This lesson allows students to investigate the slope criteria and characteristics of parallel lines using graphing calculators and school staircases. Students will also use equations and graphs. Students will work cooperatively to develop and justify ideas/conjectures.
This is a College- and Career-Ready Standards showcase lesson plan.
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.
Students will discover and use the properties of parallel lines.
Students will find equations of parallel lines given other equations of lines passing through other points.
Students will use slope definitions with rise over run and formulas to solve problems and justify reasoning for developed discoveries.
Students will work cooperatively to discover patterns in the graph table of values while problem solving.
Students will verify conclusions by finding slope and understanding properties of paralell lines.
Students will measure and document lengths of stairs and compare values to determine parallel slopes.
ENGAGE
1. As students enter the classroom, they should be given a group indicator that tells them where to sit until dismissed to staircase work location. Inform the students that their mission will be to determine whether a pair of equations of lines are parallel.
EXPLORE
2. Student groups should measure the rise and the run of the steps to find the slope of the stairs. They should record these findings on their own paper (this information is to be used to key into their graphing calculators).
3. The students should come back to the classroom and key their information into their graphing calculators (using the list key on the graphing calculator) to determine if the staircases make parallel lines and have parallel slopes. They should look for patterns, develop equations based on data, and list slope conclusions based on data. The groups must agree on findings and be able to justify.
3. If students are unable to identify rise and run values, provide necessary feedback to move them forward with their thinking. Refer to Rise over Run: https://www.youtube.com/watch?v=zTa0xTu9Yv4 (if your school system does not allow YouTube access, you may download the video using http://www.keepvid.com/)
EXPLAIN
4. The teacher should be sure that students are using slope correctly to verify parallel lines.
5. Groups will discuss properties discovered and begin justifying their ideas; along with creating equations and graphs to match their tables in the calculator.
6. Allow students time to prepare attractive posters to share with the class to begin discussions about parallel, along with having the groups share their findings using the Smartview function of the calculator.
EVALUATE
Use the rubric provided to assess student work individually and as a group. Students should justify all reasoning stated on poster. The Assessment Process is on-going. The teacher should visit each group and ask questions to make sure students apply the properties of parallel line definitions. Post the posters in the classroom and have students present conclusions. As students present posters and graphing calculator finds, they should compare posters for other information not listed on their group's poster.
For extra practice or for students who were absent, have them visit What is the slope of a staircase? (if your school system does not allow YouTube access, you may download the video using http://www.keepvid.com/).
Teacher:
Students:
Poster Paper or Poster with grid lines
Sticky notes of different types
Straight edge
Markers
Student may use their own devices or teacher-issued graphing calculators.
Computer with Internet access
LCD Projector and Document camera to share student work (helpful but not necessary)
Smartview with calculator is needed
