Instrumentation in Mathematics

By: Fate Jacaban
PREPARED BY:
JACABAN, FATE S.
BSED MATH -IV

• Fraction wall
• Number Line Wall
• Algebra tiles
• Gridline Wall
• Geoboard
• Pie
• Platonic and Archemedean solids
• Perimeter
• Area
• Surface area
• Volume
• Instrcutional Materials

OBJECTIVE
This instructional material is made for
students to :
• easily review on the basic concepts on
fractions
• identify the basic skills in using
fractions
• solve algebraic operations with fractions
and for mastery of any problems
involving fractions.

The fraction table has two horizontal lines.
The lower horizontal line is for the fractions
(numbers) and the upper horizontal line is
where students will put the number of blocks
to be added, subtracted, multiplied or
divided. These blocks are colorful rectangles.

• Basic operation on fractions
• Solving algebraic equations involving fractions
• Solving word problems involving fractions

students to master :
• the rules in solving basic operations on
integers (the laws of signed numbers)
• Solving problems on integers.

ADDITION
To add a positive on the number line, move to the
right, towards the larger numbers. To add a negative
on a number line you move to the left.
Simple rule
Rule for adding integers with different signs:
Subtract the absolute values of the numbers and the use the
sign of the larger absolute value.

SUBTRACTION
To subtract a positive number, move to the left
on the number line. This is the same thing
that happens when we add a negative
number.

SUBTRACTION
Subtract a negative number we need to move to
the right.
Simple Rule:
KEEP the first number the same. CHANGE the
subtracting to adding. Then CHANGE the sign of the
second number

MULTIPLICATION AND DIVISION
Multiplying is really just showing repeated
adding. To add 2 three times. 2 + 2 + 2 = 6

• With negatives.
Examples:-2 x 3 = -6
Add -2 three times. That means that -2 + -2 + -2 = -6.

• Two Negatives
Examples:-2 x -3 = 6
Meaning add -2 negative 3 times.
The negative symbol means "the opposite". So
if there are two negative numbers/terms
being multiplied then move to the .

SIMPLER RULES
Rule #1:If the signs are the same, the answer is positive.
Examples:
Rule #2:If the signs are different, the answer is negative.
Dividing integers are the same as the rules for multiplying
integers.
Remember that dividing is the opposite of multiplying. So we can
use the same rules to solve.
Rule #1:If the signs are the same, the answer is positive.
Rule #2:If the signs are different, the answer is negative.

• Introduction of integers
• Basic operations on integers
• Solving algebraic equations

This instructional material is made
for the learners to:
• better understand ways of
algebraic thinking and the
concepts of Algebra.

Each tiles represents to a certain variable/
constant
x2
x
1

2X2 + x+ 3
See: http://mathbits.com/MathBits/AlgebraTiles/AlgebraTiles/AlgebraTiles.html

• Concepts on Algebra
 basic operations on signed numbers
 Simple substitution
 Solving equations
 Distributive property
 Representing polynomials
 Basic operations on polynomials
 Factoring polynomials
 Completing the square
• Geometric figures on square and parallelogram

This instructional material will help the
learners :
• be introduced with the concepts of plane
figures
• to master the skill in solving areas and
perimeter of plane figures.

The Geometry Grid Wall is composed of two areas. The
upper area is to where the figure be pasted and the
lower area is the grid area where a figure be drawn/
illustrated

This instructional material will help the learners :
• be introduced with the concepts of plane
figures and its characteristics
• to use concrete material on finding the area
and perimeter of plane figures
• to master the skill in solving areas and
perimeter of plane figures

• Geoboard consists of a physical
board with a certain number of
dots. If these dots are connected
it will serve as the measurement
of a certain side or the figure
itself.
• The unit of area on the
geoboard is the smallest square
that can be made by connecting
four nails:
• We will refer to this unit as 1
square unit.

• On the geoboard, the unit
of length is the vertical or
horizontal distance
between two nails.
Perimeter is the distance
around the outside of a
shape and is measured
with a unit of length.
• Use a white board pen to
draw a figure.

OBJECTIVES
the students to:
• solve for the area and circumference
of a circle
• identify the relationship between a
circle and a parallelogram.

Each slices of the pie is detachable making it
easy to explain the learners how to get
the circumference and area of a circle.
Example: If the radius is 5 inches.
5 inches

In finding the relationship between a circle and
a parallelogram

• Concept of a circle; area and perimeter
• Relationship of a parallelogram and a
circle
• Fraction
• Division of numbers

The instructional material is made for the
learners to:
• identify the concepts of solid figures;
Surface area and volume; faces, edges and
vertices
• recognize the relationship between
platonic and archimedian solids

The instructional material is
made with a pattern
being followed.
The following information are
already given:
• faces
• edges
•Vertices
Learners will investigate the
surface area and volume of
these figures as well as the
relationship between Platonic
and Archimedean solids. The
figures made will serve as their
basis for this investigation

• Concepts on plane figures
and solid figures
• Surface area and volume of
solid figures
• Mathematical
investigations on the
relationships of these solid
figures
• Dice for various activities

OBJECTIVES
 Define Perimeter and Area.
 Illustrate the formulas on
finding the perimeter and
area of plane figures.
 Find the perimeter and area
of common plane figures.

