3.G.A.2

Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

 

Summary:

This standard moves beyond the previous grade's similar standard in that students now partition "shapes", instead of just circles and rectangles as we saw in 2 G.A.3. Notice that the standard still calls only for the use of unit fractions. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.


Understanding the Standard:

    • Students should be given a variety of shapes that can be partitioned into equal pieces. Shapes that work well for this are circles, squares, rectangles, regular hexagons, and equilateral triangles.
    • Students should partition shapes into unequal sized pieces and determine the area of each shape. For example, a rectangle drawn on grid paper can easily be partitioned into a variety of pieces; the area of each can be easily counted.

      Questions to Focus Instruction:

        • Can students partition a shape in multiple ways? For example, can students partition a rectangle into four parts in multiple ways?
        • Can students express partitions with the symbols we use for fractions?
        • Can students determine the area of a partition when they know the area of the whole?

          Skills


          Prior to: Students can partition circles and squares.  Go to 2.G.A.2 and 2.G.A.3 to see previous skills in this progression.

          At Grade Level:
          Students partition shapes, express the partitions as unit fractions, and determine the area of a partition.

          Beyond: Students begin investigating ways to partition triangles and express them as fractions.