Maths
What is an array in maths?
Quick answer
An array is a set of objects arranged in equal rows and columns. 3 rows of 4 dots is an array that shows 3 × 4 = 12, so arrays help children see multiplication.
In one sentence
An array is a group of objects set out in neat rows and columns, with the same number in every row.
Explained
Look at an egg box. It has 2 rows, and each row holds 6 eggs. That is an array. Rows go across, from left to right. Columns go up and down. The one rule that makes something an array is that every row has the same number of objects (and so every column does too).
egg
cupcake
cookie
Arrays are the clearest picture of multiplication. The number of rows times the number in each row gives the total. 3 rows of 4 dots is 3 × 4 = 12. You do not need to count every dot one by one: count one row (4), then skip-count down the rows: 4, 8, 12. That is the same as the repeated addition 4 + 4 + 4.
Now turn the array on its side. The 3 rows of 4 become 4 rows of 3. Nothing was added or taken away, so the total is still 12. This shows that 3 × 4 = 4 × 3: you can multiply in either order (mathematicians call this the commutative property). One array, two multiplication facts, and half as many times tables facts to learn.
Arrays work backwards too. Start with 12 cookies and put them into 3 equal rows: each row gets 4, so 12 ÷ 3 = 4. Put them into rows of 4 instead and you get 3 rows, so 12 ÷ 4 = 3. A single array gives a whole fact family: 3 × 4 = 12, 4 × 3 = 12, 12 ÷ 3 = 4 and 12 ÷ 4 = 3.
Arrays also help with bigger multiplications. To find 6 × 7, draw 6 rows of 7 and cut it into two smaller arrays: 6 rows of 5 (30) and 6 rows of 2 (12). Together that is 30 + 12 = 42. Later on, the dots turn into squares, and the array becomes a rectangle whose area is length × width. The "grid method" for long multiplication is the same idea.
Examples
| Array | Rows | In each row | Multiplication | Total |
|---|---|---|---|---|
| Egg box | 2 | 6 | 2 × 6 | 12 |
| Muffin tray | 3 | 4 | 3 × 4 | 12 |
| Chocolate bar | 4 | 5 | 4 × 5 | 20 |
| Window panes | 3 | 3 | 3 × 3 | 9 |
| Carrots in a garden | 5 | 10 | 5 × 10 | 50 |
Worked example: chairs in a classroom are set out in 4 rows with 6 chairs in each row. Skip-count by 6: 6, 12, 18, 24. So 4 × 6 = 24 chairs. Turned around it would be 6 rows of 4, and 6 × 4 is also 24.
Common mistakes
- Rows with different numbers. A row of 5 and a row of 3 is not an array. Fix: line the objects up on a grid and check every row has the same count.
- Mixing up rows and columns. Fix: rows go across, like rows of seats in a cinema; columns stand up tall, like the columns holding up a building.
- Counting every dot one by one. It is slow and easy to lose your place. Fix: count one row, then skip-count by that number.
- Thinking 3 × 4 and 4 × 3 give different answers. Fix: turn the paper sideways. It is the same array.
Step by step
Step by step
- Count the rowsHow many rows go across?
- Count one rowHow many objects are in each row? Check that every row has the same number.
- Write the multiplicationNumber of rows × number in each row, for example 3 × 5.
- Find the totalSkip-count down the rows (5, 10, 15) or use a times table fact: 3 × 5 = 15.
- Turn it to checkRead the columns as rows to get the other fact: 5 × 3 = 15.
To draw an array for a multiplication such as 4 × 2, draw 4 rows with 2 dots in each row, keeping the dots in straight columns.
Practice questions
Arrays
Try each one, then check your answer.
- An array has 2 rows of 5 dots. How many dots?
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2 × 5 = 5 + 5 = 10 - An array has 3 rows of 3 apples. How many apples?
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3 × 3 = 9 - An array has 4 rows of 2 cars. How many cars?
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4 × 2 = 2 + 2 + 2 + 2 = 8 - An array has 5 rows of 4 stars. How many stars?
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5 × 4 = 20 - Write the multiplication for 3 rows of 6.
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3 × 6 = 18 - Write the repeated addition for 4 rows of 3.
