lp in geometry

A Detailed Lesson Plan in Mathematics IIIGeometry

I. ObjectiveAt the end of an hour class discussion, 85% of the students are expected to:a. identify the parts of a coordinate plane;b. participate actively in the activity using coordinates; andc. plot the coordinates in a Cartesian plane.

II. Subject Mattera. Unit: Chapter 7: Plane Coordinate Geometryb. Topic: Parts of the Cartesian planec. Reference: Bernabe, Julieta G., et.al, Geometry III, JTW Corporation, Quezon

City, 2002, pp. 221-222.

III. Procedures

A. Pre Discussion

Teacher’s Activity Students’ ActivityGood morning class! Good morning Ma’am!Please arrange your chairs before we start and keep those unnecessary materials not related to our subject.

(students follow)

Okay, I’ll be assigning numbers in each one of you. For the first student in the first column is number 1. For the second number 1 is for the first row.As I call you’re a pair of corresponding number, the student in the intersection of the points that I called will stand to be recognized. Let’s practice if you are aware of your number. Ready, may I have student number (1,4)

(student will stand)

Good! That’s the mechanics of our activity okay. Failure to stand in their corresponding number will eliminate them from the activity until a student is left to stand.

B. Discussion Proper

Teacher’s Activity Students’ ActivityAlright, did you enjoy the activity? Yes Ma’am!Our activity has something to do with our lesson for today. Who are familiar with this

Ma’am.

plane? Not an airplane but a plane with horizontal and vertical lines.Yes? The Cartesian Plane Ma’am?Exactly! Thank you! Yes, this is the Cartesian plane invented by Rene Descartes. Every point in the plane can be located in terms of numbers, specifically an ordered pair. When we say ordered pair, it has an x and y intercept.So, generally, an ordered pair is the representation of x and y. What letter comes first in our English alphabet? x or y?

X.

Okay, and so we will write our ordered pair as (x,y).Another term for x is abscissa and ordinate for the y. Take a look at the diagram we have here on the board.

Teacher’s Activity Students’ ActivityYou can observe that there are two perpendicular lines in our plane intersecting at the origin.What do we call the horizontal line? X-axis.How about the other line aligned vertically? Y-axis.Correct! You can also observe that the two lines divide the plane into four quadrants represented by Roman Numerals.For every point in the coordinate plane, there corresponds an ordered pair, there corresponds a point.Let us show a point from an ordered pair (3,4).

I

III

II

IV

origin

X-axis

Y-axis

C. Post Discussion

Teacher’s Activity Students’ ActivityAfter we have identified the parts of the coordinate plane, most probably you can try plotting the points now.

Yes Ma’am.

Okay, now, can you relate our activity earlier on our lesson for today. Show in front what you have observed using this coordinate plane.

Ma’am!

IV. Evaluation

Graph the ordered pair.

1. A (3,8 ) 6. F (7,2)

2. B (−2,5 ) 7. G(−6,8)

3. C (−1 ,−1 ) 8. H (3,1)

4. D (5,9 ) 9. I (3 ,−7)

5. E(2,−7) 10. J (−6 ,−9)

V. Agreement

Draw the graph and then write the answer.

1. Three of the vertices of a square are points (2, 2), (-3, 2), and (-3, -2). What are the coordinates of the fourth vertex?

2. Three of the vertices of a rectangle are points (2, 1), (-4, 1), and (-4, -3). What is the fourth vertex of the rectangle?

Prepared By:

Kimberly MiraflorBSED-Mathematics


I. ObjectiveAt the end of an hour class discussion, 85% of the students are expected to:a. define what slope is;b. participate actively in class discussion; andc. find the slope of the line with the given points.

II. Subject Mattera. Unit: Chapter 7: Plane Coordinate Geometryb. Topic: Slope of a Linec. Reference: Bernabe, Julieta G., et.al, Geometry III, JTW Corporation, Quezon

City, 2002, pp. 225-227.

III. Procedures

A. Pre-Discussion

Teacher’s Activity Students’ ActivityGood morning class! Good morning Ma’am!Ms. Secretary have you checked the attendance?

Yes Ma’am!

Alright, are you ready for a new lesson? Yes Ma’am!I have here pieces of cut out letters. I will be giving you two minutes to identify what is the word that I want you to guess but upon guessing I’ll be supplementing you with definitions of this specific word.First definition: To be inclined from the level or vertical.To move on an inclined path.Any slanting surface or line.Last definition, the degree of inclination of a line or surface from the plane of the horizon.Any answer? Who wants to answer?

Ma’am slope?

Are you sure? Ma’am why are there excess letters?Are you sure with the ‘slope’? Yes.Correct!


