Being curious

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

Explore ways of colouring this set of triangles. Can you make symmetrical patterns?

What is the greatest number of squares you can make by overlapping three squares?

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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

We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?

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?

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