Halves, thirds, and sixths

The purpose of this task is for students to use their understanding of area as the number of square units that covers a region, to recognize different ways of representing fractions with area, and to understand why fractions are equivalent in special cases. Determining the fraction of the area that is shaded for rectangles A-D in part (b) is increasingly complex. Rectangles E, F, and G show that there are many ways for of the area to be shaded blue, which implies that there are many ways to represent the fraction with area. Rectangle H requires students to see the equivalence of two fractions, neither of which is a unit fraction.