Geometrical Constructions

These are "construction" problems. The idea is to build facility with geometical concepts.

Two-Triangle Constructions

Using two triangles, how many different shapes can you make? Rules: The triangles can overlap, or touch at an edge, but they cannot be separated or touch at just one point. The student can use any shape of triangle, but it of course must have three straight sides.

A student might be inclined to show how to make different kinds of 4-sided shapes. But sooner or later, the goal is a list by number of sides. For example, can you make a 7-sided shape? And if you can, can you make an 8-sided shape?

Splitting a Rectangle

An easier problem, perhaps as a beginning or for younger children. (1) Draw a line through a rectangle to make 2 rectangles; (2) Draw a line through a rectangle to make 2 triangles; (3) Draw a line through a rectangle to make a triangle and a 5-sided figure. A six-year-old could easily do the first two but not the third, leading to even easier problems.....

Easiest

Draw a 5-sided shape. Draw a 6-sided shape. My 6-year-old could do these problems, but she had to think and it was not easy.

Draw a line through a circle to split it into 2 equal parts. Draw a line through a circle to split it into two unequal parts, one big and one small. The latter problem is designed to teach the rule that the line does not have to go through the center of the shape.