We've already discussed here how children's literature provides an engaging, meaningful, and cross-curricular way to get students interested in mathematics. Quilting is yet another way to get students to reconsider math concepts like fractions, geometry, and area in a very hands-on and visual way. No needles, thread, or fabric required!
Smaller children can explore the tiling aspects of simple geometric figures like squares and triangles. For the five and six year olds, the challenge will be to see how to fit their smaller shapes within a larger quilt square (i.e. 9 x 9 piece of white paper) without overlapping them or leaving any white space. This is a great lesson in the properties of shapes - the number of sides, how polygons fit together, and what can be created with some very simple shapes.
Your older children will be able to construct more complex designs, and can explore additional areas of mathematics as they do so. Take their completed quilt squares and question them about fractions. What fraction of your quilt square is red? Yellow? For students who have begun exploring the concept of area, ask them to calculate the area of their quilt square. You can even ask your more challenge-ready students to calculate the area of their square that is white, blue, green, etc. All students in the upper elementary grades should be able to measure and then calculate the perimeter of their square and the class-made quilt. All of these are excellent math extensions from what seems at first glance to be a fancy art project.