Numbers & Maths
Teaching Numbers 1 to 10 at Home: Counting, Subitising and When to Show the Numerals
Published · 9 minute read
Reciting one to ten is not the same as understanding it. A practical guide to one-to-one correspondence, subitising, and the order to introduce written numerals, with what to say when your child counts the same button twice.
Your child can chant one to ten, sometimes to twenty. But ask them to fetch three spoons and you get a random handful. Ask which card shows the 6 and they guess. This gap is a common one, and on its own it is not a sign that anything has gone wrong. Reciting numbers and understanding numbers are two different skills, they tend to arrive in that order, and the second one usually takes longer. This guide sets out what to teach, in a rough order, and what to say when it goes sideways.
Counting out loud is a song, not maths
Many children learn the number sequence much the way they learn a nursery rhyme. It is a string of sounds with a fixed order. A two year old chanting to ten has, more often than not, memorised a tune. That is genuinely useful, because the sequence has to be in place before it can be attached to anything, but on its own it tells you very little about what the child understands.
You can see the gap clearly with one question. Put out five buttons, ask your child to count them, and let them finish. Then ask, calmly, how many are there. If they start counting again from one, they have not yet grasped that the last number said is the answer. Practitioners call this the cardinal principle. It generally comes well after the chant is fluent, and it tends to come for small quantities first, so a child may be certain about three long before they are certain about eight.
So do not treat the chant as the goal. Treat it as the raw material. Everything that follows is about attaching that string of sounds to real quantities, and only then to written symbols.
One-to-one correspondence, in practice
One-to-one correspondence means one number word for one object, every time. No object skipped, none counted twice, no words rattled off faster than the finger moves. It sounds trivial. It is one of the most common places young children slip, and it is what makes a counted answer wrong even when the sequence itself is perfect.
The fix is physical. Have the child move each object as it is counted, rather than pointing at a static row. Sliding a button from one side of the table to the other brings the hand and the voice into step. Posting counters into a jar does the same. If your child races ahead of their hand, put your hand gently over theirs and count together, slowly, once. Then let them do it alone.
Build it into things you already do. Lay the table and hand over the forks one at a time. Put socks into the drawer, one word per sock. Count the stairs, one word per step, which tends to look after itself because the feet set the pace. Two minutes here is usually worth more than twenty minutes at a table.
- Move each object as you count it, do not just point
- Sweep counted objects into a separate pile so counted and uncounted stay visibly apart
- Count things that are already in a line before things in a heap
- Start with three or four objects, not ten
- Ask how many at the end, every single time
- When the answer is wrong, recount together rather than correcting the number
Subitising: seeing how many without counting
Subitising is recognising a small quantity instantly, without counting. You do it every day. You glance at a dice and see five, you do not count the pips. It only works for small amounts, roughly four or five for most adults and fewer for a young child, and it tends to appear early, often before a child can count a set accurately.
It matters because a child who has to count from one every time is doing a lot of work for very little. A child who sees three at a glance has a quantity they can hold in their head and use. Familiar, repeated arrangements seem to make this easier, which is why practitioners tend to reach for dice patterns, domino patterns and fingers rather than random scatterings of stickers.
To practise, show a pattern for a second, cover it, and ask how many. Do not let them count. If they are unsure, show it again briefly. Use dice faces, fingers held up the same way each time, and dots arranged in the same layouts. Keep to five and below at first, and add a sixth only once five is easy. Once they are quick, ask how they knew, and accept answers like two and two. Two things are happening in that answer. They are seeing a group, and they are breaking it into parts, which is the habit that later makes adding feel like something known rather than something counted.
Knowing that five is four and one more is a different kind of knowing from being able to count to fifty.
The order to introduce written numerals
A written numeral is an arbitrary squiggle. There is nothing about the shape of 7 that suggests seven of anything. So the symbol is usually best left until after the child can count that quantity accurately and, ideally, recognise it in a pattern. Working through 1 to 10 as a set of flashcards before quantity is secure can leave you with a child who names symbols confidently and still cannot fetch three spoons.
