List

Practical activity

Making Maths: String and Circles
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Making maths: string and circles

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.
Making Maths: Link-a-Cube
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Making maths: link-a-cube

Make a cube with three strips of paper. Colour three faces or use the numbers 1 to 6 to make a die.
Making Maths: Make a Pendulum
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Making maths: make a pendulum

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?
Hoops/Rope
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Hoops/rope

Ideas for practical ways of representing data such as Venn and Carroll diagrams.
Making Maths: Kites and Darts
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Making maths: kites and darts

Using these kite and dart templates, you could try to recreate part of Penrose's famous tessellation or design one yourself.
Watch those Wheels
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Watch those wheels

Have you ever noticed the patterns in car wheel trims? These questions will make you look at car wheels in a different way!
Building Patterns
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Building patterns

Can you deduce the pattern that has been used to lay out these bottle tops?
Making Maths: Clinometer
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Making maths: clinometer

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.
Making Maths: Rolypoly
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Making maths: rolypoly

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

These models have appeared around the Centre for Mathematical Sciences. Perhaps you would like to try to make some similar models of your own.

Turning the Place Over
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Turning the place over

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: Stars
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Making maths: stars

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

In this article for primary teachers, Fran describes her passion for paper folding as a springboard for mathematics.

Baked Bean Cans
problem

Baked bean cans

Age
5 to 7
Challenge level
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Is there a best way to stack cans? What do different supermarkets do? How high can you safely stack the cans?
Paper Patchwork 2
problem

Paper patchwork 2

Age
5 to 7
Challenge level
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Have a go at making a few of these shapes from paper in different sizes. What patterns can you create?

Chairs and Tables
problem

Chairs and tables

Age
5 to 7
Challenge level
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Make a chair and table out of interlocking cubes, making sure that the chair fits under the table!

problem

Pairs of numbers

Age
5 to 7
Challenge level
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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?

Rearrange the Square
problem

Rearrange the square

Age
5 to 7
Challenge level
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We can cut a small triangle off the corner of a square and then fit the two pieces together. Can you work out how these shapes are made from the two pieces?
Building with Solid Shapes
problem

Building with solid shapes

Age
5 to 7
Challenge level
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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?

Tangram Pictures
game

Tangram pictures

Age
5 to 14
Challenge level
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Use the tangram pieces to make our pictures, or to design some of your own!
Paper Partners
problem

Paper partners

Age
5 to 7
Challenge level
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Can you describe a piece of paper clearly enough for your partner to know which piece it is?

Triangle Shapes
problem

Triangle shapes

Age
5 to 11
Challenge level
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This practical problem challenges you to create shapes and patterns with two different types of triangle. You could even try overlapping them.
project

How many?

This project challenges you to work out the number of cubes hidden under a cloth. What questions would you like to ask?

Data shapes
problem

Data shapes

Age
5 to 7
Challenge level
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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?

Repeating Patterns
problem

Repeating patterns

Age
5 to 7
Challenge level
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Try continuing these patterns made from triangles. Can you create your own repeating pattern?

How Tall?
problem

How tall?

Age
5 to 11
Challenge level
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A group of children are discussing the height of a tall tree. How would you go about finding out its height?

Two-digit targets
problem

Two-digit targets

Age
5 to 7
Challenge level
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You have a set of the digits from 0 to 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?

Well balanced
problem

Well balanced

Age
5 to 18
Challenge level
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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.
Jig Shapes
problem

Jig shapes

Age
5 to 11
Challenge level
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Can you each work out what shape you have part of on your card? What will the rest of it look like?

Take One Metre
problem

Take one metre

Age
5 to 7
Challenge level
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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?
Bottles (1)
problem

Bottles (1)

Age
5 to 7
Challenge level
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For this activity which explores capacity, you will need to collect some bottles and jars.

Sizing them Up
problem

Sizing them up

Age
5 to 7
Challenge level
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Can you put these shapes in order of size? Start with the smallest.

It's a Fence!
problem

It's a fence!

Age
5 to 11
Challenge level
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In this challenge, you will work in a group to investigate circular fences enclosing trees that are planted in square or triangular arrangements.
Car Journey
problem

Car journey

Age
5 to 7
Challenge level
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This practical activity involves measuring length/distance.

Bottles (2)
problem

Bottles (2)

Age
5 to 7
Challenge level
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In this activity focusing on capacity, you will need a collection of different jars and bottles.

