I.               Course Title:  Algebra

II.             Unit: Graphing Lines

III.           Anticipated Grade Level:  7th or 8th grade.

 

IV.           Lesson Objectives: Students will be able to graph a variety of lines given a point slope equation of a line.  Students will also be able to write point slope equations given a point and a slope.

 

V.             Prologue: My lesson plan is designed to use the Direct Instruction Model.  My introduction relates directly to the last class period in order to promote learning in the form of making connections.  I have a great warm up activity where the students get to plot lines in a very new and exciting way.  The students will use my computer and the GeometerÕs Sketchpad program to digitally graph lines.  This will be fun for the students because the program is new to them and is extremely interactive.  The actual content from the warm up also reviews previous material and creates a lead in for the new material, and simultaneously relates the content to the real world application of graphic design.

I also have an extremely organized and detailed presentation in which I demonstrate the material with definitions and examples and then give examples for guided practice and independent practice.  The examples vary and highlight the different properties of the definitions so that the students can gain an in depth understanding of the content.  I will also be able to alter the pace of my lesson to better suit the students by my use of assessment throughout the lesson.  I will assess using a thumbs up strategy, listening to student responses and questions, observing work on examples, and grading a well designed homework.

I also have hints of constructivism in my lesson.  In my lesson, I ask students to make conjectures about what they expect or think should be the outcome or the next logical step.  I will use these student-generated ideas to shape the definitions of the lesson.  I also ask the students to think about and come up with a conjecture about an untaught concept for the next class.  This part of the lesson relies on the students to take ownership and control of their learning. 

 

VI.           Curricular Material:

a.     I have created an original handout homework sheet.  The homework sheet contains instructions, and ample space to do what is asked.

b.     A PowerPoint will also be paired with the introduction of the lesson to give the students a visual aid to promote learning.

c.     I also have prepared a note card for each student with a point and slope.  The students will take their card to the board and attempt the graph the line for the class and I to see as an active warm up exercise.

d.     To be paired with the note card I have created a simple coordinate axis on a computer program that will allow the students to graph lines on the computer to be projected onto the screen.  I have done this because it is more exciting than just graphing them on graph paper or the board.  It also involves technology in the classroom.

 

 

VII.         Content:

a.     Review:

                                               i.    

                                             ii.     Rise is the change in y

                                            iii.     Run is the change in x

b.     New Content:

                                               i.     Slope intercept equations:  where m is the slope and  is a point. 

                                             ii.     Take a given point and slope and substitute into the formula to create an equation of a line.

                                            iii.     We can also take an equation of a line to graph a line.

1.     Look at the equation and find the given point and slope.

2.     The slope will be multiplied with the xÕs and the points will be subtracted from x and y respectively.

a.     If it is  then the point is a positive 2.  If it is  then the point is a negative 2, because a negative minus a negative is a positive.

 

VIII.       Instructional Procedures:

a.     Before class begins: generate the coordinate axis and three lines graphed from the previous class. Slide One

b.     Introduction:  Remember last time we had class we focused on how to graph lines given a point and a slope.  Well, today we are going to extend this concept and find a general equation to represent a line.  But first, I want everyone to wake up with a warm up exercise.

c.     Warm Up:  Slide Two Everyone is going to get a note card with a point and a slope.  One at a time I want you to come up and graph your line on our coordinate axis.  This will help us review and wake up.  HereÕs how we are going to graph the linesÉ on the computer Open Sketchpad and demonstrate how to graph the lines for the first four. 

                                               i.     Help students graph their lines on the computer program by asking guiding questions when necessary. 

                                             ii.     Ask the students if they see any hidden messages in the graph on the board.  The M will be revealed.

1.     Erase the excess lines, and tell the students that this is a very simple, but relevant example of how graphing lines can be used in graphic design.

d.     After the warm up:

                                               i.     What if we want to represent a line with just one piece of information, instead of two, such as a point and slope?

1.     Accept student suggestions and guide them to the idea of an equation of a line.

                                             ii.     In the real world, where do we see or use lines and their equations?

1.     Maybe you are a scientist and want to find the relationship between sunlight and the growth of plants.  Or rainfall and the growth of plants.

a.     So the sciences use equations of lines to graph and record relationships between two variables.

2.     Maybe you want to record the relationship between how many hours you get to sleep and your grades in school Slide Three. 

a.     Draw a graph of a possible sleep vs grade relationship.

b.     So we could use graphs of lines and their equations in our every day life. 

