These are the instructional materials/manipulative that I made in our Instrumentation in Mathematics class.

2. Topic Slide No.
Operations of Signed Numbers 6
Fraction 11
Operations in Algebraic Expressions 16
Plane Figures PPT 22
Polygons (Geoboard) 41
Area and Perimeter of Irregular Polygons PPT 46
Platonic Solids PPT 60
Platonic and Achimedean Solid Model 84
Circle 89
Contents

3. •Instructional materials are devices that assist the
facilitator in the teaching-learning process.
•Instructional materials are not self-supporting;
they are supplementary training devices
•This includes power point presentations, books,
articles, manipulatives and visual aids.

4. Values and Importance
•To help clarify important concepts
•To arouse and sustain student’s interests
•To give all students in a class the
opportunity to share experiences necessary
for new learning
•To help make learning more permanent

6. Operations of Signed
Numbers
(negative and positive)

7. Number Line Route
Objectives:
The operations of signed numbers instructional
material will be able to:
• Define signed numbers
• Apply the operations of signed numbers using
number line
• Visualize the operations of signed numbers
• Manipulate the operations of signed numbers
• Value the importance of signed numbers through
cultural integration

8. How to use:
• Introduce the positive and negative numbers in a number line. Write
the values in the number line using whiteboard pen on the octagon-
shaped space; positive numbers on the right of the zero and negative
numbers on the left of the zero.
• Move the jeepney on the desired “JEEPNEY STOP”. Attach on the
jeepney stop post the “STOP 1” card.
 For addition
Move the jeepney forward if you want to add a positive number.
Move the jeepney backward if you will add a negative number
 For subtraction
Move the jeepney backward if you want to subtract a positive
number. Move the jeepney forward if you want to subtract a negative
number.

9. Number Line
Route

10. Other pedagogical uses:
• In counting
• In measurement
• In addition and subtraction
• And in decimals and
fractions
• Developmental issues

11. Fraction
s

12. Fraction
Tiles
Objectives:
The fraction tiles instructional material will be
able to:
• Define fraction numbers
• Apply the operations of fraction numbers using
tiles
• Visualize the operations of fraction numbers
• Manipulate the operations of fraction numbers
• Value the importance of fraction numbers
through daily encounter when buying

13. How to use:
• Place a number of tiles on the pink board that corresponds a
whole/denominator. (ex. 5 tiles corresponds a whole)
• On the top of the tiles, place the another tiles with another
color that will correspond the part/numerator. (ex. 2 tiles,
makes 2/5)
For addition
Place a same colored tiles of the numerator tiles next to
the numerator tiles, then count the total numerator tiles.
For addition
Get a number of numerator tiles, then count the
remaining numerator tiles

14. Fraction
tiles

15. Another Pedagogical uses:
• In counting
• In operations of algebraic
expressions
• In basic operations
• In equality, inequality, and
ratios

16. Operations of
Algebraic Expressions

17. Algebra
Tiles
Objectives:
The algebra tiles instructional material will be able
to:
• To represent positive and negative integers using
Algebra Tiles.
• Manipulate operations of positive and negative
integers using Algebra Tiles

18. How to use:
• Introduce the unit squares.
• Discuss the idea of unit length, so that the area of the
square is 1.
• Discuss the idea of a negative integer. Note that we can
use the yellow unit squares to represent positive integers
and the violet unit squares to represent negative
integers.
• Show students how two small squares of opposite colors
neutralize each other, so that the net result of such a pair
is zero.

19. Algebra
Tiles

20. Another Pedagogical uses:
• In counting
• In basic operations
• In equality, inequality, and ratios
• In fractions
• In operation of signed numbers

22. Plane
Figures
Area and Perimeter

23. Plane Figures
- are flat shapes
- have two dimensions: length and width
- have width and breadth, but no thickness.

25. Area
•The area of a plane figure refers to the number
of square units the figure covers.
•The square units could be inches, centimeters,
yards etc. or whatever the requested unit of
measure asks for.

26. Perimeter
•The distance around a two-dimensional shape.
•The length of the boundary of a closed figure.
• The units of perimeter are same as that of
length, i.e., m, cm, mm, etc.

27. Triangles
A triangle is a closed plane geometric figure formed by
connecting the endpoints of three line segments
endpoint to endpoint.

