Resources tagged with: Practical Activity

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Broad Topics > Mathematical Thinking > Practical Activity

Rolling Triangle

Age 11 to 14 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.

Sea Defences

Age 7 to 14 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?

Triangles to Tetrahedra

Age 11 to 14 Challenge Level:

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

Nine Colours

Age 11 to 16 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?

Cubic Conundrum

Age 7 to 16 Challenge Level:

Which of the following cubes can be made from these nets?

Getting an Angle

Age 11 to 14 Challenge Level:

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

Making Maths: Double-sided Magic Square

Age 7 to 14 Challenge Level:

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

Constructing Triangles

Age 11 to 14 Challenge Level:

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

Cunning Card Trick

Age 11 to 14 Challenge Level:

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

Factors and Multiples Game

Age 7 to 16 Challenge Level:

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

Tower of Hanoi

Age 11 to 14 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.

Factors and Multiples Game for Two

Age 7 to 14 Challenge Level:

Factors and Multiples game for an adult and child. How can you make sure you win this game?

Amazing Card Trick

Age 11 to 14 Challenge Level:

How is it possible to predict the card?

Marbles

Age 11 to 14 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?

Tangram Pictures

Age 5 to 14 Challenge Level:

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

Making Maths: Snake Pits

Age 5 to 14 Challenge Level:

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

More Marbles

Age 11 to 14 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?

Drawing Celtic Knots

Age 11 to 14 Challenge Level:

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

Back to the Practical?

Age 7 to 14

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. . . .

Attractive Rotations

Age 11 to 14 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...

Factors and Multiples Puzzle

Age 11 to 14 Challenge Level:

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

Sociable Cards

Age 11 to 14 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?

Notes on a Triangle

Age 11 to 14 Challenge Level:

Can you describe what happens in this film?

The Best Card Trick?

Age 11 to 16 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?

First Forward Into Logo 5: Pen Up, Pen Down

Age 7 to 16 Challenge Level:

Learn about Pen Up and Pen Down in Logo

Modular Origami Polyhedra

Age 7 to 16 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.

Well Balanced

Age 5 to 18 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.

Which Solids Can We Make?

Age 11 to 14 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?

Making Rectangles, Making Squares

Age 11 to 14 Challenge Level:

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

First Forward Into Logo 3: Repeat REPEAT

Age 7 to 16 Challenge Level:

More Logo for beginners. Now learn more about the REPEAT command.

Celtic Knotwork Patterns

Age 7 to 14

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

Making Maths: Walking Through a Playing Card?

Age 7 to 14 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?

Whirling Fibonacci Squares

Age 11 to 16

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

Fractions Jigsaw

Age 11 to 14 Challenge Level:

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

Making Maths: Equilateral Triangle Folding

Age 7 to 14 Challenge Level:

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

Making Maths: Clinometer

Age 11 to 14 Challenge Level:

You can use a clinometer to measure the height of tall things that you can't possibly reach to the top of, Make a clinometer and use it to help you estimate the heights of tall objects.

Paper Folding - Models of the Platonic Solids

Age 11 to 16

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

First Forward Into Logo 10: Count up - Count Down

Age 11 to 18 Challenge Level:

What happens when a procedure calls itself?

Straw Scaffold

Age 11 to 14 Challenge Level:

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

Cool as Ice

Age 11 to 16 Challenge Level:

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

First Forward Into Logo 2: Polygons

Age 7 to 16 Challenge Level:

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

Making Maths: Archimedes' Spiral

Age 7 to 14 Challenge Level:

Make a spiral mobile.

First Forward Into Logo 12: Puzzling Sums

Age 11 to 18 Challenge Level:

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

Turning the Place Over

Age 11 to 18 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?

Making Maths: Celtic Knot Tiles

Age 7 to 16 Challenge Level:

Make some celtic knot patterns using tiling techniques

Making Maths: Make a Pendulum

Age 7 to 14 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 4: Circles

Age 7 to 16 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

Age 11 to 18 Challenge Level:

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

Making Maths: String and Circles

Age 7 to 14 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.

First Forward Into Logo 7: Angles of Polygons

Age 11 to 18 Challenge Level:

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