Online Maths Courses for Primary Schoolers

Register today! Courses are running from April 19th – July 17th, 2021.

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Whether you’re on the lookout for something to keep the kids occupied during the school holidays, or are trying out a more unconventional approach when it comes to learning maths, this page has it all. The teachers at Think Academy have diligently created some new, interactive KS2 maths games for your child to enjoy!

Below you’ll discover two virtual maths escape rooms. The first is spaceship-themed and has been designed for children in Years 3 and 4. The second is set in what we’ve decided to call a maths dungeon and has been designed with children in Years 5 and 6 in mind.

Each of the escape rooms has a degree of interactivity to help keep children engaged. We’ve included some video and audio clips to help your child follow the storyline as they put their maths knowledge to practice and complete the escape room. Most importantly, these KS2 maths games are free to enjoy, and so if your child has fun, you can easily share this page with your friends.

Years 3 and 4, prepare to blast off into outer space!

We’re ready to welcome you on-board our alien spaceship-themed virtual escape room this half-term. You’ll be completing brain teasers and maths challenges to unlock new clues that’ll help you escape, all while learning about Fractions, Area, Time, and more.

This escape room, including all content and materials, is designed for 8-9-year-olds for some fun maths practice. So, if you’re ready to go intergalactic and use the power of maths to fight extraterrestrials, tap the button below!

Click the button below to get access for free!

Blast Off to Space

Years 5 and 6, will you brave the maths dungeon?

This is the ultimate maths test. Guided only by your knowledge of maths, you need to escape the maths dungeon and flee the evil teacher’s wrath! Your storyline will involve watching video clips from Think Academy tutors as they give you clues to progress to the next level.

This escape room will test your knowledge on more complex areas of maths such as Geometry, Calculations, Fractions, Sequences and Sudoku-style problems!

This escape room is designed for 10-11-year-olds, for some fun but challenging maths practice.

Click the button below to get access for free!

Enter the Maths Dungeon

More KS2 maths games & online learning resources.

In this section, you’ll find links to websites with free online maths games, in addition to our own KS2 maths worksheets to help your child progress in maths. Our team are continually developing new resources. Therefore, we encourage you to follow our resources pages for new updates.

While many of the resources below are for children, we have helpful articles for parents too!

Free KS2 maths worksheets:

Below you can find links to helpful pages that contain a number of free, printable maths worksheets to support pupils in Years 3-6.

Year 3 maths worksheets

Year 4 maths worksheets

Year 5 maths worksheets

Year 6 maths worksheets

Listen to our free maths podcast for kids.

Learning maths isn’t all about memorising calculations and times tables; it’s so much more than that! Discover Think Academy’s maths podcast for children, Perfect Numbers. Click here to listen for free.

Created by our Year 3 teacher Ross, Perfect Numbers will spark your child’s imagination, encouraging them to see mathematics in a new and exciting way. Each episode is full of incredible facts and stories that are bound to inspire your child to love maths as much as we do!

Free Maths Worksheets for Years 1 - 6

Download and print our teacher-approved study packs, for free!

Download now

The post KS2 Maths Games: Think Academy UK’s Free Virtual Escape Rooms appeared first on Think Academy Blog.

The most common reason children complain about the struggles of maths is that it is too difficult, or they are not smart enough. This could not be further from the truth and it’s important that both you and your child understand this. This mistaken belief could have serious consequences on your child’s lifelong relationship with numbers and problem-solving abilities.

That’s why it’s important to identify which parts they struggle with. What makes sense to some children might not to others. As teachers use a standard method, many children don’t understand and are ‘left behind’. On the other hand, keep in mind that this problem is not just limited to a child struggling with maths. It can sometimes be an undiagnosed learning difficulty.

Why do some children experience problems with maths?

There can be several reasons why some pupils find it hard to understand maths. Even if they do understand the concept of maths, children still feel anxious about ‘doing’ maths. The idea of just learning maths can be stressful. Both parents and teachers need to understand that all children are not the same, just like we as adults are not the same. Children learn at different paces; some will excel at maths and some may take a bit more time.

Additionally, some children will experience learning and thinking differences. This is what is called dyscalculia, this is a learning difficulty that affects a pupil’s ability to understand and do maths. Children with dyscalculia, usually have difficulty understanding numbers, symbols, and related concepts that they need to succeed in math.

In every class, several pupils struggle with at least a mild form of dyscalculia, this, as a result, affects their maths potential. This is why it is important to identify signs that your child is struggling with maths.

How can I tell if my child struggles with maths?

Identifying the signs that your child is struggling with maths is important to help understand and make plans accordingly. These are some of the common signs that your child is struggling with maths:

– Negative comments
– Getting stressed or frustrated
– Low grades in maths but higher grades in other subjects
– Trouble connecting maths families i.e. 4+5=9 or 5+4=9
– Difficulty managing time
– Difficulty applying maths to real-world contexts.

