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

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Cool as Ice

Age 11 to 16 Challenge Level:

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

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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?

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Straw Scaffold

Age 11 to 14 Challenge Level:

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

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Make Your Own Pencil Case

Age 11 to 14 Challenge Level:

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

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Paper Folding - Models of the Platonic Solids

Age 11 to 16

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

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Next Size Up

Age 7 to 11 Challenge Level:

The challenge for you is to make a string of six (or more!) graded cubes.

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Making Maths: Link-a-cube

Age 7 to 11 Challenge Level:

Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.

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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?

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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?

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Stringy Quads

Age 7 to 11 Challenge Level:

This practical problem challenges you to make quadrilaterals with a loop of string. You'll need some friends to help!

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Making Maths: Stars

Age 7 to 11 Challenge Level:

Have a go at drawing these stars which use six points drawn around a circle. Perhaps you can create your own designs?

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Making Maths: Rolypoly

Age 5 to 11 Challenge Level:

Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?

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It's a Fence!

Age 5 to 11 Challenge Level:

In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.

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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.

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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?

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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?

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Little Boxes

Age 7 to 11 Challenge Level:

How many different cuboids can you make when you use four CDs or DVDs? How about using five, then six?

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Two Squared

Age 7 to 11 Challenge Level:

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

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Straight to Curves

Age 5 to 11 Challenge Level:

How can you make a curve from straight strips of paper?

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Making Cuboids

Age 7 to 11 Challenge Level:

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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It's a Tie

Age 7 to 11 Challenge Level:

Kaia is sure that her father has worn a particular tie twice a week in at least five of the last ten weeks, but her father disagrees. Who do you think is right?

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A Patchwork Piece

Age 7 to 11 Challenge Level:

Follow the diagrams to make this patchwork piece, based on an octagon in a square.

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Hoops/rope

Age 7 to 11 Challenge Level:

Ideas for practical ways of representing data such as Venn and Carroll diagrams.

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Paper Curves

Age 7 to 11 Challenge Level:

This is a simple paper-folding activity that gives an intriguing result which you can then investigate further.

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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?

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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.

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Jomista Mat

Age 7 to 11 Challenge Level:

Looking at the picture of this Jomista Mat, can you decribe what you see? Why not try and make one yourself?

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Folding Flowers 1

Age 7 to 11 Challenge Level:

Can you visualise what shape this piece of paper will make when it is folded?

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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.

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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?

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Folding Flowers 2

Age 7 to 11 Challenge Level:

Make a flower design using the same shape made out of different sizes of paper.

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Regular Rings 1

Age 7 to 11 Challenge Level:

Can you work out what shape is made by folding in this way? Why not create some patterns using this shape but in different sizes?

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Regular Rings 2

Age 7 to 11 Challenge Level:

What shape is made when you fold using this crease pattern? Can you make a ring design?

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Pyramid Numbers

Age 7 to 11 Challenge Level:

What are the next three numbers in this sequence? Can you explain why are they called pyramid numbers?

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Triangular Faces

Age 7 to 11 Challenge Level:

This problem invites you to build 3D shapes using two different triangles. Can you make the shapes from the pictures?

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Cereal Packets

Age 7 to 11 Challenge Level:

How can you put five cereal packets together to make different shapes if you must put them face-to-face?

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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.

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Plaited 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.

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Folding, Cutting and Punching

Age 7 to 11 Challenge Level:

Exploring and predicting folding, cutting and punching holes and making spirals.

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First Forward Into Logo 9: Stars

Age 11 to 18 Challenge Level:

Turn through bigger angles and draw stars with Logo.

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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.

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Construct-o-straws

Age 7 to 11 Challenge Level:

Make a cube out of straws and have a go at this practical challenge.

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First Forward Into Logo 5: Pen Up, Pen Down

Age 7 to 16 Challenge Level:

Learn about Pen Up and Pen Down in Logo

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First Forward Into Logo 8: More about Variables

Age 11 to 18 Challenge Level:

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

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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.

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Jig Shapes

Age 5 to 11 Challenge Level:

Can you each work out what shape you have part of on your card? What will the rest of it look like?

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First Forward Into Logo 10: Count up - Count Down

Age 11 to 18 Challenge Level:

What happens when a procedure calls itself?

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Fractional Triangles

Age 7 to 11 Challenge Level:

Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.

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Let Us Reflect

Age 7 to 11 Challenge Level:

Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

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Making Maths: Snowflakes

Age 7 to 11 Challenge Level:

It's hard to make a snowflake with six perfect lines of symmetry, but it's fun to try!