Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

It Figures

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Bracelets

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

Divide it Out

Divide it Out

Why do this problem?

This problem requires logical thinking about factors and much multiplication! Learners must first find out what is the lowest number which divides exactly by all the numbers from $2$ to $10$ and then decide how this helps to answer the question asked. A calculator could be useful for checking.

Key questions

How are you going to start on this problem?
Why not start by listing all the numbers from $2$ to $10$?
Which numbers do you not need because they are factors of other numbers you are using?

Possible extension

Learners could find the lowest number which always leaves a remainder of $1$ when divided by any of the numbers from $2$ to $12$, or $2$ to $20$, etc.

Possible support

Suggest starting by finding the lowest number which divides exactly by all the numbers from $2$ to $6$. A calculator might be very helpful.