Does maths anxiety lead to experiencing problems with maths?

As previously pointed out, some pupils even when they do understand maths suffer from anxiety of carrying out maths problems. There is this feeling of tension and anxiety that goes through your child’s head with solving mathematical problems

In the midst of hardship, it’s easy to feel as though we’re the only ones going through a certain problem. For parents of a child struggling with math, it’s no different. And while it is alarming, we hope parents everywhere find comfort in knowing their child is not the only one who may experience anxiety when it comes to math.

In 2019, a BPS study had found that one-third of children aged four to six felt anxious about their maths ability. There are some symptoms you can look out for if you feel your child is suffering from math anxiety.

• Avoidance
• Low achievement
• The negative reaction of their ability
• Intense emotional reactions

If this is not tackled head-on the children will struggle with this throughout both their childhood and adulthood

Could problems with maths be a sign of learning difficulties?

There are several learning difficulties that are associated with learning maths including the most common dyscalculia or what may be also called maths dyslexia. This actually affects 1 in 20 children in the UK. It is much more common than you think. Understanding if your child suffers from this can help you in the long run

• Mistaking a number – e.g. 6 as 9
• Difficulty counting backwards
• Weak mental arithmetic skills
• Having problems with understanding the relationship between numbers and connecting numbers to objects
• High levels of Maths anxiety
• Telling the time

This learning difficulty as common as it is is not really heard off. This is because there are not enough resources to introduce the help that is needed for these students at schools.

However, if your child is currently affected by that, we would highly recommend talking about this with your child’s teachers. This advice is also relevant to really find out what areas your child is struggling with. Your child’s teacher is the best person to actually give you detailed insights and help do a full diagnostic assessment of your child’s knowledge.

What can I do if my child has problems with maths?

Your role as a parent is important in helping your child to succeed, giving them the confidence and help is crucial at this point. However, as previously pointed out the first step in helping your child is looking out for the signs. This will help you identify any problems your child may be experiencing. There are also further points that can help your child.

Making Maths fun

This may change the child’s perspective of maths completely, as said before not each child is the same. Hence, each child may react to different methods in different ways. Traditional sitting down and doing maths problems can be overwhelming for some.

You can try and change this by introducing maths games, there are plenty of free online games to help. You have worksheets that can also help. You can also be creative with objects at home.

Hint: Children learn more through games

Practice makes perfect!

Children respond well when parents are more involved with their education. Sitting down with them after school and helping them with a bit of maths practise every other night can help them more than you think

This will help your child to keep the maths knowledge fresh in their head. However, if they don’t feel up to it. Do not enforce it.

Activities

You can use maths in almost every activity, even as simple as something like baking. Let the child take control of the recipe, this will help them develop the skills without realising. This can even be done when you are grocery shopping

Get a tutor

This can be also an incentive as well, some children generally do need that extra bit of help, providing them with a tutor may help them in the long run.

Please note that if your child has a learning difficulty this will need to be professionally assessed. Please talk to your child’s teacher before taking any further steps.

Use CODE:  247HYP7In5 to redeem £12.00 off Think Academy’s January 2021 maths courses! Enter your code at the checkout here! Give your child a confidence boost in maths and help them to prepare for the 11+ exam, SATs, or simply catch up and make progress in maths!

Perfect for Covid catch-up, KS2 SATs or 11 Plus exam preparation, Think Academy is offering affordable online maths tuition for children at £6.00 (KS1) or £8.00 (KS2) per class. New classes are available for January 2021. Easy-to-use, minimal supervision required.

Read more:

Year 6 SATs Revision Guides 2021: The Top 8 Guides for UK Primary School Pupils 

Help with Maths: The Top 5 Reasons Parents Choose Group Tuition in 2021

What is Distance Learning? Helping Your Child to Learn Remotely

The post Problems with Maths? – Here’s What to do if Your Child is Struggling with Maths at Primary School appeared first on Think Academy Blog.

Online Maths Courses for Primary Schoolers

Register today! Courses are running from April 19th – July 17th, 2021.

Learn more

Free Maths Worksheets for Years 1 - 6

Download and print our teacher-approved study packs, for free!

Download now

The post Year 6 Maths – Resources to Help Your Child in 2021 appeared first on Think Academy Blog.

Online Maths Courses for Primary Schoolers

Register today! Courses are running from April 19th – July 17th, 2021.

Learn more

Free Maths Worksheets for Years 1 - 6

Download and print our teacher-approved study packs, for free!

Download now

The post Year 4 Maths Worksheets: Discover the Best Games, Puzzles, and Learning Resources appeared first on Think Academy Blog.

There’s also a stronger focus on preparing for the Year 6 SATs. Above all, they’re starting to learn independently in preparation for the transition to secondary school.

