### 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?

# Number Tracks

##### Age 7 to 11 Challenge Level:

Ben's class were making number tracks and cutting them up.

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First they cut them into twos. Ben started with zero

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but Miles started with one:

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Then they both added up the numbers on each piece.

Ben wrote: $0 + 1 = 1$, $2 + 3 = 5$, $4 + 5 =$... ... ...

Miles wrote: $1 + 2 = 3$, $3 + 4 = 7$, $5 + 6 =$ ... ... ...

What patterns could they see?

Alice cut her number track into $3$s and added up the numbers on each one.

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Winston made a longer number track which he cut into $5$s and he added up the numbers on each one.

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What could they discover about the sum of the numbers on their strips of number track?

What other patterns can you find?