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Resources tagged with: Square numbers

There are 39 NRICH Mathematical resources connected to Square numbers , you may find related items under Properties of numbers .

Always, Sometimes or Never? Number

Are these statements always true, sometimes true or never true?

Square Subtraction

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

Filling the Gaps

Which numbers can we write as a sum of square numbers?

Generating Triples

Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?

Light the Lights Again

Each light in this interactivity turns on according to a rule. What happens when you enter different numbers? Can you find the smallest number that lights up all four lights?

Sticky Numbers

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

Picture a Pyramid ...

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

Factors and Multiples Puzzle

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

Up and Down Staircases

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

Odd Squares

Think of a number, square it and subtract your starting number. Is the number you're left with odd or even? How do the images help to explain this?

Picturing Square Numbers

Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

Cycling Squares

Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

Two Primes Make One Square

Can you make square numbers by adding two prime numbers together?

One Wasn't Square

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

Fractions in a Box

The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

Odd Differences

The diagram illustrates the formula: 1 + 3 + 5 + ... + (2n - 1) = n² Use the diagram to show that any odd number is the difference of two squares.

Making Boxes

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

Swimming Pool Tiles

This activity creates an opportunity to explore all kinds of number-related patterns.

Few and Far Between?

Can you find some Pythagorean Triples where the two smaller numbers differ by 1?

Robert's Spreadsheet

Robert noticed some interesting patterns when he highlighted square numbers in a spreadsheet. Can you prove that the patterns will continue?

Four Coloured Lights

Imagine a machine with four coloured lights which respond to different rules. Can you find the smallest possible number which will make all four colours light up?

Summing Squares

Discover a way to sum square numbers by building cuboids from small cubes. Can you picture how the sequence will grow?

Numbers as Shapes

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?

Triangles Within Squares

Can you find a rule which relates triangular numbers to square numbers?

Smith and Jones

Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!

A Square Deal

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

Graphing Number Patterns

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

Seven Square Numbers

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Augustus' Age

In 1871 a mathematician called Augustus De Morgan died. De Morgan made a puzzling statement about his age. Can you discover which year De Morgan was born in?

Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.

A Right Charlie

Can you use this information to work out Charlie's house number?

Triangular Triples

Show that 8778, 10296 and 13530 are three triangular numbers and that they form a Pythagorean triple.

What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A

Square Routes

How many four digit square numbers are composed of even numerals? What four digit square numbers can be reversed and become the square of another number?

Time of Birth

A woman was born in a year that was a square number, lived a square number of years and died in a year that was also a square number. When was she born?

Little Squares

Look at the squares in this problem. What does the next square look like? I draw a square with 81 little squares inside it. How long and how wide is my square?

Cuisenaire Squares

These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?

Square and Cube Numbers

By the end of this unit, students will be able to:

• Understand the concepts of square and cube numbers.
• Identify square and cube numbers and their properties.
• Recognize number patterns related to square and cube numbers.
• Apply knowledge of square and cube numbers to solve problems and analyze patterns.

What's Included

• Three-part Lesson
• Self-marking Activities
• Fluency, Reasoning and Problem-solving Questions.
• Engaging Drag and Drop Activities
• Interactive Self-marking Worksheet
• Printable Worksheets to Consolidate Learning

Year 6 Number: addition-subtraction-multiplication-and-division

• solve problems involving addition, subtraction, multiplication and division
• England & Wales: Year 6
• Scotland: Primary 6
• Rep. Ireland: Fifth Class
• Australia: Grade 5
• USA: Grade 5

Connected Resources

Multiplying Decimals-Single Digits

Short Divisions

Using Estimation to Check Answers

Prime and Composite Numbers

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Square and Cube Numbers - PowerPoint

In a Year 6 mathematics lesson, students delve into the world of square and cube numbers. The lesson objectives are to identify these numbers, explore their relationships, and use reasoning and problem-solving skills to work through various exercises. Square numbers are the product of a number multiplied by itself, such as 2 squared (2²), which equals 4. Cube numbers, on the other hand, involve a number multiplied by itself twice more, such as 2 cubed (2³), resulting in 8. Students are encouraged to write down square numbers up to 100 and discuss the patterns they observe, such as the progression found in times tables (1x1, 2x2, 3x3, etc.). They also learn that square numbers can be visually represented as a square of dots, with each square number corresponding to the number of dots along each side of the square.

Cube numbers up to 100 are also explored, with students quickly listing them and discussing the patterns, which can be represented as 2x2x2 for 8, or 3x3x3 for 27, and so on. These cube numbers can be visualized as a three-dimensional cube made up of smaller unit cubes. The lesson includes activities where students compare square and cube numbers using greater than and less than signs, as well as exercises involving missing square numbers in calculations. Towards the end of the lesson, students apply their knowledge to reasoning and problem-solving questions, such as placing numbers in a Carroll diagram according to certain criteria. The lesson aims to solidify the students' understanding of square and cube numbers, as well as their ability to identify and use them in various mathematical contexts.

Square Numbers Worksheet

FREE DOWNLOAD

Help your students prepare for their Maths GCSE with this free square numbers worksheet of 30+ questions and answers

• Section 1 of the square numbers  worksheet contains 20+ skills-based square numbers  questions, in 3 groups to support differentiation
• Section 2 contains 3 applied square numbers  questions with a mix of word problems and deeper problem solving questions
• Section 3 contains 3 foundation and higher level GCSE exam style square numbers  questions 
• Answers and a mark scheme for all square numbers  questions are provided
• Questions follow variation theory with plenty of opportunities for students to work independently at their own level
• All questions and maths activities created by fully qualified expert secondary maths teachers
• Suitable for GCSE maths revision for AQA, OCR and Edexcel exam boards

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Raise maths attainment across your school with hundreds of flexible and easy to use GCSE maths worksheets and lessons designed by teachers for teachers.

