Key takeaways
- An array is a set of objects arranged in equal rows and columns — like a chocolate block or an egg carton.
- You read an array as rows × columns: a 3 × 4 array is 3 rows of 4, which equals 12.
- Arrays make the commutative property visible — rotate a 3 × 4 array and you can see 4 × 3 gives the same total.
- The same array models multiplication, repeated addition and division, so it links the three ideas in one picture.
- The Australian Curriculum introduces arrays in Year 2, then builds on them for the area model in later years.
Ask a class "what is 4 × 6?" and you will get a mix of confident chanters, careful skip-counters, and a few students who freeze. An array gives every one of them the same solid picture to fall back on. It is the single most useful visual model in primary multiplication, because one arrangement of dots or counters explains times tables, division and the properties of multiplication all at once.
This guide covers what an array is, how to read one, how to teach it through the concrete–pictorial–abstract sequence, and the hands-on activities that make it stick.
What is an array in maths?
An array is a collection of objects arranged in equal rows and columns. The key word is equal: every row holds the same number of objects, and every column does too. That regularity is what makes an array countable by multiplying rather than by counting one by one.
Students meet arrays everywhere once they start looking: the squares in a block of chocolate, the cups in an egg carton, windows on a building, muffins in a tin, dots on dominoes, and the seats in a classroom. Naming these real examples early helps students see arrays as a description of the world, not just a maths exercise.
- A row runs across, horizontally (left to right).
- A column runs down, vertically (top to bottom).
- The maths convention is to read an array as rows × columns.
How to read an array: rows and columns
Picture 3 rows of 4 counters. Because the rows are equal, you do not have to count all 12 — you can say "3 groups of 4" and write it as 3 × 4 = 12. That single move, from counting-all to multiplying, is the whole point of the array.
Now rotate the same array a quarter turn. What was 3 rows of 4 becomes 4 rows of 3. The counters have not moved, so the total is still 12 — you have just shown that 3 × 4 = 4 × 3. This is the commutative property of multiplication, and an array proves it in a way a memorised rule never can.
The array also holds the two related division facts. If 3 × 4 = 12, then covering up the rows shows that 12 ÷ 3 = 4 and 12 ÷ 4 = 3. Teaching multiplication and division together from the same picture builds the idea of a fact family and cuts the amount students have to memorise roughly in half.
| What the array shows | Read it as | Number sentence |
|---|---|---|
| 2 rows of 5 counters | Repeated addition | 5 + 5 = 10 |
| 2 rows of 5 counters | Multiplication | 2 × 5 = 10 |
| 10 counters shared into 2 rows | Division (sharing) | 10 ÷ 2 = 5 |
| A 3 × 4 array turned on its side | Commutative property | 3 × 4 = 4 × 3 = 12 |
| A 6 × 7 array split into 6 × 5 and 6 × 2 | Distributive property | 30 + 12 = 42 |
How to teach arrays step by step
Arrays work best taught through the concrete–pictorial–abstract (CPA) sequence: students build an array with real objects, then draw it, then write the matching number sentence. Rushing to the symbols is the most common reason arrays fail to stick.
- 1
Build it with objects (concrete)
Give each student counters, buttons or cubes and a target like "make 3 rows of 5". Insist that rows are straight and equal — a wonky arrangement is not an array. Have them count the total, then say the two facts: "3 rows of 5" and "15 altogether".
- 2
Draw it (pictorial)
Move to dot arrays on squared paper or a printed grid. Drawing forces students to keep rows and columns aligned and frees them from needing counters for every problem.
- 3
Name the structure with language
Fix the sentence stem "___ rows of ___" before any symbols. Consistent language (rows, columns, equal groups) prevents the classic mix-up of counting rows as columns.
- 4
Write the multiplication fact (abstract)
Connect the picture to 3 × 5 = 15, then to the repeated addition 5 + 5 + 5. Show that both describe the same array so students see multiplication as a shortcut for equal groups.
- 5
Turn it to prove commutativity
Rotate the array to reveal 5 × 3 = 15 and discuss why the total did not change. This is a rich, low-floor high-ceiling discussion that suits mixed-ability classes.
- 6
Extend to division and the distributive property
Cover rows to reveal 15 ÷ 3 and 15 ÷ 5, then split larger arrays (e.g. 6 × 7 into 6 × 5 + 6 × 2) to introduce partitioning and, later, the area model.
Hands-on array activities
Egg carton arrays
A standard carton is a ready-made 2 × 6 array. Drop counters in to model 2 × 6 = 12, then challenge students to find other 12-arrays (3 × 4, 1 × 12).
Array city
Students draw buildings and fill each with a grid of windows, then label the rows × columns fact under each one. Great for a display and for spotting equal groups in the real world.
Dot-sticker challenge
Give a total (say 24) and a sheet of dot stickers. Students make every array they can (1 × 24, 2 × 12, 3 × 8, 4 × 6) — a concrete introduction to factors.
Array photo hunt
Students photograph or sketch real arrays around school — muffin trays, tiles, lockers, garden beds — and write the number sentence each one shows.
Cover-and-solve
Show an array, cover part of it, and ask what is hidden. This turns arrays into a reasoning task and previews the distributive property.
Fact-family cards
From one array, students write all four facts (two multiplication, two division). A quick, printable warm-up that reinforces the array as one connected picture.
Common misconceptions to watch for
A few predictable errors show up every year:
- Unequal rows. Students scatter objects and still call it an array. Keep insisting that every row and column must be equal — this is the defining property.
- Confusing rows and columns. "3 rows of 4" and "4 rows of 3" look different on the page even though the total matches. Use a consistent sentence stem and colour rows and columns differently at first.
- Counting all instead of multiplying. Some students draw a perfect array and then count each dot. Prompt them with "How could you find the total without counting every one?" to nudge them toward the multiplication fact.
- Thinking rotation changes the answer. Rotating a 3 × 4 array unsettles students who believe 3 × 4 and 4 × 3 must be different. Physically turning a card is the fastest way to resolve it.
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Try the AI worksheet generatorFrequently asked questions
An array is a set of objects arranged in equal rows and columns, such as counters in a grid or the cups in an egg carton. Because the rows and columns are equal, an array can be counted by multiplying — you read it as rows × columns.
In the Australian Curriculum, arrays are introduced in Year 2 as a way to represent multiplication as equal groups. They are revisited in Years 3–4 to build multiplication facts and division, and later underpin the area model for larger multiplication.
A 3 × 4 array has 3 rows and 4 columns — that is 3 rows of 4, which equals 12. Rotate it and it becomes a 4 × 3 array (4 rows of 3), which also equals 12, showing that multiplication is commutative.
The same array holds two division facts. If a 3 × 4 array shows 3 × 4 = 12, then sharing the 12 counters into 3 rows shows 12 ÷ 3 = 4, and into 4 rows shows 12 ÷ 4 = 3. Teaching them together builds fact families.
They describe the same thing from two angles. A 2 × 5 array can be read as the repeated addition 5 + 5 = 10 or as the multiplication 2 × 5 = 10. Arrays help students see multiplication as a faster way to add equal groups.