The science behind
Take Away & Find the Difference

A two-minute read for parents — why subtraction deserves its own practice, how it connects to addition, and what research says about the best way to build subtraction fluency.

1 Subtraction is not just addition in reverse

Many parents assume that once a child knows 5+3=8, they automatically know 8−3=5. Research consistently shows this transfer is far from automatic. Subtraction activates different retrieval pathways in the brain, and children who are fluent at addition often still need explicit practice with subtraction before those facts become equally fast and reliable.

This is why Take Away and Find the Difference exist as separate games rather than being folded into the addition games. The same number relationships are being trained, but from a different direction — which is exactly what builds durable, flexible number knowledge.

      The research: Studies by Geary, Fayol and others show that children who practise arithmetic from multiple directions — both the operation and its inverse — show stronger retention and better transfer to novel problems than those who practise in one direction only.
    

2 Two games, two complementary skills

Take Away — A − B = ?

Trains direct subtraction: given a number and a subtrahend, find the difference. Builds the core subtraction fact network.

Find the Difference — A − ? = C

Trains missing subtrahend reasoning: given a starting number and result, find what was taken away. Closely related to algebra and equation solving.

Together these two games — alongside Add It Up and Fill the Gap — give children practice with all four basic fact-retrieval directions for any number relationship: a+b, a+?=c, a−b, and a−?=c. Research in mathematical cognition calls this fact family fluency, and it is strongly predictive of later success in algebra.

3 Why answers are never below zero

Both games are carefully designed so that no question ever has a negative answer. At every level, the subtrahend B is always less than or equal to the minuend A. This keeps the game accessible and avoids introducing negative numbers before children are ready — while still making the questions genuinely challenging as the numbers get larger.

The one case where the answer reaches zero — for example 5 − 5 = ? — appears at most once per round. Zero as an answer is valid and worth knowing, but seeing it too often would make the game feel strange. One occurrence keeps it present without it dominating.

4 How levels and thresholds work

Both games start at level 5|5, meaning A ranges from 1 to 5 and B from 0 to 5 (with B always ≤ A). As the child gets faster, the upper bounds increase one step at a time, up to a maximum of 20|20.

The threshold to move up is 8 + (A+B) × 1.5 seconds for 10 questions — the same formula as the addition games, reflecting comparable cognitive difficulty. Two rounds under the threshold in a row triggers a level-up. One slow round resets the streak but never steps down.

      Why the same formula as addition? Subtraction of small numbers requires similar cognitive effort to addition of the same numbers. The threshold is proportionate to level difficulty — easy levels have tight thresholds, harder levels allow more time.
    

5 What to expect over time

First sessions: Subtraction is typically harder than addition at first. Slower times and more mistakes are normal.

After regular play: Times drop as retrieval replaces counting-back. The child stops working the sum out and starts just knowing it.

Alongside addition practice: Playing both addition and subtraction games on the same day reinforces the full fact family, producing faster gains in both.

Long term: Fluent subtraction is the foundation for column subtraction, mental arithmetic, fractions, and all equation solving in secondary school.