach, well established in special education research, describes exactly this progression: first physical objects (concrete), then pictures or diagrams (representational), and finally numerical symbols (abstract). A synthesis of evidence-based practices classifies CRA as an effective instructional framework specifically for students with learning disabilities in mathematics.

A simple pictorial activity for one-to-one correspondence: show the child a picture with rabbits drawn on one side and carrots on the other – with more carrots than rabbits. Ask the child to draw a line connecting each rabbit to one carrot. This activity keeps the correspondence concept alive while introducing the idea of symbolic representation. At the same time, it naturally introduces “more than” – the child can see that there are more carrots than rabbits because some carrots have no line connecting them.

After practising with such one-to-one picture tasks, introduce comparison pictures – three birds and five worms, or four children and six balloons. Ask the child to identify which group has “more” and which has “less.” This builds the child’s ability to apply their concrete quantity understanding to visual representations, which is the bridge toward recognising written numbers as meaningful symbols.

Why this sequence matters for children with intellectual disabilities 🔗

Children with intellectual disabilities do not develop mathematical understanding in a fundamentally different way from their peers – but they do need more time, more repetition, and more carefully structured input at each stage. A systematic review of mathematics interventions for this population found that the most effective approaches are those that use explicit instruction with manipulatives, provide immediate feedback, and are structured as well-sequenced, high-intensity learning experiences adapted to each child’s level.

Rushing a child from rote counting to formal number operations – skipping pre-number work – creates gaps that are extremely difficult to fill later. A child who has genuinely mastered matching, comparing, sorting, ordering, and one-to-one correspondence has the cognitive scaffolding in place to understand what counting actually means. That understanding is far more valuable, and far more durable, than any memorised number sequence. Experts in disability and mathematics education stress that making math visual, concrete, and relevant to a child’s real world is consistently more impactful than drilling abstract skills in isolation.

What do you think? If a child can recite numbers accurately but struggles to count a small group of real objects, which pre-number skill would you prioritise first – and how would you decide when they are genuinely ready to move to the next stage? Is there one pre-number concept from this list that you find children most often skip over or rush through?

References

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