Search by Topic

Resources tagged with Shape, space & measures - generally similar to Euclid? No, but Carol, Yes:

Filter by: Content type:
Stage:
Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

There are 22 results

problem Icon

Euclid? No, but Carol, Yes

Stage: 4

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

problem Icon

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.

problem Icon

Natural Shapes

Stage: 4 Challenge Level: Challenge Level:1

What mathematical shapes occur in the natural world?

problem Icon

Fitting Flat Shapes

Stage: 4 Challenge Level: Challenge Level:1

How efficiently can various flat shapes be fitted together?

problem Icon

Squareo'scope Determines the Kind of Triangle

Stage: 4

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

problem Icon

All Square

Stage: 3 Challenge Level: Challenge Level:1

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?

problem Icon

Farmers Field

Stage: 3 Challenge Level: Challenge Level:1

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. . . .

problem Icon

What Is the Circle Scribe Disk Compass?

Stage: 3 and 4

Introducing a geometrical instrument with 3 basic capabilities.

problem Icon

Appearing Square

Stage: 3 Challenge Level: Challenge Level:1

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. . . .

problem Icon

Arclets

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 NFRICH website.

problem Icon

Black and Red Tiles

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

A rectangular floor is covered with 315 black and red tiles. There is a border of single black tiles round the edge of the floor, and inside that a pattern of 2 interlocking black squares which do. . . .

problem Icon

Disappearing Square

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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. . . .

problem Icon

Long Short

Stage: 4 Challenge Level: Challenge Level:1

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. . . .

problem Icon

Lawnmower

Stage: 4 Challenge Level: Challenge Level:1

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. . . .

problem Icon

Circumspection

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

problem Icon

Triangle Incircle Iteration

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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. . . .

problem Icon

Fitting In

Stage: 4 Challenge Level: Challenge Level:1

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. . . .

problem Icon

Painting Cubes

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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?

problem Icon

Christmas Boxes

Stage: 3 Challenge Level: Challenge Level:1

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

problem Icon

Paving Paths

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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?

problem Icon

The Old Goats

Stage: 3 Challenge Level: Challenge Level:1

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. . . .

problem Icon

All in the Mind

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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. . . .