Integrated Science SME

Key Unit competence: Explain the concept of Integrated science and use accurately   

                                             different tools to measure physical quantities in sciences.

Introductory Activity 1
Look carefully the following illustrations and answer the questions below:

Questions:
a). Describe the illustration A, B, C, D.
b). Based on your knowledge from O-level, what are scientific concepts
can you associate to each of those illustrations? Group the noted
concepts in their science subject areas.
c). Is there any one illustration in which you find application of many
science subjects area? Justify your answer by providing other
examples found in everyday life.
d). Can you explain how and why every person should have integrated
understanding of those science subject areas?
e). What kind of physical quantities that can be measured in the
illustration above? Suggest the names of the tools used in the
illustration above?

f). Outline other examples of physical quantities and the corresponding
measuring tools
g). What can be considered to select the best tool(s) to be used in
measuring a given measurable quantity?

1.1. Introduction to Integrated science

Activity 1.1

Task 1

It is known that an Integrated Science course serves the purpose of
unifying sciences in a whole one subject covering both the physical and
life sciences. These courses are integrated in that the fields of science
are not segmented. For example, in describing the physics of light, we
show how this applies to the inner workings of our eyes, which, in turn, are
sensitive to visible light in great part because of the chemical composition
of our atmosphere.
Use the paragraph above to answer the following questions:
a). What does the term integrated science mean?
b). Explain why Integrated Science is very important in finding
appropriate solutions in various complex situations? Justify your
answer based on the paragraph above and other examples
observed in everyday life.

Task 2

Suppose you visited two industries and took the photos A and B below
and saw that distinguished science subjects are involved in the process
of production. Write a paragraph about your visit identifying how Physics,
Biology and Chemistry are integrated in the process.

1.1.1. Definition and rationale of Integrated science

Human survival depends on knowledge through the exploration of the
environment. Science provides knowledge while technology provides ways
of using this knowledge. It is therefore very important to be aware of the
global dimension of science needed in our lives in order to effectively deal
with every day situation.
The word “integrated” means “to restore the whole, to come together, to be
a part of, to include.” Integrated science is a subject which incorporates
the knowledge base of all the science fields, both physical and life sciences
and these science fields are included in one subject as a whole “integrated
science” in that the fields of science are not segmented. It is a subject
which offers experiences which help people to develop an operational
understanding of the structure of science that should enrich their lives and
make them more responsible citizens in the society.
Hence, integrated approach of learning science is appropriate as science
knowledge is a tool to be used by every person to effectively deal with real
world problems and life.
For examples, when you are studying digestion process of animals, you will
need the knowledge of chemical processes. Another example, in describing
the physics of light, we show how this applies to the inner workings of our
eyes, which, in turn, are sensitive to visible light in great part because of the
chemical composition of our atmosphere.

Aims of Integrated Science subject

The overall aim of the integrated science subject is to enable students

develop scientific literacy so that students can participate actively in the
rapidly changing knowledge based society, prepare for further studies or
careers in fields where the knowledge of science will be useful.
However, the broad aims of integrated science subject are to enable students
to:
• Develop interest in and maintain a sense of wonder and curiosity about
the natural and technological world;
• Acquire a broad and general understanding of key science ideas and
explanatory framework of science and appreciate how the ideas were
developed and why they are valued;
• Develop skills for making scientific inquiries;
• Develop the ability to think scientifically, critically and creatively and
to solve problems individually or collaboratively in science related
contexts;
• Use the language of science to communicate ideas and views on
science – related issues;
• Make informed decisions and judgments about science related issues;
• Be aware of the social, ethnical, economic, environmental and
technological implications of science and develop an attitude of
responsible citizenship; and
• Develop conceptual tools for thinking and making sense of the world.

