A small square is a square unit. What is the area of this rectangle? Explain.
What fraction of the area of each rectangle is shaded blue? Name the fraction in as many ways as you can. Explain your answers.
Shade \(\frac12\) of the area of rectangle in a way that is different from the rectangles above.
Shade \(\frac23\) of the area of the rectangle in a way that is different from the rectangles above.
Commentary
The purpose of this task is for students to use their understanding of area as the number of square units that covers a region (3.MD.6), to recognize different ways of representing fractions with area (3.G.2), and to understand why fractions are equivalent in special cases (3.NF.3.b). 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 \(\frac12\) of the area to be shaded blue, which implies that there are many ways to represent the fraction \(\frac12\) with area. Rectangle H requires students to see the equivalence of two fractions, neither of which is a unit fraction. Students get a chance to demonstrate what they have learned in part (b) by generating their own representations of fractions in parts (c) and (d).
Note that in third grade, students are limited to working with halves, thirds, fourths, sixths, and eighths. While it would be acceptable in instructional situations to work with other fractions, students should have an opportunity to work extensively with the fractions mentioned in order to develop a deep and flexible understanding of them. In particular, summative assessment should be strictly limited to fractions with denominators 2, 3, 4, 6, and 8.
This is an instructional task. Students would benefit from having tracing paper, colored pencils, and multiple blank copies of the rectangle as they work. Students would also benefit from working in pairs or small groups so they can compare their answers and explain the fraction equivalences to each other.