Title - Geometry of Shape and Size
Second Year Level
Time Frame: 1 session (Day 1)
Competence A1. Undefined Terms
1.1 Describe the ideas of point line and plane
1.2 Describe, identify and name the subsets of a line
  • segment
  • ray

Time Frame 1 session
At the end of the session, the students must be able to:
1. Describe the ideas of point, line and plane
2. Define, identify and name the subsets of a line
a. segment
b. ray

Development of the Lesson:
A. Introduce the concept of a point by asking the students this question: "Have you ever watched the stars at night"?
Let the students draw a picture of the stars as seen on the night sky
Then explain that the stars in the sky suggest the idea of a point. A point is represented by a dot and has no dimensions. It is used to describe location.
Explain further that a point is named by capital letters.
Example .A .C
B. Let the sutdents observe a thin wire and give their description of it. Then ask one student to draw a picture of the wire on the board.
State that the wire is good representation of a line alghough a line has no width and extends indefinitely on both sides. It is drawn with two arrowheads on both sides to remind us that it extends indefinitely.
Explain that lines are named using two capital letters or "l" like at the end of the line.
The line above can be named in different ways: line AB or AB, AC or line l. All these describe the same line. The notation implies that a line is determined when two points are given.
C. Now, let the students consider the example above and ask them to imagine cutting the line at point A and point B.
Then ask one student to draw a ;icture showing the pieces of t he line after cutting.
The student might possibly draw the folllowing:

Let the students observe each figure and ask them to describe each.
Explain that each figure is a subset of the give line. The portion from point A to point B is called a SEGMENT. Points A and B are called the endpoints of the segment.

Discuss further that segments are named using two capital letters with a bar on top.
This may be referred to as segment AB,AB or BA. Mention here that every segment has exactly one midpoing. Point M on segment AB is said to be a midpoint if AM=MB.
D. Present the other piece of the line.

Ask the students this question: "How does this figure differe from a line?"
Let the students explain their answers.
State that the figure is an example of a RAY. It has a starting point called the initial point of the ray.
Explain that a ray is named using capital letters with an arrow at the top. The initial point is always written first. The second letter indicates the direction of the ray.

Descuss that each example above may be called ray AB or AB.

E. Present the concept of a plane by placing a clean board paper on the fllor and asking the students to imagine the bond paper expanding on all directionsl. Ask them to describe wthat they see.
Explain that the bond paper, the wall and other flat surfaces are good representations of the idea of a PLANE. Stress that a plane is a never ending flat surface; this means that it has no limits or boundaries. Thus, when we illustrate a plane, we are just representing a part of it as shown in the diagram below.
Let the students give other examples of good representations of a plane. The plane above can be denoted as plane E. In general, a plane is denoted using a capital letter.

F. Ask the students to work on p.4 numbers 1-10. They should be able to give their answers orally.

Suggested Teaching Strategies:
1. Provisions for Integration of Content Areas in language teaching
- Go over the descriptions of points, lines and planes as well as the meaning of segments and rays.
2. Provision for Miltiple Intelligence
- Ask the students to identify things around them which represent a point, line, plane, segment or ray.

