EXPLORING AREA and PERIMETER
In this unit, students explore area and perimeter relationships in response to the following problem. "You want to create an enclosed play area for children and you have exactly 320 feet of fence. What shapes and sizes of play areas can you make?" Students use interactive sketches to explore possible shapes and areas for triangular, rectangular, pentagonal, hexagonal, octagonal, and circular play areas. Questions designed to encourage exploration, reflection, synthesis, and extension are provided with each sketch. The Summary page asks students to reconsider their work and decide to what extent it helps them answer the original question. Students may work in groups of two or three, share computers, or work individually. Students working individually should be encouraged to discuss ideas with other students frequently and compare answers. Although the Summary page asks students to read each other's writing, students may be instructed to work alone, if the teacher wishes to use this page for individual assessment.
The interactive sketches provided for each shape are easy to use and are accessible to students from upper elementary through high school. However, its is important that students have had experiences which promote conceptualization of area as space within a boundary (perimeter) prior to using this web site. Questions provided to guide each explorations are geared toward upper middle school or high school students.
In the Curriculum and Evaluation Standards for School Mathematics (1989), the National Council of Teachers of Mathematics (NCTM) describes the following goals for all students: (1) that they learn to value mathematics, (2) that they become confident in their ability to do mathematics, (3) that they become mathematical problem solvers, (4) that they learn to communicate mathematically, and (5) that they learn to reason mathematically (p.5). To reach these goals, students must be encouraged to engage in problem solving activities which provide opportunities for exploration of important mathematical ideas, making and testing conjectures and building arguments, and reading, writing, and discussing mathematics (NCTM, 1989).
The Exploring Area and Perimeter Unit uses a simple, relatively open problem (creating a play area with 320 feet of fence) as a means to focus on the relationships between shape and area for a given perimeter. Students use interactive sketches to help them visualize the relationship between shape and area. Questions encourage students to make and test conjectures, reflect on their thinking, and write and discuss ideas. Because the computer does the area calculations, students are free to focus on the effect of changing side lengths on the enclosed area. In short, this unit attempts to engage students in explorations related to important mathematical content as suggested by the NCTM.
Assessment of student understanding should be ongoing throughout the explorations. Questions are used to encourage students to reflect on their understanding and make connections between explorations. For specific assessment guidelines click on Assessment
Area 10 Mathematics and Technology Professional Development Center
Permission is granted to duplicate these materials for classroom use.
Last updated on 1/30/1999