Ms. Bauserman’s third and fourth graders in Title I math class worked with manipulatives to demonstrate combining and subdividing polygons. These are students at Christ the King Catholic in Norfolk.


Ms. Bauserman knows when you give students math manipulatives for the first time, the best thing to do is let them play with them – because they are going to do it anyway!

house of shapes

girl with bow


So the third and fourth grade math students first played with the shapes for a bit.

standing shapes

manipulative shapes

different shapes

Then Ms. Bauserman dove into her lesson about combining polygons. Students learned, for example, the following combinations:



  • Two squares make a rectangle.
    2 squares make a rectangle
  • Four squares make another square.4 squares makes another square
  • Two trapezoids make a hexagon.2 trapezoids make a hexagon
  • Two triangles make a rhombus.
    2 triangles make a rhombus

What happens when polygons are subdivided? The students discovered the following about their manipulatives:

  • Dividing a hexagon in half results in two trapezoids.
    Combining and Dividing Polygons - Hexagon in half
  • Subdividing a rectangle in half can result in two squares.
    dividing a rectangle in half
  • Dividing a rhombus in half can result in two triangles.
    divide a rhombus into 2 triangles
  • And, finally, dividing a square into four equal parts can result in four squares.
    Combining and subdividing square polygons. One square into 4 squares


While playing and working with the manipulatives, combining and subdividing the polygons, students discussed

  • the names of the shapes,
  • the types of angles in each shape, and
  • number of vertices in each polygon.