1.1.2. Interconnection between science subjects

The purpose of science is to produce useful models of reality which are used
to advance the development of technology, leading to better quality of life for
human being and the environment around him or her.
There are many branches of science and various ways of classifying them.
One of the most common ways is to classify the branches into natural
sciences, social sciences, and formal sciences.
Natural sciences: the study of natural phenomena (including cosmological,
geological, physical, chemical, and biological factors of the universe).
Natural science can be divided into two main branches: physical science
and life science (or biological science). Social sciences: the study of human
behavior and societies. The social sciences include, but are not limited to:
anthropology, archaeology, communication studies, economics, history,
musicology, human geography, jurisprudence, linguistics, political science,
psychology, public health, and sociology. Formal science is a branch of

science studying formal language disciplines concerned with formal systems,
such as logic, mathematics, statistics, theoretical computer science, artificial
intelligence, information theory, game theory, systems theory, decision
theory, and theoretical linguistics.

Note:
• Chemistry mainly deals with the study of matter’s properties and
behaviors as well as reactions between them to produce new useful
products. For a physicist to understand the working mechanism of
chemical cells, help is sought from a chemist. On the other hand, the
reasons behind the various colours observed in most of the chemical
reactions are explained by a physicist.
Petroleum products are dealt with by the chemist, but the transportation
of such products make use of the principles of physics.
• In Biology, the study of living cells and small insects by a biologist
requires magnification. The concept of magnification using simple or
compound microscope is a brain child of a physicist. A good physicist
needs to have good health.

1.1.3. Relationship between Integrated science with other subjects

As science is about observation and experimentation of things in the physical
and natural world, the relationship of Integrated science and other subjects
might be explained in broader senses and will also predict much broader
interconnections as applications of science are useful in human daily life.
Below are some examples of relationship between Integrated science with
other subjects:

Science with Mathematics:

A large number of scientific principles and rules are represented in the form of
mathematical expressions, for which it is very necessary for person intending
to get advanced study of science subjects to have sound mathematical basis.
Without making use of mathematical expressions and rules, it is not possible
to learn science in effective manner. Therefore, mathematics is considered
to be sole language of science because of which real understanding of
science is considered to be impossible without adequate knowledge of
mathematics. Some of the useful mathematical tools which are generally
used in the science are algebraic equations, geometrical formulas, graphs
etc. For example, Astrology is an advanced branch of science in which it
is predicted or enumerated that which planet revolves at which speed and
when it will get appeared to the people of earth.

Science with History:
It sounds quite amazing that some kind of correlation can exist in between
the science and history as earlier subject is practical in nature while nature
of later subject is purely theoretical. However, it is possible to co-relate
these subjects with each other. For example, in History, the determination of
age fossils by historians and archaeologists use the principle developed by
physicists. The medicine science lists the incidences which inspired various
scientists to found out the medical remedies of various diseases.

Science with Geography:
Geography is the subject in which various concepts relating to earth on which
we live are dealt with. Everything existing on earth, on different planets of the
universe are also main subjects of geography. Which kind of crop should be
sown in which kind of soils, how many kinds of rocks are found on the earth
are some of the main topics which are covered by Geography. These topics
are also covered by the subject of Science.
In science, there are various concepts relating to the atmosphere and earth
in which living and non-living beings. For this reason, temperature, wind
directions and measurement of rainfall are conducted in the subject of
science by making use of various apparatus. For example, in Geography,
weather forecast, a geographer uses a barometer, wind gauge, etc. which
are instruments developed by a physicist.
Results obtained by the science in terms of climate and the manner in which
it affects the human beings and earth are being interpreted by subject of
Geography. The manner in which it is mentioned by the geography how
soil gets produced through crushing process of rocks makes the subject a
special branch of science.
As there are various topics which are of common interest for geographers
and scientists, it can be said that both of these subjects are very near to
each other and complementary to each other.

Science with Social Studies:
Various evidences can be found in our life which can show the significant way
in which life style of human beings have got affected by inclusion of scientific
developments in their life. Today, there are various kinds of machines for
performing different functions, about which primitive men even did not think.
As a result of these machines, human life has become very easy and
smooth and now we can accomplish complex functions within short period
of time, which were considered to be very time consuming. Again, scientific

researches have led to development of various medicines with the help of
which physicians have found the remedies of various diseases, which were
once considered to be incurable and were responsible for bringing about
heavy loss of life in earlier times.

