Instructional Materials in Mathematics

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

•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.

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

Operations of Signed Numbers

(negative and positive)

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

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 additionMove the jeepney forward if you want to add a

positive number. Move the jeepney backward if you will add a negative number

For subtractionMove the jeepney backward if you want to

subtract a positive number. Move the jeepney forward if you want to subtract a negative number.

Number Line Route

Other pedagogical uses:

• In counting

• In measurement

• In addition and subtraction

• And in decimals and

fractions

• Developmental issues

Fractions

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

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 additionPlace 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

Fraction tiles

Another Pedagogical uses:

• In counting

• In operations of algebraic

expressions

• In basic operations

• In equality, inequality, and

ratios

Operations of Algebraic

Expressions

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

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.

Algebra Tiles

Another Pedagogical uses:

• In counting

• In basic operations

• In equality, inequality, and ratios

• In fractions

• In operation of signed numbers

Plane Figures

Area and Perimeter

Plane Figures

- are flat shapes

- have two dimensions: length and width

- have width and breadth, but no thickness.

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.

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.

TrianglesA triangle is a closed plane geometric

figure formed by connecting the endpoints

of three line segments endpoint to

endpoint.

h

b

a c

Perimeter = a + b + c

Area = bh21

The height of a triangle is measured perpendicular to the base.

ParallelogramA parallelogram is a quadrilateral with

both pairs of opposite sides parallel. It

has no right angle.

b

a h

Perimeter = 2a + 2b

Area = hb Area of a parallelogram = area of rectangle with width = h and length = b

RectangleA rectangle is a quadrilateral that has four right angles.

The opposite sides are parallel to each other.

Not all sides have equal length.

Rectangle

w

l

Perimeter = 2w + 2l

Area = lw

Square

A square is a quadrilateral that has four right angles. The

opposite sides are parallel to each other. All

sides have equal length.

Squares

Perimeter = 4s

Area = s2

TrapezoidsIf 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.

Trapezoidc 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)21

h

CircleA 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.

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

Find the Circumference• The circumference, C,

of a circle is the distance around the circle. C = 2pr

• C = 2pr• C = 2p(1.5)• C = 3 p cm

1.5 cm

Find the Area of the Circle• The area of a circle is A = pr2

• d=2r• 8 = 2r• 4 = r

• A = pr2

• A = (4)p 2

• A = 16 p sq. in.

8 in

Polygons

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

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 PolygonsTo 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 PolygonsTo 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 polygons, then add the results to find the area of the irregular polygon

Geoboard

Other pedagogical uses:

• Identify simple geometric shapes

• Describe their properties

• Develop spatial sense• Similarity • Co-ordination• In counting• Right angles; • Pattern; • Congruence

Area and Perimeter of Irregular Polygons

Irregular Polygons

All sides are not equal

All angles are not equal

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 upThe perimeter is 134 yd

19yd

30yd

37yd

23yd

7yd18yd

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.

19in7in

3in

13in

20in

9in

20in

13in

What is the perimeter? The perimeter is 104 in

19 in7 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.

Exercises

Area and perimeter of irregular polygons

5cm

10cm

6cm9cm

1.

2.

12m

4m

7m

2m

2m

3.

7cm

11cm

4cm

6cm

4cm

10cm

7cm

11cm

4cm

6cm

4cm

4.

15cm

16cm

20cm

3cm

3cm

15cm

Example

Work out the area shaded in each of the following diagrams

1.

8 cm

6 cm 4 cm

2 cm

2.

18cm

17cm

15cm

14cm

3.

34m

9m 7m

5m

5m

5m

Platonic Solids

• 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.

• 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.

Regular Tetrahedron

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

Characteristics of the Tetrahedron

Number of faces: 4.

Number of vertices: 4.

Number of edges: 6.

Number of concurrent edges at a vertex: 3

Surface Area of a Regular Tetrahedron

Volume of a Regular Tetrahedron

Regular Hexahedron or Cube

A cube or regular hexahedron is a regular polyhedron composed of 6 equal squares.

Characteristics of a cube

•Number of faces: 6.

•Number of vertices: 8.

•Number of edges: 12.

•Number of concurrent edges at a vertex: 3.

Surface Area of a Cube

Volume of a Cube

Diagonal of a Cube

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.

Characteristics of a Octahedron

• Number of faces: 8.

• Number of vertices: 6.

• Number of edges: 12.

• Number of concurrent edges at a vertex: 4.

Surface Area of a Regular Octahedron

Volume of a Regular Octahedron

Regular Dodecahedron

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

Characteristics of a Dodecahedron

• Number of faces: 12.

• Number of vertices: 20.

• Number of edges: 30.

• Number of concurrent edges at a vertex: 3.

Surface Area of a Regular Dodecahedron

Volume of a Regular Dodecahedron

Regular Icosahedron

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

Characteristics of an Icosahedron

• Number of faces: 20.

• Number of vertices: 12.

• Number of edges: 30.

• Number of concurrent edges at a vertex: 5.

Surface Area of a Regular Icosahedron

Volume of a Regular Icosahedron

Platonic and Archimedean

Solids

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

Platonic Solids

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

Archimedean Solids

Circle

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

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

Pie Chart

Parallelogram

Other pedagogical uses:

• In fraction

• In percentage

• In parallelogram

• In trigonometric functions