Lesson Title: ______________________________________________ Course: ___________________________ Date: _____________ Teacher(s): ____________________ Start/end times: _________________________ Lesson Standards/Objective(s): What mathematical skill(s) and understanding(s) will be developed? Which Mathematical Practices do you expect students to engage in during the lesson? G.GPE.B.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. G.CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. MP1: Make sense of problems and persevere in solving them. MP5: Use appropriate tools strategically. MP6: Attend to precision. Lesson Launch Notes: Exactly how will you use the first five minutes of the lesson? Lesson Closure Notes: Exactly what summary activity, questions, and discussion will close the lesson and connect big ideas? List the questions. Provide a foreshadowing of tomorrow. Have students design a floor plan for their dream home. Allow students to use rulers, graph paper, protractors, etc. during the design process. Specify that students must include at least three angles that Have students complete the Strengths and Weaknesses Closure activity to be handed in. are not 90 degrees in their floor plan, and that all walls must be straight. No particular scale needs to be designated. (NOTE: You may decide to require more than 3, depending on the level of rigor desired and the time allowed.) Lesson Tasks, Problems, and Activities (attach resource sheets): What specific activities, investigations, problems, questions, or tasks will students be working on during the lesson? Be sure to indicate strategic connections to appropriate mathematical practices. 1. Have students transfer their floor plan design to a coordinate plane. Students should use each of the quadrants and make sure that all vertices are plotted on integer coordinates. Students may have to modify their design slightly in order to transfer the diagram successfully. Allow students access to patty paper, graph paper, rulers, and protractors for this task. If possible or necessary, students can use Geometer’s Sketchpad or Geogebra to recreate their image. 2. Have students devise a method to determine the length of each of their walls and the total perimeter of their floor plan. (NOTE: This can serve as a formative assessment of what students remember from Common Core 8. Do students use the distance formula or Pythagorean theorem? As a class, discuss the different methods used, and review the distance formula and Pythagorean theorem if necessary.) Have students assign an appropriate scale to their coordinates and convert the measurements, using what they know about ratios. Be sure that students specify units. All work can be tracked on the Dream Home Measurements sheet. 3. Have students add a yard, with a pool around their floor plan. Using the coordinates and the scale they created, have students find the perimeter of the yard, the perimeter of the pool, and the area of their yard that would need to be covered with sod. Students may need to cut the yard up into more manageable shapes in order to determine the area. 4. Have students use the prices of fencing, stone and sod to calculate how much the landscaping materials would cost. Work can be tracked on the Dream Home Measurement sheet. HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student achievement. Portsmouth, NH: Heinemann. Lesson Title: ______________________________________________ Course: ___________________________ Date: _____________ Teacher(s): ____________________ Start/end times: _________________________ 5. As a class, discuss the different methods students used to find their measurements and the cost of landscaping. What did students find difficult? What tools were necessary? Was precision an issue? 6. Divide students into small groups or partners, and have them complete as many Coordinate Stations as they can within the time available. If the class is large, you may wish to have a set of the stations posted at the front of the room and an additional set in the back to give students more space. Evidence of Success: What exactly do I expect students to be able to do by the end of the lesson, and how will I measure student success? That is, deliberate consideration of what performances will convince you (and any outside observer) that your students have developed a deepened and conceptual understanding. Students should be able to calculate perimeter and area of given figures using coordinates. Students may use the distance formula or the Pythagorean Theorem to determine distance. They should understand how diagramming situations using coordinates may be helpful in a real-world situation. A student who has mastered this objective should be able to successfully complete the Coordinate Stations, particularly 1-3, with few errors by using the distance formula or Pythagorean theorem. Notes and Nuances: Vocabulary, connections, anticipated misconceptions (and how they will be addressed), etc. Students have used Pythagorean Theorem and the distance formula in middle school, starting in the 20122013 school year. Prior to 2012, students have had exposure to Pythagorean theorem. They should be able to apply these methods in order to calculate perimeter and area in the context of a real-world situation. Students often make computational errors when using the distance formula. Resources: What materials or resources are essential for students to successfully complete the lesson tasks or activities? Homework: Exactly what follow-up homework tasks, problems, and/or exercises will be assigned upon the completion of the lesson? Dream Home Measurements sheets Graph paper Rulers Geometry Software (optional) Stations (to be posted around the room) Have students create a figure with at least five sides and without any 90 angles on a coordinate plane and calculate the perimeter of their figure using the coordinates. As an extension or extra credit, have students calculate the area of the figure. Lesson Reflections: How do you know that you were effective? What questions, connected to the lesson standards/objectives and evidence of success, will you use to reflect on the effectiveness of this lesson? Were students able to use the coordinate plane in order to determine perimeter and area? Did they use the distance formula or Pythagorean Theorem? Were students able to find are on a more complex diagram by cutting the shape into parts? HCPSS Secondary Mathematics Office (v2.1); adapted from: Leinwand, S. (2009). Accessible mathematics: 10 instructional shifts that raise student achievement. Portsmouth, NH: Heinemann.