8 th Grade Pythagorean Theorem Lesson

Transcription

1 8 th Grade Pythagorean Theorem Lesson Date(s): October 4, 2010 Course: EDS 541 Teaching Practicum Contents: Lesson Plan from 10/04/10 lesson Observation Report by K. Colossale from 10/04/10 lesson

2 Lesson Plan Template Lesson Information Subject: Period / Time: Date: Grade: Name: Mathematics 2 nd, 3 rd 10/04/ Schomaker/Dawson Goal for Lesson: Topic: Standard(s): Transition from unit on square roots and exponents to new unit on right triangles and the Pythagorean Theorem. Make connections between old and new units Right Triangles, Squares and the Pythagorean Theorem M8G2: b. Recognize and interpret the Pythagorean Theorem as a statement about areas of squares on the sides of a right triangle Materials and Resources: Understanding(s): What deep understanding will students have as a result of this lesson? Essential Question(s): What ideas or concepts will students seek answers for during this lesson? Knowledge and Skills: Performance Task: How will students be assessed? Task / Activity: Consider what Quality Plus Teaching Strategy will best support this task or activity ActiveInspire flipchart, Notes pages, 5x5 grids Students will understand that line segments can be measured through construction of right triangles and use of the Pythagorean Theorem. How do the sides of a square relate to the side of a right triangle? Time: :05 Sequence of Activities Description (provide step by step instructions to include teacher activity, student activity, and transitions): Warm Up: Display warm up on the active board. Use word document October4WarmUp.docx. Give students 5-10 minutes to complete the activity. Review: Work problems from the warm up Engage Students / Hook: How will I begin so that students are engaged? :10 Have two students stand in opposite corners of the room and pose question to the class about how we might determine the distance between students without physically measuring it. Pose 1

3 Lesson Plan Template Lesson Introduction (I Do, You Watch): How can I best teach new concepts, content, or skills to students to ensure they learn? How can I model strategies or techniques for students? What visual tools or organizers would assist students in grasping new concepts? Guided Practice (I Do, You Help You Do, I Help) Can students describe what you modeled for them and why? What steps can you take to have students practice the strategy? How will you check for understanding? question about how surveyors measure lots w/out use of physical measure, or astronomers and distances to the Moon and planets. :15 Hand out one notes sheet to each student Show active flipchart presentation, called Pythagorean_Theorem_ flp. Have students take notes Skip skills check questions already covered during warm up. STOP at slide showing geometric proof of the Pythagorean Theorem. Make a connection with previous unit about squares and sides and square roots :10 Open the FivebyFiveDotGrid.pdf file into a new active board window. Start with simple examples of segments and ask students how long the segment is. Show how long the segment is by creating a square on the grid and calculating the area of the square and taking the square root to find the side or segment length. This will be easy at first w/ squares with area = 1, 4 and 9. Note: students may want to count the number of dots to determine the length of a side rather than the number of unit segments. Independent Practice (You Do, I Watch) What independent task(s) will students demonstrate understanding of the concept or strategy? Did I word directions clearly so students can understand? Did I provide written directions for students to refer back to at another time? Closing / Wrap- Up / Reflect / Review :10 :05 Progress to more difficult examples, such as a diagonal segment w/ length sqrt(2) or 2sqrt(2). Invite students to come up to the board to work out one example with square with area = 8 square units, shaped like diamond with vertices at midpoints of a five- by- five dot grid. Segment runs from midpoint of left column of grid to midpoint of top row of grid. Let them figure out a strategy for calculating the area of the square with the segment in question as one side. Segment length = 2sqrt(2) Now work some of the same segment problems, but this time 2

4 Lesson Plan Template How will students summarize and share their learning? What reflective questions will help students think deeply about their learning? How will you connect back to the Essential Questions or Understandings? Is there a product that should be turned in? How will that product be collected? When will you assess student learning? use the Pythagorean theorem to calculate the segment length. Hand out homework sheet on calculating segment lengths using areas of squares. Let students know that each segment length can be calculated using the area measuring techniques shown in class, but that there is a short cut using an important theorem about right triangles. 3

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