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Learning the 9 Times Table: Tricks and Teaching Tips

At first glance, the 9 times table can look intimidating. The numbers get big quickly, and many children feel a little overwhelmed when they first meet it. But the truth is, the 9s are one of the most satisfying tables to learn – once you know how to spot the patterns.

In fact, many children end up loving the 9 times table once they’re shown how it works. From finger tricks to number patterns, this table is full of clever ways to make learning easier, faster and more fun.

Whether you’re a parent helping at home or a teacher looking for a new way to engage your class, this blog will guide you through how to teach, explain and remember the 9 times table – and why it might become your child’s favourite.

How to learn the 9 times table fast?

Times tables can take a while to understand. But the 9s lend themselves to quick learning because of how full of patterns they are! The key to learning the 9 times table fast is in helping your child notice these patterns, then giving opportunities to practise in lots of different ways (like singing, practical examples and tricks like finger counting). Visual tools like multiplication grids also make a big difference.

A good place to start is showing your child where the 9s sit in the wider world of multiplication. Take a look at a multiplication grid like this:

1	2	3	4	5	6	7	8	9	10
2	4	6	8	10	12	14	16	18	20
3	6	9	12	15	18	21	24	27	30
4	8	12	16	20	24	28	32	36	40
5	10	15	20	25	30	35	40	45	50
6	12	18	24	30	36	42	48	54	60
7	14	21	28	35	42	49	56	63	70
8	16	24	32	40	48	56	64	72	80
9	18	27	36	45	54	63	72	81	90
10	20	30	40	50	60	70	80	90	100

Pointing out how the 9s feature in times tables your child already knows (like the 2s, 5s or 10s) helps them see they’re not learning something completely new – they’re building on something familiar. You can also challenge your child to fill in the 9s themselves, or play a game where they find and circle all the multiples of 9!

If your child is preparing for GCSE Maths, a solid grasp of times tables makes a huge difference. Not only does it boost their confidence, but it also helps them work faster and more accurately. It’s one of those foundational skills that keeps paying off—not just for GCSEs, but right through secondary school.

And it doesn’t stop there. Whether they go on to study A Level Maths, Chemistry, Economics or even subjects like Accounting or Finance at university, quick recall of multiplication facts is a real asset.

Is there a pattern in the 9 times table?

Yes, there is a pattern in the 9 times table. In fact, it’s one of the most fascinating patterns of all the times tables. Children often light up when they notice it for the first time because it feels like they’ve cracked a secret code!

Here are the first 10 multiples of 9:

1 × 9 = 9
2 × 9 = 18
3 × 9 = 27
4 × 9 = 36
5 × 9 = 45
6 × 9 = 54
7 × 9 = 63
8 × 9 = 72
9 × 9 = 81
10 × 9 = 90

Have you noticed anything yet?

The tens digit increases by 1 each time (0, 1, 2, 3, 4, 5, 6, 7, 8, 9)
The ones digit decreases by 1 each time (9, 8, 7, 6, 5, 4, 3, 2, 1, 0)
They also all add up to nine. 1+8, 2+7, 3+6 (etc) = 9. It’s pretty incredible really!

So while the numbers get bigger, they follow a clear and comforting pattern. This makes the 9s one of the easiest tables to predict once children get the hang of it.

How do you explain the pattern of the 9 times table?

To help children understand and remember this pattern, make it feel like a discovery. Don’t just tell them the answers – get them to explore. You might:

Ask them to write out the 9s from 1 to 10
Encourage them to spot what’s happening in each digit
Point out how the digits in each answer always add up to 9

For example:

2 × 9 = 18 → 1 + 8 = 9
4 × 9 = 36 → 3 + 6 = 9
9 × 9 = 81 → 8 + 1 = 9

This digit-sum pattern is not only helpful for memory – it also gives children a built-in error-checking tool. If their answer to 6 × 9 doesn’t add up to 9, they know they’ve made a mistake somewhere!

Mastering times tables lays the groundwork for bigger leaps in learning. Once the foundations are there, children are much better equipped to tackle challenges like square numbers, cube numbers and beyond.

What’s the trick to the 9 multiplication?

One of the most famous multiplication tricks is the finger trick for the 9s – and it works brilliantly, especially for younger children.

Here’s how to do it:

Hold both hands up in front of you with fingers spread.
To work out 3 × 9, fold down your third finger (left to right).
Count the fingers to the left of the one that’s down. That’s your tens digit.
Count the fingers to the right. That’s your ones digit.

So 3 × 9 = 2 fingers left, 7 fingers right = 27

Children love how physical and visual this is. It turns maths into something they can hold in their hands.

Why does the 9 multiplication trick work?

This trick works because of how the number 9 behaves in our base-10 system. Each time you multiply by 9, it’s the same as multiplying by 10 and then subtracting one group.

For example:

9 × 4 = (10 × 4) – 4 = 40 – 4 = 36

The finger trick cleverly represents that subtraction with physical movement. By putting down one finger, you’re splitting 10 into two parts (one on either side) representing the digits in the answer. It works up to 10 × 9, which makes it perfect for KS1 and lower KS2 learners.

