Angles and Transversals

Lesson Notes
Calculator Notes
Homework Sheet
Student Sample One
Student Sample Two
Student Sample Three

Name: Lori D. Rafferty
Grade: 8
School: Ogdensburg Free Academy

1. Title/Context Of Learning Experience
   The objective is to investigate the relationship of angles formed when lines are cut by a transversal. The exploration investigates angle relationships when two parallel and two non-parallel lines are cut by a transversal.

   Learning Standards and Performance Indicators:

   Process:
   8.RP.2 - Use mathematical strategies to reach a conclusion
   8.CM.1 - Provide a correct, complete, coherent, and clear rational for thought process used in problem solving
   8.CM.4 - Share organized mathematical ideas through the manipulation of objects, numerical tables, drawings, pictures, charts, graphs, tables, diagrams, models and symbols in written and verbal form
   8.CM.9 - Increase their use of mathematical vocabulary and language when communicating with others
   8.CN.4 - Model situations mathematically, using representations to draw conclusions and formulate new situations
   8.R.1 - Use physical objects, drawings, charts, tables, graphs, symbols, equations or objects created using technology as representation
   8.R.6 - Use representation to explore problem situations

   Content:
   8.G.1 - Identify pairs of vertical angles as congruent
   8.G.4 - Determine angle pair relationships when given two parallel lines cut by a transversal
   8.G.5 - Calculate the missing angle measurements when given two parallel lines cut by a transversal

   The students will need to know the difference between parallel and non-parallel lines. They will also need to know what supplementary and vertical angles are.

2. Essential Question
   What types of angles are formed when two lines are cut by a transversal?
3. Assessment Plan
   Rubric used to grade homework:
   2 - Consistent and appropriate use of mathematical vocabulary; appropriately identified angle pairs and their measurements
   1 - Some appropriate use of mathematical vocabulary; shows some understanding of naming angle pairs and measurements according to directions
   0 - Did not use mathematical vocabulary appropriately; could not name angle pairs and measurements according to directions
4. Procedure
   Pass out notes; state objective; review supplementary and vertical angles.

   Discuss the new vocabulary on the first page of the notes, giving students enough time to complete the first page. I will then review the answers with them in order to check for understanding.

   Discuss the new vocabulary on the second page of the notes, giving students enough time to complete this page. I will then review the answers with them in order to check for understanding.

   The students will then turn their graphing calculators (TI-84 Plus) on and I will guide them on how to turn on Cabri Jr. The construction will be loaded on every calculator before class begins. The students will be given a handout with all the calculator instructions listed.

   The students will .open. the construction named .PAR.. I will have the construction visible on the views screen panel.

   I will guide the students through the rest of the notes, carefully explaining how to use the graphing calculator.

   The students will be asked to measure

   I will check for understanding by reviewing the vocabulary from the notes and discuss the angle measures they see on their graphing calculators.

   The technology enhances the learning because it allows the students to measure the angles themselves and get a better understanding of the relationship of angles formed when a transversal cuts through parallel lines.

5. Resources
   Student -
   • graphing calculator (TI-84 Plus)
   • notes

   Teacher -

   • graphing calculator (TI-84 Plus)
   • View Screen Panel for the overhead
   • overhead notes, (notes were taken from Cabri Jr.: Interactive Geometry Activities and Investigations; written by Charles Vonder Embse and Eugene Olmstead; published by Texas Instruments)
6. Instructional/Environmental Modifications
   The construction was transferred onto each calculator before beginning the lesson. The construction would take a great deal of time for the students to do completely. Because the objective is for the students to investigate the relationship of angles formed when lines are cut by a transversal, I felt that it was important for them to spend as much time as possible investigating the angles rather than constructing the figure.
7. Time Required
   Two 40-minute periods
8. Reflection
   I believe that using the graphing calculator to investigate the relationship of angles formed when lines are cut by a transversal is a good way to teach this lesson. It was important for the students to discover that the lines must be parallel in order to form certain angle relationships. They were more involved with the lesson than similar lessons in the past. They really enjoyed using the graphing calculator.
   When I teach the lesson next year, I will spend a day to introduce the necessary vocabulary before using the graphing calculator. I think that the lesson would have gone more smoothly if the students had prior knowledge of the types of angles formed when two lines are cut by a transversal. The students had a difficult time with the new vocabulary and trying to use the calculator.