Introduce numerals a few at a time, in roughly this order, and do not move on because a week has passed. Move on when the child is right most of the time without prompting.
- 1, 2 and 3 first. Small enough to see at a glance, and 3 is often the first quantity a child truly owns.
- 4 and 5 next, linked to fingers on one hand. Show the hand and the numeral together.
- Recognition before writing. Point to the 4 among a few cards before asking them to form a 4.
- 0, once 1 to 5 are solid. Introduce it as the empty plate, the number of biscuits left. It is abstract, so it needs a concrete story.
- 6 to 10, in pairs. Anchor each one to five and some more, so 7 is a full hand and two fingers.
- Matching numeral to quantity. Put the card next to the right number of counters, and work in both directions.
- Ordering. Lay 1 to 10 in a line, then remove one and ask what is missing.
- Forming the numerals. Trace with a finger, then a chunky pencil. The starting point is usually worth more attention than neatness.
Expect 6 and 9 to be confused, and 2 and 5 to be reversed when written. Both are common at four and five, and reversals usually settle as writing gets more practised, so on their own they are not something to act on. If you have a wider worry about how your child is getting on, their nursery or school and your child's doctor are the people to ask. Say the shape out loud as you form it, using the same words every time, so the child has a verbal handle to reach for.
A rough sequence by stage
Ages here are very approximate, children move through this at different speeds, and some meet these stages out of order. Use the description of what the child can do to work out where you are, not the ages.
| Stage | Roughly when | What the child can do | What to work on next |
|---|---|---|---|
| Chanting | 2 to 3 | Says the sequence, may skip numbers | Accuracy of the sequence to five, counting stairs and steps |
| Tagging | 3 to 4 | Touches objects while counting, sometimes doubles up | One-to-one correspondence, moving each object |
| Cardinality | 3 to 5 | Knows the last number said is the total | Asking how many after every count, small sets first |
| Subitising | 3 to 5 | Sees three or four at a glance | Dice and finger patterns, quick flashes, up to five |
| Symbols | 4 to 6 | Recognises and names numerals | Matching numeral to quantity, then forming the numerals |
What to do when it goes wrong
If your child counts the same object twice, do not say no. Say let us do that one again, and move the objects into a line so the counting has a direction. If they consistently lose track past five, work only within five for a fortnight. Shrinking the range is not going backwards, it is removing the thing that is causing the errors, and five counted accurately is worth more than ten counted hopefully.
If they name numerals but cannot produce the quantity, put the cards away for a while and go back to objects. Ask for the number rather than showing it. Bring me two shoes. Give the dog three biscuits. Put four cars in the box. The instruction has to be acted on, which is the whole point, and you will hear straight away whether the number means anything yet.
If they refuse, stop. Number work at three and four is usually best kept to two or three minutes at a time, and it does not have to happen every day. A short, cheerful count of the buttons on a coat is worth more than a long session that ends in a standoff. Come back to it tomorrow.
If you want something on paper, keep it simple. A printable pack is useful here mainly because it puts the same thing in front of your child each day without you having to invent it, and that repetition is most of the work at this stage. Ours are printable PDF packs for A4 and US Letter, mostly black and white, so a page that gets scribbled on can just be printed again.
A ten minute routine that fits a real week
You do not need a curriculum. You need a handful of moments that happen anyway. Pick three of these and do them most days for a month, then look back and see what has shifted.
- Counting the stairs on the way up, one word per step
- One quick dice flash at the table before a meal, ask how many
- Handing over cutlery one piece at a time when laying the table
- Finding one numeral in the wild, a house number, a bus, a page number
- Two minutes tracing one numeral with a finger before it goes anywhere near a pencil
- One instruction a day that has a number in it, fetch two apples, find three socks
Progress in this is slow and lumpy. A child can sit on five for weeks and then pick up six to ten in a few days, and neither the pause nor the jump means very much on its own. Judge it by whether they can act on a number, not by how far they can chant. When they can fetch you three spoons without counting on their fingers, the work is doing what it should.
