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I Have a Box

Age 3 to 5

In this activity, there's a mystery box! What could be inside it? How do you know?

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I Like ...

Age 5 to 7 Challenge Level:

Mr Gilderdale is playing a game with his class. What rule might he have chosen? How would you test your idea?

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I Love Musical Stars

Age 14 to 16 Short Challenge Level:

Each row and column has the total given. What is the value of the heart symbol?

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I Spy Numbers

Age 3 to 5 Challenge Level:

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I Wonder ... What If ...?

Age 5 to 11

This feature explores how teachers can harness the power of curiosity by using some tasks that may cause children to wonder!

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I Wonder ...?

Age 7 to 11

Have you ever started a mathematics task and then stopped and wondered about something in it? We think these tasks might make you do this.

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I Wonder ...?

Age 5 to 7

We hope these tasks make you wonder what if ...?

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I Wonder... What If...?

Age 11 to 16 Challenge Level:

Problems to provoke curiosity and questioning

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I'm Eight

Age 5 to 11 Challenge Level:

Find a great variety of ways of asking questions which make 8.

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I'm Stuck but ....!

Age 7 to 11

These tasks are tough! Can you keep going and find a solution?

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I'm Stuck but ....!

Age 5 to 7

These tasks are tough! Can you keep going and find a solution?

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I'm Stuck!

Age 5 to 11

Being stuck is usually thought of as being a negative state of affairs. We want our pupils to succeed, not to struggle. Or do we? This article discusses why being stuck can be fruitful.

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I've Submitted a Solution - What Next?

Age 5 to 18

In this article, the NRICH team describe the process of selecting solutions for publication on the site.

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Ice Cream

Age 7 to 11 Challenge Level:

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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Ice Cream Pie

Age 11 to 14 Short Challenge Level:

The pie chart shows the different types of ice creams on sale. How many chocolate ice creams were sold?

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Ice Cream Tangent

Age 14 to 16 Short Challenge Level:

The diagram shows a semi-circle and an isosceles triangle which have equal areas. What is the value of tan x?

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Icosian Game

Age 11 to 14 Challenge Level:

This problem is about investigating whether it is possible to start at one vertex of a platonic solid and visit every other vertex once only returning to the vertex you started at.

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Ideal Axes

Age 16 to 18 Challenge Level:

Explore how can changing the axes for a plot of an equation can lead to different shaped graphs emerging

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Ideal Gases

Age 16 to 18 Challenge Level:

Problems which make you think about the kinetic ideas underlying the ideal gas laws.

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Ideas for the Secondary Classroom

Age 11 to 18

Articles about mathematics which can help to invigorate your classroom

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Identical Digit Multiplication

Age 11 to 14 Short Challenge Level:

77 is multiplied by another two-digit number with identical digits. What is the product?

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Identifying Trigonometry

Age 16 to 18 Challenge Level:

These CMEP resources explore the use of trigonometric identities and other trig features

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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?

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Iff

Age 14 to 18 Challenge Level:

Take a triangular number, multiply it by 8 and add 1. What is special about your answer? Can you prove it?

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Iffy Logic

Age 14 to 18 Challenge Level:

Can you rearrange the cards to make a series of correct mathematical statements?

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IFFY Triangles

Age 14 to 18 Challenge Level:

Can you prove these triangle theorems both ways?

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Illusion

Age 11 to 16 Challenge Level:

A security camera, taking pictures each half a second, films a cyclist going by. In the film, the cyclist appears to go forward while the wheels appear to go backwards. Why?

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Imagine This!

What if we could find the square root of negative numbers?

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Immersion

Age 14 to 16 Challenge Level:

Various solids are lowered into a beaker of water. How does the water level rise in each case?

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Impedance Can Be Complex!

Age 16 to 18 Challenge Level:

Put your complex numbers and calculus to the test with this impedance calculation.

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Implicitly

Age 16 to 18 Challenge Level:

Can you find the maximum value of the curve defined by this expression?

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Impossibilities

Age 11 to 14 Challenge Level:

Just because a problem is impossible doesn't mean it's difficult...

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Impossible Picture?

Age 14 to 16 Challenge Level:

Under what circumstances can you rearrange a big square to make three smaller squares?

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Impossible Polyhedra

Age 16 to 18

Is it possible to make an irregular polyhedron using only polygons of, say, six, seven and eight sides? The answer (rather surprisingly) is 'no', but how do we prove a statement like this?

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Impossible Sandwiches

Age 11 to 18

In this 7-sandwich: 7 1 3 1 6 4 3 5 7 2 4 6 2 5 there are 7 numbers between the 7s, 6 between the 6s etc. The article shows which values of n can make n-sandwiches and which cannot.

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Impossible Square?

Age 16 to 18 Challenge Level:

Can you make a square from these triangles?

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Impossible Triangles?

Age 16 to 18 Challenge Level:

Which of these triangular jigsaws are impossible to finish?

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Improving Problem Solving in Mathematics Through Inquiry-based Learning

Age 11 to 16

Publicity for the one day event at the Royal Society, London on Monday 11th November, 2013

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Improving Reasoning: Analysing Alternative Approaches

Age 5 to 18

In this article, Malcolm Swan describes a teaching approach designed to improve the quality of students' reasoning.

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Impuzzable

Age 16 to 18

This is about a fiendishly difficult jigsaw and how to solve it using a computer program.

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In a Box

Age 14 to 16 Challenge Level:

Chris and Jo put two red and four blue ribbons in a box. They each pick a ribbon from the box without looking. Jo wins if the two ribbons are the same colour. Is the game fair?

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In a Box Poster

Age 11 to 14 Challenge Level:

In A Box

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In a Spin

Age 14 to 16 Challenge Level:

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?

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In Between

Age 16 to 18 Challenge Level:

Can you find the solution to this algebraic inequality?

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In Constantly Passing

Age 14 to 16 Challenge Level:

A car is travelling along a dual carriageway at constant speed. Every 3 minutes a bus passes going in the opposite direction, while every 6 minutes a bus passes the car travelling in the same. . . .

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In or Out?

Age 14 to 16 Short Challenge Level:

Weekly Problem 52 - 2014
Four arcs are drawn in a circle to create a shaded area. What fraction of the area of the circle is shaded?

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In Order

Age 7 to 11 Challenge Level:

Can you rank these quantities in order? You may need to find out extra information or perform some experiments to justify your rankings.

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In Particular

Age 14 to 16 Challenge Level:

Can you find formulas giving all the solutions to 7x + 11y = 100 where x and y are integers?

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In Proportion

Age 11 to 16

Understanding ratio and proportion is vital in science and in design technology.