So as a parent, how can you help? Below is a guide for parents with all the resources you need to ensure you can support your child outside of the classroom. This article is part of Think Academy UK’s Covid catch-up series, designed for parents to help their child catch-up and progress in maths with tons of tips and resources after months of lost learning.

Year 5 maths: What will my child learn about?

Year 5 maths will involve a review of some of the topics covered in Year 4 maths class. However, your child will also be introduced to new topics.

These will include practising their mental arithmetic skills in preparation for the KS2 SATs, and written calculation methods. The written calculation method is more commonly known as ‘showing the method of working-out’ – important in gaining extra marks in exams!  Your child will also practise solving problems using the operations.

Additionally, your child will be focusing on how to calculate perimeters and areas, whilst also drawing and measuring angles. They will also be learning how to convert between units of time and learn some imperial measures.

Long multiplication and short division will also be a part of the curriculum, as they start to learn how to multiply fractions and learn more about decimals. This will be a core learning in Year 5 maths class. This can all be easily practised at home, with worksheets, activities, and a bit of encouragement!

A closer look at the Year 5 maths curriculum

You’ll have gathered by now that in Year 5 maths there’s a lot to cover! To make your job even more difficult, the way your child is learning to problem-solve will be different from the methods you were taught in school. So, is it possible to help them? Thanks to Think Academy – yes, it is!

Number and place value

In Year 5 your child will be expected to read, write, order, and compare numbers up to 1,000,000. They will also need to recognise the place value of each digit.

Addition and subtraction

Year 5 maths covers how to solve addition and subtraction problems with up to four digits.

Multiplication and division

Year 5 maths is when your child is first introduced to long multiplication and short division. They will also be expected to know how to divide four-digit numbers by one-digit numbers and interpreting remainders.

Fractions, decimals, and percentages

Year 5 Maths is especially important for fractions as your child will be expected to find fractions of numbers and quantities.

Geometry

Solving problems about shapes is key in Year 5, your child will be expected to use their knowledge of geometric properties to help them.

Measurement

Learning how to convert between metric units of measurements and solving problems involving decimal measurement, money and time will be the main subject in this topic.

Statistics

By the end of Year 5, your child will be expected to successfully interpret and present data in a range of ways.

Are games helpful for Year 5 maths pupils?

Games can be helpful for Year 5 pupils as they help to engage the learner. It helps simplify various topics for the pupil, which ultimately helps to test maths ability.

Top free games for Year 5 maths

Maths Frame

Use interactive games that your child can easily understand. This can be useful as an alternative way of explaining something if your child cannot fully understand the teacher.

Oxford Owl

We have repeated this a couple of times, however, it is a teacher’s favourite and of course ours. It has all levels, with really fun games to play!

Top Marks

This website is simple and user-friendly. Minimal supervision required (although we always believe in closely monitoring your child’s internet use. It has both English and maths subjects to choose from and a range of levels.

Primary Games Arena

This website includes various options and game types. What is great about this one is that it will gives you reviews from previous users, so you can better find the perfect game for your child!

Timestables

This is an excellent way for students to learn their multiplication in an easy and accessible way. There are various games included all of which are interactive.

Are Year 5 maths worksheets helpful?

Year 5 may not have SATS or tests, however, supporting them during this time can help you prepare them for next year’s SATS. They will already be expected to draw on what they have previously learned during their time in primary school.

Giving them the time to prepare earlier allows them to become confident enough with the various topics they will be given. These worksheets will help them to see how maths fits into everyday life.

Of course, similarly to games, this can be hard and overwhelming to find hence why Think Academy has made an easy access way of finding them.

Top Free Year 5 maths printable worksheets

Twinkl

This is recommended by schools themselves, with teachers using them in their lessons. There are various worksheets for the topics that are required.

Ed Place

This website has a variety of worksheets created by teachers, they not only have various class groups but also various levels. They have put in mind for children who are struggling to keep up.

MathsSphere

This website has a variety of Maths topics to choose from for all levels. This also includes ‘booster’ worksheets to give that extra help.

Additional resources:

There are plenty of resources around the web to aid your child with Year 5 maths including here at Think Academy.

Perfect for Covid catch-up, KS1 & KS2 SATs or 11 Plus exam preparation, Think Academy is offering affordable online maths tuition for children at £6.00 per class (Year 1 & 2) and £8.00 per class (Years 3 – 6). New classes are available for January 2021. Easy-to-use, minimal supervision required. Free 1-hour taster sessions are also available.

Read more:

30 Fun Maths Games to Help Kids Learn Maths for Free!

Top 50 Home Learning Resources for UK Primary School Maths

11 Plus Exam: What Age Should You Start Preparing Your Child?

The post Year 5 Maths Worksheets, Games and Learning Resources to Help Study at Home appeared first on Think Academy Blog.

With this article, you’ll find everything you need, from Year 3 maths worksheets to games and useful websites. Perfect for giving your child a healthy head start at Key Stage 2 primary school maths.

