Fact Family Forge

Three numbers make four facts. Find the missing one.

Game Multiplication and division 3.OA.B.63.OA.C.7 ARF · Multiplication facts ARF · Division facts
▤ Print this All of 3rd grade

For grown-ups

  • How long: 5 to 10 minutes is plenty. Short and frequent beats long and occasional — the early-numeracy trials with the largest effects ran eight weeks or less.
  • The strategy to reinforce: “Use the family” — Three numbers make four facts. If 6 × 7 = 42, then 42 ÷ 7 = 6. If they stall, remind them of this rather than giving the answer.
  • When they get one wrong: the page shows the working. Read it together rather than moving straight on. Feedback that explains is worth several times more than feedback that only marks right or wrong, and that gap is wider in maths than in any other subject.
  • On the timer: it is off unless you turn it on, and it is never needed. Use it only once the skill is comfortable, never to introduce it.
  • Print it too: doing the same problems on paper a few days later is worth more than doing twice as many today.

What this practises

Linking multiplication and division as the same fact seen two ways.

Multiplication and division are one fact seen from two directions, and practising them together roughly halves what has to be memorised. Division facts usually lag precisely because they are rarely rehearsed as the inverse.

The underlying idea
Multiplication and division are one relation viewed from two directions.
Where this sits in Illustrative Mathematics
3rd grade Unit 4: Relating Multiplication to Division
Sources
Illustrative Mathematics / Kendall Hunt (2024) · Codding et al. (2011)  all references →

Related measured skills: ARF · Multiplication facts, ARF · Division facts. What this means