Once children understand why it works, the trick becomes a tool rather than a crutch – one they can build on with mental maths.

What’s the rule for the 9 times table?

If there’s one standout pattern in the 9 times table, it’s this:

The digits in each answer always add up to 9.

It’s a simple rule, but surprisingly powerful – and children love it once they spot it. For example:

2 × 9 = 18 → 1 + 8 = 9
4 × 9 = 36 → 3 + 6 = 9
9 × 9 = 81 → 8 + 1 = 9

This pattern isn’t just fun. It’s useful. It can be used to:

Check answers quickly: if the digits don’t add to 9, something’s off
Boost memory: the rule sticks in children’s heads and helps with recall
Build number confidence: children start to see multiplication as logical and structured, not just a list of random facts.

Recognising this kind of pattern also shows children that maths has its own rhythm and order – and that discovering those patterns can actually be fun. For many children, noticing this in the 9 times table is a real lightbulb moment.

Looking for fun, interactive ways to boost Maths skills? Check out our detailed reviews of top revision platforms like Corbett Maths, Maths Genie, Seneca Learning, MathsWatch and Physics and Maths Tutor – perfect for finding the right fit for your child.

How do you teach the 9 times table?

The 9 times table is full of clever patterns and tricks that make it surprisingly enjoyable to teach. With the right approach, children can move beyond memorisation and understand how the 9s work. The key is focusing on patterns, using practical tools and building fluency through regular, playful practice.

Here are five practical tips for teaching the 9s in a way that builds understanding, confidence and long-term fluency:

1. Start with patterns

Begin by laying out the 9 times table and letting children explore what they notice. The digits in each answer go up in the tens and down in the ones – and the digits always add up to 9. Encourage children to spot these patterns for themselves before explaining. Discovery often sticks better than instruction.

2. Use the finger trick for early fluency

The finger trick is a brilliant visual aid for the 9s. It’s fun, easy to remember, and gives children a quick way to check their answers – perfect for building early confidence.

3. Link it to the 10 times table

Help children use what they already know:

9 × a number = 10 × that number – the number itself.
So, 9 × 7 = (10 × 7) – 7 = 63.

This reinforces place value and strengthens mental maths skills too.

4. Practise in different ways

Variety is key. Try chanting, flashcards, number games, multiplication apps, or even making a song or rap. Short, lively sessions keep it fun and stop things from feeling repetitive.

5. Keep revisiting

Times tables are best learned through repetition. Quick-fire questions over breakfast, skip counting in the car, or singing the 9s while getting ready for school – every bit helps. The goal is long-term recall, not cramming.

Whether your child is preparing for SATs or heading towards A Levels, we’ve created clear, helpful overviews to support them at every step. From key GCSE Maths topics and exam board comparisons to dedicated guides for Core Maths and A Level Maths students – we’re here to make the journey smoother.

What order should I teach the times tables?

There’s no one-size-fits-all rule on the order of teaching times tables. But most successful teachers and tutors follow a progression that builds on what children already know. The idea is starting with the simplest, most pattern-based tables and then moving towards the more complex ones. This helps confidence grow step-by-step.

Here’s a suggested order that supports steady progress:

2 times table: Often the first to be taught, because it’s based on doubling and feels intuitive.
10 times table: With a clear, predictable pattern (just add a zero), making it great for early success.
5 times table: Rhythmic and familiar, especially when counting in 5p or 5-minute intervals.
3 times table: Introduces trickier odd-number patterns, but connects well to 6s and 9s.
4 times table: Builds on 2s (double the double), helping children feel more secure.
6 times table: A bit tougher, but can be introduced as double the 3s.
9 times table: Packed with patterns and logic, great for children ready to spot structure.
8 times table: Can be more difficult, but essentially double the 4s.
7 times table: Often saved for later as it lacks obvious shortcuts or patterns.
11 and 12 times tables: These go beyond the core KS2 requirement but help with fluency and mental maths speed in upper primary.

This order isn’t set in stone, but gives a helpful framework. By introducing the easiest and most useful tables first, you help build your child’s confidence. This makes it much easier for them to tackle the trickier ones later on.

In summary: what’s the secret of the 9 times table?

The 9 times table might seem tough at first, but once children start spotting the patterns, it quickly becomes one of the most enjoyable to learn! With digit patterns, the finger trick, and a strong link to the 10 times table, there are multiple ways to master it.

At Achieve Learning, we support children at every stage of their maths journey – from their first times tables to success in the 11 Plus, SATs and GCSE Maths. With over 20 years’ experience, our expert tutors offer 1-1 support tailored to your child’s needs. To help your child feel confident and thrive in Maths, get in touch with Achieve Learning today.

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Learning the 6 Times Table: Tricks and Teaching Tips

Learning times tables is one of those building blocks that opens so many doors in maths. For many children, the early ones (2s, 5s and 10s) come fairly easily. They’re rhythmic,follow neat patterns and pop up often in real life – counting socks, hands, coins and fingers.

But when children hit the 6 times table, it can feel like the safety net has been taken away.