This article is part of our Covid catch-up series, designed for parents to help their child catch-up and progress in maths with tons of tips and resources after months of lost learning.

What will my child be learning in Year 3 maths?

As your child enters Key Stage 2, you’ll notice that maths lessons focus more on the times tables. While this would likely have been touched upon in Year 2 with children learning multiples of 2 and 5; now they will focus on 3, 4 and 8. This is to help prepare them for the Year 4 times tables test.

With the revised national curriculum’s mastery approach, your child can expect to develop a deep understanding of the following topics:

• Times tables
• Fractions of quantities
• Equivalent fractions
• Angles
• Parallel and perpendicular
• Area
• Perimeter
• Shapes

Year 3 maths topics

Times tables

Using times table number rules, e.g. how to calculate multiples of 2, your child will now be introduced to several, more challenging times tables. In Year 3 maths your child will start to learn multiples of 3, 4, 6, 7, 8, and 9. However, this will depend on your child’s ability.

Fractions of quantities

Your child will learn how to find the fraction of an amount, adding and subtracting simple fractions, and use mixed fractions.

Equivalent fractions

Introduction to fractions that are different numbers but can still represent the same part of a whole and can be simplified into smaller ones.

Angles

In Year 3 maths children are introduced to angles, learning to recognise different types of angles e.g. right, acute, obtuse, and reflex.

Parallel and Perpendicular

Your child will learn about parallel and perpendicular lines, including measuring lines that are an equal distance apart and lines that cross at 90 degrees.

Area and Perimeter

In this topic, your child will learn how to measure the perimeter of 2D shapes. In some cases, Year 3 maths touches upon the area of shapes too. E.g. understanding that the area of a rectangle is length x width.

Shapes

In Year 3 maths geometry focuses on the properties of 2D shapes and learning how to identify them. Pupils will be encouraged to draw 2D shapes and create 3D models, including triangles, rectangles, squares, circles, and hexagons.

Are there any fun games to help my child with Year 3 maths?

Games are a great way to help children learn. That’s because they are more engaging and help to motivate students, encouraging them to want to learn about maths.

With the transition to learning online, maths games have become even more interactive. There are tons of websites to help your child learn KS2 maths, as well as popular online courses.

Think Academy UK

With a number of online maths courses available at the touch of a button, Think Academy UK supports students in learning maths via an interactive online learning platform.

Pioneering a new style of online maths tuition, Think Academy UK uses ‘game-based’ learning, inviting children to take part in fun maths challenges alongside their peers. Children can win exciting rewards that can be exchanged for virtual stickers, encouraging positive attitudes towards learning maths.

Maths Frame

With a library of interactive maths games designed for students in Key Stage 2, this resource is perfect for Year 3 students. Free to use, the website is regularly updated with the UK’s most popular children’s maths games.

Topmarks

Another free website for you to check out, Topmarks has great games to help your child practise mental maths. With an increased focus on mental arithmetic in Key Stage 2, practising these skills online is an effective way to keep your child engaged while developing maths fluency.

How can Year 3 maths worksheets help my child?

Worksheets are an awesome supplementary learning tool to help your child continue practising what they have been learning at school.

That’s why during periods of primary school closures, your child’s teacher will no doubt have included worksheets within their home learning pack or suggested additional resources.

Free printable Year 3 maths worksheets

We’ve compiled a list of websites where you can download worksheets for free! Including from our own blog, check out the list below:

White Rose Maths Worksheets

White Rose Maths is known as the primary school teacher’s go-to maths online resource. In fact, many teachers use their resources to plan the lessons that take place at school!

But they now have a section for parents to download free workbooks for their children! Parent and teacher-approved, this is a resource you can trust!

Twinkl

Twinkl has some free resources such as worksheets for parents to download. If you’re on the lookout for more Year 3 maths worksheets, you can easily download them using the link above without having to pay for them. For those parents looking for even more resources, you can get access to even more for a fee.

Hamilton-Trust

This is a resource for teachers, but that doesn’t mean that parents can’t benefit from it too. Using the link above, you’ll find pre-made home learning packs for children who are living within lockdown restrictions. They have plenty of maths resources available which can be easily used for learning at home with your child. This includes free Year 3 maths worksheets.

Additional Year 3 maths resources

As with some of the resources above, teachers have access to the premium features on many primary school maths websites. It’s likely they will frequently make these available to you and your child.

With that said, don’t forget you can always reach out to them and request further resources. No doubt they’ll be only too happy to help you where they can! This way, you’re not solely restricted to low-quality resources from free websites and can be sure your child is learning from trusted, teacher-approved resources.

Perfect for Covid catch-up, KS1 & KS2 SATs or 11 Plus exam preparation, Think Academy is offering affordable online maths tuition for children at £8.00 per class. New classes are available for January 2021. Easy-to-use, minimal supervision required. Free 1-hour taster session also available.

Read more:

SATs 2021: Complete Guide on KS2 SATs and How to Prepare Your Child!

