English: Two mathematics teachers are evaluating a new teaching tool under development. The tool, a set of pie-shaped models of foam paper, is designed to help students to understand fractions.

The size of the pies have been chosen carefully so that it should be handy for children. Different colors designate fractions with different denominators in their simplest form. On the left, you can see a series of calculations with fractions (from top to bottom): 19/16 + 2/8 (pink), 10/12+2/12 (orange), 1/2+2/4 (brown), 3/4+2/12 (pink and orange), 8/16+2/12+4/12 (brown, orange and blue), 3/9+3/12+1/6+3/12 (blue, pink and purple), 1-3/12 (green and pink), 1/2+1/2-1/3 (brown and blue).

The result of the 3/9+3/12+1/6+3/12 operation is rather close to 1, but not so much that the gap would be negligible. This is an important aid for the students, so that they do not assume equalities that do not hold, however, it poses a constraint on the available fractions in the set.

English: Foam paper fraction pies