The 6s are trickier: the numbers are bigger, patterns less obvious and the shortcuts fewer. But that doesn’t mean they have to be scary. With the right approach, the 6 times table can be a brilliant opportunity to stretch your child’s number sense, build connections to other tables and develop understanding.

In this guide, we’ll explore patterns, tricks, memory tools and strategies to make the 6 times table much more approachable. Let’s get started.

How to learn the 6 times table easily

Before you jump into repetition or memory tools and tricks, it’s helpful to introduce the 6 times table in context – as part of a bigger system. To help children learn the 6 times table easily, introduce it as just part of the times tables they already know. One of the best tools for this is the multiplication grid, where children can see how the 6s relate to other numbers.

Here’s an example of a 1-10 multiplication grid, with the 6s highlighted:

1	2	3	4	5	6	7	8	9	10
2	4	6	8	10	12	14	16	18	20
3	6	9	12	15	18	21	24	27	30
4	8	12	16	20	24	28	32	36	40
5	10	15	20	25	30	35	40	45	50
6	12	18	24	30	36	42	48	54	60
7	14	21	28	35	42	49	56	63	70
8	16	24	32	40	48	56	64	72	80
9	18	27	36	45	54	63	72	81	90
10	20	30	40	50	60	70	80	90	100

Grids like these are a great way to show that multiplication facts aren’t random – they’re connected.

Children who are visual learners especially benefit from seeing the 6s in context. Encourage your child to explore: What do they notice? How do the 6s fit in with the 3s? Can they spot the same numbers appearing in different rows? Can they find all the multiples of 6 in a longer grid?

This is especially powerful when combined with activities that encourage active discovery. For instance, you could even turn the grid into a colouring activity, a memory game or a speed challenge. Reinforcing the 6 times table in multiple ways helps ensure it sticks.

If your child is approaching GCSE Maths, feeling totally secure with times tables will help confidence and speed. It’s a core skill that will stand them in good stead throughout secondary education, especially if they choose A Level Maths (and related subjects like Economics or Chemistry).

Of course, times tables are also essential tools that will stay with your child through university (particularly helpful for courses like Economics or Accounting and Finance) and beyond.

What’s the rule for the 6 times table?

Unfortunately, there’s no magic rule for multiplying by 6, unlike the neat “add a 0” trick we have for 10s. But there are key ideas that help children make sense of what’s going on.

Firstly, the 6 times table always produces even numbers – because 6 itself is even. This is a great pattern to point out to children who like certainty. If the answer to a 6 multiplication question isn’t even, something’s gone wrong.
Secondly, 6 is made up of 3 × 2 – which means every multiple of 6 is also a multiple of 3 and 2. This is especially useful if your child already knows their 3 times table. You can say, “If you know 3 × 4 is 12, then just double it – 6 × 4 is 24.” This strategy reinforces what they know and stretches their thinking without overwhelming them.

These “rules” are more like shortcuts to understanding. They help your child feel more secure and capable when facing unfamiliar multiplication problems.

Is there a pattern in the 6 times table?

Yes! And patterns are often the key to making learning ‘click’! Many children find comfort in spotting something repeatable and predictable. The 6 times table has several lovely patterns to explore.

Here are the 6s up to 10:

1 × 6 = 6
2 × 6 = 12
3 × 6 = 18
4 × 6 = 24
5 × 6 = 30
6 × 6 = 36
7 × 6 = 42
8 × 6 = 48
9 × 6 = 54
10 × 6 = 60

You might have spotted some patterns yourself. Here are a few to share with your child:

The ones digits repeat in a cycle: 6, 2, 8, 4, 0, then start again. Neat, right?
It might be obvious to us, but remember to point out to your child that the difference between each number is always 6. This reinforces the idea of multiplication as repeated addition.
Each answer is a multiple of 2 and 3 – perfect for making links across other known tables.
The digit sums (adding the digits together) often give 3, 6 or 9. For example:
- 1 × 6 = 6 → 6
- 2 × 6 = 12 → 1 + 2 = 3
- 3 × 6 = 18 → 1 + 8 = 9
- Can you spot the odd one out in the list above? Clue: take a look at 8 x 6.

These patterns turn the 6 times table into a logic puzzle rather than a list to memorise. For many children, especially those who enjoy structure and order, this can be a turning point in their confidence.

Once key concepts like times tables stick, children can move on to topics like square numbers and cube numbers with ease.

What’s the trick for multiplication by 6?

When children begin to see the 6 times table connected to what they already know, they feel much more confident. There might not be one universal trick, but there are several useful techniques that make multiplication by 6 quicker and less stressful.

Here are a few handy ones:

Double the 3s: This is probably the most effective trick. If your child knows 3 × 7 = 21, they can double the answer to get 6 × 7 = 42. It helps reinforce the idea that multiplication builds on known facts.
Break down into parts (5 + 1): You can think of 6 × a number as 5 × that number plus 1 × that number. This works especially well for mental maths:
- 6 × 9 = (5 × 9) + (1 × 9) = 45 + 9 = 54
Use familiar facts: As a similar tip, build on tables they already feel confident with. For example, if they know 5 × 6 = 30, they can find 6 × 6 by adding one more group of 6.
Turn it into a chant or rhyme: Musical memory is powerful. Clapping, chanting, or singing multiplication facts in rhythm helps them stick. Use 6 times table songs from school, YouTube or create your own together.

