Multiplication Arrays Game: Array Builder
Array Builder is a free multiplication game that shows what times tables really mean. Children build arrays of cookies on a tray, seats in a cinema and flowers in a garden bed, write the number sentences, turn the array round to see that 3 × 4 = 4 × 3, split big arrays into easy ones, and find every rectangle for a number.
Array Builder
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- Ages
- 6–9
- School years
- Year 2–Year 5
- Skills
- Understanding multiplication as equal rows (arrays), Writing multiplication number sentences from an array, The commutative property: 3 × 4 = 4 × 3 (turnaround facts)
- Time
- 5–10 minutes a game
- Cost
- Free, no sign-up
- Updated
How to play Array Builder
- Choose a level and press Play. Level 1 builds arrays up to 5 × 5, Level 2 up to 10 × 10, Level 3 splits arrays, and Level 4 finds factor pairs.
- To build “3 rows of 4”, tap or drag on the board to stretch the array, or use the + and − buttons (arrow keys work too). Rows go across and columns go up and down. Press Check.
- The array counts itself in 4s. Type the answer on the number pad: 3 × 4 = 12. Then press Turn it, and write the new number sentence: 4 × 3 = 12.
- In Level 3, tap between two rows to split the array, then work out each part and add them. In Level 4, choose how many rows to use and save every tray that makes a rectangle with nothing left over.
What your child learns
- Understanding multiplication as equal rows (arrays)
- Writing multiplication number sentences from an array
- The commutative property: 3 × 4 = 4 × 3 (turnaround facts)
- Skip counting along the rows of an array
- The distributive property: splitting 6 × 7 into 5 × 7 + 1 × 7
- Factor pairs, factors, prime numbers and square numbers
About Array Builder
Arrays are how teachers show what multiplication means. An array is a rectangle of things in equal rows, so 3 rows of 4 cookies shows 3 × 4, and counting along the rows in 4s (4, 8, 12) gives the answer. Arrays are taught in Year 2 and Year 3, and they are the model behind times tables, the commutative property and later the area model and long multiplication. In Array Builder, children build each array themselves, see it count itself row by row, and write both number sentences. Turning the array round shows why 3 × 4 and 4 × 3 give the same answer, which almost halves the number of times table facts to learn.
Level 3 is for Year 4 and Year 5: a tricky fact such as 6 × 7 is split into two easier arrays, 5 × 7 and 1 × 7, then the parts are added (35 + 7 = 42). This is the distributive property, and it is exactly how confident children work out facts they have forgotten. Level 4 turns the question round: with 12 cookies, how many different rectangular trays can you make? Rows that do not work leave cookies over, so children see why 5 is not a factor of 12, and they meet prime numbers (only one long row) and square numbers along the way. There is no timer, and every wrong answer comes with a hint.
Which level should my child play?
| School year | Suggested level |
|---|---|
| Year 2 | Level 1: arrays up to 5 × 5, such as 3 rows of 4 |
| Year 3 | Level 1, then Level 2: arrays up to 10 × 10 and turnaround facts |
| Year 4 | Level 2, then Level 3: splitting arrays, such as 6 × 7 = 5 × 7 + 1 × 7 |
| Year 5 | Level 3, then Level 4: factor pairs (every rectangle for 12, 16 or 24) |
Move up a level after getting three stars two or three times in a row.
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Frequently asked questions
What is an array in maths?
An array is a set of objects arranged in equal rows and columns, like eggs in a box or seats in a cinema. 3 rows of 4 is an array for 3 × 4 = 12. Arrays help children see multiplication as equal groups instead of a fact to memorise.
Why does 3 × 4 equal 4 × 3?
Build 3 rows of 4, then turn the array round: now it is 4 rows of 3, but there are still 12 things. This is called the commutative property. The game asks children to turn every array and write both facts.
How do arrays help with times tables?
Children can count along the rows (4, 8, 12), see turnaround facts, and split a hard fact into easy ones, such as 7 × 6 = 5 × 6 + 2 × 6. These are the strategies that make times tables stick.
What are factor pairs?
Factor pairs are two numbers that multiply to make a number. The factor pairs of 12 are 1 × 12, 2 × 6 and 3 × 4, which match the three rectangles you can make with 12 cookies. Level 4 asks children to find them all.
Which level should my child start on?
Start on Level 1 if your child is new to multiplication, and Level 2 if they know some times tables. Level 3 suits children learning their 6, 7, 8 and 9 times tables, and Level 4 suits children learning about factors.
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