**I.
****Course
Title: Algebra**

**II.
****Unit:
Graphing Lines**

**III.
****Anticipated
Grade Level:** 7^{th} or
8^{th} 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 *x*Õs
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.

**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