These tricks don’t just build speed, they help develop flexible problem-solving. And for many children, that’s the key to moving from memorisation to mastery.

For fun and interactive Maths learning, don’t miss our in-depth reviews of revision websites, including: MathsWatch, Seneca Learning, Physics and Maths Tutor, Maths Genie and Corbett Maths.

What’s the strategy for learning 6 times tables?

The best strategy for learning the 6 times table is a combination of understanding, regular exposure, and playful practice. Children are far more likely to remember facts when they feel involved in the learning process, and when the material feels connected to what they already know.

With this in mind, start by identifying what your child is confident with. If they’ve got their 2s, 3s or 5s in place, you can use those as stepping stones. Remind them that the 6s are not entirely new territory – they’re just the next logical step!

Here are some strategies that work well:

Use concrete materials: Counters, building blocks, or even spoons and socks! Let your child group them into sets of six and physically count them.
Group in real life: Make it relevant. Six legs on an insect? Six petals on a flower? Six eggs in a box? When maths shows up in everyday life, it feels more meaningful.
Skip count in sixes: Use chants and claps: “6, 12, 18, 24…” March around the room or hop as you say each number.
Connect to other times tables: Ask your child, “What’s 3 × 5? What’s double that?” It encourages reasoning, not just remembering.
Mix it up: Don’t always go in order. Try 6 × 7, then 6 × 2, then 6 × 9. This helps your child recall facts independently, not just through rhythm.

Children learn best when they feel capable and curious, and these strategies should support both!.

What’s the best way to memorise the times tables?

Memorising times tables takes time, but as we’ve seen, it’s much easier when children understand the patterns and structure behind the numbers. Once that understanding is in place, it’s all about regular, varied exposure.

Here are some memory techniques to try:

Flashcards: Simple, effective, and easy to tailor to your child’s level. Make your own or use an app like Quizlet.
Call and response games: You say “6 times 7”, they shout “42!” These quick-fire games are great in the car or on a walk.
Times table songs: There are so many catchy times table songs, including the 6s. They’re fun and great for auditory learners.
Draw it out: Use visual organisers like multiplication wheels or bar models. These help children see how the numbers fit together.

Most importantly, keep it positive and pressure-free. Praise effort over speed, and celebrate small wins. A confident child will keep trying, and that’s what builds lasting knowledge.

How do you teach multiplication in 6 easy steps?

Finally, it’s important to note that teaching multiplication doesn’t have to mean diving straight into times tables! In fact, it’s far more effective (and less stressful) to build up your child’s understanding step by step.

This six-step approach works well across Key Stage 1 and Key Stage 2, and it can be easily adjusted depending on your child’s confidence level, age and learning style. Each step helps children move from concrete ideas to more abstract thinking, laying the foundations for both memory and understanding. And most importantly, it keeps learning fun, approachable, and connected to the real world.

Start with repeated addition: Show that 6 × 3 is the same as 6 + 6 + 6. Use real objects to link addition and multiplication.
Use concrete materials: Then, group items into sixes. This helps children understand multiplication as ‘equal groups’ rather than abstract numbers.
Introduce the multiplication symbol (×): Explain that 6 × 4 means six groups of four. Write it out in different ways to reinforce understanding – building on what you spoke about with household items.
Practise skip counting in sixes: Once they’ve understood the concept of multiplication, chant, sing, stomp, clap – whatever keeps your child engaged! Rhythm and movement make learning stick.
Build a multiplication grid: Let your child help fill in their own grid. Highlight the 6s (or other times tables) and look for patterns. This boosts both memory and understanding.
Apply it to real-life situations: Finally, ask questions like “If there are 6 pencils in each box and you have 4 boxes, how many pencils?” Real-world questions make maths feel relevant.

These steps don’t need to be done all at once. Spread them over a week or revisit them regularly. The goal is to build confidence, not rush. And once your child has confidence with times tables like the 6s, you can repeat the same steps with other times tables like 7s, 8s and 9s!

To help your child at every stage of their Maths journey, we’ve compiled introductions (including key Maths GCSE content, exam boards and their respective difficulty!), as well as guides for Core Maths and A Level Maths students.

Does your child need help with Maths?

At Achieve Learning, we believe every child deserves to feel confident in maths. Whether your child is just getting to grips with the 6 times table or preparing for major milestones like SATs, the 11 Plus or GCSE Maths and English, we’re here to help.

With over 20 years’ experience, our expert 1-to-1 tutors create a supportive, tailored environment that helps children succeed and thrive. Get in touch today to find out more.

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What Are Cube Numbers? Definitions and Examples

When it comes to maths, some numbers have special properties that make them stand out. You might have heard of square numbers, but what about cube numbers? If you’ve ever wondered what cube numbers are, why they matter, and how to explain them to children, you’re in the right place.

