1. Lesson Plan for Math
Prepared for: Summer Bridge Students
Prepared by: Tariqul Islam
March 28, 2014
MATHEMATICS

2. Objective
Cartesian plane, distance formula, midpoint formula, slope, point slope formula, function, and graphs.
Goals
Students should be able to demonstrate their understanding of some basic math concepts such as
quadrants in a Cartesian plane, distance formula, midpoint formula, slope, point slope formula,
function, and some basic graphs.
Cartesian plane
Cartesian plane is a coordinate system that has two axis (x-axis, y-axis), and four quadrants. Example
of a cartesian plane is following…
Distance formula
MATHEMATICS

3. Distance formula can be used to find distance between two given points such that (x1, y1), (x2, y2). To
find the distance between two points we use the distance formula: 𝑑 = √( 𝑥1 − 𝑥2
)2 + ( 𝑦1 − 𝑦2
)2.
Midpoint formula
To find a point that is in the middle of two given points, we use the midpoint formula that can be
expressed as: 𝑚 = (
(𝑥1+𝑥2
2
,
𝑦1+𝑦2
2
).
Slope
Slope represents how a graph is changing its direction. We can also define slope as change in y over
change in x, which can be represented as 𝑚 =
∆𝑦
∆𝑥
=
𝑦2−𝑦1
𝑥2−𝑥1
. For example, if you’re to find slope of two
points (5,3), (2,1), you’d do: 𝑚 =
3−1
5−2
=
2
3
.
Point slope formula
Point slope formula could be found by deriving slope, 𝑚 =
∆𝑦
∆𝑥
=
𝑦−𝑦1
𝑥−𝑥1
 𝑦 = 𝑦1 + 𝑚 (𝑥 − 𝑥1). So, if a
point p = (5,7) and the slope, m= 3 are given, you can write an equation using the point slope
formula.
Solutions: 𝒚 = 𝟕 + 𝟑 ( 𝒙 − 𝟓)  𝒚 = 𝟑𝒙 − 𝟏𝟓 + 𝟕  𝒚 = 𝟑𝒙 − 𝟖
Function
Function is a kind of relation in math where every input has exactly one output in other word, for
every value of x, there is only one y value. If a graph has two y values for one x, that is not a graph of a
function. Example: {(0,1), (0,2)}  not a function because x is repeating; {(5,0), (3,0)} a function
because x is not repeating.
Graphs

4. There are some graphs that student should know for pre-calculus, and calculus I-III are following…

5. Classroom activity
For the classroom activity, I may ask students random questions from what they have learned in the
class. I think asking students about graphs would be a good classroom activity. Before showing them
the graphs above, I may put all of the equations on the board and ask if any student wants to come to
the front to draw graph of any equations that are on the board. This way at least 13 students would be
able to participate in the class by drawing graphs on the board.