Building Polygons (Part 2)
5 min
Teacher Prep
Setup
Narrative
The purpose of this warm-up is to remind students that when you have a fixed starting point, all the possible endpoints for a segment of a given length form a circle (centered around the starting point). The context of finding Lin’s position in the playground helps make the geometric relationships more concrete for students. Since there are many possible distances between Lin and the swings (but not infinitely many), this activity serves as an introduction to formalizing rules about what lengths can and cannot be used to form a triangle.
Monitor for students who come up with different locations for Lin, as well as for students who recognize that there are many possible locations, and ask them to share during the whole-class discussion.
Launch
Arrange students in groups of 2. If necessary, remind students of the directions north, south, east, and west and their relative position on a map. Provide access to geometry toolkits. Give students 2 minutes of quiet work time, followed by a partner discussion and a whole-class discussion.
During the partner discussion, have students compare their reasoning with a partner and to discuss until they reach an agreement.
Student Task
At a park, the slide is 5 meters east of the swings. Lin is standing 3 meters away from the slide.
- Draw a diagram of the situation including a place where Lin could be.
- How far away from the swings is Lin in your diagram?
- Where are some other places Lin could be?
Sample Response
- Answers vary. See diagram.
- There is no way to know for sure, because we don’t know what direction Lin is from the slide. She could be anywhere between 2 and 8 meters away from the swings.
- Lin could be at any position along a circle that is centered on the slide and that has a radius of 3 meters.
Activity Synthesis (Teacher Notes)
Begin by inviting selected students to share their diagrams of where Lin is located. Discuss the following questions with the whole class:
- “Do we know for sure where Lin is?” (No, because we don’t know what direction she is from the swings.)
- “What shape is made by all the possible locations where Lin could be?” (a circle)
- “What is the closest Lin could be to the swings?” (2 m)
- “What is the farthest Lin could be away from the swings?” (8 m)
Consider displaying the applet to show all the locations where Lin could be.
Anticipated Misconceptions
Some students might assume that the swings, the slide, and Lin are all on a straight line, and that she must be 8 meters away. Ask these students if the problem tells us which direction Lin is from the slide.
Some students may confuse the type of compass discussed in the Launch and the type of compass discussed in the Activity Synthesis. Consider displaying a sample object or image of each of them and explain that the same name refers to two different tools.
Standards
- 7.G.2·Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
- 7.G.A.2·Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
15 min
15 min
Knowledge Components
All skills for this lesson
No KCs tagged for this lesson
Building Polygons (Part 2)
5 min
Teacher Prep
Setup
Narrative
The purpose of this warm-up is to remind students that when you have a fixed starting point, all the possible endpoints for a segment of a given length form a circle (centered around the starting point). The context of finding Lin’s position in the playground helps make the geometric relationships more concrete for students. Since there are many possible distances between Lin and the swings (but not infinitely many), this activity serves as an introduction to formalizing rules about what lengths can and cannot be used to form a triangle.
Monitor for students who come up with different locations for Lin, as well as for students who recognize that there are many possible locations, and ask them to share during the whole-class discussion.
Launch
Arrange students in groups of 2. If necessary, remind students of the directions north, south, east, and west and their relative position on a map. Provide access to geometry toolkits. Give students 2 minutes of quiet work time, followed by a partner discussion and a whole-class discussion.
During the partner discussion, have students compare their reasoning with a partner and to discuss until they reach an agreement.
Student Task
At a park, the slide is 5 meters east of the swings. Lin is standing 3 meters away from the slide.
- Draw a diagram of the situation including a place where Lin could be.
- How far away from the swings is Lin in your diagram?
- Where are some other places Lin could be?
Sample Response
- Answers vary. See diagram.
- There is no way to know for sure, because we don’t know what direction Lin is from the slide. She could be anywhere between 2 and 8 meters away from the swings.
- Lin could be at any position along a circle that is centered on the slide and that has a radius of 3 meters.
Activity Synthesis (Teacher Notes)
Begin by inviting selected students to share their diagrams of where Lin is located. Discuss the following questions with the whole class:
- “Do we know for sure where Lin is?” (No, because we don’t know what direction she is from the swings.)
- “What shape is made by all the possible locations where Lin could be?” (a circle)
- “What is the closest Lin could be to the swings?” (2 m)
- “What is the farthest Lin could be away from the swings?” (8 m)
Consider displaying the applet to show all the locations where Lin could be.
Anticipated Misconceptions
Some students might assume that the swings, the slide, and Lin are all on a straight line, and that she must be 8 meters away. Ask these students if the problem tells us which direction Lin is from the slide.
Some students may confuse the type of compass discussed in the Launch and the type of compass discussed in the Activity Synthesis. Consider displaying a sample object or image of each of them and explain that the same name refers to two different tools.
Standards
- 7.G.2·Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.
- 7.G.A.2·Draw (freehand, with ruler and protractor, and with technology) geometric shapes with given conditions. Focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.