Lesson 2 of 7
Objective: SWBAT identify and apply properties of line segments to problems.
Line Constructions and Notes
Congruent Segments Construction:
We will then work on completing 2 constructions using a straight edge and a compass. In the first construction, we will ask students to construct a congruent segment to a given segment. The steps have been provided for students to work through in pairs but as this is the first construction of the year, you may want to work step by step with students who are using a compass for the first time. It’s also critical to get students to think about the deeper reasoning behind why this construction works and how it relates to the ideas in this lesson. We can do this by asking students some follow-up questions like,
- Why must these segments be congruent?
- How can we prove these segments are congruent?
Students will respond with answers like, we could measure each of the segments to ensure that the segments are congruent.
Midpoint/Line Bisector Construction:
In the second construction, we will find the bisector for a line. To engage students in deeper level thinking about this idea, students are presented with a challenge question asking them how to find the midpoint of a given line without a ruler. Many students may fold their paper or try to use marks. The notes included scaffolded steps and space for students to create circles using the endpoints of the given line segment as the center. Students will be asked to explore and determine how and when we have overlapping circles and what the intersection points (or lack of!) means in relation to the line segment and midpoint.
Teachers can then introduce the steps to constructing a line bisector or finding a midpoint and connect this with the exploration and circles that students have previously drawn.
Each construction has two examples, one for students to work on with the teacher in a whole class setting and the second example for students to work with independently or with a partner. I’ve also included links to these constructions being done which is a great resource for absent students or for review.
Activity: If time remains, teachers can have students work on the short activity - Points, Lines and Planes and then review the answers to ensure that students understood the key concepts from the lesson. Once this is done, students can continue working on the activity from the previous lesson called points, lines and planes. This connects with MP #4 where students are asked to model mathematics.
Exit Ticket: Students will complete an Exit Ticket question that asks them to use the segment addition property to find missing lengths.
Homework: Students will be asked to finish activity and will be assigned questions in the textbook.