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#### Resources tagged with Visualising similar to Transformations on a Pegboard:

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### Framed

##### Stage: 3 Challenge Level:

Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .

### Inside Seven Squares

##### Stage: 2 Challenge Level:

What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

### Tetra Square

##### Stage: 3 Challenge Level:

ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.

### Trice

##### Stage: 3 Challenge Level:

ABCDEFGH is a 3 by 3 by 3 cube. Point P is 1/3 along AB (that is AP : PB = 1 : 2), point Q is 1/3 along GH and point R is 1/3 along ED. What is the area of the triangle PQR?

### Tied Up

##### Stage: 3 Challenge Level:

In a right angled triangular field, three animals are tethered to posts at the midpoint of each side. Each rope is just long enough to allow the animal to reach two adjacent vertices. Only one animal. . . .

### More Pebbles

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

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

### A Square in a Circle

##### Stage: 2 Challenge Level:

What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?

### Nine-pin Triangles

##### Stage: 2 Challenge Level:

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

### Zooming in on the Squares

##### Stage: 2 and 3

Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?

##### Stage: 2 Challenge Level:

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

### Dissect

##### Stage: 3 Challenge Level:

It is possible to dissect any square into smaller squares. What is the minimum number of squares a 13 by 13 square can be dissected into?

### Convex Polygons

##### Stage: 3 Challenge Level:

Show that among the interior angles of a convex polygon there cannot be more than three acute angles.

### Getting an Angle

##### Stage: 3 Challenge Level:

How can you make an angle of 60 degrees by folding a sheet of paper twice?

### Square Corners

##### Stage: 2 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?

### Two Squared

##### Stage: 2 Challenge 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?

### Four Triangles Puzzle

##### Stage: 1 and 2 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?

### World of Tan 16 - Time Flies

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of the candle and sundial?

### World of Tan 29 - the Telephone

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of this telephone?

### Travelling Salesman

##### Stage: 3 Challenge Level:

A Hamiltonian circuit is a continuous path in a graph that passes through each of the vertices exactly once and returns to the start. How many Hamiltonian circuits can you find in these graphs?

### Coloured Edges

##### Stage: 3 Challenge Level:

The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?

### World of Tan 28 - Concentrating on Coordinates

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of Little Ming playing the board game?

### Putting Two and Two Together

##### Stage: 2 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?

### World of Tan 26 - Old Chestnut

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

### World of Tan 22 - an Appealing Stroll

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of the child walking home from school?

### World of Tan 21 - Almost There Now

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

### World of Tan 24 - Clocks

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of these clocks?

### Cubes Within Cubes

##### Stage: 2 and 3 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?

### World of Tan 25 - Pentominoes

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of these people?

### World of Tan 27 - Sharing

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of Little Fung at the table?

### Triangular Faces

##### Stage: 2 Challenge Level:

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

### Dodecamagic

##### Stage: 2 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?

### World of Tan 17 - Weather

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of the watering can and man in a boat?

### All in the Mind

##### Stage: 3 Challenge Level:

Imagine you are suspending a cube from one vertex (corner) and allowing it to hang freely. Now imagine you are lowering it into water until it is exactly half submerged. What shape does the surface. . . .

### Folding Flowers 2

##### Stage: 2 Challenge Level:

Make a flower design using the same shape made out of different sizes of paper.

### World of Tan 1 - Granma T

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of Granma T?

### Jomista Mat

##### Stage: 2 Challenge Level:

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

### The Old Goats

##### Stage: 3 Challenge Level:

A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't. . . .

### Isosceles Triangles

##### Stage: 3 Challenge Level:

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

### Map Folding

##### Stage: 2 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?

### Sea Defences

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

These are pictures of the sea defences at New Brighton. Can you work out what a basic shape might be in both images of the sea wall and work out a way they might fit together?

### World of Tan 18 - Soup

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of Mai Ling and Chi Wing?

##### Stage: 3 Challenge Level:

Can you mark 4 points on a flat surface so that there are only two different distances between them?

### Fractional Triangles

##### Stage: 2 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.

### Regular Rings 1

##### Stage: 2 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?

### Regular Rings 2

##### Stage: 2 Challenge Level:

What shape is made when you fold using this crease pattern? Can you make a ring design?

### World of Tan 20 - Fractions

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of the chairs?

### World of Tan 19 - Working Men

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of this shape. How would you describe it?

### World of Tan 15 - Millennia

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outlines of the workmen?

### World of Tan 14 - Celebrations

##### Stage: 2 Challenge Level:

Can you fit the tangram pieces into the outline of Little Ming and Little Fung dancing?