Cube numbers are fascinating because they grow quickly and have unique properties that make them useful in real-life situations. They also open doors to bigger mathematical ideas.

So whether you’re a parent or teacher looking for teaching ideas and examples, a student tackling the concept, or just someone after a simple explanation, here’s everything you need. We’ll explain cube numbers in a way that’s simple, engaging and full of practical examples.

What is a cube number in maths?

Let’s start with a simple definition.

A cube number is the result of multiplying a whole number by itself three times. So in mathematical terms, it’s a number “raised to the power of three”. For example, 8 is a cube number. Why? Well, 2 multiplied by 2 is 4. Then, times 4 by 2 again. And there’s your answer. 2 x 2 x 2 = 8. Although they may sound complicated, that’s all there is to cube numbers!

Here are a few more examples:

1 × 1 × 1 = 1 → So, 1 is a cube number.
2 × 2 × 2 = 8 → So, as we’ve seen, 8 is a cube number.
3 × 3 × 3 = 27 → So, 27 is a cube number.
4 × 4 × 4 = 64 → And 64 is a cube number too.

If you’ve ever worked with square numbers (where you multiply a number by itself), cube numbers follow a similar pattern. Except this time, you’re multiplying three times instead of two. The difference is cube numbers grow much faster than square numbers. For example, squaring 4 gives you 16, but cubing it gives you 64—a much bigger jump!

Cube numbers also help us understand the concept of dimensions. A square number represents an area (length × width), whereas a cube number represents a volume (length × width × height). This brings us nicely to the question—why are cube numbers important?

Why are cube numbers important?

Cube numbers aren’t just a fun maths trick. They have real-world uses in maths, science, and even technology. At school, cube numbers are mostly used to calculate volume, but learning them helps build a strong foundation for future maths and problem-solving skills.

Here’s why they matter:

Volume calculations: Cube numbers help us work out the space inside a cube. Imagine a cube 3 blocks wide, 3 blocks deep, and 3 blocks tall. To find out how much space it takes up, you multiply 3 × 3 × 3 = 27 cubic units. Cube numbers make volume calculations quick and simple!
Building blocks for advanced maths: Knowing cube numbers makes it easier to understand cube roots, indices (powers) and exponential growth. These topics are important for GCSEs and A Levels, appearing in algebra, problem-solving and even economics.
Science and engineering: Many real-world formulas involve cube numbers, especially in physics, chemistry and engineering. They help scientists calculate things like gravity, energy and force, which are essential for designing everything from buildings to roller coasters.
Computing and technology: Cube numbers are used in computer programming and data organisation. They help speed up algorithms, which makes technology like search engines and game development more efficient.
Spotting patterns: Cube numbers appear in many maths puzzles and number sequences. They help us recognise trends and relationships between numbers, which is useful in problem-solving and logical thinking (helpful if you’re preparing for non-verbal reasoning sections of the 11 Plus).

What are cube numbers for kids?

Cube numbers might sound fancy, but they’re just what happens when you multiply a number by itself three times—like 2 × 2 × 2 = 8. Children usually meet cube numbers in Key Stage 2 (ages 9–11), where they start spotting patterns. But the real magic kicks in during Key Stage 3 and beyond, when cube numbers pop up in volume, algebra, and even real-world problems.

So, how do you make cube numbers exciting and easy to understand? Start with what they already know and use plenty of visual, hands-on examples to bring the idea to life.

Here are a few ideas.

Cube numbers for Key Stage 2

At this stage (ages 9-11), it’s all about making cube numbers feel real—the more hands-on, the better!

Stack up some fun: Grab some building blocks, sugar cubes, or dice. Ask them to stack 2 × 2 × 2 cubes and count them. It’s a great way to show that 2³ = 8 in a way they can actually see.
Spot the pattern: Write out cube numbers (1³, 2³, 3³…) and compare them to square numbers. Kids will love noticing how quickly cube numbers shoot up compared to squares!
Make it a real-world puzzle: “If a chocolate box is shaped like a cube and holds smaller chocolates inside, how many chocolates fit inside a 3 × 3 × 3 box?” This makes cube numbers feel useful (and a little delicious).

Cube numbers for Key Stage 3

By now (ages 11-14), students get the basics, so it’s time to connect cube numbers to real-world maths.

Make it about volume: Ask, “If a cube-shaped box has sides of 5 cm, how much stuff can it hold?” Cube numbers naturally appear in volume calculations, so this helps the idea click.
Real-World Cubes: Find cube-shaped objects around the house or classroom—things like dice, Rubik’s cubes, or storage boxes. Talk about how their volume can be calculated using cube numbers, making the maths more practical and relevant.
Let them experiment: Ask them to cube their age, their house number, or a random number and compare results. They’ll love seeing just how big the numbers can get.
Cube number bingo: Create bingo cards with different cube numbers on them. Call out the cube roots (e.g., “the cube of 4”), and players match them to the correct answer. This is a fun way to memorise cube numbers and their roots.

Cube numbers for Key Stage 4

At this stage (ages 14-16 and GCSE study), cube numbers aren’t just about spotting patterns—they start appearing in algebra, problem-solving and even science.

