Conjecturing and generalising

problem

Crossings

Age

7 to 11

Challenge level

2 out of 3

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?
problem

Button-Up Some More

Age

7 to 11

Challenge level

2 out of 3

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

Walking the Squares

Age

7 to 11

Challenge level

2 out of 3

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.
problem

Bundles of Cubes

Age

7 to 11

Challenge level

2 out of 3

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
problem

Truth or Lie

Age

7 to 11

Challenge level

2 out of 3

Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?
problem

Lost Books

Age

7 to 11

Challenge level

3 out of 3

While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?
problem

Oddly

Age

7 to 11

Challenge level

3 out of 3

Find the sum of all three-digit numbers each of whose digits is odd.
problem

Triangle Pin-Down

Age

7 to 11

Challenge level

3 out of 3

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.
problem

Dotty Circle

Age

7 to 11

Challenge level

3 out of 3

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?
problem

Polygonals

Age

7 to 11

Challenge level

3 out of 3

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.