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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# 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

- Problem
- Getting Started
- Student Solutions
- Teachers' Resources

You may find it helpful to use some blocks to make the staircase each time, or to draw a picture of the staircase.

How will you record the total number of blocks used in each staircase?

Have you noticed that you can rearrange the blocks in each staircase to make a square shape?

Have a go yourself. How might this help you work out the total number of blocks in each staircase?

You can click below to see a picture.

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?