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For younger learners

  • Early Years Foundation Stage

Up and Down Staircases

Age 7 to 11
Challenge Level Yellow star
Primary curriculum
  • Problem
  • Getting Started
  • Student Solutions
  • Teachers' Resources

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.

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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?

Bracelets

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

Sweets in a Box

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?

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The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice.

NRICH is part of the family of activities in the Millennium Mathematics Project.

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