Troublesome Triangles
Age 7 to 14
Challenge Level
Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple simulation game to investigate the properties of such systems.
Flip Your Mat!
Age 7 to 14
Challenge Level
What shape and size of drinks mat is best for flipping and catching?
Chocolate Cake
Age 11 to 14
Challenge Level
If I don't have the size of cake tin specified in my recipe, will the size I do have be OK?
Toad in the Hole
Age 11 to 14
Challenge Level
Is it cheaper to cook a meal from scratch or to buy a ready meal? What difference does the number of people you're cooking for make?
Temperature
Age 11 to 14
Challenge Level
Is there a temperature at which Celsius and Fahrenheit readings are the same?
Does This Sound about Right?
Age 11 to 14
Challenge Level
Examine these estimates. Do they sound about right?
Fill Me Up
Age 11 to 14
Challenge Level
Can you sketch graphs to show how the height of water changes in different containers as they are filled?
Place Your Orders
Age 11 to 14
Challenge Level
Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?
Make Your Own Pencil Case
Age 11 to 14
Challenge Level
What shape would fit your pens and pencils best? How can you make it?
Pinhole Camera
Age 11 to 14
Challenge Level
Make your own pinhole camera for safe observation of the sun, and find out how it works.
Designing Table Mats
Age 11 to 16
Challenge Level
Formulate and investigate a simple mathematical model for the design of a table mat.
Investigating Epidemics
Age 11 to 16
Challenge Level
Simple models which help us to investigate how epidemics grow and die out.
Gym Bag
Age 11 to 16
Challenge Level
Can Jo make a gym bag for her trainers from the piece of fabric she has?
Big and Small Numbers in the Living World
Age 11 to 16
Challenge Level
Work with numbers big and small to estimate and calculate various quantities in biological contexts.
Witch's Hat
Age 11 to 16
Challenge Level
What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
3D Drawing
Age 11 to 16
The design technology curriculum requires students to be able to represent 3-dimensional objects on paper. This article introduces some of the mathematical ideas which underlie such methods.
A Question of Scale
Age 14 to 16
Challenge Level
Use your skill and knowledge to place various scientific lengths in order of size. Can you judge the length of objects with sizes ranging from 1 Angstrom to 1 million km with no wrong attempts?
Counting Dolphins
Age 14 to 16
Challenge Level
How would you go about estimating populations of dolphins?
Electric Kettle
Age 14 to 16
Challenge Level
Explore the relationship between resistance and temperature
Far Horizon
Age 14 to 16
Challenge Level
An observer is on top of a lighthouse. How far from the foot of the lighthouse is the horizon that the observer can see?
Guessing the Graph
Age 14 to 16
Challenge Level
Can you suggest a curve to fit some experimental data? Can you work out where the data might have come from?
Big and Small Numbers in Physics
Age 14 to 16
Challenge Level
Work out the numerical values for these physical quantities.
How Do You React?
Age 14 to 16
Challenge Level
To investigate the relationship between the distance the ruler drops and the time taken, we need to do some mathematical modelling...
Big and Small Numbers in Biology
Age 14 to 16
Challenge Level
Work with numbers big and small to estimate and calulate various quantities in biological contexts.
Fill Me up Too
Age 14 to 16
Challenge Level
In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
Biology Measurement Challenge
Age 14 to 16
Challenge Level
Analyse these beautiful biological images and attempt to rank them in size order.
Choose Your Units
Age 14 to 16
Challenge Level
Which units would you choose best to fit these situations?
Carbon Footprints
Age 14 to 16
Challenge Level
Is it really greener to go on the bus, or to buy local?
Big and Small Numbers in the Physical World
Age 14 to 16
Challenge Level
Work with numbers big and small to estimate and calculate various quantities in physical contexts.
Constantly Changing
Age 14 to 16
Challenge Level
Many physical constants are only known to a certain accuracy. Explore the numerical error bounds in the mass of water and its constituents.
Speed-time Problems at the Olympics
Age 14 to 16
Challenge Level
Have you ever wondered what it would be like to race against Usain Bolt?
Big and Small Numbers in Chemistry
Age 14 to 16
Challenge Level
Get some practice using big and small numbers in chemistry.
Investigating the Dilution Series
Age 14 to 16
Challenge Level
Which dilutions can you make using only 10ml pipettes?
Perfect Eclipse
Age 14 to 16
Challenge Level
Use trigonometry to determine whether solar eclipses on earth can be perfect.
Robot Camera
Age 14 to 16
Challenge Level
Could nanotechnology be used to see if an artery is blocked? Or is this just science fiction?
Stadium Sightline
Age 14 to 18
Challenge Level
How would you design the tiering of seats in a stadium so that all spectators have a good view?
Approximately Certain
Age 14 to 18
Challenge Level
Estimate these curious quantities sufficiently accurately that you can rank them in order of size
Construct the Solar System
Age 14 to 18
Challenge Level
Make an accurate diagram of the solar system and explore the concept of a grand conjunction.
Back Fitter
Age 14 to 18
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?
What's That Graph?
Age 14 to 18
Challenge Level
Can you work out which processes are represented by the graphs?
A Very Shiny Nose?
Age 16 to 18
Challenge Level
This problem explores the biology behind Rudolph's glowing red nose, and introduces the real life phenomena of bacterial quorum sensing.
NRICH is part of the family of activities in the Millennium Mathematics Project.