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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?
Age 7 to 11
Challenge Level
Flora had a challenge for her friends.
She asked, "Can you make square numbers by adding two prime numbers together?"
Ollie had a think.
"Well, let me see... I know that 4 = 2 + 2. That's a good start!"
Have a go yourself. Try with the squares of the numbers from 4 to 20.
Once you have had some initial ideas, take a look at how three more of Flora's friends started the problem:
Bailey said:
Dina said:
Shameem said:
Did you go about the task in the same way as any of these children?
What do you like about each method?
Continue working on the problem. You might like to adopt Bailey's or Dina's or Shameem's approach.
Did you find any square numbers which cannot be made by adding two prime numbers together? Why or why not?
You could print off this sheet which includes the problem and the three approaches.
NRICH is part of the family of activities in the Millennium Mathematics Project.