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### Number and algebra

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# Up and Down Staircases

## You may also like

### Pebbles

### Bracelets

### Sweets in a Box

Links to the University of Cambridge website
Links to the NRICH website Home page

Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

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Age 7 to 11

Challenge Level

One block is needed to make an up-and-down staircase, with one step up and one step down.

Four blocks make an up-and-down staircase with two steps up and two steps down.

How many blocks would be needed to build an up-and-down staircase with three steps up and three steps down?

What about for four steps up and four steps down?

What do you notice about the number of blocks needed each time?

Can you predict how many blocks will be needed to build an up-and-down staircase with five steps up and five steps down?

Were you right?

Explain how you would work out the number of blocks needed to build a staircase with *any number* of steps.

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?

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

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?