                                            iii.     Today we have the following lesson objectives Slide Four:

                                            iv.     And once again, throughout the lesson IÕm going to be asking to see your thumbs Slide Five.

e.     Content:  So if we have determined we want to represent a line in an equation, what kind of information do we want to have in that equation?  What do we want to relate?

                                               i.     Accept student suggestions and guide them to wanting to represent a slope and a point in an equation, because we know how to graph lines with points and slopes.

f.      The way we can represent a point and a slope in a single equation is called point slope form.  We write point slope form as:  where  is a point and m is a slope.

 

g.     Write:  So what do we need if we wanted to write these equations ourselves? 

                                               i.     All we need to know is a point and a slope and then we can substitute into the formula to find an equation.

h.     Examples:

                                               i.     Point: (1, 1), Slope: -2

                                             ii.     Point: (0, -2), Slope: .

i.      Now try these at your seat.  Talk with your neighbor if you would like and I will be around to help.

                                               i.     Point: (2, 1), Slope: .

                                             ii.     Point: (0, 0), Slope: 1.

 

j.      Graph:  Good, now that we know how to write these equations and recognize the different parts of them, what do you think the next thing we want to be able to do is? 

                                               i.     We want to graph a line using these point slope equations.

                                             ii.     How do you suppose we do this?

1.     We can look at an equation in point slope form and pull out or find a point and slope.  With this point and slope we can then graph the lines.  Just as we did last class, and in the warm up. 

 

k.     Examples:

                                               i.    

1.     Point: (3, 2)

2.     Slope:

                                             ii.    

1.     Point: (1, -2)

2.     Slope: 5

                                            iii.    

1.     Point: (-4, -2)

2.     Slope:

l.      Now try these at your seat on your graph paper.  Again, talk with your neighbor if you would like.  IÕll be around to help if you need it.

                                               i.    

                                             ii.    

                                            iii.    

 

m.   Good, it seems every body is really getting the hang of point slope form.  Can anybody foresee any time or situation where we would not be able to use point slope form?

                                               i.     Accept student suggestions, while guiding them to the idea of undefined or zero slope.

n.     The problems that we would run into would be when the slope is undefined or zero.  This is because our point slope form would look like this:

                                               i.     , or

                                             ii.      which would equal y = 0. 

o.     For the next class I want you guys to think about possible ways or methods we could use to overcome these two situations. 

p.    Also, for the next class, since you need to practice, I want you to complete this homework sheet where you will practice graphing lines from point slope form equations and writing equations from a given point and slope. 

HH

IX.           Closure: 

a.     The closure of this lesson will be the summary of what we did in class today.  I will go over the key points and the lesson objectives again.  I will also talk about how we reached our lesson goals.  I will also remind the students of the real world applications of finding equations of lines. 

b.     Another closing segment of my lesson will be when I ask the students to think about a special situation when a point slope equation would not work.  This will require the students to apply all that they have learned from the lesson, and use critical thinking strategies to come up with a conjecture.

 

X.             Assessment and Evaluation:

a.     The students will self assess throughout the entire lesson, by constantly having to think whether or not they should have their thumbs up or thumbs down. 

                                               i.     When I ask to see their thumbs the students have to think about whether or not they understand enough to give a thumbs up or if they need to call attention to the fact that they need more instruction

                                             ii.     As a teacher this is a good, quick way to see if students are understanding and comprehending the material throughout the lesson. 

                                            iii.     In order to make this strategy effective however, I must carefully choose my placement and frequency of asking to see their thumbs.  If I ask too many times it will become a joke and the students will not think about their understanding, but rather, just have an automated response.

b.     I will be able to assess the students throughout my lesson by listening to and interpreting their responses to my questions.

1.     If students give appropriate and on target responses I know that the material is being comprehended.

2.     If responses are limited and off target I know more instruction is necessary. 

c.     I will also be able to assess students during independent work, when they work through examples of the material covered in that segment of the class.  I will be able to assess all of the students while I circulate the room.

d.     I will also be able to assess the students individually as they come to the computer and attempt to graph their lines.  This assessment will not just be a total hit or miss like the thumbs up and down assessment, but I will be able to monitor varying levels of comprehension and ability.

e.     My final form of assessment will come in terms of homework.  The homework problems given are attached.  The homework has the students practicing similar but not exact problems that were demonstrated in class.  The slight differences will be important for me to be able to measure understanding, because understanding is different than being able to copy examples from class.  If the students understand they will be able to apply the concepts to new problems. 

 

Green = Slide Show

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