This story about some troublesome dogs encourages children to find and model doubles of different numbers.
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?
Show that the edges $AD$ and $BC$ of a tetrahedron $ABCD$ are mutually perpendicular if and only if $AB^2 +CD^2 = AC^2+BD^2$. This problem uses the scalar product of two vectors.
Can you find a way to break one of these rods so that one of the pieces is equal to the mean of the other two?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
