The science behind
Add It Up & Fill the Gap
A two-minute read for parents — why practising addition with increasing difficulty builds lasting maths fluency, and how the two game formats train different but complementary skills.
1 Why addition fluency matters beyond primary school
Addition is the first arithmetic operation children learn, but it remains fundamental throughout all of maths. Every multiplication is repeated addition. Every algebraic equation involves addition. Every mental calculation in daily life uses it.
The goal is not just accuracy — it is fluency: the ability to add without conscious effort, so that mental energy is free for the actual problem at hand. Research consistently shows that children who automatise addition facts in the early years show significantly better outcomes in algebra, mental arithmetic and estimation well into secondary school.
2 Two games, two complementary skills
Trains forward addition: given two numbers, find their sum. This is the most direct form and builds the basic fact network.
Trains additive reasoning: given a starting number and a target, find the difference. This is the foundation of subtraction, change problems and algebraic thinking.
Playing both games trains the same number relationships from two directions — which is exactly how memory researchers recommend building robust fact retrieval. A fact learned from one direction only is more fragile than one accessed from multiple angles.
3 Why multiple choice for addition
For facts that are still being built, multiple choice outperforms fill-in-the-blank. This is not because multiple choice is easier — it is because it is better designed for learning.
When a child sees five plausible options and must select the right one, they are actively processing each alternative. Rejecting wrong answers strengthens the correct one in memory. Cognitive science calls this the generation effect and the retrieval practice effect: the mental effort of choosing, even when uncertain, encodes the fact more deeply than passive reading or a blank stare at an empty box.
The distractors are deliberately chosen to be close to the correct answer — never random, never trivially different. This forces genuine engagement with the actual value rather than guessing by elimination.
4 How the levels work
Both games start with numbers from 0 to 5, giving sums up to 10. The level is defined by two upper bounds, A and B. As the child gets faster, the upper bounds increase — first A goes up, then B, then A again — so the range of numbers grows gradually and systematically.
The threshold to move up is 8 + (A+B) × 1.5 seconds for a 10-question round. At the starting level (5|5) that is 23 seconds — about 2.3 seconds per question, which is brisk but achievable. At a higher level like 10|10 it is 38 seconds, reflecting the greater difficulty of larger numbers.
Two rounds under the threshold in a row triggers a level-up. One slow round resets the streak — but never steps down. The game is designed to be encouraging, not punishing.
5 The +15s mistake penalty
A wrong answer adds 15 seconds to the running time. This creates a real cost for guessing — but it does not end the round or disrupt flow. The child sees the correct answer flash green, then moves on immediately. The penalty teaches that speed and accuracy are both part of the goal, which is exactly the condition needed to drive genuine automaticity rather than hasty guessing.
6 Short sessions, spaced over time
Each round takes 20–60 seconds. That is short enough to play three or four times between other activities. Spaced practice — many short sessions spread across days — produces far stronger long-term retention than one long session, as Ebbinghaus demonstrated in the 1880s and decades of subsequent research has confirmed.
The leaderboard gives children a personal benchmark to beat, which motivates them to return. Returning is what produces the spacing. The game is engineered so that the most effective learning strategy is also the most fun one.