Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Can you describe this route to infinity? Where will the arrows take you next?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
What can you say about the angles on opposite vertices of any
cyclic quadrilateral? Working on the building blocks will give you
insights that may help you to explain what is special about them.
Can you find the values at the vertices when you know the values on
Polygons drawn on square dotty paper have dots on their perimeter
(p) and often internal (i) ones as well. Find a relationship
between p, i and the area of the polygons.
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?
Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?
Can all unit fractions be written as the sum of two unit fractions?
Imagine a large cube made from small red cubes being dropped into a
pot of yellow paint. How many of the small cubes will have yellow
paint on their faces?
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
Is this a fair game? How many ways are there of creating a fair
game by adding odd and even numbers?
Can you find a way to identify times tables after they have been shifted up?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
This interactivity invites you to make conjectures and explore
probabilities of outcomes related to two independent events.