A Game to Teach Kids Addition and Subtraction (Free, with Dots)

See numbers as groups, not one-by-one

Fast calculators don’t count "●●●●●" one dot at a time — they see "a group of five" at a glance. This ability to know a quantity without counting (number sense, or subitizing) largely determines the speed and accuracy of addition and subtraction.

That’s why showing dots alongside the numbers helps at first. Present "5 and 3" as clusters of dots and kids can see them combine into 8, or see that taking 3 from 8 leaves 5. Learning the make-up of numbers as pictures (5 is 2 and 3; 10 is 6 and 4…) is the groundwork for later mental math.

• Pair numerals with dots to grasp "number groups"
• Learn composition/decomposition as pictures (5 = 2 and 3, 10 = 6 and 4)
• Thinking in tens makes carrying much easier
• Value how they thought about it, not just the answer

Dots for addition and dots for subtraction have to look different

Simply showing dots is not enough, because addition and subtraction need to make different things visible.

What matters in addition is that two sets become one. For 3 + 2, Kids Math lays out three dots and two dots in separate colours — blue and orange. Five dots in a single colour would just be "five"; the fact that a 3 and a 2 came together would have vanished. Splitting the colours keeps the original parts visible inside the answer.

Subtraction is harder, because "taking away" is an invisible action. Here the app lays out the full starting quantity and then crosses out the ones being removed. The dots do not simply appear in their reduced number — something that was there gets struck through. That difference is what makes the operation land.

Why the problem is spoken and the answer is one of three

Ask a five-year-old to read the equation and decoding the digits and symbols uses up everything they have, leaving nothing for the maths. Reading it aloud removes that load entirely. Hear it, check it against the dots, tap the answer — the more senses involved, the better it holds.

Three choices rather than free entry is the same reasoning. Operating a keypad or forming digits is effort unrelated to the calculation. Narrowing it to "which one?" keeps the attention where it belongs, and a miss costs nothing but a retry.

Three choices have a side benefit too. Scanning the options and ruling one out as obviously wrong quietly builds estimation. If 7 + 5 offers a 3, no calculation is needed to reject it — and being able to make that judgement is a real numerical skill.

The difficulty levels also decide when the dots go away

The three levels change more than the range of numbers: they change whether the dots are shown from the start.

Easy is addition only, each term 1–5, no carrying, and dots on. Normal adds subtraction, keeps sums within 10 and still has no carrying — dots on here too. Hard brings in carrying and borrowing with sums up to 18, and it is the only level where dots default to off.

That is not meanness; it is the handover to mental arithmetic. As long as dots are available, counting always produces an answer, so children keep counting. By the time they reach Hard, most have begun to internalise the sums up to ten, and the natural pattern becomes: try without dots, and call them up with the button only when stuck. The dots have not been removed — they have become something you summon when needed.

How to play (Kids Math)

A round is ten questions. Speech uses the voice built into your device and the chimes are generated on the fly, so no record of the practice leaves the browser.

• Open Kids Math, choose a difficulty and press start
• The problem is read aloud; "hear it again" replays it as often as needed
• Turn on the dots if you want to check the quantity by eye
• Tap the answer from three choices; a wrong choice is marked on the spot
• Ten questions per round, with a best score kept per difficulty on the device

From finger-counting to mental arithmetic — when to make the switch

Counting on fingers is fine at the start; fingers are the first tool for linking numbers to quantity. But starting from 1 every time caps how far they can get, so use the dots to draw attention to groups of five and ten, and move towards counting on — "after 5 comes 6, 7". Once counting on arrives, the time per question drops visibly.

The carrying barrier is crossed by making a ten. For 9 + 4: "9 needs 1 to reach 10, and 3 is left, so 13." Working through that split while looking at the dots turns it into a mechanism rather than a memorised procedure. Conversely, a child who answers 9 + 4 = 13 without dots but cannot explain why is still at the memorising stage.

For gauging progress, watch the pause before the answer rather than the score. Ten correct with a long think before each one still means counting. When the pauses shorten, it is time to move up a level.