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Rectangular Coordinate System Lesson Plan
- 1. 4 Prepared by: Realyn Alcobilla MAEd – Mathematics The Rectangular Coordinate System Objectives/ Setting Targets At the end of the lesson, the Grade 8 students must have: a. defined whatis coordinate, real line, origin and Cartesian plane; b. familiarized the x – axis, y – axis, quadrants, abscissa, ordinate and the Cartesian coordinate system or the rectangular coordinate system and c. determined the coordinates of a given point on a coordinate plane. Time Frame 2 sessions Content Illustration and uses of the rectangular coordinate system. Let’sExplore! Do youknow the person in the middle? Indeed, he is the great mathematician Rene Descartes who discovered the Cartesian Coordinate Plane. Do youknow that the ceiling and a fly are the things that help him discoverit? Write your guess on the space provided below.
- 2. 5 Prepared by: Realyn Alcobilla MAEd – Mathematics Abstraction Rene Descartes was a French man who lived in the 1600s. And this a story of some people on how he discovered the Rectangular Coordinate System. One day, Descartes noticed a fly crawling around on the ceiling. He watchedthe fly fora long time. He wanted toknow how to tell someone else where the fly was. Finally, he realized that he could describe the position of the fly by its distance from the walls of the room. When he got out of bed, Descartes wrotedownwhathe had discovered.Then he tried describing the positions of points, the same way he described the position of the fly. Descartes had invented the coordinate plane! In fact, the coordinate plane is sometimes called the Cartesian plane, in his honor. Illustrated below is a Cartesian Plane. Unlocking of Terms Origin/ Axes – thepointof intersection of twoperpendicular lines. x – axis – verticalline y – axis – horizontalline Coordinate – pairof numbers that corresponds to a real number equal to its distance from 0, positive if to the right and above, or negative if to the left and below. Real Line- thelinewhere a positive number has a corresponding negative number from 0. Cartesian Plane / Coordinate System System/ Rectangular Coordinate -consistsof two perpendicular lines.
- 3. 6 Prepared by: Realyn Alcobilla MAEd – Mathematics How do you think we can apply this in real life? Let’s try the next activity? Example Suppose Jane and Joy belong to the class withthe followingseating arrangement. To plot points in a Cartesian Plane: 1. Determine the quadrant where the coordinates belong. Note: The signs of the coordinates will help you identify where what quadrant it belongs. Q1 (+, +), Q2 (-, +), Q3 (-, -) and Q4 (+, -). 2. Locate the abscissa on x – axis and ordinate on y – axis. 3. Put a dot where the line intersects. Quadrant I Quadrant II Quadrant III Quadrant IV x -axis y -axis Origin
- 4. 7 Prepared by: Realyn Alcobilla MAEd – Mathematics C1 C2 C3 C4 C5 C6 R5 R4 R3 R2 R1 Solutions: 1. Jane’s seat is at the intersection of Column 2 and Row 3. Joy’sseat is at the intersection of Column 4 and Row 2. In symbols, we can write (2, 3) and (4, 2), respectively, if wetake the column as the x – axis and the row as y – axis. 2. We locate the seat of Jane’s and Joy’sclassmates by using column and row. We can use ordered pair (Column #, Row #) to locateit. 3. Here is the set of ordered pairs: {(C1, R1), (C2, R1), (C3, R1), (C4, R1), (C5, R1), (C6, R1), (C1, R2), (C2, R2), (C3, R2), (C4, R2), (C5, R2), (C6, R2), (C1, R3), (C2, R3), (C3, R3), (C4, R3), (C5, R3), (C6, R3), (C1, R4), (C2, R4), (C3, R4), (C4, R4), (C5, R4), (C6, R4), (C1, R5), (C2, R5), (C3, R5), (C4, R5), (C5, R5), (C6, R5)} Activity 1.1 Locate your Classmate! Direction: Locateyour seat and seats of groupmates in the classroom. Complete the table below: NAME LOCATION JANE JOY Teacher’s Table Questions: 1. Using ordered pairs, how do we describe Jane’s seat? How about Joy’sseat? 2. Using ordered pairs, how do we locatethe seat of any classmate of Jane and Joy? 3. Can we make a set of ordered pairs? If yes, state so.
- 5. 8 Prepared by: Realyn Alcobilla MAEd – Mathematics How do youlocate the seat of yourclassmate in the classroom? Activity 1.2 FOOD ESTABLISHMENT’S POSITION
- 6. 9 Prepared by: Realyn Alcobilla MAEd – Mathematics Pictures are got from google.com Direction: From yourhouse locate these fast foodchains by drawing it on the space provided. I have prepared stickers foryou to label the location. Describe the location of each fast food chains that you have pasted by completing the followingtable. An example is done for you. Possible student’s work. Food Establishment Coordinate Quadrant/Axis
- 7. 10 Prepared by: Realyn Alcobilla MAEd – Mathematics Example: Your House (0,0) At the origin ASSESSMENT: SELF CHECK! Direction: Write thecoordinates of each point. Identify the quadrant/ axis where each point lies. Complete the table below.
- 8. 11 Prepared by: Realyn Alcobilla MAEd – Mathematics Coordinates Quadrant/ Axis 1. M (______,______) 2. A (______,______) 3. T (______,______) 4. H (______,______) 5. E (______,______) 6. M (______,______) 7. A (______,______) 8. T (______,______) 9. I (______,______) 10. C (______,______) 11. S (______,______) B. Direction: Draw a Cartesian plane. Plot and label the followingpoints.
- 9. 12 Prepared by: Realyn Alcobilla MAEd – Mathematics 1. C (0, 7) 2. A (5, 4) 3. R (6, -3) 4. T (3, -5) 5. E (7, 0) 6. S( 1 2 , 5 ) 7. I (11, - 7) 8. A ( -1, 6) 9. N (8, 3 4 ) EXTENSION: A. Constellation Art Direction: Group yourselves into 5 – 10 members. Research constellations and their names. Choose the one that you like most. Make yourown constellation using graphing paper, ruler, pencil or ballpeen and any coloring materials. B. Plotthe followingpoints in a graphing paper. Connect the points followingthe sequence of the alphabet. What figure have youformed? A (4, 2), B (2,0), C (-1, -3), D (4, -3), E (9, - 3), F (6, 0)