Factors and multiples

problem
What's in the box?

Age

7 to 11

Challenge level

This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
problem
Multiplication square jigsaw

Age

7 to 11

Challenge level

Can you complete this jigsaw of the multiplication square?
problem
Music to my ears

Age

7 to 11

Challenge level

Can you predict when you'll be clapping and when you'll be clicking if you start this rhythm? How about when a friend begins a new rhythm at the same time?
problem
Clapping times

Age

5 to 7

Challenge level

If you count from 1 to 20 and clap more loudly on the numbers in the two times table, as well as saying those numbers loudly, which numbers will be loud?
problem
Rarity

Age

16 to 18

Challenge level

Show that it is rare for a ratio of ratios to be rational.
problem
Factors and multiples puzzle

Age

11 to 14

Challenge level

Using your knowledge of the properties of numbers, can you fill all the squares on the board?
problem
Multiples grid

Age

7 to 11

Challenge level

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
problem
There's always one isn't there

Age

14 to 16

Challenge level

Take any pair of numbers, say 9 and 14. Take the larger number, fourteen, and count up in 14s. Then divide each of those values by the 9, and look at the remainders.
problem
Numbers as shapes

Age

5 to 7

Challenge level

Use cubes to continue making the numbers from 7 to 20. Are they sticks, rectangles or squares?
problem
Coin collection

Age

14 to 16

Challenge level

When coins are put into piles of six 3 remain and in piles of eight 7 remain. How many remain when they are put into piles of 24?