To assess students' prior geometric knowledge, make a KWL Chart
as a group. Record on the overhead projector or on a chart in the classroom. You and the students can refer to this chart in the future.
Compare this list with the learning objectives for this lesson. This focuses students’ attention on the mathematical content of the lesson.
Direct students to the Virtual Geoboard, part of the NCTM E-Examples on the Principles and Standards Web site.
Give students at least five minutes to make designs on their own using the geoboards. Tell them that this is the time to experiment and explore. Ask students to share what they learned from the activity. Then have them clear their boards.
Ask students to model geometric figures and discuss the online questions after creating each figure.
Note: It is important for students to process what they are doing to create the various figures so that they will understand the relationships among the figures. Talking helps students clarify and extend their thinking. It also helps you understand what students are learning.
Ask students to make a three-sided figure on their personal geoboards. Then, pose the following questions to guide students’ thinking about the properties of this three-sided figure.
- What is the name of this figure? [triangle]
- How many vertices does this figure have? [3]
- Show me an example of a vertex by holding your geoboard up and pointing to the vertex. Model this on the Virtual Geoboard E-Example.
- What is the relationship between the number of sides and the number of vertices?
Ask students to make a four-sided figure on their geoboards. Then ask the following questions to guide students’ thinking about the properties of this four-sided figure.
- What is the name of this figure? [quadrilateral]
- Why is it so named? Are the sides of your quadrilateral the same? Why or why not? This discussion helps focus on the equilateral quadrilateral.
- How many vertices does this figure have? [4]
- How do the four-sided figures compare with the three-sided figures? What are the primary similarities? What are the major differences?
Ask students to show you a right angle on the Virtual Geoboard E-Example using two rubber bands. Pose the following questions to guide their thinking about the properties of the right angle.
- How would you describe this shape to a partner who has never seen such a shape?
- What words can you use to describe the right angle? How is an understanding of these words important to an understanding of the shape you created?
- How is an understanding of these words important to an understanding of other shapes you might make?
Ask students to show you an acute angle on the Virtual Geoboard E-Example using two rubber bands.
- How would you describe this shape to a partner who has never seen such a shape?
- What words can you use to describe the acute angle?
- How does this activity compare with the previous ones?
- Why is it important to know the difference between acute and right angles?
Ask students to show you an obtuse angle on the Virtual Geoboard E-Example using two rubber bands. Ask a volunteer to model how to construct an obtuse angle using the virtual geoboard.
- How would you describe this shape to a partner who has never seen such a shape?
- What words can you use to describe the obtuse angle? How is an understanding of these words important to an understanding of the shape you created?
- Why is it important to know the difference between acute, right, and obtuse angles?
- What important knowledge is necessary for you to describe the difference among the three types of angles?
When students have made and discussed each of the figures, ask them to discuss the similarities among the figures. It may be helpful for students to display a sample of each figure or angle during this discussion.
Encourage students to consider the common properties that define each figure. Ask them to pose any questions they may have about each figure.
Bring closure to the lesson by having students write a brief summary of what they have learned and the questions they want to explore. Collect these work samples so that you can review and identify students’ knowledge and understanding to guide the next instructional activities.
