The science behind
Divide It & Split It

A two-minute read for parents — why division needs its own practice, how it connects to multiplication, and why only whole-number questions are used.

1 Division is not automatic from multiplication

A child who knows 6×7=42 does not automatically know 42÷7=6. Research on arithmetic fact retrieval consistently shows that the inverse operation activates a different retrieval pathway and needs to be practised separately. Children who are fluent multipliers often still count or guess when faced with division — because the "division direction" of the fact has never been reinforced.

Divide It and Split It close that gap. They use exactly the same number facts as Times Tables, but approach them from the division direction — training the full fact family rather than just one half of it.

      The research: Campbell and Fugelsang (2001) showed that division facts are retrieved more slowly and less accurately than multiplication facts even when both are well practised, because division is cognitively processed differently — as a search for a missing factor rather than a direct retrieval. Explicit division practice accelerates that retrieval significantly.
    

2 Two games, two directions

Divide It — A ÷ B = ?

Trains direct division: given a dividend and divisor, find the quotient. The most direct form — mirrors how division appears in everyday maths.

Split It — A ÷ ? = C

Trains missing divisor reasoning: given a dividend and quotient, find the divisor. Closely related to algebraic thinking and proportional reasoning.

Together with Times Tables, these two games give children practice in all three fact-retrieval directions for any multiplication fact: A×B=?, A÷B=?, and A÷?=C. Research in mathematical cognition shows that accessing the same fact from multiple directions produces significantly stronger and more durable memory than one-directional drill.

3 Why only whole-number questions

Both games are carefully restricted to questions that produce clean integer answers. At level 4|4, for example, every question is drawn from the 2–4 × 2–4 multiplication grid — so 12÷3=4, 16÷4=4, 6÷2=3, and so on. There are no remainders, no fractions, no decimals.

This is intentional. The goal at this stage is to build fact fluency, not to introduce the concept of non-integer division. That is a separate skill taught in the classroom. Keeping answers clean lets the child focus entirely on retrieval speed.

As levels increase, the question pool grows — level 8|9 draws from the full 2–8 × 2–9 multiplication table, giving a large variety of challenging but always exact division facts.

4 Levels, thresholds and variety

Both games start at level 4|4 and use the same threshold formula as Times Tables: 10 + (A+B) × 2 seconds for 10 questions. At 4|4 that is 26 seconds — about 2.6 seconds per question, which is achievable once the facts are becoming automatic.

Each question in the pool can appear in two forms — for example, 12÷3=? and 12÷4=? are both valid questions from the fact 3×4=12. This doubles the variety within any level, keeping rounds from feeling repetitive even when the fact pool is small.

      Note on variety: When A equals B (e.g. 4|4), only one division form exists per fact (since 16÷4=4 is the only question from 4×4). As A and B diverge, variety increases quickly. By level 6|8, each round draws from over 40 distinct questions.
    

5 What to expect over time

First sessions: Division is typically harder than multiplication at the same level. Slower times and more mistakes are normal and expected.

After regular play alongside Times Tables: Times drop noticeably as the child stops working backwards and starts retrieving directly.

Long term: Fluent division underpins fractions, ratios, algebra, and all of secondary mathematics. A child who can retrieve 56÷8=7 instantly has a significant advantage when manipulating fractions or solving equations.