30 Fun Maths Games to Help Kids Learn Maths for Free!

Top 50 Home Learning Resources for UK Primary School Maths

The post Year 3 Maths Worksheets: Everything Your Child Needs to Learn at Home appeared first on Think Academy Blog.

This is how to help your child fully get to grips with square numbers. Moreover, we’ve included a square numbers worksheet with fun practice examples and solutions.

What is a square number?

A square number is a number multiplied by itself. It can also be called ‘a number squared,’ and all square numbers are formed by finding the product of an integer with itself.

In mathematics, the symbol used to represent any number squared is written in superscript, like this:  ²  for example 3² = 3 x 3 = 9.

Mathematically speaking, a square number is a number of the form n x n, or n² where n is any integer (an integer is any whole number including 0 and negative numbers).

To understand this better, we will take a look at an unknown variable c (we don’t know what c is, but that doesn’t matter…)

c²  is ‘c  to the power of 2’  most commonly known as ‘c squared’

c³ is ‘c to the power of 3’  most commonly known as ‘c cubed’

c⁴ is ‘c to the power of 4’

c⁵ is ‘c to the power of 5’

A number can be raised to any power (or index) that you like, however today we will focus on just the squares, the result of a number raised to the power of 2.

Why is a square number called a ‘square number’?

The real life representation of multiplying a number by itself or squaring a number, for example 4², is calculating the area of a square with side length 4. These numbers are called square numbers for the simple reason that they form the area of a square.

Let’s take a look at the most basic square, the unit square. The area of a rectangle is given by the formula:

 Area = length x width

It is easy to see that using the formula, the area of the unit square is 1 x 1 = 1 square unit. In fact because squares have equal sides, you just need to pick one side and ‘square’ it.

In this example a square of width 4cm is made up of 4 rows and 4 columns of 1cm² squares. To calculate the area, you can count the total number of squares inside the square, each having an area of 1 square centimeter.

In this case the area of the square is 4cm x 4cm = 16cm² or 16 square centimeters.

What are the square numbers up to 1000

0² = 0 x 0 = 0                 10² = 10 x 10 = 100                   21² = 21 x 21 = 441

1² = 1 x 1 = 1                 11² = 11 x 11 = 121                   22² = 22 x 22 = 484

2² = 2 x 2 = 4                 12² = 12 x 12 = 144                   23² = 23 x 23 = 529

3² = 3 x 3 = 9                  13² = 13 x 13 = 169                   24² = 24 x 24 = 576

4² = 4 x 4 = 16               14² = 14 x 14 = 196                   25² = 25 x 25 = 625

5² = 5 x 5 = 25               15² = 15 x 15 = 225                   26² = 26 x 26 = 676

6² = 6 x 6 = 36               16² = 16 x 16 = 256                   27² = 27 x 27 = 729

7² = 7 x 7 = 49               17² = 17 x 17 = 289                   28² = 28 x 28 = 784

8² = 8 x 8 = 64               18² = 18 x 18 = 324                   29² = 29 x 29 = 841

9² = 9 x 9 = 81               19² = 19 x 19 = 361                   30² = 30 x 30 = 900

20² = 20 x 20 = 400                   31² = 31 x 31 = 961

Learning square numbers

This list does not contain all of the square numbers; any number can be squared so the list could go on forever. You are also not expected to know all of these numbers in KS2 primary school maths, so do not worry!

What is the square root?

To find the square root of a number you must find some number that when multiplied by itself gives you the original number you started with. The square root is the inverse function of squaring a number.

For example: 3 squared = 9, and so the square root of 9 is equal to 3

Primary school children may have already encountered the inverse functions of addition, subtraction, multiplication and division as the opposite operation, used to reverse a calculation that you have just done (or to check your work). This inverse function is very important because if you know the area of of a square then in order to work out the length of the sides, you must calculate the square root. Here are some examples of square roots for the first square numbers up to 20:

1² = 1 x 1 = 1                                        square root of 1 = 1

2² = 2 x 2 = 4                                        square root of 4 = 2

3² = 3 x 3 = 9                                        square root of 9 = 3

4² = 4 x 4 = 16                                     square root of 16 = 4

Question: The area of a square is 25cm², calculate the side length?

In this example here, we are given the area and asked to work backwards. Alarm bells should be ringing here that we need to use the square root.

We need to consider what number when multiplied by itself gives us 25.

In KS2 primary school maths, you are not expected to know all of the square numbers off by heart, but it will definitely help to recognize the first few.

In this case, it is easy to spot that 25 = 5 x 5 = 5² which gives us the dimensions of the square.

Length = 5cm

Width = 5cm

When will my child learn about square numbers in school?

It is not until Year 5 maths classes that students will encounter squaring numbers. From Year 4, students are taught to recall multiplication and division facts for multiplication tables up to 12 x 12 so your child may already be familiar with some the square numbers up to 144, and should definitely recognize the square numbers up to 50.

