X Tables
Times Table Methods

Multiplication as arrays

Use rows and columns to make multiplication visible and prepare for area.

Quick answer

Multiplication as arrays means arranging objects in rows and columns to show how many groups there are and how many objects are in each group. This helps us understand multiplication and prepares us for learning area.

Learning outcome

By the end of this page, you will understand how to use arrays to show multiplication problems and solve them by counting rows and columns. Success signs:
  • You can draw arrays for multiplication problems
  • You can count rows and columns to find the total
  • You can match arrays to multiplication sentences
  • You can solve multiplication problems using arrays

Why this matters

Arrays help you understand multiplication better. When you see objects arranged in rows and columns, you can quickly see how many groups there are and how many are in each group. This skill is important for:
  • Learning times tables
  • Understanding area in maths
  • Solving word problems
  • Building mental pictures for maths
Arrays are used in games, cooking, and everyday life when you need to count things in groups.

How it works

Arrays are like grids of objects. Each row has the same number of objects, and each column has the same number of objects. To solve a multiplication problem using arrays:
  1. Draw the rows (horizontal lines)
  2. Draw the columns (vertical lines)
  3. Count the number of rows
  4. Count the number of objects in each row
  5. Multiply rows × objects per row
Arrays help you see multiplication visually and make it easier to understand.

Examples you can see

Let's look at some examples of arrays to understand how they work. Example 1: 3 × 4
  • Draw 3 rows
  • Each row has 4 objects
  • Count all objects: 4 + 4 + 4 = 12
  • So 3 × 4 = 12
Example 2: 5 × 2
  • Draw 5 rows
  • Each row has 2 objects
  • Count all objects: 2 + 2 + 2 + 2 + 2 = 10
  • So 5 × 2 = 10
Example 3: 2 × 6
  • Draw 2 rows
  • Each row has 6 objects
  • Count all objects: 6 + 6 = 12
  • So 2 × 6 = 12
You can draw arrays with any objects: counters, toys, stickers, or even your fingers!

Try it as a mini adventure

Adventure: The Garden Plot You are a gardener planning a new vegetable garden. You want to plant carrots in rows. You decide to plant 4 rows of carrots, with 5 carrots in each row.
  1. Draw 4 rows
  2. Draw 5 carrots in each row
  3. Count all the carrots
  4. Write the multiplication sentence
Your garden has 4 rows of 5 carrots each. How many carrots do you plant in total? Answer: 4 × 5 = 20 carrots You can also make the garden bigger by planting 6 rows of 3 carrots each. How many carrots do you plant now? Answer: 6 × 3 = 18 carrots

Common mistakes

  • Mistake: Counting the rows and columns separately instead of multiplying them together.
    Why it happens: Confusing counting with multiplication.
    Fix: Remember that rows × columns = total objects.
  • Mistake: Drawing arrays with different numbers in each row or column.
    Why it happens: Not understanding that arrays must have equal groups.
    Fix: Make sure each row has the same number of objects and each column has the same number.
  • Mistake: Forgetting to count all the objects in the array.
    Why it happens: Rushing or not looking carefully.
    Fix: Count row by row or column by column to make sure you don't miss any.
  • Mistake: Writing the multiplication sentence in the wrong order.
    Why it happens: Not understanding which number is rows and which is columns.
    Fix: Remember: rows × columns = total.

Parent and carer guide

You can help your child understand arrays in just a few minutes:
  • Use everyday objects like buttons, coins, or crayons to make arrays
  • Ask your child to show you how many rows and columns there are
  • Encourage them to count by groups instead of one by one
  • Play array games using stickers or drawings
  • Look for arrays in the real world: egg boxes, window panes, or chocolate bars
Don't worry if they make mistakes – arrays are a new way of thinking, and practice helps!

Practice questions

  1. Draw an array for 3 × 4. How many objects are there?
  2. Draw an array for 5 × 2. How many objects are there?
  3. Draw an array for 2 × 7. How many objects are there?
  4. Draw an array for 6 × 3. How many objects are there?
  5. Draw an array for 4 × 5. How many objects are there?
Answers:
  1. 3 rows of 4 objects = 12 objects
  2. 5 rows of 2 objects = 10 objects
  3. 2 rows of 7 objects = 14 objects
  4. 6 rows of 3 objects = 18 objects
  5. 4 rows of 5 objects = 20 objects

Times table facts: 3 times table as arrays

3 × 0 3 × 1 3 × 2 3 × 3 3 × 4 3 × 5 3 × 6 3 × 7 3 × 8 3 × 9 3 × 10 3 × 11 3 × 12
0 3 6 9 12 15 18 21 24 27 30 33 36

FAQ

What is an array in maths?

An array is a way to arrange objects in rows and columns to show multiplication. Each row has the same number of objects, and each column has the same number of objects.

How can I use arrays to solve multiplication problems?

You can draw rows and columns of objects, then count how many rows there are and how many objects are in each row. Multiply rows by objects per row to find the answer.

Why are arrays useful for learning multiplication?

Arrays help you see multiplication visually. They make it easier to understand how groups work and prepare you for learning area and more advanced maths.

Can I use arrays with any multiplication problem?

Yes! Arrays work for any multiplication problem. You can make arrays with 1 row, 2 rows, 10 rows, or any number of rows.

How do arrays connect to real life?

Arrays appear everywhere: egg cartons, window panes, chocolate bars, and garden plots. Understanding arrays helps you count things more quickly and understand how groups work in the world around you.