Learn Maths, Step by Step

The 6 stages

Sort, match, compare (age 2-4) — Sorts, matches and compares: big and small, same and different, what comes next.
Count to ten (age 3-4) — Counts to ten with one touch for each thing, and sees small amounts at a glance.
Numbers to twenty (age 4-5) — Counts to twenty, knows what comes before and after, and who is first, second, third.
Add and take away (age 4-6) — Knows the pairs that make ten, and adds and takes away within ten.
To a hundred (age 5-6) — Counts to a hundred, sees tens and ones, and counts in twos, fives and tens.
Numbers in the world (age 5-6) — Uses numbers in the world: halves, measuring, time, money and simple charts.

Ticks are saved only in this browser — there is no account, and nothing is sent anywhere. Play on a different phone and the ladder starts empty; that is the price of not tracking your child.

Number sense before sums

A child who can recite one to a hundred has learned a song. A child who knows that five is one more than four, that it can be three and two or four and one, and that it looks like the dots on a dice, has learned a number. The second child will find every later piece of maths easier, which is why this ladder spends its first two stages on sorting, comparing, patterns and small amounts before any sum appears.

The order follows how children actually learn

These stages follow the early-maths learning trajectories described by Clements and Sarama and used, in one form or another, by the US Common Core kindergarten standards, England's EYFS and Singapore's nursery curriculum: compare and sort, count with one-to-one matching, see small quantities without counting (subitising), learn the number line to twenty, find the pairs that make ten, and only then add and subtract. Place value — tens and ones — comes after that, because it depends on all of it.

Fingers are fine

Counting on fingers is not a bad habit; it is the first number line a child owns, and research on early maths finds that children who use their fingers well at five calculate better at eight. Let them. The fingers retire by themselves when they are no longer needed.

Most of it happens away from the screen

Lay the table for four. Share six biscuits between two plates. Count the stairs, going up and coming down. Which glass holds more? These are the real lessons, and the games on this ladder are practice for them. The things to do at home page has a balance scale, a ramp race and a tidy-up sorting game that teach more maths than any worksheet.

Now do it for real

When the screen goes off, do something with your hands. Try 🕐 Make a clock — an easy craft for ages 5-6, with every step read aloud in your language. You will need a paper plate or a card circle, two card strips for hands, a pin or a paper fastener (grown-up); nothing that needs a trip to a shop.

There are 56 more on the things to do at home page, and free printable worksheets if you would rather have something on paper. Ten minutes on a screen and twenty minutes off it is a good shape for a day at this age.