The national curriculum states that a Year 5 maths student should be taught to:

• Recognize and use square numbers and cube numbers, and the notation for squared (²) and cubed (³).
• Solve problems involving multiplication and division including their knowledge of factors and multiples, squares and cubes.

The non-statutory notes and guidance state that Year 5 pupils should be able to:

• Use and understand the terms factor, multiple and prime, square and cube numbers
• Use them to construct equivalence statements (for example, 4 x 35 = 2 x 2 x 35; 3 x 270 = 3 x 3 x 9 x 10 = 9² x 10.

This learning will be consolidated in Year 6, particularly when learning about the order of operations where they will be introduced to the mathematical term ‘index.’ They will also begin to perform mental calculations with higher numbers, increasing their fluency through the use of multiplication tables.

Square number practice questions

• What are the first 5 square numbers?
• If the length of a square is 6cm, what is the area of the square?
• Explain why 1 is a square number?
• A square has an area of 64mm², what is the length of the square?
• Fill in the table:

• Bonus questions:

This question was taken from the 2019 KS2 maths SATs exam, testing children’s application of their knowledge of square numbers

• Another question on area taken from the 2019 KS2 Mathematics reasoning paper

Solutions

• 0, 1, 4, 9, 16
• 6cm x 6cm = 36 cm²
• 1 is a square number because it is the product/ result of multiplying 1 with itself 1 x 1 = 1. 1 square unit is the area of the unit square
• 64 = 8 x 8 so length = 8mm
• There are many solutions to this problem. The first column must contain two even numbers (ending in 0, 2, 4, 6 or 8), the first being a square number and the second not.

The second column must contain two odd numbers (ending in 1, 3, 5, 7, or 9)

E.g

6) Rectangle divided as shown (different orientations also work)

7)    Perimeter of hexagon = 8 x 6 = 48 (There are six sides each with length 8cm).

A square with perimeter 48 has sides of length 48/4 = 12cm

So area of square = 12²  = 144cm²

You may also like to read:

Your Must Have Guide to KS2 Fractions

What are Cube Numbers? How to Explain Cube Numbers to Primary School Students?

Why Online Maths Tutors are More Popular than Ever in 2020?

The post What are Square Numbers? – An Easy Guide for Primary Schoolers appeared first on Think Academy Blog.

We will look at what cube numbers are, why they are called cube numbers, how to calculate the inverse, and we will give you all the information required to help your child get up to speed on this topic. There are also some fun worked examples with solutions to try at the end!

What is a cube number in maths?

Cube numbers are the product of three identical numbers. Basically, you need to multiply a number by itself, and then by itself again! This can also be called ‘a number cubed.’

In maths, the symbol used to represent any number cubed is written in something called – superscript. Here’s an example:  ³ for example 3³ = 3 x 3 x 3 = 27.

To understand this better, we will use unknown variable c (we don’t know what c is yet, but it doesn’t matter…)

First consider, c²  is ‘c  to the power of 2’  most commonly known as ‘c squared’

It’s good to note that c³ is ‘c to the power of 3’ most commonly known as ‘c cubed’

Then, c⁴ is ‘c to the power of 4’

Finally, c⁵ is ‘c to the power of 5’

A number can be raised to any power (or index) that you like, however today we will focus on just the cubes, the result of a number raised to the power of 3.

You may have already noticed that a number cubed is the same as multiplying the original number by its square number.

2 squared = 2 x 2 = 4

2 cubed = 2 x 2 squared = (2 x 2) x 2 = 8

For each time you multiply a number by itself you must raise the power by 1.

Why are cube numbers called cube numbers?

The real-life representation of multiplying a number by itself twice over, for example 4 x 4 x 4, is finding the volume of a cube with side length 4.

So in this example a square of length 4cm is made up of 4 rows and 4 columns of 1cm² squares, and to calculate the area you must count the total amount of squares, each with an area of 1cm²

In this case area of the square = 4 x 4 = 4² = 16 so we call this 4 ‘squared’

We are now going to use the exact same method to calculate the volume of a cube.

This time, the shape has another dimension, and now we must also consider the depth. Volume means the amount of 3-dimensional space a shape takes up, so not only do we need the area of one face, we need the total amount of 1cm³ blocks.

Now there are 4 x 4 x 4 little cubes, giving us a volume of 64cm³

A cube by definition has equal height, width, and depth, and so to calculate the volume of a cube you must multiply these dimensions together. This is where the name cube comes from. Cube numbers can be used to calculate the volume of a cube.

What are the cube numbers from 1-100?

0³ = 0 x 0 x 0 = 0

1³ = 1 x 1 x 1 = 1

2³ = 2 x 2 x 2 = 8

3³ = 3 x 3 x 3 = 27

4³ = 4 x 4 x 4 = 64

5³ = 5 x 5 x 5 = 125

6³ = 6 x 6 x 6 = 216

7³ = 7 x 7 x 7 = 343

What is a cube root?