Teacher’s Activity Students’ ActivitySlope is the ratio of the rise to the run, written None Ma’am.

asriserun

.

Lines always have slopes. Another simple definition of slope is the steepness of the line.Questions so far?

Take a look at the example of a line I the coordinate plane. Focus on the vertical and horizontal change of the line.

Teacher’s Activity Students’ ActivityThe slope of a line containing two points (x, y) and (x1, x2) can be determined using the

formula m=y2− y1

x2−x1 where x2≠ x1

Questions? Can you still recall now this formula?

Yes Ma’am!

Good!

C. Post Discussion

Teacher’s Activity Students’ ActivityLet’s try the formula. On the board, find for the slope of points (5,1) and (1, 8)

Ma’am!

Yes.

IV. Evaluation

Find the slope of the line with the given points.

1. (-4,-1) and (1,8)

2. (a, b) and (c, d)

3. (0, 0) and (1, 8)

4. (0, a) and (b, 0)

V. Agreement

Prepare for a short quiz for tomorrow.

\

Prepared By:

Kimberly MiraflorBSED-Mathematics II


I. ObjectiveAt the end of an hour class discussion, 85% of the students are expected to:a. recall the points of the Cartesian plane;b. utilize the given formulas wisely and effectively in doing the activity; andc. solve for the slope, coordinates in the given points.

II. Subject Mattera. Unit: Chapter 7: Plane Coordinate Geometryb. Topic: Parts of the Cartesian plane and Slope of a Linec. Reference: Bernabe, Julieta G., et.al, Geometry III, JTW Corporation, Quezon

City, 2002, pp. 221-227.

III. Procedures

A. Recall

Teacher’s Activity Students’ ActivityWe already have tackled the different parts of the Cartesian plane and also the slope of a line and how it is obtained using a formula. And today, we’ll have more exercises regarding the lessons. In a sheet of paper, copy the given and answer.

(students follow)

B. Activity Proper

A

B

C

D

EF

G

H

I

K

J

1. Describe all the ordinate of all points on the x-axis.2. Describe all the abscissa of all points on the y-axis.3. Describe the coordinates of all points in the first, second, third, and fourth

quadrant.4. Write the coordinates of each point.5. Two vertices of a square are points (4, 2) and (-4, 2). State the coordinates

of 2 possible pairs of points for the other 2 vertices.6. Find the slope of points B and G.7. Find the slope of points K and D.8. Find the slope of points I and F.


I. ObjectiveAt the end of an hour class discussion, 85% of the students are expected to:a. answer 70% out of the 10-items correctly;b. strictly follow the directions; andc. solve for the slope and the intercepts of the line.

II. Subject Mattera. Unit: Chapter 7: Plane Coordinate Geometryb. Topic: Slope of a Line, Interceptsc. Reference: Bernabe, Julieta G., et.al, Geometry III, JTW Corporation, Quezon

City, 2002, pp. 225-231.III. Procedures

A. Recall

Teacher’s Activity Students’ ActivityGood morning class! Good morning Ma’am!As what we have agreed yesterday, we’ll have the quiz today. But before that, let us recall your formulas, for the slope, we have?

m=y2− y1

x2−x1

How about for the intercepts? m=−ba

Are you ready now? Yes Ma’am!Okay, get a sheet of paper and work quietly.

B. Test Proper

Directions: Find for the x- and y-intercepts for each of the following:1. 2 x+ y=62. 5 x+3= y3. y=6x+54. 3 x−7= y5. 5 x+ y=10

Find for the slope of the given lines.

Prepared By:



I. ObjectiveAt the end of a forty-minute class period, 90% of the students are expected to:a. recall the previous lessons such as intercepts, slope, equation of a line through

exercises;b. follow the directions strictly and carefully; andc. solve for what is asked regarding intercepts, slopes, and equation of a line.

II. Subject Mattera. Unit: Chapter 7: Plane Coordinate Geometryb. Topic: Slope, Intercepts, and Equation of a Linec. Reference: Bernabe, Julieta G., et.al, Geometry III, JTW Corporation, Quezon

City, 2002, pp. 225-235.

III. Procedures

A. Recall

Teacher’s Activity Students’ ActivityGood morning class! Good morning Ma’am!Please distribute the workbooks so we can start the activity.

(students follow)

B. Workbook Exercisespp. 76-80

Prepared By:


A Semi-Detailed Lesson Plan in Mathematics IIIGeometry

I. ObjectiveAt the end of a forty-minute class period, 90% of the students are expected to:a. identify if the linear equations is in general form;b. participate actively in class discussion; andc. complete the table of ordered pairs.

