Lesson Plan 2

Coordinate GeometryLesson 3Name: Kelly Griffin Date May 3, 2004Today’s Lesson: DAR with manipulatives and cooperative groups: Slopes of Paralleland perpendicular lines.Unit Topic: Coordinate Geometry Course: Math 1NYS Mathematics, Science, and Technology Learning Standards AddressedStandard 1: Students will use mathematical analysis, scientific inquiry, andengineering design, as appropriate, to pose questions, seek answers, anddevelop solutions.Standard 3: Students will understand mathematics and become mathematicallyconfident by communicating and reasoning mathematically, by applyingmathematics in real-world settings, and by solving problems through theintegrated study of number systems, geometry, algebra, data analysis,probability, and trigonometry.Standard 6: Students will understand the relationships and common themes thatconnect mathematics, science, and technology and apply the themes to these andother areas of learning.Standard 7: Students will apply the knowledge and thinking skills ofmathematics, science, and technology to address real-life problems and makeinformed decisions.ObjectivesMaterialsStudents will recall their previous knowledge of y = mx + b form andapply this knowledge in order to compare horizontal and vertical lines inorder to discover the form of their equations as well as their slopes todetermine a significant difference (Knowledge, Synthesis, Application)2 page group task sheet- 1 per student (There should be a different versionof the worksheet for each group)Geo boards for each studentGeo board overheadProblem Sheet- 1 per studentGriffinLesson 31

Anticipatory Set“We have learned how to put an equation in y = mx + b form andhow to graph this type of equation. Let’s use this knowledge todiscover what happens to two equations with the same slope oreven similar slopes.”Lesson Body1. ExperimentingI will split the class into groups of 4 and instruct each group to assign a communicator, arecorder/time keeper, a materials person, and a reporter. I will instruct the materialssupervisor to make sure their group has 4 geo boards as well as rubber bands. I will meetwith the communicators and explain to them the following:- For each section put the 4 geo-boards together, connect them and choose youraxis near the middle.- Use a different color rubber band for each of the functions and create the graphon the geo board.- Draw the graph on the grid provided.- Once you are done with both grids, discuss the similarities of the equationsand of the graphs and try to make a general conclusion. (This includescompleting the questions for that section).2. Reflecting and ExplainingAfter the first page is complete, I will bring the group back together and ask each group’sreporter to share their findings. The reporter will use the overhead geo board to showwhat their graphs looked like. The other students will check that their graphs match thestudent reporter’s. The students will then complete the second page of the worksheet andthis will be repeated for that page. I will be sure to ask the students “what conclusions canwe make about the relationship between the graph and the equation of a line so far?”3. Hypothesizing and ArticulatingOnce each group has reported their findings, I will use these graphs and lead the studentsto a general idea of what is happening in each case. I will ask them “what are the generalsimilarities of the graphs in the first group?” “what about the second group?” I will alsoask “can you come up with a general thesis about what is happening?” Once we havediscussed both sections, I will ask the students “why do you think there is a directrelationship between a slope and graph of an equation?” and “in what ways can we besure our conclusion is correct?”4. Verifying and RefiningGriffinLesson 32

I will give the students practice problems to work on within their small groups. I willalso ask them to create their own examples of parallel lines and perpendicular lines.They should complete part A and create 2 parallel pairs and 2 perpendicular pairs in partB. As they work on these questions, they should check that our general thesis works inevery case. Once they are done with these practice problems, we will discuss the resultsas a class and finalize our decision about our thesis.Closure“When an equation is in y = mx + b form, the following generalizations can be made:Two lines are parallel if their slopes are equalTwo lines are perpendicular if their slopes are negative reciprocals.”Homework/AssessmentStudents should complete the questions part C and create 2 more examples of eachparallel pairs and perpendicular pairs from the in class practice sheet (also part C).ExtensionsGriffinLesson 33

Name ___________________Date ____________Worksheet – Slopes of parallel and perpendicular linesGraph the following functions on the same grid: [Note: Each group willreceive different equations to graph]Grid 1 Grid 2y = xy = 3xy = x + 1 y = 3x + 2y = x – 4 y = 3x + 5y = x + 4 y = 3x - 1y = x - 2 y = 3x – 3Observations:1. What is the same about the equations on grid 1? Grid 2?2. How do the graphs of each equation on grid 1 compare to each other? Grid 2?GriffinLesson 34

Graph the following functions on the same grid:Grid 1 Grid 22y = 2x + 1 y = x − 431 3y = − x + 3y = − x + 222Observations3. How do the equations of each pair compare?4. What do you notice about the graphs of each pair?GriffinLesson 35

Name________________________Practice/ Homework – Parallel and perpendicular linesDo the following problems on your own sheet of paper.Part ADetermine whether the following pairs are parallel or perpendicular and explain why.y = x − 71. 2.y = x + 171 15y = x −2 163.y = −2x+ 224x= 2y− 41y = − x + 824.5x= 3y−1y =5x + 63Part BCreate two of your own pairs of parallel and perpendicular lines and explain why they fitour definition.Part C5.y = 7x2 − 41y = − x − 476.14 = 3x− y− 3y= x7.y = 5x− 6− 5x+ 10 = − y8.4 1 7x = − y +3 2 820 155y− = x3 89.19y= x − 731y = 9x+ 5310.15y= 3x+ 55x= − y + 13Create two more pairs of parallel line and two more pairs of perpendicular lines andexplain why they fit our definition.GriffinLesson 36