These pictures show some different activities that you may get up
to during a day. What order would you do them in?
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
These pictures show squares split into halves. Can you find other ways?
In this game you throw two dice and find their total, then move the appropriate counter to the right. Which counter reaches the purple box first? Is this what you would expect?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
This 100 square jigsaw is written in code. It starts with 1 and
ends with 100. Can you build it up?
How many different sets of numbers with at least four members can
you find in the numbers in this box?
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
A country has decided to have just two different coins, 3z and 5z
coins. Which totals can be made? Is there a largest total that
cannot be made? How do you know?
Can you arrange the numbers 1 to 17 in a row so that each adjacent
pair adds up to a square number?
Charlie and Lynne put a counter on 42. They wondered if they could
visit all the other numbers on their 1-100 board, moving the
counter using just these two operations: x2 and -5. What do you
Which of these games would you play to give yourself the best possible chance of winning a prize?
Explore when it is possible to construct a circle which just
touches all four sides of a quadrilateral.
Is it really greener to go on the bus, or to buy local?
Can you make sense of these three proofs of Pythagoras' Theorem?
Investigate the properties of quadrilaterals which can be drawn
with a circle just touching each side and another circle just
touching each vertex.
How do these modelling assumption affect the solutions?
Why MUST these statistical statements probably be at least a little
Was it possible that this dangerous driving penalty was issued in
Have a go at being mathematically negative, by negating these
Did you break the spells? We had some very clear explanations of
how to complete these sequences.
This problem was very well answered by many of you using a
systematic approach. You knew that you hadn't missed out any
possibilities because of the way you ordered the solutions. Well
Harry sent us a very clear algebraic solution to this problem, and
we also received lots of ideas on how to solve it numerically.
Is the process fair? This question often gives rise to
disagreements and discussion. Tom gives a clear logical explanation
and uses a tree diagram and a spreadsheet.
This fascinating article delves into the world of talk in the
classroom and explains how an understanding of talking can really
improve the learning of mathematics.
A train building game for 2 players.
This article stems from research on the teaching of proof and
offers guidance on how to move learners from focussing on
experimental arguments to mathematical arguments and deductive
An article demonstrating mathematically how various physical
modelling assumptions affect the solution to the seemingly simple
problem of the projectile.