Conjecturing and generalising

problem
Seven squares

Age

11 to 14

Challenge level

Watch these videos to see how Phoebe, Alice and Luke chose to draw 7 squares. How would they draw 100?
problem
What was in the box?

Age

5 to 7

Challenge level

This box does something to the numbers that go into it. If you know the numbers that come out, what might be going on inside the box?
problem
Vector journeys

Age

14 to 18

Challenge level

Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?
problem
Irrational arithmagons

Age

16 to 18

Challenge level

Can you work out the irrational numbers that belong in the circles to make the multiplication arithmagon correct?
problem
Largest even

Age

5 to 11

Challenge level

How would you create the largest possible two-digit even number from the digit I've given you and one of your choice?
problem
What numbers can we make?

Age

11 to 14

Challenge level

Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
problem
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
Button-up some more

Age

7 to 11

Challenge level

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
problem
Which is bigger?

Age

14 to 16

Challenge level

Which is bigger, n+10 or 2n+3? Can you find a good method of answering similar questions?
problem
Which is cheaper?

Age

14 to 16

Challenge level

When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?