California Common Core Standard: High School Geometry
Stage 2: Performance Task: The race - Students collect data from the 2003 New York Marathon, in which rapper Sean "P. Diddy" Combs participated. Students create a graphs of Sean's race and compare it to a graph of Martin Lel's (the winner) race. They explore the slope of each graph and how they differ and what that means for how the race is run. Then students use a marathon calculator to find their projected finishing time and compare that with the two other racers.
Stage 3: Learning Plan 1. The lesson introduction sets up the situation: the 2003 New York City Marathon, in which rapper, P. Diddy received a lot of media attention for participating. 2. Students explore the graphing tool to remember what they know about slope and to experience slope before formulating a definition. 3. Students are presented with the definition and equation of slope and are providing ample examples and practice opportunities. 4. Students find other internet resources on slope, justify them, and share them5. Student complete a study guide (Training Manual) as they complete section 1. 6. Students complete the practice sheet. 7. Students explore the "Moving Man" applet as an introduction to distance vs. time graphs. 8. Students explore other internet resources on distance vs. time graphs. 9. Students collect and graph data for Martin Lel and P. Diddy. 10. Students create theoretical data for their own race. 11. Students evaluate and interpret the graphs. 12. Students fill out study guide, "Race Log" to record their data, graphs, and reflections. 13. Students reflect on the unit in a discussion forum. 14. Students are given opportunity to review content before taking the quiz. 15. Students take a quiz covering the skills and ideas from the unit
Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
Established Goals: Demonstrate knowledge of coordinate geometry and graphing functions and relations.
Desired Understandings:• Slope is a single number that describes the "slant" of a line• Slopes of linear data represent the rate of change of the data. • A slope of zero means that the line has no vertical change. • An undefined slope means that the line has no horizontal change.
Students will know...• The definition of slope• That the slope of a distance vs. time graph represents speed.
Students will be able to...• Recognize positive, negative, zero, and undefined slopes from looking at a graph.• Find the slope of a line from it's graph or from two points on the line. • Interpret the slope of linear data as a rate of change.
Essential Questions: • What is slope? • What kind of situations can be modeled with linear functions? • What can the slope of linear data tell us?
Student Self-Assessment and Reflection:• In the first discussion students collect resources and share what they learned that was not covered in the lesson. • In the "Race Log" students create data for a theoretical race, in which they evaluate if they think how they would be able to perform and what their graph would look like. • In the discussion at the end of the race section students reflect on the unit and give adice to other students.
Technology Resources: 1. P Diddy Marathon Article: 2. Create a Graph: 3. Definition of Slope:
Other Evidence:• "Training Manual" - Students record discoveries and examples as they work through the content of section 1 in develop definitions and methods of finding slopes. • Finding Resources - Students find resources on linear equations and share them with each other in a discussion forum. • Practice Sheet - A problem set that covers the basic skills covered in this section and introduces the idea of distance vs. time graphs. • "Race Log" - Students collect and graph data from 2 participants in the 2003 NYC marathon. In addition they collect and graph data for their own hypothetical race, based on a marathon calculator. • Discussion - Students share their thoughts about the lesson in a discussion forum• Quiz - At the end of the unit students take part in a quiz