problem
Parallel lines
Age
11 to 14
Challenge level
How does the position of the line affect the equation of the line?
What can you say about the equations of parallel lines?
problem
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
Elevenses
Age
11 to 14
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?
problem
Reflecting Lines
Age
11 to 14
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.
problem
Translating Lines
Age
11 to 14
Challenge level
Investigate what happens to the equation of different lines when
you translate them. Try to predict what will happen. Explain your
findings.
problem
Cyclic Quadrilaterals
Age
11 to 16
Challenge level
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
problem
Growing Surprises
Age
11 to 14
Challenge level
Can you find the connections between linear and quadratic patterns?
problem
Days and Dates
Age
11 to 14
Challenge level
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
problem
What's it worth?
Age
11 to 16
Challenge level
There are lots of different methods to find out what the shapes are worth - how many can you find?
problem
Largest product
Age
11 to 14
Challenge level
Which set of numbers that add to 100 have the largest product?
problem
Cinema Problem
Age
11 to 14
Challenge level
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
problem
Special Numbers
Age
11 to 14
Challenge level
My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?
problem
Tilted Squares
Age
11 to 14
Challenge level
It's easy to work out the areas of most squares that we meet, but what if they were tilted?
problem
Mixing Paints
Age
11 to 14
Challenge level
Can you work out how to produce different shades of pink paint?
problem
Twisting and Turning
Age
11 to 14
Challenge level
Take a look at the video and try to find a sequence of moves that will untangle the ropes.
problem
Terminating or not
Age
11 to 14
Challenge level
Is there a quick way to work out whether a fraction terminates or recurs when you write it as a decimal?
problem
Marbles in a box
Age
11 to 16
Challenge level
How many winning lines can you make in a three-dimensional version of noughts and crosses?
problem
Think of Two Numbers
Age
11 to 14
Challenge level
Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
problem
Sending a Parcel
Age
11 to 14
Challenge level
What is the greatest volume you can get for a rectangular (cuboid)
parcel if the maximum combined length and girth are 2 metres?
problem
How Many Miles To Go?
Age
11 to 14
Challenge level
How many more miles must the car travel before the numbers on the milometer and the trip meter contain the same digits in the same order?
problem
Generating Triples
Age
14 to 16
Challenge level
Sets of integers like 3, 4, 5 are called Pythagorean Triples, because they could be the lengths of the sides of a right-angled triangle. Can you find any more?
problem
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?