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Resources tagged with Working systematically similar to Squares:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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Working systematically. Generalising. Visualising. Squares. Logo. Area.

There are 314 results

Broad Topics > Using, Applying and Reasoning about Mathematics > Working systematically

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Tiling

Stage: 2 Challenge Level: Challenge Level:1

An investigation that gives you the opportunity to make and justify predictions.

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Making Squares

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

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Area and Perimeter

Stage: 2 Challenge Level: Challenge Level:1

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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Geoboards

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

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Tiles on a Patio

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

How many ways can you find of tiling the square patio, using square tiles of different sizes?

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My New Patio

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

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Intersection Sums Sudoku

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

A Sudoku with clues given as sums of entries.

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Making Boxes

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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An Introduction to Magic Squares

Stage: 1, 2, 3 and 4

Find out about Magic Squares in this article written for students. Why are they magic?!

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Two and Two

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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Numerically Equal

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you draw a square in which the perimeter is numerically equal to the area?

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A-magical Number Maze

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

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The Naked Pair in Sudoku

Stage: 2, 3 and 4

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

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Newspapers

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

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Zargon Glasses

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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Shaping Up

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

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Lots of Lollies

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

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Polo Square

Stage: 2 Challenge Level: Challenge Level:1

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

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Sandwiches

Stage: 2, 3, 4 and 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's there is one digit, between the two 2's there are two digits, and between the two 3's there are three digits.

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Rabbits in the Pen

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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Twinkle Twinkle

Stage: 2 and 3 Challenge Level: Challenge Level:1

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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Magnetic Personality

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

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More Transformations on a Pegboard

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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Sitting Round the Party Tables

Stage: 1 and 2 Challenge Level: Challenge Level:1

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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Journeys in Numberland

Stage: 2 Challenge Level: Challenge Level:1

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

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Two Egg Timers

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

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The Pied Piper of Hamelin

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

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Consecutive Numbers

Stage: 2 and 3 Challenge Level: Challenge Level:1

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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Prison Cells

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

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Making Maths: Double-sided Magic Square

Stage: 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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Magic Vs

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

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Square Corners

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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Problem Solving, Using and Applying and Functional Mathematics

Stage: 1, 2, 3, 4 and 5 Challenge Level: Challenge Level:1

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

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Fault-free Rectangles

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Find out what a "fault-free" rectangle is and try to make some of your own.

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The Moons of Vuvv

Stage: 2 Challenge Level: Challenge Level:1

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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Torn Shapes

Stage: 2 Challenge Level: Challenge Level:1

These rectangles have been torn. How many squares did each one have inside it before it was ripped?

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Button-up Some More

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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Ice Cream

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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The Add and Take-away Path

Stage: 1 Challenge Level: Challenge Level:1

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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Maths Trails

Stage: 2 and 3

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

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Pouring the Punch Drink

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

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Games Related to Nim

Stage: 1, 2, 3 and 4

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

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Fencing Lambs

Stage: 2 Challenge Level: Challenge Level:1

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

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Broken Toaster

Stage: 2 Short Challenge Level: Challenge Level:1

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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Calcunos

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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Teddy Town

Stage: 1, 2 and 3 Challenge Level: Challenge Level:2 Challenge Level:2

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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Round the Three Dice

Stage: 2 Challenge Level: Challenge Level:1

What happens when you round these three-digit numbers to the nearest 100?

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Round the Dice Decimals 1

Stage: 2 Challenge Level: Challenge Level:1

Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?

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Round the Dice Decimals 2

Stage: 2 Challenge Level: Challenge Level:1

What happens when you round these numbers to the nearest whole number?

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Halloween Investigation

Stage: 2 Challenge Level: Challenge Level:1

Ana and Ross looked in a trunk in the attic. They found old cloaks and gowns, hats and masks. How many possible costumes could they make?