To find the cube root of a number you must find some number that when multiplied by itself twice gives you the original number you started with. The cube root is the inverse function of cubing a number.

Cube root examples:

For example: 2 cubed = 8, and so the cube root of 8 is equal to 2

You will have already encountered the inverse functions of addition, subtraction, multiplication and division as the opposite operation, used to reverse a calculation that you have just done (or to check your work). This inverse function is very important because if you know the volume of a cube, then in order to work out the dimensions of the cube, you must calculate the cube root.

1³ = 1 x 1 x 1 = 1                                cube root of 1 = 1

2³ = 2 x 2 x 2 = 8                                 cube root of 8 = 2

3³ = 3 x 3 x 3 = 27           ——–>          cube root of 27 = 3

4³ = 4 x 4 x 4 = 64                               cube root of 64 = 4

5³ = 5 x 5 x 5 = 125                            cube root of 125 = 5

Question: The volume of a cube is 27m³, calculate the height?

In this example here, we are given the volume and asked to work backwards. Alarm bells should be ringing here that we need to use the cube root.

We need to consider what number when multiplied by itself 2 consecutive times gives us 27.

In KS2 primary school maths, you are not expected to know all of the cube numbers off by heart, but it will definitely help to recognise the first few.

In this case, it is easy to spot that 27 = 3 x 3 x 3 = 3³ which gives us the dimensions of the cube.

Length = 3m

Height = 3m

Depth = 3m

What age will my child start learning about cube numbers?

Children are first introduced to square numbers to calculate the area of a square in Year 5. They will be expected to recognise the notation ² and to be able to calculate the area of basic squares and rectangles. They will also begin to estimate the area of shapes by counting how many 1cm² squares make up the shape.

The Year 5 national curriculum for maths indicates that pupils should:

• recognize and use square numbers and cube numbers, and the notation for squared (²) and cubed (³)
• solve problems involving multiplication and division, including using their knowledge of factors and multiples, squares and cubes

The non-statutory notes and guidance state that Y5 pupils should be able to:

• Use and understand the terms factor, multiple and prime, square and cube numbers
• Use them to construct equivalence statements (for example, 4 x 35 = 2 x 2 x 35; 3 x 270 = 3 x 3 x 9 x 10 = 9² x 10

In Year 5 they will have a brief introduction to cube numbers and begin to learn about the capacity of 3 dimensional objects, applying the same theory they learnt about for square numbers, this time using 1cm³ building blocks to estimate the volume of a cuboid. They should be familiar with some of the different units, i.e cm³, m³ and mm³ (cubic centimetres, cubic metres and cubic millimetres respectively). Consolidation of this will be in Year 6.

Often in 11+ exams and secondary school entrance exams students will be given a pattern of squared or cubed numbers and be expected to spot the pattern and continue it.

What is a perfect cube?

When we talk about cube numbers, we usually mean perfect cube numbers. A perfect cube is an integer (or whole number) that can be written as another integer to the power of 3.

For example, 125 is a perfect cube, because it is the product of an integer multiplied by itself 2 times, 5 x 5 x 5 = 125

Using a calculator we can see 121 is not a perfect cube because there doesn’t exist an integer that when cubed gives the value 121. Using a calculator we can see ∛121=4.94608744. This means that the cube root of 121 is approximately 4.95

This is a scary looking number and in KS2 primary school maths the only cube numbers you only need to be able to recognize are the nicely fitting, perfect cube numbers.

Cube numbers: Examples and practice questions

1. What is the cube root of 64?
2. A dice has volume 216mm³, what is the area of one face?
3. Order these from smallest to largest: 5², 3², 3³, 2³
4. Find two cube numbers that total 3²
5. Use long multiplication to calculate 7³

Solutions

1. ∛64 = ∛(4 x 4 x 4) = 4
2. We must spot that 216 = 6³ so the dice has measurements 6mm x 6mm x 6mm. The length of every edge in a cube is the same so to calculate the area of a face we just need to multiply 6mm x 6mm = 36mm² (take note of how the units become mm² now we are calculating area instead of volume.
3. 2³ = 8 | 3² = 9 |5² = 25 |3³ = 27
4. 3² = 9 The only solution to this equation using perfect cubes is 2³ + 1³
5. 7³ = 7 x 7² Can spot first that 7² is 49? Then long multiplication used to calculate 49 x 7.

You may also like to read:

How to Work Out Area of Different Shapes at KS2

The KS2 Long Multiplication Method – The Step by Step Guide for Parents and Kids

What is BODMAS? A Parent’s Guide to BODMAS, BIDMAS, and The Order of Operations

The post What are Cube Numbers? – Mastering Primary School Maths appeared first on Think Academy Blog.

What does my child need to know about calculating area?

