### 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?

##### Stage: 2 Challenge Level:

You may like to look at Are you well Balanced? before trying this problem.
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I hang three weights on the 8 hook on the left-hand side of the equaliser.
If I have a maximum of four weights left, where could I hang them on the right-hand side of the equaliser so that it balances?
Are there any other ways of doing it? (I don't need to use all four weights.)

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Now I hang three weights on the 10 hook and one on the 6 hook on one side of the equaliser.
If I have six weights, where could I hang them on the other side to make it balance?

### Why do this problem?

In a similar way to Are you well Balanced? , factors and multiples are at the heart of this problem as well as addition and subtraction, even though this may not be the route through which children solve it. It is important, therefore, to discuss ideas of multiplication with the class, perhaps after children have first thought about the problem on their own for a few minutes and then talked to a partner about possible ways to the solutions.

### Key questions

Where have you tried hanging weights so far?
How will you know that you have got all the ways of making the equaliser balanced?
Is it possible to balance the equaliser with just one weight? With two weights ... three ...?

### Possible extension

Learners could experiment with the equaliser by trying other numbers and trying to find all the ways of balancing it.

### Possible support

Chldren could try Are you Well Balanced? and Number Balance before trying this problem.