28. h
b
a c
Perimeter = a + b + c
Area = bh
2
1
The height of a triangle is
measured perpendicular to the
base.

29. Parallelogram
A parallelogram is a quadrilateral with both pairs of
opposite sides parallel. It has no right angle.

30. b
a h
Perimeter = 2a + 2b
Area = hb  Area of a parallelogram
= area of rectangle with
width = h and length = b

31. Rectangle
A rectangle is a quadrilateral that has four right angles.
The opposite sides are parallel to each other. Not all sides
have equal length.

32. Rectangle
w
l
Perimeter = 2w + 2l
Area = lw

33. Square
A square is a quadrilateral that has four right angles. The
opposite sides are parallel to each other. All sides have
equal length.

34. Square
s
Perimeter = 4s
Area = s2

35. Trapezoids
If a quadrilateral has only one pair of opposite sides that
are parallel, then the quadrilateral is a trapezoid. The
parallel sides are called bases. The non-parallel sides are
called legs.

36. Trapezoid
c d
a
b
Perimeter = a + b + c + d
Area =
b
a
 Parallelogram with base (a + b) and height = h
with area = h(a + b)
 But the trapezoid is half the parallelgram 
h(a + b)
2
1
h

37. Circle
A circle is the set of points on a plane that are equidistant
from a fixed point known as the center. A circle is named
by its center.

38. Circle
• A circle is a plane figure in which all points are equidistance from the center.
• The radius, r, is a line segment from the center of the circle to any point on
the circle.
• The diameter, d, is the line segment across the circle through the center. d =
2r
• The circumference, C, of a circle is the distance around the circle. C = 2pr
• The area of a circle is A = pr2.
r
d

39. Find the Circumference
• The circumference, C,
of a circle is the distance
around the circle. C = 2pr
• C = 2pr
• C = 2p(1.5)
• C = 3p cm
1.5 cm

40. Find the Area of the Circle
• The area of a circle is A = pr2
• d=2r
• 8 = 2r
• 4 = r
• A = pr2
• A = p(4)2
• A = 16p sq. in.
8 in

41. Polygon
s

42. Geoboard
Objectives:
The geoboard instructional material will be able to:
• Define polygons
• Solve for the area of polygons
• Solve for the perimeter of polygons
• Visualize the area and perimeter of polygons
• Manipulate the geoboard to find the area and
perimeter of polygons

43. How to use:
• Connect the dots on the geoboard to form a polygon
• Count the connected dots to have the length of the sides
Regular Polygons
To find the perimeter of regular polygons, count all the dots that was
connected.
To find the area of regular polygons, count the square units enclosed by
the connected dots.
Irregular Polygons
To find the perimeter of an irregular polygon, count all the connected
dots.
To find the area of an irregular polygon, visualized a regular polygon
inside the irregular polygon. Use the formulas of the area of regular

44. Geoboard

45. Other pedagogical uses:
• Identify simple geometric shapes
• Describe their properties
• Develop spatial sense
• Similarity
• Co-ordination
• In counting
• Right angles;
• Pattern;
• Congruence

46. Area and Perimeter of
Irregular Polygons

47. Irregular Polygons
All sides are not equal
All angles are not equal

48. 19yd
30yd
37yd
23 yd
7yd18yd
What is the perimeter of this irregular polygon?
 Find the missing length of other sides.
 Add all of the sides up
The perimeter is 134 yd

49. 19yd
30yd
37yd
23yd
7yd
18yd
What is the area of this irregular shape?
Find the area of each rectangle now
133
851
Add the area of the first and second rectangle. The area is 984 sq. yd.

50. 19in
7in
3in
13in
20in
9in
20in
13in
What is the perimeter? The perimeter is 104 in

51. 19 in
7 in
3 in
13in
20 in
9 in
20 in
13 in
What is the area?
7
39
117
133
The area is 289 sq. yd.

52. Exercises

53. Area and perimeter of
irregular polygons
5cm
10cm
6cm9cm
1.

54. 2.
12m
4m
7m
2m
2m

55. 3.
7cm
11cm
4cm
6cm
4cm
10cm
7cm
11cm
4cm
6cm
4cm

56. 4.
15cm
16cm
20cm
3cm
3cm
15cm

57. Example
Work out the area shaded in each of the following diagrams
1.
8 cm
6 cm 4 cm
2 cm

58. 2.
18cm
17cm
15cm
14cm

59. 3.
34m
9m 7m
5m
5m
5m

60. Platonic Solids

61. • The Platonic Solids, discovered by the Pythagoreans
but described by Plato (in the Timaeus) and used by
him for his theory of the 4 elements, consist of
surfaces of a single kind of regular polygon, with
identical vertices.

