Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
AGENDAS FOR THE WEEK: September 30 – October 4 MONDAY Objective(s): SWBAT *complete an assessment evaluating their understanding of the material covered in Chapter 2 TUESDAY WEDNESDAY Objective(s): SWBAT * identify skew and parallel lines, planes, and lines cut by a transversal *classify types of angles created by a transversal *use prior knowledge to prove theorem 3-1: If two parallel lines are cut by a third plane, then the lines of intersection are parallel. Objective(s): SWBAT * use technology to identify the relationship between angles and parallel lines cut by a transversal * solve problems using the properties parallel lines Objective(s): SWBAT * use technology identify the relationship between angles and parallel lines cut by a transversal * solve problems using the properties parallel lines Objective(s): SWBAT *prove that two lines are parallel by using theorems and postulates outlined in Ch. 3-3 CCSS/NGSSS: CCSS/NGSSS: MACC.912.G-CO.1.1: 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. MACC.912.G-CO.1.1: 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. MACC.912.G-CO.3.9: Prove theorems about lines and angles. CCSS/NGSSS: MACC.912.G-CO.1.1: 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. THURSDAY FRIDAY CCSS/NGSSS: MACC.912.G-CO.3.9: Prove theorems about lines and angles. MACC.912.G-CO.3.9: Prove theorems about lines and angles. CH. 2 TEST TODAY P Move students’ desks to face the front of the room, rather than in their groups. Test forms A and B can be distributed amongst the students in each class to further deter the temptation to cheat. Engage Engage Engage Engage Bring in a cereal box modeling parallel planes cut by a third plane as visuals for the students. Ask them at the beginning of class, what does a cereal box have to do with geometry? Based on their homework students should be able to name the types of lines and planes contained in the construction of the box. Show students the optical illusion with parallel lines. A lot can be done with parallel lines, and with the addition of surrounding shapes and colors, one can change the effect that the image has on the human eye. Display the math humor about parallel lines on the board for students as they get settled at the beginning of class. Have a student volunteer come to the board and explain to the class how he/she completed the proof from last night on the SmartBoard. TI-Nspire Warm-up: Have students answer the questions outlined in the Warm-up document on their TI-Nspires. Discuss the answers together as a class. TI-Nspire Warm-up: Have students answer the questions outlined in the Warm-up document on their TI-Nspires. Discuss the answers together as a class. TI-Nspire Warm-up: Have students answer the questions outlined in the Warm-up document on their TI-Nspires. Discuss the answers together as a class. Students will have the whole class period to complete their tests. Elaborate *Online Homework: students will watch the following You Tube video http://www.youtube.com/watch ?v=Q2ByDKh7Y0g on the definitions concerning parallel lines and planes, via the course website. L Explore Explore Explore Explore Students will be working in teams to complete the parallel lines and planes activity worksheet. Ex. 1 Students must name the angles created as alternate interior, same-side interior, or corresponding angles. Ex. 2 Students will be drawing a six sided box and using it to classify types of lines in relation to each other. Ex. 3 Students will then use their knowledge of definitions, properties and theorems to prove theorem 3-1 in the textbook: If two parallel lines are cut by a third plane, then the lines of intersection are parallel. The students will engage in a TI-Nspires activity in which they will explore and observe the properties of angles creates by parallel lines cut by a transversal. Students will follow directions given to them to complete an activity sheet that corresponds to the TINspire activity—instructing them on what to do, and asking probing questions for them to consider. Address terms such as linear angles versus supplementary angles. Wrap up the TI-Nspires activity from yesterday in which they will explore and observe the properties of parallel lines cut by a transversal. Students will be working in groups to complete the 3-3 Proofs worksheets. Circulate throughout the room answering any questions students may have, and posing probing questions to them. (Students will be saving their document in the folder that corresponds to their period, so that they will be able to pick up where they left off tomorrow, if necessary) Elaborate Explain Call student’s attention to the front of the room. Display each problem/diagram on the SmartBoard for students to see. Call on volunteers to come to the board to explain their reasoning for classifying the lines and angles in the diagram. For the last exercise, pass around a 3-D model of the figure described by the theorem, for students to physically see. Explain After the activity/during the activity call students’ attention to the board to discuss their results and observations after certain important concepts arise. (i.e. When two parallel lines are cut by a transversal, corresponding angles have the same angle measure.) Elaborate If time remains, have students use classroom protractors to measure the angles formed by the transversal and the parallel lines in the first exercise. Students will begin to see a trend occurring as they record the angle measurements. This activity serves as a great Segway Address the theorems from last night (3-2) that pertain to the activity on parallel lines. Prompt students to take notes and/or refer to their notes from last night. (*Note: Students will probably not finish the activity. Provide them with a brief overview of the new concepts that they have Explain Call students’ attention to the front of the room to review their results, and discuss their findings. Elaborate on the theorems and postulates that pertain to their results. Continue to discuss the theorems and postulates in Ch. 3.2 and 3.3 as a class by having students work a couple proofs at their desks presented to them on the SmartBoard (these proofs are listed in the in-class proofs document). Then take a volunteer to come to the SmartBoard to explain/teach the class their reasoning. Pass out the 3-3 Worksheet, and have the students work in their groups to complete. Circulate throughout the room answering questions and asking probing questions. Most likely students will not be able to get through the entire worksheet. Pick a few harder questions that multiple groups had questions about to work together as a class on the board. Students should complete the worksheet, if Explain Students will volunteer to come to the SmartBoard to explain each proof. (Advanced Prep: The teacher should copy and paste the proofs into a SmartBoard document so that students will be able to fill in the blanks with the pen tool, while “teaching” the class. The teacher should clarify student reasoning for further understanding. Elaborate *Online HW: Students will be taking notes on the following proof of the theorem: the sum of the measures of the angles in a triangle is 180 degrees. You Tube video: https://www.khanacademy.or g/math/geometry/paralleland-perpendicularlines/triang_prop_tut/v/proof--sum-of-measures-of-anglesin-a-triangle-are-180 into tomorrow’s exploration on properties of parallel lines! discovered, and continue where they left off tomorrow) they hadn’t already done so, as homework in addition to the proof discussed below. *Online HW: Students will be taking notes on the 3.2 You Tube video: http://www.youtube.com/watch? v=AztmdWk_BF4 given to them via the course website, as well as the 3-2 PowerPoint Elaborate Evaluate and Summary Evaluate and Summary Evaluate and Summary Evaluate and Summary The evaluation of tonight’s homework will be assessed in tomorrow’s warm-up. The evaluation of tonight’s homework will be assessed in tomorrow’s warm-up The evaluation of tonight’s homework will be assessed in tomorrow’s warm-up Students will be completing a proof given to them via the online website, and bringing it to class tomorrow. Chapter 2 Tests (form A and B) Warm-up Questions Parallel Lines & Planes Worksheet 3-2 PPT TI-Nspires Protractors Cereal Box Intersecting planes model Warm-up Questions TI-Nspires Activity Sheet TI-Nspires directions 3-3 PPT TI-Nspires Math Humor Warm-up Questions TI-Nspires Activity Sheet TI-Nspires directions In-class proofs 3-3 Worksheet Online HW: Proof TI-Nspires Students will be taking notes on the 3.3 video given to them via the course website. You Tube video: http://www.youtube.com/watc h?v=ubDalX0vokQ as well as on the 3-3 PowerPoint slides. A N Resources: Evaluate and Summary 3-3 Proofs Worksheet SmartBoard