II. Subject Mattera. Unit: Chapter 7: Plane Coordinate Geometryb. Topic: Linear Equationc. Reference: Bernabe, Julieta G., et.al, Geometry III, JTW Corporation, Quezon

City, 2002, pp. 229-230.

III. Procedures

A. Pre DiscussionGood morning class!Is there any absent for today?Good.Take a look at the coordinates posted here. Anyone who wants to plot the points?What figure is formed?

B. Discussion ProperWe have noticed that the above points formed a straight line.Take note that if an equation written in the formax+by=c, where a and b are

not both 0, then the graph of the equation is a line.

C. Post DiscussionOkay, count one to four and then go to your respective groups.Now, I want you to graph the following equations.a. 6 x+2 y=4b. − y=−3+2x

IV. EvaluationDetermine whether each of the following equations is linear.1. y=−52. x−2 y=4

3.12x−2 y=6

V. AgreementDetermine whether each of the following is a linear equation.1. 8 y=x−2

2. ( 1x )+( 3 y

2 )=6


I. ObjectiveAt the end of a forty-minute class period, 90% of the students are expected to:a. differentiate the two-point form from the slope-intercept from;b. participate actively in class discussion; andc. find for the equation of the line using the two-point form

II. Subject Mattera. Unit: Chapter 7: Plane Coordinate Geometryb. Topic: Equation of a Linec. Reference: Bernabe, Julieta G., et.al, Geometry III, JTW Corporation, Quezon

City, 2002, pp. 232-234.

III. Procedures

A. Pre Discussion

Good morning class!Do we have an assignment?Okay, on the board, number one.


An even shorter process in finding the equation of a line is, y− y1

x−x1

=y2−¿ y1

x2−x1

¿

where (x, y) is the arbitrary point on the line.Let’s have some examples.1. (1, 3) and (5, -4)2. (0, 1) and (0, 3)3. (-1, 2) and (5, 8)

C. Post Discussion

Solve the following points to find for the equation of the line using two-point formula.

1. (-1, 3) and (4, 1)2. (3, 2) and (2, -3)

IV. Evaluation

Find the equation of the line passing througha. (3, 5) and (-2, 4)b. (6, 1) and (2, 3)

V. Agreement

Find the equation of the line passing througha. (-1, 0) and (1, 0)b. (2, 6) and (6, 5)

Prepared By:



I. ObjectiveAt the end of a forty-minute class period, 90% of the students are expected to:a. recall the last two forms of the equation of a line;b. participate actively in class discussion; andc. find for the equation of the line using the point-slope form.

II. Subject Mattera. Unit: Chapter 7: Plane Coordinate Geometryb. Topic: Equation of a Linec. Reference: Bernabe, Julieta G., et.al, Geometry III, JTW Corporation, Quezon

City, 2002, pp. 232-234.

III. Procedures

A. Recall

Good morning class!Yesterday we have tackled the two-point slope formula in finding the slope to

have the equation of a line.What is again our two-point formula?


There is another derivation of the equation of a line. It is the point-slope form that shows the line satisfying the given point (x, y) and the slope m.

The point slope form of the equation of a line is:y− y1=m(x−x1) where (x, y) is an arbitrary point on the line. Let’s have an example.

m=3 ; (1,5 ) m=−2 ; ( 4 ,2 )

C. Post Discussion

Solve the following on your notebook.

1. m=13; (3,1 )

2. m=−5 ; (6 ,1 )

IV. Evaluation

Find the equation of the line witha. a slope of 3 and passing through a point (-1, -1)

b. a slope of 12

and passing through a point (3, -3)

V. AgreementFind the equation of the line with

a. a slope of 34

and passing through a point (4, 3)

b. a slope of -2 and passing through a point (-4, -3)

Prepared By:



I. ObjectiveAt the end of a forty-minute class period, 90% of the students are expected to:a. recall the previous lessons such as plotting of points, slope of a line and linear

equation;b. participate actively in class discussion; andc. find for the x- and y- intercepts of the given linear equation.

II. Subject Mattera. Unit: Chapter 7: Plane Coordinate Geometryb. Topic: The Interceptsc. Reference: Bernabe, Julieta G., et.al, Geometry III, JTW Corporation, Quezon

City, 2002, pp. 230-231.

III. Procedure

A. Recall

Good morning class!Ms. Secretary please check the attendance.Let us recall our previous lessons, in getting the slope of a line.What is our equation?


Consider the graph of the linear equation2 x+3 y=6. The set of ordered pair which satisfies the equations are (-3, 4), (0, 2), (3, 0), (6, -2). Notice that two of the ordered pairs have as 0 as one of their coordinates and the point whose coordinates consists of the number pair (0, 2) intersects in the y-axis, thus the ordinate of 2 is called the y-intercept. The point whose coordinates consist of the number pair, (3, 0) intersects the x-axis, thus the abscissa 3 of this point is called the x-intercept.