Science with Physical education and sports:
In games and sports, different instruments developed by physicists are used
for accurate measurement of time, distance, mass and others.

Application activity 1.1

1. Write a paragraph to convince someone that science is related to
other subjects. Use clear examples to support your arguments and
reasoning.
2. How can you describe the interconnections between science and
technology, using at least three specific examples?

1.2. Measurement of physical quantities

Activity 1.2

Task 1:

Look around the place and identify possible physical quantities that can
be measured? Explain the meaning of the physical quantities you have
identified? Mention the SI units of the identified physical quantities?

Task 2:
It is possible to determine the nature and magnitude of the physical
quantities that are measurable. Which of the following situations can be
determined with the guidance of measurements? Support your answer
with explanations and mention the physical quantity to be measured if
possible.
a). Love between a boy and girl.
b). Size of the body
c). Size of the garden?
d). Amount occupied by water in a tank.

1.2.1. Physical quantities and their measurements
A quantity is any observable property or process in nature with which a
number may be associated.
A physical quantity is defined as a property of a material that can be quantified
by measurement.
Physical quantities are classified into fundamental and derived quantities.

Fundamental physical quantities
A quantity may be defined as any observable property or process in nature
with which a number may be associated. This number is obtained by the
operation of measurements. The number may be obtained directly by a single
measurement or indirectly, say for example, by multiplying together two
numbers obtained in separate operations of measurement. Fundamental
quantities are those quantities that are not defined in terms of other quantities.
In physics there are 7 fundamental quantities of measurements namely
length, mass, time, temperature, electric current, amount of substance and
luminous intensity.

Derived physical quantities
Quantities which are defined in terms of the fundamental quantities via a
system of quantity equations are called derived quantities. Examples of
derived quantities include area, volume, velocity, acceleration, density,
weight and force.
The SI units of derived quantities are obtained from equations using
mathematical expressions
Note that some derived units have been given special names. For example,
force is measured in kg m/s2 and has been given a named unit called a
newton (N).

1.2.2. International system of units (SI)
In order to measure any quantity, a standard unit (base unit) of reference
is chosen. The standard unit chosen must be unchangeable, always
reproducible and not subject to either the effect of aging and deterioration or
possible destruction.
In 1960, an international system of units was established. This system is
called the International System of Units (SI).

The International System of Units is an internationally agreed metric system
of units of measurement. The value of a physical quantity is usually expressed
as the product of a number and a unit.

Name, Symbol and factor of metric prefixes in everyday use at workplace.SI
prefixes used to form decimal multiples and submultiples of SI units (table 2
below).

Example for length
• 10 mm= 1cm
• 1m= 106μm
• 1m=10-9Gm
• 1m2=(1012pm)2=1024pm2

Note: Numbers in the SI system are based on the number 10. Units in the SI
system can therefore be multiplied or divided by 10 to form larger or smaller
units.

1.2.3. Measuring fundamental physical quantities

Measuring length and distance

We use different tools for measuring length: metre rule, ruler, tape measure,
vernier caliper and the micrometer screw gauge based on the kind of length
to measure. Straight distances that are less than one metre in length are
generally measured using metre rules. Straight distances that are more than
one metre in length are generally measured using tape measure.
A tape measure or measuring tape is a flexible ruler and used to measure
distance. A tape measure is in form of a strip of metal, plastic or cloth that has
numbers marked on it as shown in figure below and is used for measuring.
The instruments A and B in the figure 1.4. below represent examples of tape
measures:

It is a common measuring tool purposely designed to allow for a measure
of great length to be easily carried out and permits one to measure around
curves or corners. Surveyors use tape measures in lengths of over 100 m.
Metre rules are graduated in millimetres (mm). Each division on the scale
represents 1 mm unit (Fig 1.5. below).

