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Broad Topics > Using, Applying and Reasoning about Mathematics > Visualising

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Routes 1 and 5

Age 5 to 7 Challenge Level:

Find your way through the grid starting at 2 and following these operations. What number do you end on?

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Painting Possibilities

Age 7 to 11 Challenge Level:

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

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Knight's Swap

Age 7 to 11 Challenge Level:

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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Dodecamagic

Age 7 to 11 Challenge Level:

Here you see the front and back views of a dodecahedron. Each vertex has been numbered so that the numbers around each pentagonal face add up to 65. Can you find all the missing numbers?

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A City of Towers

Age 5 to 7 Challenge Level:

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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Paw Prints

Age 7 to 11 Challenge Level:

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

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Tetrafit

Age 7 to 11 Challenge Level:

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

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Brush Loads

Age 7 to 11 Challenge Level:

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

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Cuboid-in-a-box

Age 7 to 11 Challenge Level:

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

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Map Folding

Age 7 to 11 Challenge Level:

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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Neighbours

Age 7 to 11 Challenge Level:

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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Red Even

Age 7 to 11 Challenge Level:

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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Cover the Camel

Age 5 to 7 Challenge Level:

Can you cover the camel with these pieces?

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Celtic Knot

Age 7 to 11 Challenge Level:

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

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Waiting for Blast Off

Age 7 to 11 Challenge Level:

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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Single Track

Age 7 to 11 Challenge Level:

What is the best way to shunt these carriages so that each train can continue its journey?

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Jigsaw Pieces

Age 7 to 11 Challenge Level:

How will you go about finding all the jigsaw pieces that have one peg and one hole?

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Shunting Puzzle

Age 7 to 11 Challenge Level:

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

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Counters

Age 7 to 11 Challenge Level:

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

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Tessellate the Triominoes

Age 5 to 7 Challenge Level:

What happens when you try and fit the triomino pieces into these two grids?

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Open Boxes

Age 7 to 11 Challenge Level:

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

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Hexpentas

Age 5 to 11 Challenge Level:

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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Display Boards

Age 7 to 11 Challenge Level:

Design an arrangement of display boards in the school hall which fits the requirements of different people.

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Four Triangles Puzzle

Age 5 to 11 Challenge Level:

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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Teddy Bear Line-up

Age 5 to 7 Challenge Level:

What is the least number of moves you can take to rearrange the bears so that no bear is next to a bear of the same colour?

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Square Corners

Age 7 to 11 Challenge Level:

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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Counting Cards

Age 7 to 11 Challenge Level:

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

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Quadrilaterals

Age 7 to 11 Challenge Level:

How many DIFFERENT quadrilaterals can be made by joining the dots on the 8-point circle?

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Tricky Triangles

Age 5 to 7 Challenge Level:

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

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Tangram Tangle

Age 5 to 7 Challenge Level:

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

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Putting Two and Two Together

Age 7 to 11 Challenge Level:

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

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Move a Match

Age 7 to 11 Challenge Level:

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

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Multiplication Series: Illustrating Number Properties with Arrays

Age 5 to 11

This article for teachers describes how modelling number properties involving multiplication using an array of objects not only allows children to represent their thinking with concrete materials,. . . .

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Coded Hundred Square

Age 7 to 11 Challenge Level:

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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Little Boxes

Age 7 to 11 Challenge Level:

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

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Nine-pin Triangles

Age 7 to 11 Challenge Level:

How many different triangles can you make on a circular pegboard that has nine pegs?

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Domino Numbers

Age 7 to 11 Challenge Level:

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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Three Cubed

Age 7 to 11 Challenge Level:

Can you make a 3x3 cube with these shapes made from small cubes?

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Making Maths: Rolypoly

Age 5 to 11 Challenge Level:

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

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One Big Triangle

Age 5 to 7 Challenge Level:

Make one big triangle so the numbers that touch on the small triangles add to 10.

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Midpoint Triangle

Age 7 to 11 Challenge Level:

Can you cut up a square in the way shown and make the pieces into a triangle?

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Paper Patchwork 1

Age 5 to 7 Challenge Level:

Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

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Redblue

Age 7 to 11 Challenge Level:

Investigate the number of paths you can take from one vertex to another in these 3D shapes. Is it possible to take an odd number and an even number of paths to the same vertex?

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Construct-o-straws

Age 7 to 11 Challenge Level:

Make a cube out of straws and have a go at this practical challenge.

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Dragons and Swans

Age 5 to 7 Challenge Level:

A game for two players. You'll need some counters.

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Making Tangrams

Age 7 to 11 Challenge Level:

Here's a simple way to make a Tangram without any measuring or ruling lines.

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Cubes Within Cubes

Age 7 to 14 Challenge Level:

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

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Regular Rings 1

Age 7 to 11 Challenge Level:

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

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Fractional Triangles

Age 7 to 11 Challenge Level:

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

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Paper Patchwork 2

Age 5 to 7 Challenge Level:

Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?