The National Curriculum has very clear guidance about what students need to know about calculating area. By the end of KS2 (year 6) students should be able to:

-calculate and compare the area of rectangles (including squares), including using standard units, square centimetres (cm²) and square metres (m²), and estimate the area of irregular shapes

-find the area of rectilinear shapes by counting squares

-recognise when it is possible to use formulae for area and volume of shapes

calculate the area of parallelograms and triangles

-relate the area of rectangles to parallelograms and triangles, for example, by dissection, and calculate their areas, understanding and using the formulae (in words or symbols) to do this.

In addition to this, area is a common topic in both the 11+ for Grammar schools and the Common Entrance exam used for top independent schools. Both exams usually involve using formulas for areas of triangles, rectangles, squares, parallelograms as part of more complex reasoning problems (e.g. for irregular shapes – see the bottom of this guide).

So, now the question is simple: how can I work out an area?

How to work out the area of a circle

Calculating the area of a circle is easy although many students find it a strange formula. The circular area requires you to know only one length – the radius. This is the distance between the centre of the circle and the edge. The picture below shows the radius as the red line ‘R’. We are interested in the distance of R!

Once we have R all we need to do is to plug it into the famous formula which tells us how to work out the area of a circle:

A = π R²

This means that we square R (i.e. we do R x R) and then times that by pi (π) which roughly equals 3.14.

So, for example, if the radius is 5cm, the area is:

A = π R²

A = π x 5²

A = π x 25

A = 78.5 (to one decimal place!)

And really that’s all there is to it! Once you find R just plug it in!

How to work out the area of a rectangle

The general formula for calculating the area of a rectangle is simple!

Area = Length x Width

A = L x W

So, looking at the rectangle below the length is 10cm, and the width is 6cm.

A = L x W

A = 10 x 6

A = 60

So the area is 60cm²

How to work out the area of a square

What is a square? A square is the same as a rectangle except the length and the width are the same!

So, calculating the area of a square is simple. First we take the formula for the area of a rectangle:

Area = L x W

And  then we remember that the Length and Width are the same, so we can change it to this:

Area = L x L

A = L²

For example – the area of the square below, with side length of 10m is:

Area = L²

A = 10²

A = 100

How to work out the area of a triangle

A triangle is always half a rectangle! This little piece of information gives us all we need to know to work out the area – but let’s see why it’s true first.

Look at the blue triangle above. We can split that into two other triangles which are easier to work out the area! I’ve split it into the triangle in the red rectangle and the purple rectangle.

The triangle in the red rectangle makes up half the area of the red rectangle – because there is a straight line going from one corner to the other. So the area of that section is half the area of the rectangle

A = 4 x 1 ÷ 2

A = 2

The area of the triangle in the purple section is half the purple rectangle. So we can also work that out

by using the rectangle formula:

A = 4 x 6 ÷ 2

A = 12

Therefore the overall area is 12 + 2 = 14.

However – if we look at the original triangle, we realise that we don’t need to do all this fuss. We can just measure the base and the height and half that:

A = 4 x 7 ÷ 2

A = 14

So to summarise, the formula for the area of a triangle is:

Area = ½ x Base x Height

A = ½ x B x H

How to work out the area of a parallelogram

Parallelograms are a little bit more complicated as we need to make sure we are measuring the right distances before we do the calculation for the area!

So, before you read on – have a look at the parallelogram above and ask yourself which two are we interested in out of:

distance ‘a’                                          distance ‘b’                                          distance ‘h’

The key to getting this right is to think of the parallelogram as a rectangle that has been stretched! But the area stays the same.

So we only need to know the height (distance h) and the length (distance b).

And, in fact, the formula is the same as for a rectangle:

Area = base x height

A = b x h

How to calculate the area of an irregular shape

There are two ways to calculate the area of irregular shapes.

Firstly, you can divide the irregular shape into regular shapes and then calculate the area of these and add them up.

The second option is to treat the shape as a big regular shape, and then take away the extra irregular bits.

For example, with the shape below – you could treat it as a rectangle with a square on top.

Area (rectangle) = 3 x 5 = 19

Area (square) = 2 x 2 = 4

Overall area = 15 + 4 = 19

Or you could treat it as a big square with two holes in either corner.

Area (big square) = 5 x 5 = 25

Area (square hole top left) = 2 x 2 = 4

Area (rectangular hole top right = 1 x 2 = 2

Overall area = 25 – 4 – 2 = 19

So there are two different ways to find the area of this irregular shape: as long as you work logically and carefully and split the shape into regular shapes, you will have no problem!

You may also like to read:

30 Fun Maths Games to Help Kids Learn Maths for Free

Top 50 Home Learning Resources for UK Primary School Maths

What is BODMAS? A Parent’s Guide to BODMAS, BIDMAS, and The Order of Operations

The post Working our the Area of Different Shapes at Key Stage 2 appeared first on Think Academy Blog.

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