The direct way to measure length is by means of the straight edge of a ruler
or metre ruler.

The ruler is placed alongside the object to be measured, and the number of
unit intervals of the ruler equal to the length of the object is then noted.

Metre rule is used to measure lengths up to about 100 cm and has a
sensitivity of 0.5 mm. Vernier calipers is an instrument used to measure
outer dimensions of objects inside dimensions and depths.The figure 1.6
shows the vernier calipers:

We can measure outer dimensions of objects (using the main jaws), inside
dimensions (using the smaller jaws at the top), and depths (using the stem).
The vernier calipers have a main scale and a sliding vernier scale that can
allow readings to the nearest 0.02 mm.

To measure outer dimensions of an object, the object is placed between the
jaws, which are then moved together until they secure the object.
The screw clamp may then be tightened to ensure that the reading does not
change while the scale is being read.

The first significant figures are read immediately to the left of the zero of the
vernier scale and the remaining digits are taken as the vernier scale division
that lines up with any main scale division. The internal diameter of the test
tube is given by ( MSR + (VC × LC) Whereby the main scale reading (MSR),
the vernier coincidence (VC) and The smallest reading called the least count
(LC) that can be read from vernier callipers is 1 mm – 0.9 mm = 0.1 mm or
0.01 cm .

The main scale called the vernier coincidence (VC) and multiplying it with
the least count i.e 0.01 cm. Therefore, the external diameter of the cylindrical
object is (MSR + (VC × LC)
A micrometer screw gauge is an instrument for measuring very short length
such as the diameters of wires, thin rods, and thickness of a paper.

The micrometers have a pitch of 0.50 mm (two full turns are required to
close the jaws by 1.00 mm). The rotating thimble is subdivided into 50 equal
divisions. The thimble passes through a frame that carries a millimetre scale
graduated to 0.5 mm. Thimble, which has a circular rotating scale that is
calibrated from 0 to either 50 or 100 divisions. This scale is called the head
scale (thimble scale). When the thimble is rotated, the spindle can move
either forward or backwards. Ratchet which prevents the operator from
exerting too much pressure on the object to be measured. The least count =
0.01 mm. The micrometer screw gauge reading = MSR + (HSC × LC).
When the pitch is 1 mm, the thimble has 100 divisions called head scale
divisions. In this case each division represents 0.01 mm. This is the least
count (LC) of this screw gauge.

The thimble reading called the head scale coincidence (HSC) is the value of
the mark on the thimble that coincides with the horizontal line on the sleeve.
Main scale reading is taken by considering the reading of a mark on the fixed
scale that is immediately before the sleeve enters the rim of the head scale.
The jaws can be adjusted by rotating the thimble using the small ratchet
knob. This includes a friction clutch which prevents too much tension being
applied. The thimble must be rotated through two revolutions to open the
jaws by 1 mm.

In order to measure an object, the object is placed between the jaws and the
thimble is rotated using the ratchet until the object is secured. The ratchet
knob must be used to secure the object firmly between the jaws, otherwise
the instrument could be damaged or give an inconsistent reading. The lock
may be used to ensure that the thimble does not rotate while you take the
reading.

Measuring mass
The mass of an object can be measured using a beam balance and a set
of standard masses. It is noticed that the volume of the displaced water in
measuring cylinder is equal to volume of an object lowered in the cylinder.
There are many kinds of balances used for measuring mass illustrated below:

Measuring time
Time is measured using either analogue or digital watches and clocks
and illustrated in figure below:

Application activity 1.2
1. Mention the appropriate instruments you would use to measure
each of the following:
a. The length of a football field.
b. The mass of an object.
c. The circumference of your waist.
d. The time someone uses to cover a certain length.
e. The diameter of a small ball.

