subdividing

In the first level of the POM, students view different geometric figures and
determine whether they can divide the figure into two identical pieces. Their task is
to use symmetry to answer question of same shape and equal area parts. In level B,
students are given a picture of flat geometric shapes made out of clay. Then
students are asked to find a way to make a straight line cut in order to divide the
figure into two parts of equal amounts of clay. In level C, the students are presented
with a rectangular map. The map is divided into six different regions of various
sizes. The task for the students is to determine the fractional part of each region in
terms of the whole rectangular area. In level D, students analyze a triangular region
to once again find the fractional parts of the whole. The students are then asked to
design their own map with sub‐divided regions. In the final level of the POM,
students are presented with an investigation to find five different unit fractions with
a sum of 1. Students must determine whether there is more than one set of five unit
fractions that sum to 1, and if so they must determine a general method for finding
other sets. If not, they prove why not. They also explore other size sets of unit
fractions that can be found to sum to 1.
© Noyce Foundation 2012