Resources tagged with: Square numbers

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There are 36 NRICH Mathematical resources connected to Square numbers, you may find related items under Properties of Numbers.

Broad Topics > Properties of Numbers > Square numbers

Always, Sometimes or Never? Number

Age 7 to 11
Challenge Level

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

Light the Lights Again

Age 7 to 11
Challenge Level

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?

Picture a Pyramid ...

Age 7 to 11
Challenge Level

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

Age 11 to 14
Challenge Level

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

Up and Down Staircases

Age 7 to 11
Challenge Level

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

Age 7 to 11
Challenge Level

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?

Cycling Squares

Age 7 to 11
Challenge Level

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

Age 7 to 11
Challenge Level

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

One Wasn't Square

Age 7 to 11
Challenge Level

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

Age 7 to 11
Challenge Level

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.

Iff

Age 14 to 18
Challenge Level

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

Odd Differences

Age 14 to 16
Challenge Level

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

Age 7 to 11
Challenge Level

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

Age 7 to 11
Challenge Level

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

Filling the Gaps

Age 14 to 16
Challenge Level

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

Few and Far Between?

Age 16 to 18
Challenge Level

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

Generating Triples

Age 14 to 16
Challenge Level

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?

Robert's Spreadsheet

Age 14 to 16
Challenge Level

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

Four Coloured Lights

Age 11 to 14
Challenge Level

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

Age 14 to 16
Challenge Level

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

Sticky Numbers

Age 11 to 14
Challenge Level

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

Numbers as Shapes

Age 5 to 7
Challenge Level

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

Triangles Within Squares

Age 14 to 16
Challenge Level

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

Smith and Jones

Age 14 to 16
Challenge Level

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

Age 7 to 11
Challenge Level

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

Graphing Number Patterns

Age 7 to 11
Challenge Level

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

Age 7 to 11
Challenge Level

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

Age 7 to 11
Challenge Level

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?

Special 24

Age 7 to 11
Challenge Level

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

Age 7 to 11
Challenge Level

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

Triangular Triples

Age 14 to 16
Challenge Level

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

Digat

Age 11 to 14
Challenge Level

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

Square Routes

Age 11 to 14
Challenge Level

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

Age 11 to 14
Challenge Level

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

Age 5 to 7
Challenge Level

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

Age 7 to 11
Challenge Level

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