Is there a best way to stack cans? What do different supermarkets
do? How high can you safely stack the cans?
Can you arrange fifteen dominoes so that all the touching domino
pieces add to 6 and the ends join up? Can you make all the joins
add to 7?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
"Tell me the next two numbers in each of these seven minor spells",
chanted the Mathemagician, "And the great spell will crumble away!"
Can you help Anna and David break the spell?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
What is the total area of the four outside triangles which are
outlined in red in this arrangement of squares inside each other?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
How does the position of the line affect the equation of the line?
What can you say about the equations of parallel lines?
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?
Can you decide whether two lines are perpendicular or not? Can you
do this without drawing them?
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 fractions can you find between the square roots of 65 and 67?
Four vehicles travel along a road one afternoon. Can you make sense
of the graphs showing their motion?
Can you hit the target functions using a set of input functions and a little calculus and algebra?
By tossing a coin one of three princes is chosen to be the next
King of Randomia. Does each prince have an equal chance of taking
Can you work out the equations of the trig graphs I used to make my pattern?
Which line graph, equations and physical processes go together?
Draw the graph of a continuous increasing function in the first
quadrant and horizontal and vertical lines through two points. The
areas in your sketch lead to a useful formula for finding
What functions can you make using the function machines RECIPROCAL and PRODUCT and the operator machines DIFF and INT?
You thought carefully about this problem and Luke was able to tell
us about the shortest routes very convincingly.
We had some extremely well-explained solutions to this problem.
There is still one unanswered question left, but most of this
problem has been solved. Can anyone finish it off?
2009 was clearly an interesting year! Find out which mathematical
fact about 2009 we found most interesting.
In this article, Jennifer Piggott talks about just a few of the problems with problems that make them such a rich source of mathematics and approaches to learning mathematics.
Exploring balance and centres of mass can be great fun. The
resulting structures can seem impossible. Here are some images to
encourage you to experiment with non-breakable objects of your own.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
What can you see? What do you notice? What questions can you ask?