Instructional Materials in Mathematics
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Transcript of Instructional Materials in Mathematics
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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
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•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.
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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
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Operations of Signed Numbers
(negative and positive)
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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
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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.
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Number Line Route
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Other pedagogical uses:
• In counting
• In measurement
• In addition and subtraction
• And in decimals and
fractions
• Developmental issues
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Fractions
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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
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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
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Fraction tiles
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Another Pedagogical uses:
• In counting
• In operations of algebraic
expressions
• In basic operations
• In equality, inequality, and
ratios
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Operations of Algebraic
Expressions
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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
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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.
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Algebra Tiles
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Another Pedagogical uses:
• In counting
• In basic operations
• In equality, inequality, and ratios
• In fractions
• In operation of signed numbers
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Plane Figures
Area and Perimeter
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Plane Figures
- are flat shapes
- have two dimensions: length and width
- have width and breadth, but no thickness.
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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.
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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.
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TrianglesA triangle is a closed plane geometric
figure formed by connecting the endpoints
of three line segments endpoint to
endpoint.
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h
b
a c
Perimeter = a + b + c
Area = bh21
The height of a triangle is measured perpendicular to the base.
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ParallelogramA parallelogram is a quadrilateral with
both pairs of opposite sides parallel. It
has no right angle.
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b
a h
Perimeter = 2a + 2b
Area = hb Area of a parallelogram = area of rectangle with width = h and length = b
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RectangleA rectangle is a quadrilateral that has four right angles.
The opposite sides are parallel to each other.
Not all sides have equal length.
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Rectangle
w
l
Perimeter = 2w + 2l
Area = lw
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Square
A square is a quadrilateral that has four right angles. The
opposite sides are parallel to each other. All
sides have equal length.
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Squares
Perimeter = 4s
Area = s2
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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.
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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
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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.
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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
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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
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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
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Polygons
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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
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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
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Geoboard
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Other pedagogical uses:
• Identify simple geometric shapes
• Describe their properties
• Develop spatial sense• Similarity • Co-ordination• In counting• Right angles; • Pattern; • Congruence
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Area and Perimeter of Irregular Polygons
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Irregular Polygons
All sides are not equal
All angles are not equal
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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
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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.
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19in7in
3in
13in
20in
9in
20in
13in
What is the perimeter? The perimeter is 104 in
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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.
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Exercises
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Area and perimeter of irregular polygons
5cm
10cm
6cm9cm
1.
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2.
12m
4m
7m
2m
2m
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3.
7cm
11cm
4cm
6cm
4cm
10cm
7cm
11cm
4cm
6cm
4cm
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4.
15cm
16cm
20cm
3cm
3cm
15cm
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Example
Work out the area shaded in each of the following diagrams
1.
8 cm
6 cm 4 cm
2 cm
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2.
18cm
17cm
15cm
14cm
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3.
34m
9m 7m
5m
5m
5m
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Platonic Solids
![Page 61: Instructional Materials in Mathematics](https://reader036.fdocuments.in/reader036/viewer/2022062406/55c7bc2bbb61eb7f698b4747/html5/thumbnails/61.jpg)
• 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.
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• 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.
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Regular Tetrahedron
A regular tetrahedron is a regular polyhedron composed of 4 equally sized equilateral triangles.The regular tetrahedron is a regular triangular pyramid.
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Characteristics of the Tetrahedron
Number of faces: 4.
Number of vertices: 4.
Number of edges: 6.
Number of concurrent edges at a vertex: 3
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Surface Area of a Regular Tetrahedron
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Volume of a Regular Tetrahedron
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Regular Hexahedron or Cube
A cube or regular hexahedron is a regular polyhedron composed of 6 equal squares.
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Characteristics of a cube
•Number of faces: 6.
•Number of vertices: 8.
•Number of edges: 12.
•Number of concurrent edges at a vertex: 3.
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Surface Area of a Cube
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Volume of a Cube
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Diagonal of a Cube
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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.
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Characteristics of a Octahedron
• Number of faces: 8.
• Number of vertices: 6.
• Number of edges: 12.
• Number of concurrent edges at a vertex: 4.
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Surface Area of a Regular Octahedron
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Volume of a Regular Octahedron
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Regular Dodecahedron
• A regular dodecahedron is a regular polyhedron composed of 12 equally sized regular pentagons.
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Characteristics of a Dodecahedron
• Number of faces: 12.
• Number of vertices: 20.
• Number of edges: 30.
• Number of concurrent edges at a vertex: 3.
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Surface Area of a Regular Dodecahedron
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Volume of a Regular Dodecahedron
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Regular Icosahedron
• A regular icosahedron is a regular polyhedron composed of 20 equally sized equilateral triangles.
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Characteristics of an Icosahedron
• Number of faces: 20.
• Number of vertices: 12.
• Number of edges: 30.
• Number of concurrent edges at a vertex: 5.
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Surface Area of a Regular Icosahedron
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Volume of a Regular Icosahedron
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Platonic and Archimedean
Solids
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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
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Platonic Solids
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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
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Archimedean Solids
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Circle
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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
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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
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Pie Chart
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Parallelogram
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Other pedagogical uses:
• In fraction
• In percentage
• In parallelogram
• In trigonometric functions
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