Parallel+and+Perpendicular+Lines

=__ The Importance of Parallel and Perpendicular Lines __=


 * TEACHER CANDIDATES: ** Jeff Conner, Samantha King, Kelly Rang, Sean Ruane
 * GRADE LEVEL & SUBJECT: ** 9th Grade Geometry

INTRODUCTION:
The purpose of this unit is to familiarize students with the applications of properties of parallel and perpendicular lines using mathematical technology.

OVERVIEW:
During this lesson students will learn the definitions of parallel and perpendicular lines. They will also become more familiar with the properties of parallel and perpendicular lines through the use of the program Geometer’s Sketchpad.

__ Standards: __// Mathematics: //
G.2.: Students study basic properties of parallel and perpendicular lines, their respective slopes, and the properties of the angles formed when parallel lines are intersected by a transversal. They prove related theorems and apply them to solve both mathematical and practical problems.

// Educational Technology: //
1. INTEGRATION: Students use technology within all content areas to collaborate, communicate, generate innovative ideas, investigate and solve problems.

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 * 1.1 Innovate: Demonstrate creative thinking, construct knowledge and develop innovative products and processes using technology.
 * 1.2 Collaborate: Use digital media and environments to communicate and work collaboratively to support individual learning and contribute to the learning of others.
 * 1.3 Investigate and Think Critically: Research, manage and evaluate information and solve problems using digital tools and resources.

//Communication//:
1. The student uses listening and observation skills and strategies to gain understanding.


 * 1.1 Uses listening and observation skills and strategies to focus attention and interpret information.
 * 1.2 Understands, analyzes, synthesizes, or evaluates information from a variety of sources.

Students will be able to:

 * 1) Define and describe what it means for lines to be parallel.
 * 2) Provide real-world examples of parallel lines.
 * 3) Define and describe what it means for lines to be perpendicular.
 * 4) Provide real-world examples of perpendicular lines.
 * 5) Comprehend the properties of parallel and perpendicular lines.
 * 6) Calculate and compare slopes to determine of lines are parallel or perpendicular.

** ASSESSMENT STRATEGIES: **

 * Formative ** : Active participation, paying attention, following directions, periodically ask questions to check for understanding before moving on (if not fully understood, follow with more examples).
 * Summative ** : Worksheet (provided below), quiz, or test at the end of the unit. Use grading rubric to determine full or partial credit (also provided below).


 * GROUPING OF STUDENTS FOR INSTRUCTION: **

A combination of individual class instruction and collaborative learning.

Geometer’s Sketchpad, graphing calculator, paper, pencil.
 * INSTRUCTIONAL MATERIALS, EQUIPMENT, AND TECHNOLOGY NEEDED: **


 * PRIOR KNOWLEDGE AND SKILLS: **
 * General concept of slope
 * Formula to calculate slope
 * General linear equations
 * Basic knowledge of angles
 * Some familiarity with Geometer's Sketchpad


 * NEW KNOWLEDGE: **
 * Parallel lines
 * Perpendicular lines

Students will enter the computer lab and log into their computers.
The teacher will:
 * Writing directions on the white board
 * Demonstrating on projector
 * Explaining log in procedure
 * Assisting students logging in

▪ http://www.youtube.com/watch?v=-3ODe9mqoDE
The teacher will:
 * Plays video on projector
 * Explaining video clip

▪ If students do not know, the teacher will explain what these slopes using all three methods:

 * Writing equation on the white board
 * Demonstrating on projector
 * Leading class in other examples

Students will open the Geometer’s Sketchpad program and turn on the coordinate plane.
The teacher will:
 * Writing directions on the white board
 * Demonstrating on projector
 * Explaining how to find GSP
 * Assisting students in opening GSP

▪ If students do not know properties, teacher will give some examples of parallel lines in the real world the teacher will:

 * Writing properties on the white board
 * Lead the class in another example

▪ If students cannot figure out how, teacher will show properties by:

 * Writing properties on the white board
 * Lead a discussion in another example.

▪ Two lines are perpendicular if they form right angles (90 degrees).

 * Writing definition on the white board
 * Communicate definition

▪ If students cannot figure out how, the teacher will show them on Geometer’s Sketchpad and:

 * Writing directions on the white board
 * Explain how to construct the figure

▪ Students will then verify their conjectures using Geometer’s Sketchpad. Teacher will:

 * Demonstrate on white board
 * Show other examples when needed

▪ Students must turn the worksheet in for grading the following day. The teacher will:

 * Write assignment and due date on white board
 * Explain assignment and due date
 * Pass out worksheet, answer student questions
 * Pass out worksheet, answer student questions

** Video Used **
Tron Light Bike Race

** Pictures Used **






** Extension **
We will briefly summarize parallel and perpendicular lines, in particular the 90 ° angles that they make. We will then review complementary and supplementary angles (which they have already learned about) with emphasis on the fact that there are 180 ° in a line, and then relate them to these concepts. From here we will introduce the concept of a transversal with a quick example followed by a worksheet.

The worksheet will contain the information discussed above, as well the following transversals with angles that they will calculate for homework. In particular, one of the transversals is perpendicular to the parallel lines, intersecting with another transversal, requiring them to use the 90 ° angles to determine other unknowns.



They will be given that A || B, that D is perpendicular to each, noted by angle m = 90 °. They will also be given the values of angles a and s. Their copy will be in black and white, and will not have square angle markers for the 90 ° angles.

Note that angles of the same color are equal in value, and there are several different ways in which the students can determine angles i, j, k, and l.

** Teacher Reflection **
Starting the lesson with the “Tron” video clip and class discussion about parallel and perpendicular liens in the real-world was effective and engaging for the students. Although our introduction made the lesson meaningful, we should have told the students exactly what the lesson was going to be and what they were expected to know by the end of the period.

By writing the unit's vocabulary words and definitions at the beginning of the period students were able to visualize and connect the vocabulary of the unit. However, we should have kept the definitions written for the whole period and in order to continually connect the lesson to the vocabulary.

Using Geometer's Sketchpad was also effective because it allowed the class to quickly visualize parallel and perpendicular lines. By breaking the class period into manageable tasks, students were continually engaged and busy during the lesson. Overall we believe our formative assessments were effective at checking for understanding, but that we may have covered the material too quickly for a freshman math class.