Reason with shapes and their attributes

Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.1





As students gain knowledge in the identification of geometric attributes, they are then introduced to other shapes such as trapezoids, half-circles and quarter-circles. With this introduction, students can begin to conclude that shapes may be put together to form new shapes or bigger shapes can be taken apart to show the smaller shapes that compose them. Additionally, students should have practice in creating these shapes through such methods as drawings, tracings and fashioning manipulatives together.

Understanding the Standard:

    • Students should have ample experience with manipulatives and technologies that will allow them to create two and three-dimensional shapes. For example, use tangrams and pattern block puzzles.
    • The concepts of halves and quarters are introduced and can be done so with manipulatives that show a circle segmented into pieces other than its whole.
    • Students should have experience composing a shape with previously composed shapes. For example, two quarter circles together form a half circle, and then two half circles made in this fashion can be composed to form a whole circle.


      Specific Questions to Focus Instruction:

        • Can my students combine shapes in order to successfully make a new shape?
          1. Can students put together two triangles in two different ways - one that makes a rectangle and one that makes a parallelogram?
          2. Can students put together a rectangle and a triangle to make a trapezoid?
          3. Can students put two quarter circles together to make a half circle?
          4. Can students make a cube with several rectangular patterns?


          Prior to: One skill that students have developed before being able to compose shapes, placing them edge-to-edge, is the skill of making a composite shape by touching the vertex of one shape to the part of another shape. An example would be making a girl out of pattern blocks, using a triangle block for the dress, a square for the head, and one skinny rhombus for each leg and arm. See K.G.B.6.

          At Grade Level: Students can compose a bigger shape from smaller ones and decompose a bigger shape into the smaller geometric components. Additionally, students should have an overall understanding of the separation of a circle into equal halves and fourths.

          Moving Beyond:
          Students’ knowledge of halves and fourths creates a natural progression into the study of fractions in the later grade levels.  Go to 2.G.A.2. to see the progression of related skills.

          1Students do not need to learn formal names such as “right rectangular prism.”