K-4 MATHEMATICS STANDARDS

    PROBLEM-SOLVING ACTIVITY

    Standard's bullets addressed by activity

    • use problem-solving approaches to investigate and understand mathematical content
    • verify and interpret results with respect to the original problem
    • develop and apply strategies to solve a wide variety of problems

    Materials needed

    • 5 X 5 geoboards and geobands

    Description of Activity

    • Group or classroom management practices

      • Children work in pairs or small groups.

    Have students make a triangle on the geoboard. How many pegs does the rubber band touch? Make a triangle so that the rubber band touches three pegs. Make another triangle so that the rubber band touches four pegs, and another triangle that touches five pegs. Can you make a triangle so that the rubber band touches more pegs? Is it possible to make a triangle that touches only two pegs? Is it possible to make a triangle that has the same number of pegs on two sides? On three sides?

    Make a square with the rubber band touching four pegs and a square with the rubber band touching eight pegs. What other squares can you make? Count the number of pegs on each side. Discuss why each side must have the same number of pegs. Establish a pattern with the total number of pegs on the boundary of a square: 4, 8, 12 ...

    Explore rectangles the same way. The number of pegs may not be the same for all four sides but will be the same for opposite sides. Once the children have grasped the idea of pegs on the boundary, have them illustrate what is meant by "pegs inside." Although the pegs touching the rubber band are technically "inside," for this problem, count only those pegs that are not touching the rubber band.

    Ask the children to make a triangle with two pegs inside, then with three pegs inside. What is the greatest number of pegs that can be inside a triangle on a geoboard?

    Repeat these problems using other figures, such as four-sided figures and six-sided figures. Is it possible to get more pegs inside a four-sided or a five-sided figure? Note that the answers will vary according to the figures the children make.

    Reference

    Burton, G., Clements, D., Coburn T., Del Grande, J., Firkins, J., Joyner, J., Leiva, M., Lindquist, M., & Morrow, M. (1991). Curriculum and evaluation standards for school mathematics addenda series, Grades K-6: First-grade book. Reston, VA: National Council of Teachers of Mathematics. pp. 20-21.