Drawing
problem

Drawing

Age
5 to 11
Challenge level
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This activity encourages you to measure the length of lines accurately.
Thirsty?
problem

Thirsty?

Age
5 to 7
Challenge level
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Can you lay out the pictures of the drinks in the way described by the clue cards?

Measure our heights
problem

Measure our heights

Age
5 to 7
Challenge level
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How could you measure the height of your friend without too much difficulty?
Compare the Cups
problem

Compare the cups

Age
5 to 7
Challenge level
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You'll need a collection of cups for this activity.

Exploded Squares
problem

Exploded squares

Age
5 to 7
Challenge level
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Can you create symmetrical designs by cutting a square into strips?

Shapely Lines
problem

Shapely lines

Age
5 to 7
Challenge level
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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?

Seven Sticks
problem

Seven sticks

Age
5 to 7
Challenge level
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Explore the triangles that can be made with seven sticks of the same length.
Three Fingers and a Loop of String
problem

Three fingers and a loop of string

Age
5 to 7
Challenge level
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Using a loop of string stretched around three of your fingers, what different triangles can you make? Draw them and sort them into groups.
Paper Patchwork 1
problem

Paper patchwork 1

Age
5 to 7
Challenge level
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Can you work out what shape is made when this piece of paper is folded up using the crease pattern shown?

Clapping Times
problem

Clapping times

Age
5 to 7
Challenge level
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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?

Fit These Shapes
problem

Fit these shapes

Age
5 to 11
Challenge level
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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?
A City of Towers
problem

A city of towers

Age
5 to 7
Challenge level
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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?

Star Find
problem

Star find

Age
5 to 7
Challenge level
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Can you see which tile is the odd one out in this design? Using the basic tile, can you make a repeating pattern to decorate our wall?
Making Sticks
problem

Making sticks

Age
5 to 7
Challenge level
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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?

Little Man
problem

Little man

Age
5 to 7
Challenge level
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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?

Making Longer, Making Shorter
problem

Making longer, making shorter

Age
5 to 7
Challenge level
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Ahmed is making rods using different numbers of cubes. Which rod is twice the length of his first rod?

Animated Triangles
problem

Animated triangles

Age
5 to 7
Challenge level
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Watch this "Notes on a Triangle" film. Can you recreate parts of the film using cut-out triangles?
Six to Four
problem

Six to four

Age
5 to 7
Challenge level
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Move four sticks so there are exactly four triangles.
Dienes' Logiblocs
problem

Dienes' logiblocs

Age
5 to 7
Challenge level
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This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?
Four Colours
problem

Four colours

Age
5 to 11
Challenge level
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Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
Tessellating Capitals
problem

Tessellating capitals

Age
5 to 7
Challenge level
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Have you ever tried tessellating capital letters? Have a look at these examples and then try some for yourself.
Halving
problem

Halving

Age
5 to 7
Challenge level
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These pictures show squares split into halves. Can you find other ways?

Rectangles with Dominoes
problem

Rectangles with dominoes

Age
5 to 7
Challenge level
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Can you make a rectangle with just 2 dominoes? What about 3, 4, 5, 6, 7...?
Two on Five
problem

Two on five

Age
5 to 11
Challenge level
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Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

Tangrams
problem

Tangrams

Age
5 to 11
Challenge level
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Can you make five differently sized squares from the interactive tangram pieces?

Straight to Curves
problem

Straight to curves

Age
5 to 11
Challenge level
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How can you make a curve from straight strips of paper?
Square split into a triangle and trapezium
problem

Tangram tangle

Age
5 to 7
Challenge level
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If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

Happy Halving
problem

Happy halving

Age
5 to 7
Challenge level
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Can you split each of the shapes below in half so that the two parts are exactly the same?

Four Layers
problem

Four layers

Age
5 to 11
Challenge level
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Can you create more models that follow these rules?
Three Squares
problem

Three squares

Age
5 to 11
Challenge level
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What is the greatest number of squares you can make by overlapping three squares?

Tricky Triangles
problem

Tricky triangles

Age
5 to 7
Challenge level
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Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
Back to the Practical?
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Back to the practical?

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 why the pattern occurs.
Plaiting and Braiding
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Plaiting and braiding

This article for students gives some instructions about how to make some different braids.
Celtic Knotwork Patterns
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Celtic knotwork patterns

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