Detailed Lesson Plan in Mathematics I .Content Standards The learner demonstrates understandin understanding g of key concepts concepts of geometry geometry of shapes and sizes, and geometric relationships. II. Performance Standards The learner is able to create create models of plane plane gures gures and solve accurately authentic problems problems involving sides and angles of a polygon. III. Learning Competency/Objectives At the end of the lesson 75% of the students should master the folloing ith at least 75% level of success! A. "ene "ene point point,, line, line, and and plane# plane# $. "ierentiate "ierentiate collinear collinear from from non&collinear non&collinear points# points# coplanar coplanar from from non& coplanar points# and '. (epresent (epresent point, point, line, and and plane using concrete concrete and and pictorial pictorial models )*7+&---a&/
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*. &efe &efere renc nces es Tarepe, Tarepe, ".A and velyn ara, ara, 0ractical *athematics. *athematics. 4ipa 'ity!6nited ferza Academic 0ublications 'o, 8. pp. 77& 9 1rines, :.$ et al. 2e;t century mathematics. 79&>98 velyn ara, 0ractical mathematics teacher?s manual. 4ipa 'ity! 6nited ferza Academic 0ublications 'o, 8. pp. 9@& @ C. Mate Materi rial als s 0oer0oint 0resentation 'harts 'ut&1uts
. Learning !ctivities
'#!C+#&,S !C'II'!. Preliminary !ctivities . "aily routine a. 0rayer Ask representative in the class to lead the prayer. b. +reetings +ood morning class c. 'hecking of attendance *. Strategy/proced)re . no0ledge A. *otivation 3ho pictures of magnicent buildings, gypt?s +reat 0yramid and -ndia?s TaB *ahal. 0ose the Cuestions! Dhat did the architect use in designing the buildingE Dhat did he consider in creating attractive patternsE Dhat you?ve cited are application of +eometry. Dhat is +eometryE 1. Introd)ction of the Lesson +eometry, Bust like any other mathematical system is based on undened terms, unproven statements )postulates and assumptions/ and theorems. The undened terms in geometry are point, line, and plane. ven though this terms are left undened, they used together ith ordinary ords to dene other geometric terms. 3pace, for e;ample, is dened as set of all points. a. To introduce the concept of a point, let the students close their eyes and imagine the stars in the sky at night. Then open your eyes ho do the
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The student ill lead the prayer.
+ood morning *a?am
The students ill give their observationFideas about the pictures. 3tudents ill dene +eometry.
The students ill close their eyes and imagine the given situation. The stars look like dots sparkling in the sky.
)3tudents ill bring out their research
stars in the sky look likeE Gery +ood Those dots represent points. )4et the students bring out their research assignment./
ork./
Dhat is a pointE
A point has no size and no dimension.
3tudent ill dene point.
"oes a point have size and dimensionE A point is a location that has no size and no dimension& no length, no idth, no height, and no thickness. -t could be represented by a dot )period/, a speck or even a grain of sand. A point is named by using a capital letter. ;ample !
.H .0 .A b. To illustrate the ideas of a line, sho a thin ire and ask the students to describe it. Ask the students to dra the ire on the board and add to arroheads on both ends. Dhat is a lineE 4ines are represented by small italicized letter, but they can also be identied by to points that are on the line. ;ample !
m
The student ill dra a ire on the board and describe it a lineE
3tudents ill dene hat a line is.
line m
3tudents ill cite e;amples of a line. line -+ ) -+ / 'an you give real life e;amples of a lineE 4ike for e;ample, the edge of a ruler. c. To illustrate the ideas of a plane, use a clean bond paper or the blackboard. 4et the students describe the obBects.
The bond paper and the blackboard represent a line. 3tudents ill dene plane.
Dhat is a planeE 0lane e;tends ithout end. Iou can name a plane by either a single capital letter or by at least three of its non&collinear points )points hich are not on the same line/ ;ample >!
J K
4 * plane J plane K4* COLLI(#!& !(D (O(2COLLI(#!& POI('S I R
0oints I, R, and S lie on line
l
S 2o, because point = does not lie on line l. . Dhere do points I, R and S lieE 0oints that lie on the same line are
called collinear points. . =o about point H, is point H collinear ith the other three pointsE DhyE Gery ellE 2on&collinear points are points that do not lie on the same plane.
