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Broad Topics > Using, Applying and Reasoning about Mathematics > Practical Activity

Back to the Practical?

Stage: 2 and 3

In this article for teachers, Bernard uses some problems to suggest that once a numerical pattern has been spotted from a practical starting point, going back to the practical can help explain. . . .

Making Maths: Snake Pits

Stage: 1, 2 and 3 Challenge Level:

A game to make and play based on the number line.

Enigma

Stage: 2, 3 and 4 Challenge Level:

This package contains hands-on code breaking activities based on the Enigma Schools Project. Suitable for Stages 2, 3 and 4.

Making Maths: Celtic Knot Tiles

Stage: 2, 3 and 4 Challenge Level:

Make some celtic knot patterns using tiling techniques

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?

Well Balanced

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

Exploring balance and centres of mass can be great fun. The resulting structures can seem impossible. Here are some images to encourage you to experiment with non-breakable objects of your own.

Celtic Knotwork Patterns

Stage: 2 and 3

This article for pupils gives an introduction to Celtic knotwork patterns and a feel for how you can draw them.

Making Maths: String and Circles

Stage: 2 and 3 Challenge Level:

You could use just coloured pencils and paper to create this design, but it will be more eye-catching if you can get hold of hammer, nails and string.

Making Maths: Equilateral Triangle Folding

Stage: 2 and 3 Challenge Level:

Make an equilateral triangle by folding paper and use it to make patterns of your own.

Getting an Angle

Stage: 3 Challenge Level:

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

Making Maths: Archimedes' Spiral

Stage: 2 and 3 Challenge Level:

Make a spiral mobile.

Tangram Pictures

Stage: 1, 2 and 3 Challenge Level:

Use the tangram pieces to make our pictures, or to design some of your own!

Making Maths: Clinometer

Stage: 3 Challenge Level:

Make a clinometer and use it to help you estimate the heights of tall objects.

Making Maths: Walking Through a Playing Card?

Stage: 2 and 3 Challenge Level:

It might seem impossible but it is possible. How can you cut a playing card to make a hole big enough to walk through?

Stage: 3, 4 and 5

Logo helps us to understand gradients of lines and why Muggles Magic is not magic but mathematics. See the problem Muggles magic.

The Best Card Trick?

Stage: 3 and 4 Challenge Level:

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

Conway's Chequerboard Army

Stage: 3 Challenge Level:

Here is a solitaire type environment for you to experiment with. Which targets can you reach?

Amazing Card Trick

Stage: 3 Challenge Level:

How is it possible to predict the card?

Making Rectangles, Making Squares

Stage: 3 Challenge Level:

How many differently shaped rectangles can you build using these equilateral and isosceles triangles? Can you make a square?

Making Maths: Double-sided Magic Square

Stage: 2 and 3 Challenge Level:

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Plaited Origami Polyhedra

Stage: 2, 3 and 4 Challenge Level:

These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.

Making Maths: Make a Pendulum

Stage: 2 and 3 Challenge Level:

Galileo, a famous inventor who lived about 400 years ago, came up with an idea similar to this for making a time measuring instrument. Can you turn your pendulum into an accurate minute timer?

When Will You Pay Me? Say the Bells of Old Bailey

Stage: 3 Challenge Level:

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

You Owe Me Five Farthings, Say the Bells of St Martin's

Stage: 3 Challenge Level:

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

Turning the Place Over

Stage: 3, 4 and 5 Challenge Level:

As part of Liverpool08 European Capital of Culture there were a huge number of events and displays. One of the art installations was called "Turning the Place Over". Can you find our how it works?

Straw Scaffold

Stage: 3 Challenge Level:

Build a scaffold out of drinking-straws to support a cup of water

First Forward Into Logo 9: Stars

Stage: 3, 4 and 5 Challenge Level:

Turn through bigger angles and draw stars with Logo.

First Forward Into Logo 8: More about Variables

Stage: 3, 4 and 5 Challenge Level:

Write a Logo program, putting in variables, and see the effect when you change the variables.

First Forward Into Logo 5: Pen Up, Pen Down

Stage: 2, 3 and 4 Challenge Level:

Learn about Pen Up and Pen Down in Logo

Cool as Ice

Stage: 3 and 4 Challenge Level:

Design and construct a prototype intercooler which will satisfy agreed quality control constraints.

Which Solids Can We Make?

Stage: 4 Challenge Level:

Interior angles can help us to work out which polygons will tessellate. Can we use similar ideas to predict which polygons combine to create semi-regular solids?

First Forward Into Logo 4: Circles

Stage: 2, 3 and 4 Challenge Level:

Learn how to draw circles using Logo. Wait a minute! Are they really circles? If not what are they?

First Forward Into Logo 6: Variables and Procedures

Stage: 3, 4 and 5 Challenge Level:

Learn to write procedures and build them into Logo programs. Learn to use variables.

Drawing Celtic Knots

Stage: 3 Challenge Level:

Here is a chance to create some Celtic knots and explore the mathematics behind them.

First Forward Into Logo 11: Sequences

Stage: 3, 4 and 5 Challenge Level:

This part introduces the use of Logo for number work. Learn how to use Logo to generate sequences of numbers.

First Forward Into Logo 7: Angles of Polygons

Stage: 3, 4 and 5 Challenge Level:

More Logo for beginners. Learn to calculate exterior angles and draw regular polygons using procedures and variables.

First Forward Into Logo 12: Puzzling Sums

Stage: 3, 4 and 5 Challenge Level:

Can you puzzle out what sequences these Logo programs will give? Then write your own Logo programs to generate sequences.

More Marbles

Stage: 3 Challenge Level:

I start with a red, a blue, a green and a yellow marble. I can trade any of my marbles for three others, one of each colour. Can I end up with exactly two marbles of each colour?

Cunning Card Trick

Stage: 3 Challenge Level:

Delight your friends with this cunning trick! Can you explain how it works?

Whirling Fibonacci Squares

Stage: 3 and 4

Draw whirling squares and see how Fibonacci sequences and golden rectangles are connected.

First Forward Into Logo 2: Polygons

Stage: 2, 3 and 4 Challenge Level:

This is the second in a twelve part introduction to Logo for beginners. In this part you learn to draw polygons.

Creating Cubes

Stage: 2 and 3 Challenge Level:

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

Notes on a Triangle

Stage: 3 Challenge Level:

Can you describe what happens in this film?

Triangles to Tetrahedra

Stage: 3 Challenge Level:

Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.

First Forward Into Logo 10: Count up - Count Down

Stage: 3, 4 and 5 Challenge Level:

What happens when a procedure calls itself?

Paper Folding - Models of the Platonic Solids

Stage: 2, 3 and 4

A description of how to make the five Platonic solids out of paper.

Marbles

Stage: 3 Challenge Level:

I start with a red, a green and a blue marble. I can trade any of my marbles for two others, one of each colour. Can I end up with five more blue marbles than red after a number of such trades?

Rolling Triangle

Stage: 3 Challenge Level:

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.