See also: Matching topics (16) Matching titles (122)
1194 problems, 82 games, 335 articles, 196 general resources, 7 interactive environments, 232 from Stage 1, 573 from Stage 2, 600 from Stage 3, 521 from Stage 4, 416 from Stage 5
How Steep Is the Slope?
Stage: 3 Challenge Level: 
On the grid provided, we can draw lines with different gradients. How many different gradients can you find? Can you arrange them in order of steepness?
Surprising Transformations
Stage: 3 Challenge Level:
I took the graph y=4x+7 and performed four transformations. Can you find the order in which I could have carried out the transformations?
The Greedy Algorithm
Stage: 3 Challenge Level:
The Egyptians expressed all fractions as the sum of different unit fractions. The Greedy Algorithm might provide us with an efficient way of doing this.
Keep it Simple
Stage: 3 Challenge Level:
Can all unit fractions be written as the sum of two unit fractions?
Translating Lines
Stage: 3 Challenge Level:
Investigate what happens to the equation of different lines when you translate them. Try to predict what will happen. Explain your findings.
Back Fitter
Stage: 4 Challenge Level:
10 graphs of experimental data are given. Can you use a spreadsheet to find algebraic graphs which match them closely, and thus discover the formulae most likely to govern the underlying processes?
Countdown
Stage: 2 and 3 Challenge Level:
Here is a chance to play a version of the classic Countdown Game.
Gravity Paths
Stage: 5 Challenge Level:
Where will the spaceman go when he falls through these strange planetary systems?
The Not-so-simple Pendulum 2
Stage: 5 Challenge Level:
Things are roughened up and friction is now added to the approximate simple pendulum
Reflecting Lines
Stage: 3 Challenge Level:
Investigate what happens to the equations of different lines when you reflect them in one of the axes. Try to predict what will happen. Explain your findings.
At Right Angles
Stage: 3 Challenge Level:
Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?
Aim High
Stage: 5 Challenge Level:
How do you choose your planting levels to minimise the total loss at harvest time?
Building up Friction
Stage: 5 Challenge Level:
A series of activities to build up intuition on the mathematics of friction.
Dangerous Driver?
Stage: 5 Challenge Level:
Was it possible that this dangerous driving penalty was issued in error?
Go Spaceship Go
Stage: 5 Challenge Level:
Show that even a very powerful spaceship would eventually run out of overtaking power
2009 Challenge
Stage: 3, 4 and 5 Challenge Level:
We asked what was the most interesting fact that you can find out about the number 2009. See the solutions that were submitted.
What's Your Mean?
Stage: 5 Challenge Level:
Can you work out the means of these distributions using numerical methods?
The Remainders Game
Stage: 2 and 3 Challenge Level:
A game that tests your understanding of remainders.
Power Mad!
Stage: 3 Challenge Level:
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
Hidden Dimensions
Stage: 3 Challenge Level:
Can you find rectangles where the value of the area is the same as the value of the perimeter?
Elevenses
Stage: 3 Challenge Level:
How many pairs of numbers can you find that add up to a multiple of 11? Do you notice anything interesting about your results?
Searching for Mean(ing)
Stage: 3 Challenge Level:
Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?
Direct Logic
Stage: 5 Challenge Level:
Can you work through these direct proofs, using our interactive proof sorters?
Partly Circles
Stage: 4 Challenge Level:
What is the same and what is different about these circle questions? What connections can you make?
Cops and Robbers
Stage: 2 and 3 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
Stage: 2 and 3 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?
Magic Vs
Stage: 2 Challenge Level:
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
M, M and M
Stage: 3 Challenge Level:
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
Understanding Hypotheses
Stage: 3, 4 and 5
This article explores the process of making and testing hypotheses.
Blood Buffers
Stage: 5 Challenge Level:
Investigate the mathematics behind blood buffers and derive the form of a titration curve.
The Not-so-simple Pendulum 1
Stage: 5 Challenge Level:
See how the motion of the simple pendulum is not-so-simple after all.
Stats Statements
Stage: 5 Challenge Level:
Are these statistical statements sometimes, always or never true? Or it is impossible to say?
Into the Exponential Distribution
Stage: 5 Challenge Level:
Get into the exponential distribution through an exploration of its pdf.
Which Spinners?
Stage: 3 Challenge Level:
Which spinners were used to generate these frequency charts?
Data Collection Tool
Stage: 3 and 4 Challenge Level:
An interactivity that enables you collect data from an experiment with true/false outcomes.
All in a Jumble
Stage: 3 Challenge Level:
My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.
Cannon Balls
Stage: 5 Short Challenge Level:
How high will a ball taking a million seconds to fall travel?
Weights
Stage: 3 Challenge Level:
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Escape from Planet Earth
Stage: 5 Challenge Level:
How fast would you have to throw a ball upwards so that it would never land?
Circular Circuitry
Stage: 5 Challenge Level:
What will happen when you switch on these circular circuits?
Adding and Subtracting Positive and Negative Numbers
Stage: 3 and 4
How can we help students make sense of addition and subtraction of negative numbers?
Making Functions from Their Equations
Stage: 5 Challenge Level:
Make functions from the equations which define them.
Scale Invariance
Stage: 5 Challenge Level:
By exploring the concept of scale invariance, find the probability that a random piece of real data begins with a 1.
Copyright © 2007. University of Cambridge. All rights reserved.
NRICH is part of the family of activities in the Millennium Mathematics Project, which also includes the Plus and Motivate sites.
email: nrich@damtp.cam.ac.uk
