This is part of our Secondary Curriculum collection of favourite rich tasks arranged by topic.
Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.
problem
Favourite
About average
Age
11 to 14
Challenge level
Can you find sets of numbers which satisfy each of our mean, median, mode and range conditions?
problem
Favourite
Half a minute
Age
11 to 14
Challenge level
Anna, Ben and Charlie have been estimating 30 seconds. Who is the best?
problem
Favourite
Substitution cipher
Age
11 to 14
Challenge level
Find the frequency distribution for ordinary English, and use it to help you crack the code.
problem
Favourite
In the bag
Age
11 to 14
Challenge level
Can you guess the colours of the 10 marbles in the bag? Can you develop an effective strategy for reaching 1000 points in the least number of rounds?
problem
Favourite
Reaction timer
Age
11 to 14
Challenge level
This problem offers you two ways to test reactions - use them to investigate your ideas about speeds of reaction.
problem
Favourite
M, M and M
Age
11 to 14
Challenge level
If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?
problem
Favourite
How would you score it?
Age
11 to 14
Challenge level
Invent a scoring system for a 'guess the weight' competition.
problem
Favourite
Olympic records
Age
11 to 14
Challenge level
Can you deduce which Olympic athletics events are represented by the graphs?
problem
Favourite
Statistical shorts
Age
11 to 16
Challenge level
Can you decide whether these short statistical statements are always, sometimes or never true?
problem
Favourite
Wipeout
Age
11 to 16
Challenge level
Can you do a little mathematical detective work to figure out which number has been wiped out?
problem
Favourite
Unequal averages
Age
11 to 14
Challenge level
Play around with sets of five numbers and see what you can discover about different types of average...
problem
Favourite
Searching for mean(ing)
Age
11 to 16
Challenge level
If you have a large supply of 3kg and 8kg weights, how many of each would you need for the average (mean) of the weights to be 6kg?
problem
Favourite
Who's the best?
Age
11 to 14
Challenge level
Which countries have the most naturally athletic populations?
problem
Favourite
What's the weather like?
Age
11 to 14
Challenge level
With access to weather station data, what interesting questions can you investigate?
problem
Favourite
Estimating time
Age
11 to 14
Challenge level
How well can you estimate 10 seconds? Investigate with our timing tool.
problem
Favourite
Litov's mean value theorem
Age
11 to 14
Challenge level
Start with two numbers and generate a sequence where the next number is the mean of the last two numbers...
problem
Favourite
Tree tops
Age
14 to 16
Challenge level
Can you make sense of information about trees in order to maximise the profits of a forestry company?
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You may also be interested in this collection of activities from the STEM Learning website, that complement the NRICH activities above.