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P o k l
n
0oints K, 4 and * are located on plane 0. 0oints K, 4, and * are 'oplanar points.
m 0oint 2 lies on plane 1, hence, it is not coplanar ith points K, 4 and *.
plane 0
plane 1
. Dhere can you locate point K , L, and ME . Dhen points lie on the same plane, ho ill you describe themE >. "escribe point N, is point N coplanar ith the other three pointsE
1. Process A. 3ho gures representing points, lines and planes and lots of the students identify hether it represents point, line or plane. . dge of the ruler . The tip of the pen >. A sheet of paper L. *ongo seeds 5. A piece of a yarn M. The Noor of a classroom 7. arrings 9. The tip of the nail @. A 088.88 8.A broom stick
. 4ine . 0oint >. 0lane L. 0oint 5. 4ine M. 0lane 7. 0oint 9. 0oint @. 0lane 8.4ine 3tudents ill cite e;amples.
. 3tudents ill dra intersecting lines. The intersection is a point.
line s
$. 4et the students give their on e;amples.
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3. "nderstanding !. 4ro)p !ctivity% -llustrate *e
4ine q
. -llustrate the intersection of to lines. Dhat is their intersectionE 4abel the lines and the intersection.
. 3tudents ill dra intersecting planes. The intersection is a line.
T . -llustrate intersecting line and plane. Dhat is the intersectionE 4abel the gure.
4ine z
v >. 3tudents ill dra intersecting line and plane. The intersection is a point.
4ine c
2
c plane ' >. -llustrate intersecting line and plane. Dhat is the intersectionE 4abel the gure. 3tudents ill e;plain their orks.
-t?s because e help one another *a?am.
4et the students sho their orks and e;plain it. =ave on representative in each group. Iou did your activity ell. Dhy do you think you did it ellE Alays remember that cooperation is the key for every group activity to succeed.
*. Let,s play5 T-'&TA'&T1 To players ill compete. The rst ho can make three consecutive points in a line ill be the inner. :irst round put all your dots on the plane. $lock the ay of your opponent and aim to put all your dots on a line. -f there?s no three consecutive dots formed, move your dots ith the same goal, one step at a time. $e ise to in . 4&!SPS +oal! to provide a sketchFdesign of a cabinetF divider for the sala set of you teacher. (ole! an architectFdesigner Audience! teacher and classmates 3ituation or scenario! as an aspiring architectFdesigner you have to make a sketch and design a cabinetFdivider for the 3al set of your teacher. The design should sho points, lines and planes. $e creative. 0roduct)s/ 0erformances for the assessment! present your design to the class. 'onvince your teacher that you have the best design of a cabinetFdivider. 3tandards for assessments! 0lanning, 'reativity and Justication &"*&ICS $O& PL!( O$ !C'IO(
3tudents ill play the game.
(ating
Criteria
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+ood )> pts./
:air pts./
0oor ) pts./
0lan is ell thought out.
0lan is perfunctor y.
The overall impact of the presentatio n of the sketch plan is impressive .
The overall impact of the presentati on of the sketch plan is fairly impressiv e. The purpose is fairly Bustied and shos some of the key concepts.
1verall planning is random and incomple te. The overall impact of the presentat ion of the sketch plan is poorly impressiv e. The purpose is poorly Bustied.
The purpose is ell Bustied and shos the ise use of the key concepts. The purpose is fairly Bustied and shos some of the key concepts. The purpose is poorly Bustied.
5. +eneralization Teacher?s Activity . Dhat is a pointE . Dhat is a lineE
>. Dhat is a planeE L."ierentiate collinear and non&collinear points
5."ierentiate coplanar and non&coplanar points
3tudent?s Activity A point is a specic location that has no size and no dimension. A line is of innite length but it has no idth, or no thickness A plane is a Nat surface that has no thickness. 'ollinear points are points that lie on the same line hile non collinear points are points that do not lie on the same line. 0oints are said to be coplanar if they lie on the same plane hile non&coplanar points
do not lie on the same plane.
I.!SS#SSM#(' !. no0ledge% 2ame me -dentify hat is asked on the folloing! . -t is a Nat surface that e;tends innitely in all directions. . 0oints that lie on the same line. >. -t is a specic location in space that has no dimensions. L. 0oints that lie on the same plane. 5. -t is of innite length but it is no idth and no thickness. *. Process Tell hether each represents a point, a line or a plane. . Iour desktop . The surface of the page of a notebook. >. The string on a guitar. L. The ceiling of a room. 5. A broomstick. M. lectric ire. 7. The Noor. 9. A hair strand. @. A rope. 8. A needle point. C. "nderstanding "ra and describe the intersection of the folloing! A. intersection of to lines $. intersection of to planes '. intersection of a line and a plane II. !greement / !ssignment (esearch on the folloing! . 0ostulate about points, lines and planes. . 0ostulate about intersection of lines and planes. III. &emar7s.
