Conjecturing and generalising

problem

Semi-Square

Age

14 to 16

Challenge level

3 out of 3

What is the ratio of the area of a square inscribed in a semicircle to the area of the square inscribed in the entire circle?
problem

In a Spin

Age

14 to 16

Challenge level

3 out of 3

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?
problem

Three Times Seven

Age

11 to 14

Challenge level

3 out of 3

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
problem

Next-Door Numbers

Age

5 to 7

Challenge level

1 out of 3

Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?
problem

Logic Block Collections

Age

5 to 7

Challenge level

1 out of 3

What do you think is the same about these two Logic Blocks? What others do you think go with them in the set?
problem

Two Spinners

Age

5 to 7

Challenge level

1 out of 3

What two-digit numbers can you make with these two dice? What can't you make?
problem

Unit Differences

Age

5 to 7

Challenge level

1 out of 3

This challenge is about finding the difference between numbers which have the same tens digit.
problem

Unexpected Ordering

Age

5 to 7

Challenge level

1 out of 3

Watch the video of Fran re-ordering these number cards. What do you notice? Try it for yourself. What happens?
game

Stop the Clock for Two

Age

5 to 7

Challenge level

3 out of 3

Stop the Clock game for an adult and child. How can you make sure you always win this game?
problem

Simple Train Journeys

Age

5 to 11

Challenge level

1 out of 3

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?