Square numbers at a glance

A square number is the result when a number is multiplied by itself. For example, 3 times 3=9 and so 9 is a square number. Square numbers are sometimes called perfect squares. The first 12 square numbers are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121 and 144 . 

The inverse of squaring a number is square rooting a number. The square root of a number is the number that is squared to get that number, so the square root of 9 is 3 .

It helps to be confident with times tables when exploring square numbers and square roots. 

When squaring a negative number, the answer is always positive. We must therefore be aware that the square root of a number can also have a negative solution, e.g. -4 times -4=16 and so the square root of 16 is equal to 4 and -4 .

Also, the square of an integer is always an integer (a whole number) but the square root of an integer may not always be an integer. If the square root of a number is not an integer, then this number is a surd, e.g. the square root of 3 is not an integer and so the square root of 3 is a surd.

Looking forward, students can then progress to additional powers and roots worksheets and other number worksheets , for example a multiplying and dividing decimals worksheet or an order of operations worksheet.

For more teaching and learning support on Number our GCSE maths lessons provide step by step support for all GCSE maths concepts.

Related worksheets

Money Problems Exam Questions

Place Value Exam Questions

Adding And Subtracting Negative Numbers Exam Questions

Reciprocal Exam Questions

Popular for gcse.

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Square Numbers Lesson

This  Year 5 Square Numbers  lesson covers the prior learning of finding factors of numbers, before moving onto the main skill of recognising and calculating square numbers.

The lesson starts with a prior learning worksheet to check pupils’ understanding. The interactive lesson slides recap the prior learning before moving on to the main skill. Children can then practise further by completing the activities and can extend their learning by completing an engaging extension task.

National Curriculum Objective Mathematics Year 5: (5C5d)  Recognise and use square numbers and cube numbers, and the notation for squared (2) and cubed (3)

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Lesson Slides

These lesson slides guides pupils through the prior learning of finding factors of numbers, before moving onto the main skill of square numbers. There are a number of questions to check pupils' understanding throughout.

Modelling PowerPoint

This powerpoint can be used to model the questions that the children will complete on the Varied Fluency and Reasoning & Problem Solving worksheets as part of this lesson.

These are the same as the lesson slides on Classroom Secrets. You can assign this as an activity for pupils to access individually in school or remotely from home.

Video Tutorial

In this Square Numbers Video Tutorial, Jade demonstrates square numbers and uses squared notation.

1 Prior Learning

This Year 5 Square Numbers lesson covers the prior learning of finding factors of numbers, before moving onto the main skill of recognising and calculating square numbers.

Jade shows pupils how to find the factors of different numbers using arrays in this Factors Video Tutorial.

Interactive Activity

This Year 5 Multiples and Factors Game includes five questions designed to check pupils’ understanding of multiples and factors.

2 Practical Activities

Supporting Activities

This square numbers supporting activities sheet contains suggestions for additional tasks you might wish to use to support pupils' understanding of the concepts taught in the lesson.

2 Varied Fluency

This differentiated worksheet includes varied fluency questions for pupils to practise the main skill of this lesson.

This Year 5 Square Numbers activity checks your child’s understanding of identifying square numbers.

2 Reasoning & Problem Solving

This square numbers extension task includes a challenge activity which can be used to further pupils' understanding of the concepts taught in the square numbers lesson.

Mixed Practice

This worksheet includes varied fluency, reasoning and problem solving questions for pupils to practise the main skill of square numbers.

This differentiated worksheet includes reasoning and problem solving questions to support the teaching of this step.

Discussion Problem

This worksheet includes two discussion problems which can be used in pairs or small groups to further pupils' understanding of the concepts taught in this lesson.

This Year 5 Square Numbers Maths Challenge checks pupils’ understanding of square numbers.

This differentiated worksheet includes varied fluency and reasoning and problem solving questions to support the teaching of this step.

2 Additional Activities

Home Learning Pack

This Autumn week 9 Maths pack contains varied fluency, reasoning and problem solving worksheets.

Learning Video Clip

Mara Thon and Dec Athlon are taking part in the Qatar Olympics and Paralympics. Join them as they explore the Olympic Village and find their accommodation, using square numbers to help the stewards ensure all athletes have a place to stay.

Consolidation Pack

This resource is aimed at Year 5 Expected and has been designed to give children the opportunity to consolidate the skills they have learned in Autumn Block 4 – Number: Multiplication and Division.

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Year 6 - Square and cube numbers

Subject: Mathematics

Age range: 7-11

Resource type: Lesson (complete)

Last updated

5 November 2021

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This is a whole lesson based on the Year 6 objective “Square and cube numbers". This resource includes the teacher input ( learning journey), independent worksheet and a challenge activity to deepen the children’s understanding of the concept being learned.

The questions have been inspired and adapted from the White Rose Small Steps Guidance and Teaching for Mastery documents. This document is useful for teachers who have adapted Maths Mastery and need guidance in the approach or those who are looking for variation in fluency, reasoning and problem solving or simply those who don’t want to plan it themselves but want high quality resources and quality first teaching. =)

This document is uploaded as a SMART Notebook file and it is interactive. The concrete/pictorial manipulative can be used, moved and manipulated.

This document can be downloaded on SMART Notebook and it is also available as a PDF or as a PowerPoint for those who do not have SMART Notebook, however the PDF file is not interactive.

Please note - some of my resources are available on Activinspire and some of the newer content is available on SMART Notebook, please be aware of the file you are downloading before you purchase/ download.

Thank you for taking the time to review my resources. =) I hope this helps you with your teaching and if it does please could you be kind enough to leave some positive feedback. =)

Kind regards,

@MasteryMaths01

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