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#### Resources tagged with Shape, space & measures - generally similar to Long Short:

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Broad Topics > 2D Geometry, Shape and Space > Shape, space & measures - generally

### Long Short

##### Stage: 4 Challenge Level:

A quadrilateral inscribed in a unit circle has sides of lengths s1, s2, s3 and s4 where s1 ≤ s2 ≤ s3 ≤ s4. Find a quadrilateral of this type for which s1= sqrt2 and show s1 cannot. . . .

### Fitting In

##### Stage: 4 Challenge Level:

The largest square which fits into a circle is ABCD and EFGH is a square with G and H on the line CD and E and F on the circumference of the circle. Show that AB = 5EF. Similarly the largest. . . .

### Triangle Incircle Iteration

##### Stage: 4 Challenge Level:

Start with any triangle T1 and its inscribed circle. Draw the triangle T2 which has its vertices at the points of contact between the triangle T1 and its incircle. Now keep repeating this. . . .

### Christmas Boxes

##### Stage: 3 Challenge Level:

Find all the ways to cut out a 'net' of six squares that can be folded into a cube.

### Disappearing Square

##### Stage: 3 Challenge Level:

Do you know how to find the area of a triangle? You can count the squares. What happens if we turn the triangle on end? Press the button and see. Try counting the number of units in the triangle now. . . .

### Appearing Square

##### Stage: 3 Challenge Level:

Make an eight by eight square, the layout is the same as a chessboard. You can print out and use the square below. What is the area of the square? Divide the square in the way shown by the red dashed. . . .

### 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. . . .

### Paving Paths

##### Stage: 3 Challenge Level:

How many different ways can I lay 10 paving slabs, each 2 foot by 1 foot, to make a path 2 foot wide and 10 foot long from my back door into my garden, without cutting any of the paving slabs?

### 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?

### 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. . . .

### Painting Cubes

##### Stage: 3 Challenge Level:

Imagine you have six different colours of paint. You paint a cube using a different colour for each of the six faces. How many different cubes can be painted using the same set of six colours?

### Lawnmower

##### Stage: 4 Challenge Level:

A kite shaped lawn consists of an equilateral triangle ABC of side 130 feet and an isosceles triangle BCD in which BD and CD are of length 169 feet. A gardener has a motor mower which cuts strips of. . . .

### Introducing NRICH TWILGO

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

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

### What's Inside/outside/under the Box?

##### Stage: 2 and 3

This article describes investigations that offer opportunities for children to think differently, and pose their own questions, about shapes.

### What Shape?

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

This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.

### Triangles in the Middle

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

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

### Farmers Field

##### Stage: 3 Challenge Level:

A farmer has a flat field and two sons who will each inherit half of the field. The farmer wishes to build a stone wall to divide the field in two so each son inherits the same area. Stone walls are. . . .

### Circumspection

##### Stage: 4 Challenge Level:

M is any point on the line AB. Squares of side length AM and MB are constructed and their circumcircles intersect at P (and M). Prove that the lines AD and BE produced pass through P.

### The Development of Spatial and Geometric Thinking: 5 to 18

##### Stage: 1, 2, 3 and 4

This is the first article in a series which aim to provide some insight into the way spatial thinking develops in children, and draw on a range of reported research. The focus of this article is the. . . .

### Squareo'scope Determines the Kind of Triangle

##### Stage: 3

A description of some experiments in which you can make discoveries about triangles.

### Stick Images

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

What shape and size of drinks mat is best for flipping and catching?

### Make Your Own Solar System

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

Making a scale model of the solar system

### Euclid? No, but Carol, Yes

##### Stage: 4

For teachers. About the teaching of geometry with some examples from school geometry of long ago.

### Arclets Explained

##### Stage: 3 and 4

This article gives an wonderful insight into students working on the Arclets problem that first appeared in the Sept 2002 edition of the NRICH website.

### What Is the Circle Scribe Disk Compass?

##### Stage: 3 and 4

Introducing a geometrical instrument with 3 basic capabilities.

### Natural Shapes

##### Stage: 4 Challenge Level:

How does shape relate to function in the natural world?

### Arranging Squares

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

A task which depends on members of the group working collaboratively to reach a single goal.