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Speed. Investigations. physics. Time. Vectors. Relative velocity. History of mathematics. Acceleration. sport. Maths Supporting SET.

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

Witch's Hat

Stage: 3 and 4 Challenge Level:

What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?

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: 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?

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

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.

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.

First Forward Into Logo 10: Count up - Count Down

Stage: 3, 4 and 5 Challenge Level:

What happens when a procedure calls itself?

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.

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.

Gym Bag

Stage: 3 and 4 Challenge Level:

Can Jo make a gym bag for her trainers from the piece of fabric she has?

Straw Scaffold

Stage: 3 Challenge Level:

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

Stage: 3 Challenge Level:

What shape would fit your pens and pencils best? How can you make it?

Stage: 2 and 3 Challenge Level:

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

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?

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.

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 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.

Tangram Pictures

Stage: 1, 2 and 3 Challenge Level:

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

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.

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?

Tower of Hanoi

Stage: 3 Challenge Level:

The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.

Cunning Card Trick

Stage: 3 Challenge Level:

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

Nine Colours

Stage: 3 Challenge Level:

Can you use small coloured cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of each colour?

Factors and Multiples Puzzle

Stage: 3 Challenge Level:

Using your knowledge of the properties of numbers, can you fill all the squares on the board?

Factors and Multiples Game

Stage: 2, 3 and 4 Challenge Level:

A game in which players take it in turns to choose a number. Can you block your opponent?

Fractions Jigsaw

Stage: 3 Challenge Level:

A jigsaw where pieces only go together if the fractions are equivalent.

Drawing Celtic Knots

Stage: 3 Challenge Level:

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

Sociable Cards

Stage: 3 Challenge Level:

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

Constructing Triangles

Stage: 3 Challenge Level:

Generate three random numbers to determine the side lengths of a triangle. What triangles can you draw?

Cool as Ice

Stage: 3 and 4 Challenge Level:

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

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?

Notes on a Triangle

Stage: 3 Challenge Level:

Can you describe what happens in this film?

Whirling Fibonacci Squares

Stage: 3 and 4

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

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?

Which Solids Can We Make?

Stage: 3 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?

Observing the Sun and the Moon

Stage: 2 and 3 Challenge Level:

How does the time of dawn and dusk vary? What about the Moon, how does that change from night to night? Is the Sun always the same? Gather data to help you explore these questions.

Attractive Rotations

Stage: 3 Challenge Level:

Here is a chance to create some attractive images by rotating shapes through multiples of 90 degrees, or 30 degrees, or 72 degrees or...

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?

Conway's Chequerboard Army

Stage: 3 Challenge Level:

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

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?

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.

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?

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.

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: Celtic Knot Tiles

Stage: 2, 3 and 4 Challenge Level:

Make some celtic knot patterns using tiling techniques

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?