. Grade 3, Illustrative icon

Halves, thirds, and sixths

Illustrative MathematicsVaries

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.

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