3. Grid Board
Pedagogical Uses
• Perimeter of Plane Figures
• Area of Plane Figures
• Coordinate System
• Graphing Functions
4. Grid Board
Objectives
This instructional material will help the
students:
1.To better understand the concepts of
perimeter and area of plane figures
2.To differentiate the difference between
perimeter and area of plane figures
3.To solve for the perimeter and area of
plane figures.
5. Grid Board
How to Use
PERIMETER of Plane Figures
1.Determine the desired figure to illustrate.
2.Use white board pen to shade the
corresponding square units of the desired
figure.
3.Count the number of sides in the boundary
of the figure. The resulting number will be
the perimeter of the figure.
6. Grid Board
How to Use
AREA of Plane Figures
1.Determine the desired figure to illustrate.
2.Use white board pen to shade the
corresponding square units of the desired
figure.
3.Count the number of square units of the
entire figure. The resulting number will be
the area of the figure.
9. Modified GeoBoard
Objective
This instructional material will help the
students to:
1. form different plane figures both regular
and irregular
2. find the perimeter of regular and irregular
polygons
3.find the area of regular and irregular
polygons.
10. Modified GeoBoard
How to Use
Perimeter of Regular and Irregular Polygon
1. Using a white board pen, draw a polygon
on the modified geoboard.
2. Count the number of points around the
polygon. The resulting number is the
perimeter of the polygon.
11. Modified GeoBoard
How to Use
Area of Regular Polygon
1. Using a white board pen, draw a regular
polygon on the modified geoboard.
2. Count the square units inside the
polygon. The resulting number is the area
of the regular polygon.
12. Modified GeoBoard
How to Use
Area of Arbitrary Polygon
1. Using a white board pen, draw an
arbitrary polygon on the modified
geoboard.
2. Count the number of points that touches
the boundary lines.
3.Count the points inside the polygon.
13. Modified GeoBoard
How to Use
Area of Arbitrary Polygon
4. Divide the number of boundary points by
2.
5. Add the quotient in #4 with the number of
points inside the polygon.
6. Subtract 1 from the sum in #5. The
resulting difference will be the area of the
arbitrary polygon.
16. Fraction Slider
Objectives
This instructional material will help the
students to:
1. understand the concept of adding and
subtracting of fractions
2. perform addition of fractions
3. perform subtraction of fractions.
17. Fraction Slider
How to Use
Addition and Subtraction of Fractions
1. Take the fraction bars that correspond to
the given fraction
2. Slide in the 1st fraction bar (the bigger
number). Align its left side to the origin.
18. Fraction Slider
How to Use
Addition and Subtraction of Fractions
3. From the ending point of the 1st bar, slide
in the 2nd fraction bar in the direction
indicated by the 2nd number or addend
(left if the number is negative; right if the
number is positive).
4. The ending point of the 2nd bar is the
answer.
21. Number Slider
Objectives
This instructional material will help the
students to:
1. understand the process of adding and
subtracting integers
2. perform addition of integers
3. perform subtraction of integers.
22. Number Slider
How to Use
Addition and Subtraction of Integers
1. Attach the blank number line to the
fraction slider.
2. Write the necessary numbers on the
blank number line as well as on the
number bars.
23. Number Slider
How to Use
Addition and Subtraction of Integers
3. Take the number bars that corresponds to
the given.
4. Slide in the 1st number bar. Align it to the
origin (towards the left if the 1st number is
negative; towards the right if the 1st
number is positive).
24. Number Slider
How to Use
Addition and Subtraction of Integers
5. Slide in the 2nd number bar. Align it to the
ending point of the 1st number bar
(towards the left if the 2nd number is
negative; towards the right if the 2nd
number is positive).
25. Number Slide
How to Use
Addition and Subtraction of Integers
6. The ending point of the 2nd number bar is
the answer.