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3 + 3 + 3 + 3 = 12 - An array shows 2 × 7. Turn it on its side. Which fact do you see?
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7 × 2 = 14 - Describe the array for 4 × 5.
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4 rows with 5 in each row (20 altogether) - An array has 10 rows of 2. How many altogether?
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10 × 2 = 20 - 15 counters are put into 3 equal rows. How many are in each row?
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15 ÷ 3 = 5 - 18 counters are put into rows of 6. How many rows?
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18 ÷ 6 = 3 rows - Write the fact family for the array 2 rows of 8.
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2 × 8 = 16, 8 × 2 = 16, 16 ÷ 2 = 8, 16 ÷ 8 = 2 - Which arrays can you make with 12 counters?
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1 × 12, 2 × 6, 3 × 4, 4 × 3, 6 × 2 and 12 × 1 - Split a 6 × 7 array into 6 × 5 and 6 × 2. What is the total?
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30 + 12 = 42 - Can 7 counters make an array with more than one row and more than one column?
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No. 7 can only be 1 row of 7 or 7 rows of 1.
Word problems
Arrays in real life
Try each one, then check your answer.
- A muffin tray has 3 rows with 4 muffins in each row. How many muffins?
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3 × 4 = 12 muffins - A garden has 5 rows of tomato plants with 6 plants in each row. How many plants?
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5 × 6 = 30 plants - A small cinema has 8 rows with 10 seats in each row. How many seats?
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8 × 10 = 80 seats - 24 chairs are set out in 4 equal rows. How many chairs are in each row?
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24 ÷ 4 = 6 chairs - A chocolate bar has 4 rows of 6 pieces. You eat one whole row. How many pieces are left?
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3 rows of 6 are left: 3 × 6 = 18 pieces - Sam's sticker sheet has 3 rows of 5. Mia's has 4 rows of 4. Who has more stickers, and how many more?
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Sam has 15 and Mia has 16, so Mia has 1 more.
Questions people ask
What is an array in maths?
An array is an arrangement of objects, pictures or numbers in equal rows and columns. It is used to show multiplication and division, because the total is always the number of rows times the number in each row.
What is an array in multiplication?
It is a picture of a multiplication fact. 3 × 5 can be drawn as 3 rows of 5 dots; counting them gives 15. Turning the array around shows that 5 × 3 is the same.
What is the difference between rows and columns?
Rows go across (horizontal) and columns go up and down (vertical). In an array of 3 rows of 4, there are 4 columns of 3.
How do arrays help with division?
Division is building an array from the total. To work out 20 ÷ 4, set out 20 counters in 4 equal rows: each row has 5, so 20 ÷ 4 = 5.
Why do teachers use arrays?
Arrays show why multiplication works, not just the answer. They make the commutative property easy to see, link multiplication to division, and lead straight into area and the grid method for bigger numbers.
What is an array in programming?
In computing, an array is a list of values stored under one name, such as scores = [5, 8, 3], where each value has a numbered position (in most languages, counting starts at 0). A two-dimensional array has rows and columns, just like a maths array. This page is about the maths meaning.
Quick quiz
Arrays
Check what you know with 5 quick questions.
Question 1 of 5
An egg box has 2 rows with 6 eggs in each row. Which multiplication matches it?
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For grown-ups
Related topics
Multiplication
Multiplication is adding equal groups quickly. 4 × 3 means 4 groups of 3 (or 3 groups of 4), which makes 12. The answer is called the product.
Times tables
Times tables are lists of the multiplication facts for a number, such as 3 × 1 = 3 up to 3 × 12 = 36. Knowing them by heart speeds up almost all later maths.
Division
Division is sharing into equal groups, or finding how many groups fit. The sign is ÷, so 12 ÷ 3 = 4. The answer is called the quotient.
Area
Area is the amount of flat space inside a shape, measured in square units like cm² or m². A rectangle 4 cm by 3 cm has an area of 4 × 3 = 12 cm².
Long multiplication
Long multiplication multiplies a big number by splitting the second number into ones, tens and hundreds, finding each part, then adding the results together.
The 24-hour clock
The 24-hour clock counts the hours from 00:00 at midnight to 23:59, so there is no am or pm. For afternoon times, add 12: 3 pm is 15:00.