Conjecturing and generalising

problem

Special Sums and Products

Age

11 to 14

Challenge level

3 out of 3

Find some examples of pairs of numbers such that their sum is a factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and 16 is a factor of 48.
problem

2001 Spatial Oddity

Age

11 to 14

Challenge level

3 out of 3

With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.
problem

Square Pizza

Age

14 to 16

Challenge level

3 out of 3

Can you show that you can share a square pizza equally between two people by cutting it four times using vertical, horizontal and diagonal cuts through any point inside the square?
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

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?