Title - Angles
Secondary Year Level
Time Frame - 2 session (Day 2 - 3)
1.) The student should be able to classify angles of a polygon as greater than, less
than, or equal to a right angle. (Application)
Set Induction:
The teacher will begin the lesson by giving each student a blank sheet of paper. The teacher will tell the students to fold their paper in half. She will demonstrate to the students how to fold their paper. The students will be instructed to fold their paper in half again. The teacher will again model. The teacher will point to the corner of the folded paper. She will explain to the students that this is a right angle. The teacher will state that today they students are going to learn about angles.
Activities / Content:
1a.) The teacher will place a polygon on the chalkboard. (Appendix A) she will explain that the corners of polygons are angles. The teacher will place her folded paper on top of angle A. She will state that the right angle on her paper matches
angle A; therefore, angle A is a right angle. The teacher will then place her folded paper on angle B. She will state that the right angle on her paper is smaller than angle B; therefore, angle B is greater than a right angle. The teacher will place her folded paper on angle C. The students will be asked, "Is angle C greater than or less than the right angle on the folded paper?" ( Student response : It is less than. ) The teacher will state that angle C is less than a right angle. She will place another polygon on the chalkboard. (Appendix B) The teacher will repeat the same process with this polygon that she did with the previous polygon. She will explain to the students that they just classified the angles of a polygon as greater than, less than, or equal to a right angle.
1b.) The teacher will arrange the students into groups of two. Each group will receive a paper bag with four polygons and a worksheet. (Appendix C) The students will pick a polygon out of the out of the paper bag. They will classify the specified angles of each polygon and write their answers on the worksheet. The teacher will instruct the students that they may use their folded paper to classify the angles. She will monitor. The teacher will randomly call on students to reveal their answers. The students will break up from their groups.
1c.) Each student will be given a worksheet. ( Appendix D) The students will decide if the angles of the polygons are greater than, less than, or equal to a right angle. The teacher will state that the students may use their folded paper to classify the angles. The teacher will monitor. She will randomly call on students to go to the chalkboard to write their answers.
The teacher will give each student a blank sheet of paper. Using their folded paper, the students will find at least 3 objects in the classroom, and they will classify the angles of their objects as greater than, less than, or equal to a right angle. They will write the name of the object and their answers on the blank sheet of paper. The teacher will monitor.
The teacher will end the lesson by asking the students to think about objects at home in which they can classify the object's angles as greater than, less than, or equal to a right angle. He will randomly call on students to reveal their ideas.
Classroom standards
Appendices A-D
Blank sheets of paper
Bags of four polygons (1 bag per group)
Mathworks. (1997). Grades K-8. Standard: Geo-7 page 22
Eicholz, O'Daffer, Fleenor, Young, Charles, and Barnett. Addison - Wesley
Mathematics. Addison Wesley Publishing Company. Menlo Park, California, 1991

Time Frame: 2 Sessions (Day 4-5)
1. The student will have a better understanding of how to classify triangles.
2. The student will be able to find the angle of a triangle when they already know two of the three angles.
3. The student will be able to measure and determine the value of angles using a protractor.
4. The student will have a better awareness of how many angles there are in their surroundings
Print the Angles reading and questions worksheet (see below).
Students should read the passage silently, then answer the questions. Teachers may also use the text as part of a classroom lesson plan.
Lesson Excerpt
Triangles are three-sided objects. All three sides are made up of angles. An angle is made up of two rays. These rays meet at a common endpoint.
There are different sizes, shapes, and angles for each triangle. Triangles can be classified in two ways. They can be classified by their angles or they can be classified by their shape.
Look at the following triangle. When you look at the following triangle what is your first thought? You have seen this shape more than once.
external image tri1.jpg

If you have ever been to a racetrack, the tiny flags throughout the course have this shape. You may have the same kind of flag on the back of your bike! The local high school or college banners you wave at football games have this shape, too.
You probably are not thinking about the size of each angle. Unless you are measuring something that requires the knowledge of finding the size of the angles, you may not pay attention to the angles at all.

Lesson Plan in Math IV
Topics: Linear Equations Game
Brief Description
Game cards help pair up students to solve linear equations for the value of a variable.

Students practice solving linear equations for one variable.

