# Resources tagged with: Visualising

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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?

### A Square in a Circle

##### Age 7 to 11 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?

### Two Squared

##### Age 7 to 11 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?

### Inside Seven Squares

##### Age 7 to 11 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?

### Wrapping Presents

##### Age 7 to 11 Challenge Level:

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

### Paper Partners

##### Age 5 to 7 Challenge Level:

Can you describe a piece of paper clearly enough for your partner to know which piece it is?

### Cube Drilling

##### Age 7 to 11 Challenge Level:

Imagine a 4 by 4 by 4 cube. If you and a friend drill holes in some of the small cubes in the ways described, how many will not have holes drilled through them?

### 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.

### 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?

### Six to Four

##### Age 5 to 7 Challenge Level:

Move four sticks so there are exactly four triangles.

### Seeing Squares

##### Age 5 to 11 Challenge 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.

### More Building with Cubes

##### Age 7 to 11 Challenge Level:

Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!

### 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?

### 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?

### Folding Flowers 2

##### Age 7 to 11 Challenge Level:

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

### 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?

### Dicey

##### Age 7 to 11 Challenge Level:

A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?

### Posting Triangles

##### Age 5 to 7 Challenge Level:

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

### 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?

### Diagrams

##### Age 7 to 11 Challenge Level:

A group activity using visualisation of squares and triangles.

### Happy Halving

##### Age 5 to 7 Challenge Level:

Can you split each of the shapes below in half so that the two parts are exactly the same?

### 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. . . .

### Three Squares

##### Age 5 to 11 Challenge Level:

What is the greatest number of squares you can make by overlapping three squares?

### Overlaps

##### Age 5 to 7 Challenge Level:

What does the overlap of these two shapes look like? Try picturing it in your head and then use the interactivity to test your prediction.

### Painted Faces

##### Age 7 to 11 Challenge Level:

Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?

### Sponge Sections

##### Age 7 to 11 Challenge Level:

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.

### 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?

### Reef and Granny

##### Age 7 to 11 Challenge Level:

Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?

### 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?

##### Age 7 to 11 Challenge Level:

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

### 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.

### Eight Hidden Squares

##### Age 7 to 14 Challenge Level:

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

### 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?

##### Age 7 to 11 Challenge Level:

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

### Move Those Halves

##### Age 7 to 11 Challenge Level:

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

### Ten Hidden Squares

##### Age 7 to 11 Challenge Level:

These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

### Twice as Big?

##### Age 7 to 11 Challenge Level:

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

### Right or Left?

##### Age 7 to 11 Challenge Level:

Which of these dice are right-handed and which are left-handed?

### 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?

### Hundred Square

##### Age 5 to 7 Challenge 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?

### The Development of Spatial and Geometric Thinking: the Importance of Instruction.

##### Age 5 to 11

This article looks at levels of geometric thinking and the types of activities required to develop this thinking.

### Fred the Class Robot

##### Age 7 to 11 Challenge Level:

Billy's class had a robot called Fred who could draw with chalk held underneath him. What shapes did the pupils make Fred draw?

### 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?

### The Development of Spatial and Geometric Thinking: Co-ordinating Space in Drawings

##### Age 5 to 7

This second article in the series refers to research about levels of development of spatial thinking and the possible influence of instruction.

### World of Tan 13 - A Storm in a Tea Cup

##### Age 7 to 11 Challenge Level:

Can you fit the tangram pieces into the outlines of the convex shapes?

### Coin Cogs

##### Age 7 to 11 Challenge Level:

Can you work out what is wrong with the cogs on a UK 2 pound coin?

### 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?

### Triangular Faces

##### Age 7 to 11 Challenge Level:

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

### Regular Rings 2

##### Age 7 to 11 Challenge Level:

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

### Folding Flowers 1

##### Age 7 to 11 Challenge Level:

Can you visualise what shape this piece of paper will make when it is folded?