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

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Tower of Hanoi

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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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Repeating Patterns

Stage: 1 Challenge Level: Challenge Level:1

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

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It's a Tie

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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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Music to My Ears

Stage: 2 Challenge Level: Challenge Level:1

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?

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Clapping Times

Stage: 1 Challenge Level: Challenge Level:1

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?

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Factors and Multiples Game

Stage: 2, 3 and 4 Challenge Level: Challenge Level:1

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

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Fractions Jigsaw

Stage: 3 Challenge Level: Challenge Level:1

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

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Cunning Card Trick

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Factors and Multiples Puzzle

Stage: 3 Challenge Level: Challenge Level:1

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

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Sizing Them Up

Stage: 1 Challenge Level: Challenge Level:1

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

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Brush Loads

Stage: 2 Challenge Level: Challenge Level:1

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.

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Little Man

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Stringy Quads

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Chairs and Tables

Stage: 1 Challenge Level: Challenge Level:1

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

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Fractional Triangles

Stage: 2 Challenge Level: Challenge Level:1

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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Amazing Card Trick

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

How is it possible to predict the card?

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Let Us Reflect

Stage: 2 Challenge Level: Challenge Level:1

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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Halving

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Proof Sorter - Sum of an AP

Stage: 5 Challenge Level: Challenge Level:1

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

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Triangles to Tetrahedra

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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.

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Square Corners

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Egyptian Rope

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Nine Colours

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

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.

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Building with Solid Shapes

Stage: 1 Challenge Level: Challenge Level:1

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?

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Making Sticks

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Happy Halving

Stage: 1 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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A City of Towers

Stage: 1 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Making Cuboids

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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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Compare the Cups

Stage: 1 Challenge Level: Challenge Level:1

You'll need a collection of cups for this activity.

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Bottles (2)

Stage: 1 Challenge Level: Challenge Level:1

In this activity focusing on capacity, you will need a collection of different jars and bottles.

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Car Journey

Stage: 2 Challenge Level: Challenge Level:1

This practical activity involves measuring length/distance.

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Bottles (1)

Stage: 1 Challenge Level: Challenge Level:1

For this activity which explores capacity, you will need to collect some bottles and jars.

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Take One Metre

Stage: 1 Challenge Level: Challenge Level:1

You will need a long strip of paper for this task. Cut it into different lengths. How could you find out how long each piece is?

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Factors and Multiples Game for Two

Stage: 2 Challenge Level: Challenge Level:1

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

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This Fencing

Stage: 2 Challenge Level: Challenge Level:1

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

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Domino Sets

Stage: 2 Challenge Level: Challenge Level:1

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

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Cover the Tray

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Cool as Ice

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

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Straw Scaffold

Stage: 3 Challenge Level: Challenge Level:1

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

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Gym Bag

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Witch's Hat

Stage: 3 and 4 Challenge Level: Challenge Level:1

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

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Make Your Own Pencil Case

Stage: 3 Challenge Level: Challenge Level:1

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

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Flip Your Mat!

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

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

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Constructing Triangles

Stage: 3 Challenge Level: Challenge Level:1

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

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Observing the Sun and the Moon

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

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.

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How Tall?

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

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

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Data Shapes

Stage: 1 Challenge Level: Challenge Level:1

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?

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Sports Equipment

Stage: 2 Challenge Level: Challenge Level:1

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?

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Bryony's Triangle

Stage: 2 Challenge Level: Challenge Level:1

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?

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Order the Changes

Stage: 2 Challenge Level: Challenge Level:1

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