equation, linear equation, variable, algebra
Materials Needed
    • a set of cards with equations written on them (see Before the Lesson below)
    • notebooks/paper
    • chalk and blackboard, or markers and whiteboard
The Lesson
Before the Lesson
  • This game is planned for use with 30 students; however, more cards can be made for play in a larger-sized class. Students might help you to prepare the 30 game cards, or the cards might be prepared in advance. Each card should have a letter of the alphabet (in this case, A to O) written on it along with a linear expression; there will be two different cards with the same letter and different linear expressions. For example, see the list below. For the letter A there are two cards:
  • one card has A written on it with the linear expression 4x + 2 -8x
  • the other card has A written on it with the linear expression 3x Create additional pairs of cards with the following letters and linear expressions. ||~ Card ||~ Expression
    On Card 1 ||~ Expression
    On Card 2 ||~ Answer ||
    ||~ A ||~ 4x + 2 - 8x ||~ 3x ||~ x = 2/7 ||
    ||~ B ||~ 6 x - 7 ||~ 0 ||~ x = 7/6 ||
    ||~ C ||~ 7 – 10z ||~ 17 ||~ z = -1 ||
    ||~ D ||~ 6x + 16 ||~ 2x - 12 ||~ x = -7 ||
    ||~ E ||~ 6 - 5x ||~ 13x ||~ x = 1/3 ||
    ||~ F ||~ 14y +7 ||~ -6 ||~ y = -13/14 ||
    ||~ G ||~ 8x – 4 ||~ -6 ||~ x = -1/4 ||
    ||~ H ||~ 7 - 5x ||~ -10 ||~ x = 17/5 ||
    ||~ I ||~ 6x - 17 ||~ 9x ||~ x = -17/3 ||
    ||~ J ||~ 10x + 7 ||~ 17 ||~ x = 1 ||
    ||~ K ||~ 20x + 10 ||~ 4 - 10 ||~ x = -4/5 ||
    ||~ L ||~ 15p - 5 ||~ 10p + 10 ||~ p = -3 ||
    ||~ M ||~ 11x + 33 ||~ 55 ||~ x = 2 ||
    ||~ N ||~ (6x -5)/2 ||~ (3x +6)/2 ||~ x = 11/3 ||
    ||~ O ||~ 5x – 3x + 7 ||~ -7 + 8x ||~ x = 7/3 ||
If you have a class of 30 students, shuffle the set of 30 cards and distribute a card to each student. (If you have fewer or more students, shuffle a set of letter cards for each pair of students.) Allow students who get the same alphabet cards to sit together and solve the equation for the value of the variable. For example, the pair of students who got the two cards with the letter A on them will solve for x in the linear equation

  • 4x + 2 - 8x = 3x
Once students have solved their equations, you might place lettered slips (in this game’s example, one slip with each letter A to O) in a bowl or hat. Draw out a slip and read the letter that is written on it. Invite the pair of students who have that letter on their cards to come up to the board to show how they solved their equation. If they do it correctly they win that round of the game.
Let all student pairs who correctly solved their equations play another round of the game (with new cards or the same ones). With each repeat of the game, you will eliminate more pairs of students. Play until you have a final winner (a pair of champions).
Thus, the game can be used to motivate and provide drill in solving linear equations in one variable.
Below you will find the step-by-step solution to each of the equations.
Card A
  • 4x + 2 - 8x = 3x
  • 4x - 8x - 3x = -2
  • -7x = -2
  • x = 2/7
Card B
  • 6x – 7 = 0
  • 6x = 7
  • x = 7/6
Card C
  • 7 - 10z = 17
  • -10z = 17 – 7
  • -10z = 10
  • z =10/-10= -1
Card D
  • 6x + 16 = 2x – 12
  • 6x – 2x = -12 – 16
  • 4x = -28
  • x =-28 /4= -7
Card E
  • 6 - 5x = 13x
  • -5x - 13x = -6
  • -18x = -6
  • x = -6/-18
  • x = 1/3
Card F
  • 14y + 7 = -6
  • 14y = -6 – 7
  • 14y = -13
  • y = -13/14
Card G
  • 8x – 4 = -6
  • 8x = -6 + 4
  • 8x = -2
  • x =-2/8= -1/4
Card H
  • 7 - 5x = -10
  • -5x = -10 – 7
  • -5x = -17
  • x = 17/5
Card I
  • 6x – 17 = 9x
  • 6x - 9x = 17
  • -3x = 17
  • x = -17/3
Card J
  • 10x + 7 = 17
  • 10x = 17 – 7
  • 10x = 10
  • x =10/10= 1
Card K
  • 20x + 10 = 4 – 10
  • 20x = 4 – 10 – 10
  • 20x = -16
  • x =-16/20= -4/5
Card L
  • 15p – 5 = 10p + 10
  • 15p – 10p = 10 + 5
  • -5p = 15
  • p =15/-5= -3
Card M
  • 11x + 33 = 55
  • 11x = 55 – 33
  • 11x = 22
  • x =22/11= 2
Card N
  • (6x-5)/2 = (3x+6)/2
  • [The numerators are equal as the fractions are equal and the denominators are same.]
  • 6x – 5 =3x + 6
  • 6x - 3x = 6 + 5
  • 3x = 11
  • x = 11/3
Card O
  • 5x -3x + 7 = -7 + 8x
  • 5x - 3x - 8x = -7 – 7
  • -6x = -14
  • x =-14/-6= 7/3