Working systematically

problem
Worms

Age

7 to 11

Challenge level

Place this "worm" on the 100 square and find the total of the four squares it covers. Keeping its head in the same place, what other totals can you make?
problem
Tri.'s

Age

7 to 11

Challenge level

How many triangles can you make on the 3 by 3 pegboard?
problem
3 rings

Age

7 to 11

Challenge level

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?
problem
Homes

Age

5 to 7

Challenge level

Six new homes are being built! They can be detached, semi-detached or terraced houses. How many different combinations of these can you find?
problem
Plants

Age

5 to 14

Challenge level

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
problem
Tiles on a patio

Age

7 to 11

Challenge level

How many ways can you find of tiling the square patio, using square tiles of different sizes?
problem
Chocolate

Age

7 to 14

Challenge level

There are three tables in a room with blocks of chocolate on each. Where would be the best place for each child in the class to sit if they came in one at a time?
problem
Tea cups

Age

7 to 14

Challenge level

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.
problem
Consecutive numbers

Age

7 to 14

Challenge level

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
problem
Dienes' logiblocs

Age

5 to 7

Challenge level

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?