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#### Resources tagged with Shape, space & measures - generally similar to Painting Cubes:

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

### 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?

### 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?

### 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. . . .

### 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.

### 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. . . .

### 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?

### 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. . . .

### 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.

### 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. . . .

### 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.

### 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.

### 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. . . .

### 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. . . .

### Long Short

##### Stage: 4 Challenge Level:

What can you say about the lengths of the sides of a quadrilateral whose vertices are on a unit circle?

### 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. . . .

### 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.

### 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.

### Triangle Incircle Iteration

##### Stage: 4 Challenge Level:

Keep constructing triangles in the incircle of the previous triangle. What happens?

### 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.

### Euclid? No, but Carol, Yes

##### Stage: 4

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

### Squareo'scope Determines the Kind of Triangle

##### Stage: 3

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

### 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. . . .

### What Is the Circle Scribe Disk Compass?

##### Stage: 3 and 4

Introducing a geometrical instrument with 3 basic capabilities.