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

### Tower of Hanoi

##### Stage: 4 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.

### Repeating Patterns

##### Stage: 1 Challenge Level:

Try continuing these patterns made from triangles. Can you create your own repeating pattern?

### 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?

### Clapping Times

##### Stage: 1 Challenge Level:

If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?

### Factors and Multiples Game

##### Stage: 2 and 3 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?

### Sizing Them Up

##### Stage: 1 Challenge Level:

Can you put these shapes in order of size? Start with the smallest.

### Brush Loads

##### 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.

### Little Man

##### Stage: 1 Challenge Level:

The Man is much smaller than us. Can you use the picture of him next to a mug to estimate his height and how much tea he drinks?

### Stringy Quads

##### Stage: 2 Challenge Level:

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

### Chairs and Tables

##### Stage: 1 Challenge Level:

Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

### 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's 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?

### Halving

##### Stage: 1 Challenge Level:

These pictures show squares split into halves. Can you find other ways?

### Proof Sorter - Sum of an AP

##### Stage: 5 Challenge Level:

Use this interactivity to sort out the steps of the proof of the formula for the sum of an arithmetic series. The 'thermometer' will tell you how you are doing

### 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 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.

### Building with Solid Shapes

##### Stage: 1 Challenge Level:

We have a box of cubes, triangular prisms, cones, cuboids, cylinders and tetrahedrons. Which of the buildings would fall down if we tried to make them?

### Making Sticks

##### Stage: 1 Challenge Level:

Kimie and Sebastian were making sticks from interlocking cubes and lining them up. Can they make their lines the same length? Can they make any other lines?

### Happy Halving

##### Stage: 1 Challenge Level:

Can you split each of the shapes below in half so that the two parts are exactly the same?

### A City of Towers

##### Stage: 1 Challenge Level:

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

### 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?

### 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?

### Flip Your Mat!

##### 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?

### Data Shapes

##### Stage: 1 Challenge Level:

Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?

### 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?

### 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?

### Four Layers

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

Can you create more models that follow these rules?

### 3 Sets of Cubes, 2 Surfaces

##### Stage: 2 Challenge Level:

How many models can you find which obey these rules?

### Pairs of Numbers

##### Stage: 1 Challenge Level:

If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?

### 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?

### Shapely Lines

##### Stage: 1 Challenge Level:

This challenge invites you to create your own picture using just straight lines. Can you identify shapes with the same number of sides and decorate them in the same way?

### Exploded Squares

##### Stage: 1 Challenge Level:

This practical activity challenges you to create symmetrical designs by cutting a square into strips.