Challenge them with cube roots: Once they’re confident with cubing numbers, flip it around: “What’s the cube root of 64?” (It’s 4!) Cube roots help prepare them for trickier algebra problems.
Set up a problem-solving challenge: Give them a real-world question: “If a shipping box is 4 × 4 × 4 metres, how many 1m³ boxes fit inside?” Let them figure it out like a detective.
Quickfire cube number challenge: Give a number and ask whether it’s a cube number or not. Fastest wins! You can also ask students to estimate cube roots—for example, “What is the cube root of 512?” (Again, fastest or closest wins). This makes cube numbers more interactive and develops problem-solving skills.
Spot the cube number: Write down a list of numbers, including both cube and non-cube numbers. Challenge students to identify which ones are cube numbers and explain their reasoning. This helps with pattern recognition and logical thinking.

If you’re looking for more GCSE Maths revision resources, don’t miss our guides to MathsWatch, Seneca Learning, Physics and Maths Tutor, Maths Genie and Corbett Maths.

What are examples of cube numbers?

One of the best ways to understand cube numbers is to see them in action. Maths can sometimes feel abstract, but when you work through real examples, it suddenly becomes much clearer. By looking at actual cube numbers, you can see patterns, recognise how they grow, and develop an instinct for spotting them.

Examples also help with problem-solving—if you know the first few cube numbers by heart, you can quickly figure out if a number is a cube, estimate cube roots, or apply them in real-world situations like measuring volume. This is particularly useful if you’re revising for exams like the 11 Plus, SATs, GCSEs and Maths A Levels (as well as more practical subjects like Core Maths), where cube numbers appear in number patterns, sequences and algebra questions.

Let’s go through some key examples.

What is the cube number of two?

When introducing cube numbers, it’s helpful to start with a simple example. The number 2 is a great choice because it’s small and easy to work with, yet clearly demonstrates the concept of cubing.

If we cube the number 2, it means we multiply it by itself three times:

2 × 2 = 4 (This gives us the square of 2)
4 × 2 = 8 (Now we multiply by 2 again to get the cube)

So, 2 cubed (2³) = 8. That means 8 is a cube number because it’s the result of multiplying 2 by itself three times.

A great way to visualise this is by imagining a stack of small cubes. If you had a cube that was 2 blocks wide, 2 blocks tall, and 2 blocks deep, it would contain 8 smaller cubes in total—helping show why they’re called “cube” numbers!

What are the first 10 cube numbers?

If you’re working with cube numbers, it’s useful to know the first few off by heart. These come up often in GCSE and A Level Maths problems, so being familiar with them can save time and effort.

Here are the first 10 cube numbers, starting from 1:

1³ = 1 × 1 × 1 = 1
2³ = 2 × 2 × 2 = 8
3³ = 3 × 3 × 3 = 27
4³ = 4 × 4 × 4 = 64
5³ = 5 × 5 × 5 = 125
6³ = 6 × 6 × 6 = 216
7³ = 7 × 7 × 7 = 343
8³ = 8 × 8 × 8 = 512
9³ = 9 × 9 × 9 = 729
10³ = 10 × 10 × 10 = 1,000

One thing you might notice is how quickly these numbers grow! Unlike square numbers, which increase steadily, cube numbers get much larger because we’re multiplying three times instead of just twice.

Is 27 a cube number?

Yes! 27 is a cube number because it’s the result of cubing 3:

3 × 3 = 9
9 × 3 = 27

So, 3³ = 27, which confirms that 27 is a cube number.

A great way to test if a number is a cube number is to think backwards. Can you find a whole number that multiplies by itself three times to make that number? If so, then it’s a cube number.

What are the cube numbers 1 to 100?

Between 1 and 100, only a few numbers are cube numbers. That’s because cube numbers grow rapidly, so most numbers in this range don’t fit the pattern.

Here are the cube numbers between 1 and 100:

1³ = 1
2³ = 8
3³ = 27
4³ = 64

These are the only cube numbers within this range. After 64, the next cube number is 125, which is already greater than 100.

A good way to help children identify cube numbers is to make a quick list of cubes and check if a given number is on the list. If it’s not, it’s not a cube number!

What are the rules for cube numbers?

Cube numbers follow handy patterns that make them easier to understand and work with. So, instead of trying to memorise a long, long list of cube numbers, recognising these patterns will help your child spot them more quickly—especially when they appear in schoolwork or exams.

Here are a few key rules to know:

Even numbers stay even, and odd numbers stay odd: This is a handy shortcut for checking your work! If you cube an even number (like 4), the result will always be even. If you cube an odd number (like 5), the result will always be odd. Try it for yourself!
Some numbers can never be cube numbers: If a number ends in 2, 3, 4, 5, 6, or 7, it can’t be a cube number (except for 4³ = 64). Recognising this pattern is a great way to rule out numbers that aren’t cubes.
Negative numbers can also be cube numbers: Unlike square numbers (which always give positive results), cubing a negative number still gives a negative result. For example: (-2)³ = -8, (-3)³ = -27.