The perimeter of any polygon is the sum of the
measures of the line segments that form its
sides. OR SIMPLY, the measurement of the
distance around any plane figure.
Perimeter is measured in linear units.

Triangle
The perimeter P of a triangle with sides of
lengths a, b, and c is given by the formula
P = a + b + c
a
b
c

SQUARE
The perimeter P of a square with all sides of
length s is given by the formula
P = 4s
s
s
s
s

RECTANGLE
• The perimeter P of a rectangle with length l
and width w is given by the formula
P = 2L + 2W
W
L
W
L

Can you find the perimeter for this
shape
12cm
5cm5cm
12cm

Answer
Add up all the length and width
measurements:
12cm + 12cm + 5cm + 5cm
OR
2 L + 2W
2(12) + 2(5)
= 34cm!

The amount of plane surface covered
by a polygon is called its area. Area
is measured in square units.

RECTANGLE
The area of a rectangle is the length of its base
times the length of its height.
A = bh
HEIGHT
BASE

PARALLELOGRAM
• The area of a parallelogram is the length of its
base times the length of its height.
A = bh
Why?
Any parallelogram can be redrawn as a rectangle
without losing area.
BASE
HEIGHT

TRIANGLE
The area of a triangle is one-half of the length of its
base times the length of its height.
A = ½bh
Why?
Any triangle can be doubled to make a parallelogram.
HEIGHT
BASE

TRAPEZOID
• Remember for a trapezoid, there are two parallel sides,
and they are both bases.
• The area of a trapezoid is the length of its height times
one-half of the sum of the lengths of the bases.
A = ½(b1 + b2)h
• Why?
• Red Triangle = ½ b1h
• Blue Triangle = ½ b2h
• Any trapezoid can be
divided into 2 triangles.
HEIGHT
BASE 2
BASE 1

Kite/Rhombus
• The area of a kite is related to its diagonals.
• Every kite can be divided into two congruent
triangles.
• The base of each triangle
is one of the diagonals.
The height is half of the
other one.
• A = 2(½•½d1d2)
A = ½D1D2
d1
d2

• Diameter
d=2r
• Circumference
C=2πr
• Area
A=πr2
diameter

Find the areas of the following parallelograms
12
5
6
13
5

DIFFERENCE
PERIMETER AREA
The perimeter of a
plane geometric
figure is a measure
of the distance
around the figure.
The area of a plane
geometric figure is
the amount of
surface in a region.

Rectangle P = 2l + 2w A = bh
Square P = 2l + 2w A = bh
Triangle P = side + side
+ side
A = ½ bh
Parallelogram P = 2l + 2w A = bh
Trapezoid P = 2l + 2w
Circles C = 2∏r A = ∏r²
1 2
1
( )
2
A b b h 

SURFACE AREA AND
VOLUME OF SOLID
FIGURES

WORDS TO UNLOCK
SURFACE AREA
• The total area of the
surface of a three-
dimensional object
VOLUME
• is the amount of
space enclosed in a
solid figure.

SURFACE AREA
the amount of
paper you’ll need
to wrap the shape
VOLUME
the number of cubic
units contained
in the solid.

SURFACE AREA
Total surface area:
6 (side) ² or 6(s) ²
Lateral surface area:
4(side)² or 4 (s) ²

VOLUME
CUBE/SQUARE PRISM
V = s²H
The product of its
height H and the
area of its base
s².

SURFACE AREA
Total surface area:
2(lb+bh +lh)
Lateral surface area:
2(l+b)h bl
h

VOLUME
V = lwh
The product of its
length ,
width/base and
height w
l
h

SURFACE AREA
Curved surface area
2 π rh
+
area of the circle
2 π r2
0r
Total surface area:
πrh +2 π r2
=2 π r(h+r)

VOLUME
V = Bh
V= πr²h
The product of its base
(πr²) and height (h)
h
b

SURFACE AREA
SA = ½ lp + B
Where l is the Slant
Height and
p is the perimeter and
B is the area of the Base

VOLUME
(1/3) Area of the Base x
height
Or
(1/3) Bh
Or
1/3 x Volume of a Prism
b
h

SURFACE AREA
Total surface area of
cone:
π r(s+r)
Lateral surface area of
cone-
π rs

VOLUME
V = ⅓Bh
V= ⅓ πr²h
where B is the area of the
base and h is the height
of the cone.
(1/3 the area of a cylinder)

HORIZON 101
FRONT OF ST. THERESA’S
COLLEGE (MANGO GATE)

IGLESIA NI CRISTO
(GEN. MAXILOM AVE.)

OLD BUILDING
SENIOR CITIZEN PARK

VETERAN’S
MONUMENT
PLAZA INDEPENDENCIA

MARINERS’ COURT
FRONT OF PIER 1

MIGUEL LOPEZ DE LEGAZPI
MONUMENT
PLZA INDEPENDENCIA

Sources:
msjc.edu
worldofteaching.com
taosschool.org
marianhs.org
mathbits.com

Instrumentation in Mathematics

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