problem
Favourite
Largest product
Age
11 to 14
Challenge level
Which set of numbers that add to 100 have the largest product?
problem
Favourite
Picturing triangular numbers
Age
11 to 14
Challenge level
Triangular numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
problem
Favourite
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
Favourite
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
Favourite
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
Favourite
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
Favourite
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
Favourite
Diminishing returns
Age
11 to 14
Challenge level
How much of the square is coloured blue? How will the pattern continue?
problem
Favourite
Growing surprises
Age
11 to 14
Challenge level
Can you find the connections between linear and quadratic patterns?
problem
Favourite
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
Favourite
1 step 2 step
Age
11 to 14
Challenge level
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
problem
Favourite
Tower of Hanoi
Age
11 to 14
Challenge level
The Tower of Hanoi is an ancient mathematical challenge. Working on the building blocks may help you to explain the patterns you notice.
problem
Favourite
Opposite vertices
Age
11 to 14
Challenge level
Can you recreate squares and rhombuses if you are only given a side or a diagonal?
problem
Favourite
What numbers can we make now?
Age
11 to 14
Challenge level
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
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
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
Favourite
Counting factors
Age
11 to 14
Challenge level
Is there an efficient way to work out how many factors a large number has?
problem
Favourite
Legs eleven
Age
11 to 14
Challenge level
Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?
problem
Favourite
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
Favourite
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
Favourite
Mixing more paints
Age
14 to 16
Challenge level
Can you find an efficent way to mix paints in any ratio?