Array Architect
How many squares? Then: does 4×6 match 6×4?
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: “Rows times columns” — Count one row, then count how many rows. Turning the array does not change the total. 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
Recognising a product from its shape, and knowing that order does not change it.
The commutative property is obvious in an array and invisible in a string of symbols — turning the rectangle a quarter turn is the whole proof. Seeing it halves the number of facts a child has to store.
- The underlying idea
- Commutativity is visible in an array and invisible in a symbol string.
- Where this sits in Illustrative Mathematics
- 3rd grade Unit 1: Introducing Multiplication · 3rd grade Unit 2: Area and Multiplication
- Sources
- youcubed et al. (2015) · Fyfe et al. (2014) all references →
Related measured skills: ALPACA · Elementary operations, ARF · Multiplication facts. What this means