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

### It's a Tie

##### Stage: 2 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?

### Music to My Ears

##### Stage: 2 Challenge Level:

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?

### 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.

### Cunning Card Trick

##### Stage: 3 Challenge Level:

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

### Factors and Multiples Puzzle

##### Stage: 3 Challenge Level:

A challenge that requires you to apply your knowledge of the properties of numbers. Can you fill all the squares on the board?

##### Stage: 2 Challenge Level:

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

##### Stage: 2 Challenge Level:

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

### Fractional Triangles

##### Stage: 2 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.

### Amazing Card Trick

##### Stage: 3 Challenge Level:

How is it possible to predict the card?

### Let Us Reflect

##### Stage: 2 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?

### 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.

### Square Corners

##### Stage: 2 Challenge Level:

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

### Egyptian Rope

##### Stage: 2 Challenge Level:

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

### Nine Colours

##### Stage: 3 and 4 Challenge Level:

You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.

### Making Cuboids

##### Stage: 2 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?

### Car Journey

##### Stage: 2 Challenge Level:

This practical activity involves measuring length/distance.

### Factors and Multiples Game for Two

##### Stage: 2 Challenge Level:

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

### This Fencing

##### Stage: 2 Challenge Level:

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

### Domino Sets

##### Stage: 2 Challenge Level:

How do you know if your set of dominoes is complete?

### Cover the Tray

##### Stage: 2 Challenge Level:

These practical challenges are all about making a 'tray' and covering it with paper.

### Cool as Ice

##### Stage: 3 and 4 Challenge Level:

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

### Straw Scaffold

##### Stage: 3 Challenge Level:

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

### Gym Bag

##### Stage: 3 and 4 Challenge Level:

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

### 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?

### Make Your Own Pencil Case

##### 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?

### Constructing Triangles

##### Stage: 3 Challenge Level:

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

### 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.

### How Tall?

##### Stage: 1 and 2 Challenge Level:

A group of children are discussing the height of a tall tree. How would you go about finding out its height?

### Sports Equipment

##### Stage: 2 Challenge Level:

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?

### Bryony's Triangle

##### Stage: 2 Challenge Level:

Watch the video to see how to fold a square of paper to create a flower. What fraction of the piece of paper is the small triangle?

### Order the Changes

##### Stage: 2 Challenge Level:

Can you order pictures of the development of a frog from frogspawn and of a bean seed growing into a plant?

### Four Layers

##### Stage: 1 and 2 Challenge Level:

Can you create more models that follow these rules?

### Three Sets of Cubes, Two Surfaces

##### Stage: 2 Challenge Level:

How many models can you find which obey these rules?

### 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?

### Fit These Shapes

##### Stage: 1 and 2 Challenge Level:

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

### Straight to Curves

##### Stage: 1 and 2 Challenge Level:

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

### 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...

### Next Size Up

##### Stage: 2 Challenge Level:

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

### Paper Curves

##### Stage: 2 Challenge Level:

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

### The Numbers Give the Design

##### Stage: 2 Challenge Level:

Make new patterns from simple turning instructions. You can have a go using pencil and paper or with a floor robot.

### It's a Fence!

##### Stage: 1 and 2 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.

### Sort Them Out (2)

##### Stage: 2 Challenge Level:

Can you each work out the number on your card? What do you notice? How could you sort the cards?

### 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?

### Drawing Celtic Knots

##### Stage: 3 Challenge Level:

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

### 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.

### Tangram Pictures

##### Stage: 1, 2 and 3 Challenge Level:

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

### 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.