These three rules make cube numbers much easier to work with. Once you get used to them, you can spot cube numbers quickly and use them in all kinds of maths problems.

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What are Square Numbers? Definitions and Examples

Square numbers pop up all over maths—whether it’s times tables, algebra or shapes. But what exactly are they? And how can you explain them in a way that makes sense, especially to a child?

If maths isn’t your thing, don’t worry, we’re keeping things simple. This guide will walk you through what square numbers are, why they’re useful, and some easy ways to spot them. We’ll also share tips for teaching them, a full list of square numbers up to 100, and clear up common mix-ups (like whether 2 or 20 count as square numbers).

By the end, you’ll have everything you need to explain square numbers with confidence. No complicated jargon, just straightforward, practical maths. Let’s get started!

What’s a square number in maths?

Let’s start with a definition.

A square number is a number you get when you multiply a whole number by itself. So take any number—like 1, 2, 3, or 10—and multiply it by the exact same number. The result is always a square number. For example, if you take 4 and times it by 4, you get 16. Which is a square number. The same applies if you take 7 and multiply it by 7. This gives you 49, another square number.

The key idea is that square numbers always come from whole numbers multiplied by themselves. You can’t get a square number from a fraction or a decimal multiplied by itself.

For example:

1 x 1 = 1 → a square number
2 x 2 = 4 → a square number
3 x 3 = 9→ a square number

But…

1.5 x 1.5 = 2.25 → not a square number
3.3 x 3.3 = 10.89 → not a square number

So, why are square numbers so important? Well, square numbers aren’t just a random maths fact. They’re super useful, and they pop up in all sorts of places. Whether it’s working out areas in geometry, solving algebra problems, or understanding how computers encrypt information, square numbers are a key part of maths. Learning about them early makes it much easier to tackle more advanced topics later on.

Bigger building blocks: Square numbers set the stage for trickier topics like square roots, cube numbers, indices, algebra and even Pythagoras’ theorem. If your child gets the hang of them now, GCSE and A Level maths will feel lots easier.
Spotting patterns: Knowing square numbers helps with recognising number patterns and makes times tables and division much more straightforward. It’s like having a secret shortcut to understanding how numbers work. This is particularly helpful for maths and non-verbal reasoning sections of the 11 Plus.
Essential for Geometry: Ever wondered how we calculate the area of a square? Yep, square numbers! They pop up in all sorts of shape-related maths problems.
Surprising real-life uses: Square numbers aren’t just stuck in textbooks. They show up in architecture, computer science, chemistry, economics and even online security (like encryption). Maths isn’t just for the classroom—it’s behind the scenes in everyday life!

What’s a simple definition of a square number?

At its core, a square number is a whole number multiplied by itself. But that definition can feel abstract, so let’s break it down in a way that’s easier to picture.

Think of a square number as something you can physically arrange into a perfect square.

For example:

● ●
● ● (2 × 2 = 4)

By lining up objects like this, children can see that square numbers don’t just exist in sums—they form actual shapes!

Using hands-on activities is a great way to make this concept click. Try arranging Lego bricks, counters, or even coins into squares. Letting children build and see square numbers in action can make a huge difference in their understanding.

If your child learns best through videos and animations, there are fantastic free resources online. Websites like Corbett Maths, Maths Watch, Maths Genie, Physics and Maths Tutor and Seneca Learning have engaging explanations that walk through square numbers step by step.

For instance, try these explanations from BBC Bitesize and Corbett Maths, which are aimed at primary children.

How to explain square numbers to a child?

Children are introduced to square numbers at different stages, from simple patterns in early years to square roots and algebra later on. The key to making square numbers easy to understand is explaining them in a way that makes sense for their age and learning style.

For younger children (Key Stage 1, ages 5–7), square numbers might not be taught explicitly, but they will come across them in patterns, dot arrays and counting exercises. As they move into Key Stage 2 (ages 7–11), they’ll learn square numbers up to 100, so reinforcing the idea with multiplication and hands-on activities is helpful. By Key Stage 3 (ages 11–14), square numbers become part of bigger concepts like square roots and algebra, so recognising patterns and applying them is key.

To help children grasp square numbers, explain them in a way that suits their learning style:

Building squares: Challenge your child to arrange objects like bricks, counters or biscuits into squares. Seeing that 4 can be arranged in a 2×2 square and 9 in a 3×3 square helps them understand that square numbers always form equal rows and columns.
Multiplication grids: Highlight square numbers on a multiplication chart to show how they follow a pattern (1×1, 2×2, 3×3…). This helps children spot them quickly and see how they relate to times tables.
Memorising rules: Explain that a square number is just a number multiplied by itself (e.g., 5×5=25). Some children prefer clear, logical rules they can apply straight away. This can be a helpful approach for subjects like Core Maths.

Making learning interactive keeps children engaged and helps square numbers stick. Fun activities like games and movement-based learning also reinforce the concept—particularly useful for homeschooled children.

