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Work Sample Title Your name: Lesson Title Date of Lesson Topic Grade Level Lesson Length Purpose of Lesson All About Angles: A Lesson Using Geometer’s Sketchpad 2/21/06, 2/22/06, 2/23/06 Using Geometers Sketchpad to study the properties of angles and triangles Pre-Algebra, Grades 6-8 120 min The students become familiar with Geometers Sketchpad as a tool for examining properties of angles and triangles while coming to agreement on properties of angles formed by intersecting lines in the Euclidean plane. The students will be able to… Use Geometers Sketchpad to analyze geometric properties of angles, triangles, parallel, and intersecting lines Identify complimentary, supplementary, corresponding, alternate interior, and alternate exterior angles appropriately Solve for unknown angles using triangles, intersecting lines, and given angles in a linear system Lesson Objectives Corresponding Standards Context of Lesson Materials National Standards State Standards Grades 6-8 Grade 8 Geometry Geometry-Properties and Relationships Analyze characteristics and properties of Investigate triangles and their component parts and draw two- and three-dimensional geometric conclusions about their properties shapes and develop mathematical Determine defining properties that characterize classes of arguments about geometric relationships triangles including side and angle measurements and their Connections component parts Recognize and use connections among mathematical ideas Representation Create and use representations to organize, record, and communicate mathematical ideas This lesson is meant as an entire unit on properties of angles, angles formed by intersecting lines, and triangle properties and classifications. The students are expected to be at least introduced to Geometers Sketchpad prior to this unit, but they need not be overly familiar with the program. Teachers Students (for each student, or pair of students) Computer with Geometers Sketchpad with A computer with the Geometers Sketchpad program display capabilities (optional) Paper Pencil Worksheets (for each student) Work Sample Title Assumptions Resources Used Marzano Strategies Pre-Assessment Formative Assessment Lesson Plan Details Section Time 3-Day Lesson 5 min Your name: Copy of a pre-made Geometers Sketchpad file Students should be acquainted with Geometers Sketchpad and computers in general. Students have been working with geometry terms such as right angle, line, angle, point, circle, triangle, and parallel. Students are familiar with angle measure and two angles being the same measure Students can identify an acute, an obtuse, and a right triangle Geometers Sketchpad, www.keypress.com/catalogue/products/software/sampleActivities/GeometryActivities.html, http://Teacherlink.org/content/math/interactive/geoweb/lessons/angles/home.html Non-Linguistic Representations; Cooperative Learning; Generating and Testing Hypotheses; Cues, Questions, and Advance Organizers Students, prior to this unit (or at the beginning), should be given an assessment similar to the final assessment. Each will start with a review of the information covered in the previous lessons. Formative assessment for this lesson will consist of questioning, review, and the worksheets the students fill out as they progress through the lessons. Teacher Activity DAY 1 (40 min) 1) The two teachers will introduce themselves and explain how the classes will be run. * Students will file into the computer lab and take their seats at the computers. (If there are not enough computers, students need to share) * The class will talk about what they learned thus far on the lesson, asking the students to volunteer information * The worksheets will be handed out and the students will follow the instructions and fill out the worksheets accordingly * When the class is almost over (5 min left), the students will rally again as a class and summarize what they learned that day * Students will turn in their worksheets Student Activity DAY 1 (40 min) 1) The students are listening and following instructions. Teacher Notes Try to keep the students off of the computers, reminding them of what responsible computer use looks like. Work Sample Title Your name: whether they have completed them or not and be dismissed 5 min 2) Teachers instruct students to find a computer and open the Geometers Sketchpad program. The Day 1 worksheet (All About Angles…) is handed out, one for each student 2) Students find a computer, log in, and open Geometers Sketchpad 10 min 3) The class, as a class, goes through the first construction on the worksheet, with the teachers displaying how-to on a projection screen. 3) Students follow along with the teachers and the class on the construction 7 min 4) The class turns to their computers and answers the discussion questions that follow 4) Students work on their own to answer the associated questions 8 min 5) Students attempt to finish and complete the directions on the worksheet. The class can work on the second set of directions as a class if need be. 5) Students work through the rest of the sheet including the second set of directions and questions that follow. 