Math 106 - CooleyMath for Elementary Teachers II OCC

Classroom Activity #8 – Geoboard Challenges

Learning Objectives

Students will:

  • use geoboards to create and analyze the properties of triangles, squares, and other polygons.

Materials

  • Geoboards, colored rubber bands.
  • Geoboard Challenges Activity Sheet – 1 per student
  • Geoboard Challenges Geoboard Grids – 1 per student

Instructional Plan

Have students work in pairs. Distribute the materials. Have students work through the Geoboard Challenges Activity Sheet and record their solutions on the Geoboard Grid sheet. Perhaps call out on students and have them show their solutions on the ELMO (Electronic Light-Modulated Overhead).

Extensions

Create more questions of your own. Perhaps increase difficulty and/or enlarge the geoboards.

NCTM Standards and Expectations

Geometry: Specify locations and describe spatial relationships using coordinate geometry and

other representational systems - Grades 6-8

1. Use coordinate geometry to represent and examine the properties of geometric shapes.

References

This lesson was created by Beth Schlesinger, San Diego

from the 2007-2008 Special Edition of the CMC ComMuniCator.

This lesson was modified by TopCatMath.com.

Geoboard Challenges Activity SheetNAME ______

Many different shapes meeting different requirements can be constructed using a geoboard. For example, consider Figures A and B.

Figure AFigure B

Figure A is a triangle containing 3 interior pegs.Figure B is an isosceles right triangle with legs of

length 2.

What is the perimeter of the triangle in Figure B? This will help you to answer the following questions.

Which of the following 18 shapes can be made using a geoboard?

  • Record your discoveries on the geoboard grids provided.
  • Some of your solutions may result in non-convex (concave) shapes.
  • Hint: There are 5shapes below that cannot be made.

1) / A triangle with five interior pegs. / 10) / A hexagon with three pairs of parallel sides.
2) / A triangle with six interior pegs. / 11) / A hexagon with four pairs of parallel sides.
3) / An equilateral triangle. / 12) / A hexagon with all sides of different lengths.
4) / A square with area of two square units. / 13) / A dodecagon with all twelve sides congruent.
5) / A square with area of four square units. / 14) / An octagon with all eight sides congruent.
6) / A square with area of five square units. / 15) / A convex heptagon.
7) / A square with area of seven square units. / 16) / A non-convex nonagon.
8) / A pentagon with all sides the same length. / 17) / A non-convex 24-gon.
9) / A hexagon with no two sides parallel. / 18) / A non-convex 25-gon.

Geoboard Challenges Geoboard Grids

Possible Solutions