Hopscotch challenge: Write square numbers in a hopscotch grid and have your child jump between them. This helps with number recall and pattern recognition.
Guess the square: Say a number and ask if it’s a square number. If not, can they find the closest one? This builds quick recognition skills.
Spot the pattern: Challenge older children to list the first 10 square numbers and look for patterns, like how they increase (1, 4, 9, 16…). This helps with more advanced maths later on.

By using a mix of hands-on activities, visuals and number games, children can develop a strong understanding of square numbers—without just memorising facts.

How can you check if a number is a square number?

Square numbers crop up all the time in 11 Plus, SATs, GCSE and A Level maths—so being able to spot them can save loads of time in revision and exams. The good news? There are some super simple tricks to check whether a number is a square, even if you don’t have a calculator. Once you know what to look for, you’ll start recognising them straight-away.

Take the square root: If it’s a whole number, you’ve got a square number. If it’s a decimal, it’s not.
- √25 = 5 → 25 is a square number.
- √20 ≈ 4.47 → 20 is not a square number.
Compare with nearby squares: If a number sits between two square numbers but isn’t one itself, it’s not a square.
- 50 is between 49 (7²) and 64 (8²), so it’s not a square number.
Check the last digit: Square numbers always end in 0, 1, 4, 5, 6, or 9. If a number ends in 2, 3, 7, or 8, you can rule it out straight away!
Use prime factorisation (for bigger numbers): A number is a square if all its prime factors come in pairs.
- 36 = 2 × 2 × 3 × 3 → square number (all factors are paired).
- 18 = 2 × 3 × 3 → not a square number (the 2 is unpaired).

What’s the best trick to find the square of a number?

We’ve already covered comparing with nearby squares and checking the last digits (two of the simplest and most useful tricks), but here are three more super-speedy ways to square numbers without a calculator.

Out of all the methods for finding the square of a number (especially if it’s a larger number and you’re unsure where to start), breaking it down into component parts is the best trick. Here’s how to do it.

1. Breaking it down

Instead of multiplying the number by itself the long way, split it into an easier calculation.

To square 12, think of it as (10 + 2)² and expand:
(10 + 2)² = 10² + 2(10×2) + 2²
100 + 40 + 4 = 144 → So 12² = 144

This method works well for numbers just above 10 or 20, as you can break them into 10 + something or 20 + something.

2. Squaring numbers ending in 5

If a number ends in 5, there’s an easy shortcut.

Take the first digit, multiply it by itself +1, then stick 25 on the end.
Example: 25² → 2 × (2+1) = 6, then add 25 → 625
Example: 35² → 3 × (3+1) = 12, then add 25 → 1225

Works for any number ending in 5 (45², 55², etc.), making it a great mental maths trick!

3. Using nearby squares

If you need to square a number but already know a nearby square, use this quick adjustment trick.

If you know 20² = 400, you can find 21² by adding (2 × 20) + 1 to it:
21² = 20² + (2 × 20) + 1
400 + 40 + 1 = 441 → So 21² = 441

This method works best for numbers just above or below an easy square, like 19² (using 20²) or 29² (using 30²).

Once you’ve got these tricks down, squaring numbers becomes second nature. No need for long calculations—just smart, quick maths that makes maths exams so much easier.

What are the square numbers from 1 to 100?

Square numbers are simply whole numbers multiplied by themselves. They follow a predictable pattern, making them easy to recognise once you spot how they grow. The first ten square numbers are:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

If you look at the gaps between each square number, you’ll notice an interesting pattern—the difference between consecutive squares increases by 2 each time:

4 – 1 = 3
9 – 4 = 5
16 – 9 = 7

This pattern continues as numbers get bigger, which helps when estimating square numbers and spotting them in sequences.

Is 20 a square number?

No, 20 is not a square number. This is because there isn’t a whole number you can multiply by itself to make exactly 20. If you take the square root, you get about 4.47, which isn’t a whole number.

One way to check is by looking at the nearest square numbers:

4 x 4 = 16
5 x 5 = 25

Since 20 falls between them, we know it’s not a perfect square.

Another way to think about it is visually. If you try to arrange 20 objects into a perfect square, it won’t work. This is a great trick for helping children understand square numbers.

Why is 2 not a square number?

Just like 20, the number 2 isn’t a square number because there’s no whole number that squares to make 2. Its square root is about 1.414, which isn’t a whole number. So it doesn’t fit the pattern of square numbers.

If you try to arrange 2 objects into a square, you’ll find it’s impossible—you can make a straight line, but not a full square. The closest square numbers are:

1 x 1 = 1 (1²)
2 x 2 = 4 (2²)

Since 2 falls between them but isn’t itself a square, we can say for sure that it doesn’t belong in the sequence of square numbers.

Does your child need support with maths?

Square numbers are just one of many maths concepts children need to understand as they progress through school. If your child finds maths challenging, the right support can make all the difference. Whether they’re preparing for the 11 Plus, SATs, or GCSE Maths, Achieve Learning provides expert tuition tailored to their needs.

Our friendly and experienced tutors help students build confidence, improve problem-solving skills, and develop a deeper understanding of core subjects. So if you’re looking for extra support to help your child succeed, get in touch today to find out how we can help.

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