5 min 6) The class closes out the Geometers Sketchpad programs and discusses some questions. * What is a vertical angle? * What can we say about the angles formed by intersecting lines? * What do you call a pair of angles that sums up to 180 degrees? * What is another word for an angle measuring 180 degrees? Hint: It’s straight! 6) The class closes out the Geometers Sketchpad programs and discusses some questions. DAY 2 (40 min) DAY 2 (40 min) All teachers in the room should be monitoring and assisting students Work Sample Title Your name: 5 min 1) Students talk as a class about the important information from DAY 1. The class can review the questions addressed at the closing of the previous day. 1) Students talk as a class about the important information from DAY 1. The class can review the questions addressed at the closing of the previous day. 3 min 2) Teachers instruct students to find a computer and open the Geometers Sketchpad program. The Day 2 worksheet (All About Angles (Cont)) is handed out, one for each student. 2) Students find a computer, log in, and open Geometers Sketchpad 2 min 3) The students are instructed to open a pre-made file called Day2.gsp 3) Students open the correct program on their computers 10 min 4) Depending on the class comfortibility with Geometers Sketchpad at this point, the students can either go through the first set of instructions on the worksheet as a class or individually. 4) Students work through the first set of instructions on the worksheet as a class or individually. 15 min 5) The students work through the remainder of the worksheet, getting as far as they can. 5) The students work through the remainder of the worksheet, getting as far as they can. 5 min 6) The class closes Geometers Sketchpad and logs off of their computers. The class discusses the important aspects of the lesson. * Two Complimentary angles add up to how many degrees? * What are alternate interior angles? * What is the sum of the three interior angles of a triangle? 6) Students participate in discussion, volunteering answers and answering when called upon. Students take home their worksheets for the homework assignment at the end. Work Sample Title 7 min 3 min Your name: DAY 3 (40 min) 1) Students talk as a class about the important information from DAY 2. The class can review the questions addressed at the closing of the previous day. 2) Students go to their computers, open up Geometers Sketchpad, and worksheets are handed out (Exploring Types of Triangles). 20 min 3) The class works through the constructions and associated questions. Again, if the students are having difficulty with the directions for the constructions, the teachers can go through them for the class to follow along. 5 min 4) The class wraps up with some discussion questions for DAY 3. This time, the teachers call on students for their answers to various critical thinking questions from the worksheet, focusing on the topics that were least understood in class. 5 min 5) The class goes over the main points of the last three days working with Geometers Sketchpad. Some terms to revisit are complimentary, supplementary, vertical angles, alternate interior angles, alternate exterior angles, corresponding angles, degrees in a triangle, scalene, 1) Students talk as a class about the important information from DAY 2. The class can review the questions addressed at the closing of the previous day. Students also turn in their worksheets and associated homework pages from DAY 2. 2) Students go to their computers, open up Geometers Sketchpad, and worksheets are handed out. 3) Students follow the instructions on the worksheets and ask questions of the wandering teachers if needed. 4) Students participate in discussion, asking questions and providing answers. 5) Students give answers and clear up any misconceptions or questions they may have at the end of this unit. Work Sample Title Your name: isosceles, and equilateral Homework Evaluation Plan Students also hand in their third worksheet, completed or not. DAY 1 - None DAY 2 - End of Worksheet Day 3 - None Most of the evaluation will be formative, unless the teacher does a formal summative assessment after the unit is completed. The worksheets, questions, and homework act as assessment for this class. Notes: Lesson Objectives: Write out the lesson objectives completely; don’t just refer to them by number. Context of Lesson: How does this lesson fit in with the previous lesson? How does it lead up to the next lesson? Pre- and Formative Assessments: Some lessons may not include these. Lesson Plan Details: Include questions you plan to ask along with acceptable answers in the Teacher Activity section. Teacher notes: Include organization and management strategies. May also include background notes on content. Extensions: How will you extend the lesson for students who finish early or need further challenges? Homework: Describe the homework assignment AND its purpose. Evaluation Plan: How will you know which students met the objectives? How will you help those who didn’t get ready for the next lesson?