27. Algebra Tiles
Pedagogical Uses
• Addition and Subtraction of Integers
• Modeling Linear Expressions
• Solving Linear Equations
• Simplifyings Polynomials
• Solving Equations for Unknown Variable
• Multiplication and Division of Polynomials
• Completing the Square
• Investigations
28. Algebra Tiles
Objectives
This instructional material will help the
students to:
1. Associate linear expressions with
concrete objects, specifically tiles
2. Solve addition and subtraction of integers
using tangible materials
3. Simplify polynomials using
representations.
29. Algebra Tiles
Each tile represents an area:
Area of large square = x(x) = x2
Area of rectangle = 1(x) = x
Area of small square = 1(1) = 1
x
x
x
1
1
1
40. Fraction Pie
Pedagogical Uses
• Identifying Fractions
• Circumference of a Circle
• Area of a Circle
• Perimeter of a Parallelogram
41. Fraction Pie
Objectives
This instructional material will help the
students to:
1. find the circumference of the circle
2. find the perimeter of the parallelogram
using the circumference of a circle
3. explain the relationship between the circle
and parallelogram.
42. Fraction Pie
How to Use
Finding the relationship between a circle
and a parallelogram
The radius of a circle
is the height of the
parallelogram and
the base of a
parallelogram is the
circumference of a
circle
45. Perimeter and Area
Objective
This power point presentation will
help the students to:
1. measure the perimeter of polygons
2. measure the area of polygons
46. Perimeter
It is the length of the boundary of a
closed figure.
-Concise Mathematics Dictionary
It is measured by adding all the
sides of the plane figure.
48. Area
A measure of the extent of a surface, or
the part of surface enclosed by some
specified boundary.
-Concise Mathematics Dictionary
It is measured by the number of
squares inside the figure.
68. Platonic Solids
The term platonic solids refers to the
regular polyhedra. In geometry, a
polyhedron (the word is a Greek
neologism meaning many seats) is a
solid bounded by plane surfaces, which
are called the faces; the intersection
of three or more edges is called a
vertex.
What distinguishes regular polyhedra
from all others is the fact that all of
their faces are congruent with one
another.
69. History
Pythagoras, in 5th
BCE, knew of the
tetrahedron, hexahedron or cube, and
dodecahedron. He learned these solids from
Egyptian Sacred Geometry.
Plato in his ‘Theaetetus’ dialogue, a
discussion around the question ”What is
knowledge?” that dates to about 369 BCE, added
the octahedron and the icosahedron.
Collectively, these 5 solids became known as
the Platonic Solids, after this ancient Greek
philosopher.
70. History
Plato speculated that these 5 solids were the
shapes of the fundamental components of the
physical universe, what he called the “Theory
of Everything”.
In this theory, the world was composed of
entirely of 4 elements: fire, air, water and
earth and each of the elements were made up
of tiny fundamental particles. This was the
precursor to the atomic theory. The shapes
or particles that he chose for the elements
were the Platonic Solids and the intuitive
justification for these associations were:
71. History
1. The tetrahedron was the shape of fire, because fire
is sharp and stabbing
2. The octahedron was like air, its miniscule
components being so smooth that one could barely
feel them.
3. Water was made up of icosahedra, which are the most
smooth and round of the Platonic Solids that flows
out of one’s hands when picked up as if made of
tiny balls.
4. Earth consisted of hexahedron, which are solid and
sturdy and highly un-spherical.
5. The dodecahedron left unmatched to one of the four
elements, had 12 faces that Plato decided
corresponded with the 12 constellations of the
Zodiac and was the symbol of ether or universe or
spirit, writing “God used this solid for the whole
universe, embroidering figures on it”.
87. Sphere
A sphere is a solid described y the
revolution of a semi circle about a
fixed diameter.
88. Sphere
Properties of a sphere:
A sphere has a center.
All the points on the surface of the sphere
are equidistant from the center.
The distance between the center and any
point on the surface of the sphere is the
radius of the sphere.
93. Archimedean Solids
Objectives
The model will help the students to:
1. identify the relationship between the
platonic and archimedean solids
2. investigate the surface area of the
archimedean solids
94. Archimedean Solids
How to Use
1. Use it as a model to investigate the
relationship between the archimedean and
platonic solids.
2. Allow the students to measure the surface
area of the archimedean solids.