Teacher resources and professional development across the curriculum
Teacher professional development and classroom resources across the curriculum
This class has already worked with geoboards. Students now investigate the concept of halves using the geoboard as an area model. This lesson begins with students being asked what one-half means to them. Students provide input and see two different ways to show halves modeled. The students work in pairs to find as many ways as they can to show halves on their geoboards and record each solution on geoboard paper. Students must understand that one-half means one of two equal-sized parts that do not have to be congruent but must have equal areas. The class discusses ways to prove that a figure shows halves. After time for exploration, the class reconvenes and students present some of their solutions to the class, justifying how they know they are correct.
Topics for Discussion
The following areas provide a focus for discussion after you view the video. You may want to customize these areas or focus on your own discussion ideas.
Making Mathematical Connections
- How did this lesson provide a problem-solving context for the exploration of mathematical ideas?
- Identify the mathematical ideas and connections in this lesson.
- Often one-half is defined as one of two equal parts, and it is often assumed that the parts are congruent. In this lesson the halves were not always congruent. How was the term half defined and used in this lesson and how does it compare with more common definitions?
- The need to find the areas of triangles emerged in this lesson. How did Ms. Richardson handle these situations?
- How did the geoboard facilitate connections among geometry, measurement, and fractions?
Developing Mathematical Reasoning
- How did Ms. Richardson promote the students1 reasoning and discovery?
- Some boys in this video developed a conjecture about using the pegs rather than measurements of area to verify their solutions. What was their conjecture? How did Ms. Richardson handle the situation? How else could the situation be handled?
- What was the role of the prover at the end of the lesson? What does this tell you about Ms. Richardson and her expectations of the students?
- Identify the value of using such manipulative materials as geoboards and rubber bands to facilitate the students1 reasoning.
- How does requiring students to present their discoveries to the whole class promote reasoning?
What else can you do with a geoboard? Find or create activities using geoboards. For each activity, identify the mathematical ideas being explored. For example, repeat the activity from the video lesson but divide the geoboard to show fourths in several different ways. Use the geoboard to further the students1 understanding of triangles and classification of triangles by angles.