Lesson Plan for MathPrepared for: Summer Bridge StudentsPrepared by: Tariqul IslamMarch 28, y

MATHEMATICS

ObjectiveCartesian plane, distance formula, midpoint formula, slope, point slope formula, function, and graphs.

GoalsStudents 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 planeCartesian plane is a coordinate system that has two axis (x-axis, y-axis), and four quadrants. Example of a cartesian plane is following…

Distance formulaDistance 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 formulaTo find a point that is in the middle of two given points, we use the midpoint formula that can be expressed as: m=¿.

MATHEMATICS

SlopeSlope 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− y1x2−x1

. For example, if you’re to find

slope of two points (5,3), (2,1), you’d do: m=3−15−2

=23

.

Point slope formula

Point slope formula could be found by deriving slope,m=∆ y∆ x

=y− y1x−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=3 x−15+7 y=3 x−8

FunctionFunction 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

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

following…

Classroom activityFor 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.