# Resources tagged with: Visualising

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### There are 183 results

Broad Topics > Thinking Mathematically > Visualising

### Routes 1 and 5

##### Age 5 to 7Challenge Level

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

### Painting Possibilities

##### Age 7 to 11Challenge 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. . . .

### Counters

##### Age 7 to 11Challenge Level

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

### Paw Prints

##### Age 7 to 11Challenge 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?

### Folded Number Line

##### Age 7 to 11Challenge Level

When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.

### Neighbours

##### Age 7 to 11Challenge 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?

### Map Folding

##### Age 7 to 11Challenge 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?

### Waiting for Blast Off

##### Age 7 to 11Challenge 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?

### Knight's Swap

##### Age 7 to 11Challenge Level

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

### Jigsaw Pieces

##### Age 7 to 11Challenge Level

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

### Cover the Camel

##### Age 5 to 7Challenge Level

Can you cover the camel with these pieces?

### Dodecamagic

##### Age 7 to 11Challenge 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?

### Single Track

##### Age 7 to 11Challenge Level

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

### Hexpentas

##### Age 5 to 11Challenge Level

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

### Shunting Puzzle

##### Age 7 to 11Challenge 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?

### Cuboid-in-a-box

##### Age 7 to 11Challenge 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?

### Open Boxes

##### Age 7 to 11Challenge 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?

### Tangram Tangle

##### Age 5 to 7Challenge 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?

### Display Boards

##### Age 7 to 11Challenge Level

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

### Move a Match

##### Age 7 to 11Challenge 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?

### Tricky Triangles

##### Age 5 to 7Challenge Level

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

### Triple Cubes

##### Age 5 to 11Challenge Level

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

### Taking Steps

##### Age 7 to 11Challenge Level

In each of the pictures the invitation is for you to: Count what you see. Identify how you think the pattern would continue.

### Coded Hundred Square

##### Age 7 to 11Challenge Level

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

### Little Boxes

##### Age 7 to 11Challenge Level

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

### Counting Cards

##### Age 7 to 11Challenge 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?

### Putting Two and Two Together

##### Age 7 to 11Challenge 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?

### More Pebbles

##### Age 7 to 11Challenge Level

Have a go at this 3D extension to the Pebbles problem.

### 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,. . . .

### Child's Play

##### Age 7 to 11Challenge Level

A toy has a regular tetrahedron, a cube and a base with triangular and square hollows. If you fit a shape into the correct hollow a bell rings. How many times does the bell ring in a complete game?

##### Age 7 to 11Challenge 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.

### Teddy Bear Line-up

##### Age 5 to 7Challenge 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?

### Four Triangles Puzzle

##### Age 5 to 11Challenge 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?

### Tetrahedron Faces

##### Age 7 to 11Challenge Level

One face of a regular tetrahedron is painted blue and each of the remaining faces are painted using one of the colours red, green or yellow. How many different possibilities are there?

### A City of Towers

##### Age 5 to 7Challenge 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?

### Seeing Squares

##### Age 5 to 11Challenge Level

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

### Colour Wheels

##### Age 7 to 11Challenge Level

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

### Redblue

##### Age 7 to 11Challenge 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?

### Dragons and Swans

##### Age 5 to 7Challenge Level

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

### Take One Example

##### Age 5 to 11

This article introduces the idea of generic proof for younger children and illustrates how one example can offer a proof of a general result through unpacking its underlying structure.

### One Big Triangle

##### Age 5 to 7Challenge Level

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

### Square Corners

##### Age 7 to 11Challenge 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?

##### Age 7 to 11Challenge Level

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

### Two Squared

##### Age 7 to 11Challenge Level

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

### Odd Squares

##### Age 7 to 11Challenge Level

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

### Music to My Ears

##### Age 7 to 11Challenge Level

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

### Nine-pin Triangles

##### Age 7 to 11Challenge Level

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

### Three Cubed

##### Age 7 to 11Challenge Level

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

### 28 - Upward and Onward

##### Age 7 to 11Challenge Level

Can you find ways of joining cubes together so that 28 faces are visible?

### Hundred Square

##### Age 5 to 7Challenge Level

A hundred square has been printed on both sides of a piece of paper. What is on the back of 100? 58? 23? 19?