Smart Starters · Ages 8 to 10
Array Multiplication Both Ways
Write each array as two multiplication facts. Five levels of printable practice with answer keys.
The learning journey
Every activity is one step. Here is where this one fits.
- PlayLearn the idea in a game
- Practise(you are here)Lock it in on paper
- ReviewCome back and keep it sharp
- MasterTake on a harder challenge
- AchieveEarn a certificate
About Array Multiplication Both Ways
An array is the clearest picture in multiplication, because it shows why the order of the factors does not matter. Three rows of eight and eight columns of three are the same dots seen two ways — and a child who has genuinely seen that will never need to memorise the commutative property as a rule. Every question on this page shows a rectangular array of dots and provides two lines, not one. Two lines is the whole design: a single line lets a child write one fact and stop, which is exactly the habit this worksheet exists to break. No array is ever square, because rows equal to columns would make both "orientations" the same sentence and teach nothing. Arrays grow from small to twelve a side across the levels, and the top two levels hide one dimension — giving the product and asking for the missing side, which can only be recovered by counting the array itself. Six arrays per page, each with its dots drawn at a size that stays countable when printed. Each level prints as a clean A4 sheet in black and white and downloads with its own separate answer key listing both facts. Its on-screen twin is Array Grid Architect.
Common questions
- Why are there two answer lines per array?
- Because one line lets a child write a single fact and stop. Reading the same array both ways is the entire lesson.
- Are any arrays square?
- No. Rows equal to columns would make both orientations the same sentence, which teaches nothing here.
- What happens at the highest levels?
- One dimension is hidden. The product is given and the missing side has to be recovered by counting the array.
- Which game goes with this worksheet?
- Array Grid Architect, which builds arrays and reads them both ways on screen.
A hand for grown-ups
- Before you start
- Think of it as groups: "4 × 3" is four groups of three. Have something you can arrange into equal groups.
- While they work
- Skip-counting (3, 6, 9, 12…) is a solid way in before facts are memorised. Let them use it — speed comes later.
- Afterwards
- Spot arrays in real life together — eggs in a box, tiles on a floor. Rows-and-columns is multiplication you can see.
- Watch out for
- Treating it as harder addition and losing track. Grouping objects physically keeps the "equal groups" idea in view.
- Away from the screen
- Lay out objects in rows and columns and count them two ways. Cooking with doubled recipes is multiplication too.
Where to go next
Chosen by the skills this activity practises.