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### Seeing Squares

##### Age 5 to 11 Challenge Level:

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

### Move Those Halves

##### Age 7 to 11 Challenge Level:

For this task, you'll need an A4 sheet and two A5 transparent sheets. Decide on a way of arranging the A5 sheets on top of the A4 sheet and explore ...

### Shape Draw

##### Age 7 to 11 Challenge Level:

Use the information on these cards to draw the shape that is being described.

### Car Journey

##### Age 7 to 11 Challenge Level:

This practical activity involves measuring length/distance.

### Through the Window

##### Age 7 to 11 Challenge Level:

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

### Dicey Perimeter, Dicey Area

##### Age 7 to 11 Challenge Level:

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

### Domino Sets

##### Age 7 to 11 Challenge Level:

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

### Ribbon Squares

##### Age 7 to 11 Challenge Level:

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

### School Fair Necklaces

##### Age 5 to 11 Challenge Level:

How many possible necklaces can you find? And how do you know you've found them all?

### This Pied Piper of Hamelin

##### Age 7 to 11 Challenge Level:

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

### How Do You See It?

##### Age 5 to 11 Challenge Level:

Here are some short problems for you to try. Talk to your friends about how you work them out.

### Making Spirals

##### Age 7 to 11 Challenge Level:

Can you make a spiral for yourself? Explore some different ways to create your own spiral pattern and explore differences between different spirals.

### Olympic Turns

##### Age 7 to 11 Challenge Level:

This task looks at the different turns involved in different Olympic sports as a way of exploring the mathematics of turns and angles.

### Now and Then

##### Age 7 to 11 Challenge Level:

Look at the changes in results on some of the athletics track events at the Olympic Games in 1908 and 1948. Compare the results for 2012.

### Olympic Starters

##### Age 7 to 11 Challenge Level:

Look at some of the results from the Olympic Games in the past. How do you compare if you try some similar activities?

### Round a Hexagon

##### Age 7 to 11 Challenge Level:

This problem shows that the external angles of an irregular hexagon add to a circle.

### Going for Gold

##### Age 7 to 11 Challenge Level:

Looking at the 2012 Olympic Medal table, can you see how the data is organised? Could the results be presented differently to give another nation the top place?

### Our Sports

##### Age 7 to 11 Challenge Level:

This problem explores the range of events in a sports day and which ones are the most popular and attract the most entries.

### National Flags

##### Age 7 to 11 Challenge Level:

This problem explores the shapes and symmetries in some national flags.

### If the World Were a Village

##### Age 5 to 11 Challenge Level:

This activity is based on data in the book 'If the World Were a Village'. How will you represent your chosen data for maximum effect?

### The Domesday Project

##### Age 7 to 11 Challenge Level:

Take a look at these data collected by children in 1986 as part of the Domesday Project. What do they tell you? What do you think about the way they are presented?

### Birdwatch

##### Age 7 to 11 Challenge Level:

Have a look at this data from the RSPB 2011 Birdwatch. What can you say about the data?

### How Tall?

##### Age 5 to 11 Challenge Level:

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

### Class 5's Names

##### Age 7 to 11 Challenge Level:

Class 5 were looking at the first letter of each of their names. They created different charts to show this information. Can you work out which member of the class was away on that day?

### Discuss and Choose

##### Age 5 to 11 Challenge Level:

This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.

### Jumping

##### Age 7 to 11 Challenge Level:

After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?

### The Time Is ...

##### Age 7 to 11 Challenge Level:

Can you put these mixed-up times in order? You could arrange them in a circle.

### What Is the Time?

##### Age 5 to 11 Challenge Level:

Can you put these times on the clocks in order? You might like to arrange them in a circle.

##### Age 5 to 11 Challenge Level:

How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?

### Button-up Some More

##### Age 7 to 11 Challenge Level:

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

### Dotty Six

##### Age 5 to 11 Challenge Level:

Dotty Six is a simple dice game that you can adapt in many ways.

### Count the Digits

##### Age 5 to 11 Challenge Level:

In this investigation we are going to count the number of 1s, 2s, 3s etc in numbers. Can you predict what will happen?

### Shaping It

##### Age 5 to 11 Challenge Level:

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.

### Rolling That Cube

##### Age 5 to 11 Challenge Level:

My dice has inky marks on each face. Can you find the route it has taken? What does each face look like?

### Area and Perimeter

##### Age 7 to 11 Challenge Level:

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

### The Car That Passes

##### Age 7 to 11 Challenge Level:

What statements can you make about the car that passes the school gates at 11am on Monday? How will you come up with statements and test your ideas?

### Inky Cube

##### Age 7 to 14 Challenge Level:

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

### Sorting Logic Blocks

##### Age 5 to 11 Challenge Level:

This interactivity allows you to sort logic blocks by dragging their images.

### Triple Cubes

##### Age 5 to 11 Challenge Level:

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

### What Shape?

##### Age 7 to 14 Challenge Level:

This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.

### Counters in the Middle

##### Age 7 to 11 Challenge Level:

This task depends on groups working collaboratively, discussing and reasoning to agree a final product.

### Arranging Cubes

##### Age 7 to 11 Challenge Level:

A task which depends on members of the group working collaboratively to reach a single goal.

### Next Size Up

##### Age 7 to 11 Challenge Level:

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

### The Numbers Give the Design

##### Age 7 to 11 Challenge Level:

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

### Holes

##### Age 5 to 11 Challenge Level:

I've made some cubes and some cubes with holes in. This challenge invites you to explore the difference in the number of small cubes I've used. Can you see any patterns?

### Baravelle

##### Age 7 to 16 Challenge Level:

What can you see? What do you notice? What questions can you ask?

### Venn Diagrams

##### Age 5 to 11 Challenge Level:

Use the interactivities to complete these Venn diagrams.

### Cops and Robbers

##### Age 7 to 16 Challenge Level:

Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?

### Eight Hidden Squares

##### Age 7 to 14 Challenge Level:

On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?