Area formula of a triangle

Subject: Natural science
Summary: Students learn two different ways how to find the area of a triangle through debating the pros and cons of two different methods of teaching the formula. Students’ diverse thinking processes with the development of a particular mathematical idea is illustrated by the interaction between the teacher, the students, and mathematics.
Activity length: Duration is 45 minutes.
Objectives:
  • Students understand the logic behind the area formula of a triangle.
  • Students collaborate with colleagues to teach each other different methods to solve a problem.
  • Students debate which method of calculating the area of a triangle is more suitable for teaching and learning in class.
Preparation:

Teacher prepares many copies of a triangle on papers of different colors.

Description:

Part 1: Teacher poses the main task of the lesson – finding the area of a triangle by changing its shape.

However, the first thing the teacher asks his class to do is to write down their ideas on how they might approach this task. Teacher communicates to his students that what is valued in this lesson is not just the answer, i.e. the area of the particular triangle, but also various ways students can determine the area. Students are encouraged to share ideas.

Students are expected to cut and paste the triangles to illustrate their method clearly. Cutting and re-arranging the given figure would provide an important foundation for the students to make sense of the area formula. As the students engage in their investigations, they are free to choose whatever method that makes sense to them.

Part 2: Teacher has his students share their ideas and carefully sequences students’ ideas. Student work is clearly displayed on the blackboard, both their work with paper arrangements and mathematical expressions. The teacher poses some questions to further analyze the ideas and methods shared by the students

Teacher asks students to sort the variety of methods into two types – those which transformed the given triangle to another shape without changing the area and those which created another shape by doubling the area of the given triangle.

Part 3: Dynamic group debate. The purpose of this debate is to vote for the best method.

  1. Each group tells the class its method.
  2. Individuals choose to join the group whose method they agree with most. Each group prepares the arguments in favor of their method.

Each group presents the arguments, then each group replies. Students vote for the best method.

Assessment:

Finding the area of a triangle using the chosen method.