62. • The Platonic Solids are named after Plato and were studied
extensively by the ancient Greeks, although he was not the
first to discover them. Plato associated the cube, octahedron,
icosahedron, tetrahedron and dodecahedron with the
elements, earth, wind, water, fire, and the cosmos,
respectively. Crystal Platonic Solids can be used for meditation,
healing, chakra work, grid work, and manifestation. In grid
work, they can be used together, or separately, each as a
center piece in its own crystal grid.

63. Regular Tetrahedron
A regular tetrahedron is a regular polyhedron
composed of 4 equally sized equilateral triangles.
The regular tetrahedron is a regular triangular
pyramid.

64. Characteristics of the Tetrahedron
Number of faces: 4.
Number of vertices: 4.
Number of edges: 6.
Number of concurrent edges at a vertex: 3

65. Surface Area of a Regular Tetrahedron

66. Volume of a Regular Tetrahedron

67. Regular Hexahedron or Cube
A cube or regular hexahedron is a
regular polyhedron composed of 6
equal squares.

68. Characteristics of a cube
•Number of faces: 6.
•Number of vertices: 8.
•Number of edges: 12.
•Number of concurrent edges at a vertex: 3.

69. Surface Area of a Cube

70. Volume of a Cube

71. Diagonal of a Cube

72. Regular Octahedron
A regular octahedron is a regular
polyhedron composed of 8 equal equilateral
triangles. The regular octahedron can be
considered to be formed by the union of two
equally sized regular quadrangular pyramids at
their bases.

73. Characteristics of a Octahedron
•Number of faces: 8.
•Number of vertices: 6.
•Number of edges: 12.
•Number of concurrent edges at a vertex: 4.

74. Surface Area of a Regular Octahedron

75. Volume of a Regular Octahedron

76. Regular Dodecahedron
• A regular dodecahedron is a regular polyhedron
composed of 12 equally sized regular
pentagons.

77. Characteristics of a Dodecahedron
• Number of faces: 12.
• Number of vertices: 20.
• Number of edges: 30.
• Number of concurrent edges at a vertex: 3.

78. Surface Area of a Regular Dodecahedron

79. Volume of a Regular Dodecahedron

80. Regular Icosahedron
• A regular icosahedron is a regular polyhedron
composed of 20 equally sized equilateral triangles.

81. Characteristics of an Icosahedron
• Number of faces: 20.
• Number of vertices: 12.
• Number of edges: 30.
• Number of concurrent edges at a vertex: 5.

82. Surface Area of a Regular Icosahedron

83. Volume of a Regular Icosahedron

84. Platonic and
Archimedean Solids

85. Platonic Solids Model
Objectives:
The platonic solids model instructional material will
be able to:
• Identify platonic solids
• Determine the characteristics of platonic solids
• Differentiate the different kinds platonic solids
• Differentiate Platonic solid and Archimedean solid

86. Platoni
c Solids

87. Archimedean Solids
Model
Objectives:
The archimedean solid model instructional
materials will be able to:
• Identify archimedean solids
• Determine the characteristics of Archimedean solids
• Differentiate the different kinds archimedean solids
• Differentiate archimedean solid and platonic solid

88. Archimedea
n Solids

89. Circle

90. Pie Chart
Objectives:
The pie chart instructional material will be able to:
• Define circle
• Solve for the area of a circle
• Solve for the circumference of a circle
• Manipulate the pie chart to find the area and
circumference of a circle
• Manipulate the pie chart to find the relationship
between the area of a circle and a parallelogram

91. How to use:
• Form the whole circle to define the different parts of a circle
• Manipulate the part of the circle to find the relationship of the
radius , diameter and circumference of a circle.
Circle Vs. Parallelogram
• Arrange the part of the pie chart horizontally to form a
parallelogram
• Arrange the part of the pie chart upside down to fill the spaces in
between

92. Pie Chart

93. Parallelogra
m

94. Other pedagogical uses:
• In fraction
• In percentage
• In parallelogram
• In trigonometric functions