The x-intercept is the abscissa of the point (0, p) where a graph intersects the x-axis. The y-intercept is the ordinate of the point (0, b) where a graph intersects the y-axis.

For example, 5 x+3 y=15

C. Post DiscussionFind the x- and y-intercept for each of the following.Number one, Mr. Santiago on the board.

3 x+ y=5 − y−2x=3 3 y+5 x=7

IV. Evaluation

Find for the x- and y-intercept for each of the following:

1. 2 x+ y=62. 5 x+3= y3. y=6x+54. 3 x−7= y5. 5 x+ y=10

V. AgreementFind for the x- and y-intercept for each of the following:

1. 3 x−6 y=122. 5 x+ y=103. 8 x+ y=44. y=4 x−2

5. y=12x+5

Prepared By:


An Outline Lesson Plan in Mathematics II

Geometry

I. ObjectiveAt the end of an hour class discussion, the students are expected to:a. recall the previous lessons such as plottingn of points, slope of a line and linear

equation;b. participate actively in class discussion; andc. find for the x – and y- intercept of the given linear equation.

II. Subject Mattera. Unit: Chapter 7: Plane Coordinate Geometryb. Topic: The Interceptsc. Reference: Bernabe, Julieta G., et.al, Geometry III, JTW Corporation, Quezon

City, 2002, pp. 230-231.

III. Procedure

A. Pre-Activity Routine activities Short recall Introduction of the lesson (drawing)

B. Discussion Proper Discussion Relation of the drawing to the topic Examples are given

C. Post Activity Board works

IV. Evaluation A five-item quiz

V. Agreement Five-item home work.

Prepared By:



Geometry

I. ObjectiveAt the end of an hour class discussion, the students are expected to:a. identify the different parts of and other related terms of circle;b. sustain interest in listening to class discussion; andc. label the parts of a circle

II. Subject Mattera. Unit: Chapter 7: Plane Coordinate Geometryb. Topic: The Circle (Parts of a Circle)c. Materials: Illustration of a Circle and Its Partsc. Reference: Bernabe, Julieta G., et.al, Geometry III, JTW Corporation, Quezon

City, 2002, pp. 184-186.

III. Procedure

A. Pre-Activity Routine activities ‘Spot the similarities’ game Introduction of the lesson (drawing)

B. Discussion Proper Discussion Definition of Terms Illustration

C. Post Activity Label the parts of the circle

IV. Evaluation Modified true or false

V. Agreement Name the parts in the illustration

Prepared By:



Geometry

I. ObjectiveAt the end of an hour class discussion, the students are expected to:a. recall the previous lesson which is the circle and its parts;b. identify the minor arc, major arc, semicircles and central angle; c. participate actively in class discussion; andd. manipulate the given material during class discussion.

II. Subject Mattera. Unit: Chapter 7: Plane Coordinate Geometryb. Topic: Arcs and Central Anglesc. Materials: Illustration of Arcs and Central Anglesc. Reference: Bernabe, Julieta G., et.al, Geometry III, JTW Corporation, Quezon

City, 2002, pp. 187-188.

III. Procedure

A. Pre Discussion Routine activities Recall of the previous lesson

B. Discussion Proper Discussion using the Illustration Definition of Terms Illustration

C. Post Discussion Supply the sentence with the correct term to make the statement true.

IV. Evaluation Determine the missing part

V. Agreement Measure the angle of a specific time in the clock.

Prepared By:



Geometry

I. ObjectiveAt the end of an hour class discussion, the students are expected to:a. identify the intercepted arcs and inscribed angles;b. participate actively in class discussion; andc. solve for the measures of intercepted arc ands or inscribed angles

II. Subject Mattera. Unit: Chapter 6: Circlesb. Topic: Inscribed Angles and Intercepted Arcsc. Materials: Illustration of Inscribed Angles and Intercepted Arcsc. Reference: Bernabe, Julieta G., et.al, Geometry III, JTW Corporation, Quezon

City, 2002, pp. 189-190.

III. Procedure

A. Pre Discussion Routine activities Checking of Assignments Recall of the previous lesson

B. Discussion Proper Discussion using the Figure of inscribed angles and intercepted arc Definition of Terms

C. Post Discussion Solving for the unknown measures of inscribed angles and intercepted arcs

IV. Evaluation Name and measure the indicated part of the circle.

V. Agreement Name the specified arc and angle in the figure.

Prepared By:


lp in geometry

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