2. It is possible to read and record the readings using a scale of a
vernier caliper in order to measure the external diameter of the rod.
Steps followed in using vernier
a. Place the object to be measured between the outside jaws as
shown in the figure below. Slide the jaw until they touch the rod.

b. Record the readings on the main scale and the vernier scale.
The main scale reading is the mark on the main scale that is
immediately before the zero mark of the vernier scale.

c. Multiply the vernier scale reading by 0.01 cm.

d. Add the main scale reading (in cm) and the vernier scale reading
(in cm) to get the diameter of the rod.

3. What is the diameter of the ball bearing shown in Figure below?

4.
a). What does S I Units stands for?
b). Explain why it is correct to say that SI units are very important in
measurements?
c). Suppose you wish to know the length of a big garden. How do
you get the length of your garden?

d. Look at the following physical quantities: Mass, density, length,
and time. Do all these quantities represent the fundamental
quantities? Justify your decision by identifying the ones included
in the category mentioned above.

4. Look at the table below and try to complete it based on the skills
gained in the previous activities done;

5. Choose two physical quantities with which you are familiar. Imagine
that you are skilled in physical quantities and its measurements.
Explain briefly how the values of these quantities can be obtained?
6. Express the following the indicated units and fill in blank spaces:
a). 250 m in .....cm.
b). 320 mg in ......g.
c). 5μg in .........g.
d). 7200 cm in .....m.
e). 3 kg in ......... g.

1.3. Dimensions of physical quantities

Activity 1.3

Given the formulas for the following derived quantities, try go get the
dimensions of each quantity.
a). velocity = displacement/time
b). acceleration = change of velocity/time
c). momentum = mass x velocity
d). force = mass x acceleration
e). work = force x displacement

1.3.1. Introduction to dimensions of physical quantities

The nature of physical quantity is described by nature of its dimensions.
When we observe an object, the first thing we notice is the dimensions.
In fact, we are also defined or observed with respect to our dimensions that
is, height, weight, the amount of flesh. The dimension of a body means how
it is relatable in terms of base quantities. When we define the dimension of a
quantity, we generally define its identity and existence. It becomes clear that
everything in the universe has dimension, thereby it has presence.

Note: Dimensions are responsible in defining shape of an object.

1.3.2. Definition of dimensions of physical quantities

The dimension of a physical quantity is defined as the powers to which the
fundamental quantities are raised in order to represent that quantity. The
seven fundamental quantities are enclosed in square brackets [ ] to represent
its dimensions.

Examples of assigning dimensions to physical quantities

Dimension of Length is described as [L], the dimension of time is described
as [T], the dimension of mass is described as [M], the dimension of electric
current is described as [A] and dimension of the amount of quantity can be
described as [mol]. Adding further dimension of temperature is [K] and that
dimension of luminous intensity is [Cd]
Consider a physical quantity Q which depends on base quantities like length,
mass, time, electric current, the amount of substance and temperature, when
they are raised to powers a, b, c, d, e, and f. Then dimensions of physical
quantity Q can be given as:
[Q] = [LaMbTcAdmoleKf]
It is mandatory for us to use [ ] in order to write dimension of a physical
quantity. In real life, everything is written in terms of dimensions of mass,
length and time. Look out few examples given below:

1. The volume of a solid is given is the product of length, breadth and its
height. Its dimension is given as:
Volume = Length × Breadth × Height
Volume = [L] × [L] × [L] (as length, breadth and height are lengths)
Volume = [L]3

As volume is dependent on mass and time, the powers of time and mass
will be zero while expressing its dimensions i.e. [M]0 and [T]0
The final dimension of volume will be [M]0[L]3[T]0 = [M0L3T0]

2. In a similar manner, dimensions of area will be [M]0[L]2[T]0

3. Speed of an object is distance covered by it in specific time and is given
as:
Speed = Distance/Time
Dimension of Distance = [L]Dimension of Time = [T]Dimension of Speed = [L]/[T][Speed] = [L][T]-1 = [LT-1] = [M0LT-1]

4. Acceleration of a body is defined as rate of change of velocity with
respect to time, its dimensions are given as:
Acceleration = Velocity / Time
Dimension of velocity = [LT-1]Dimension of time = [T]Dimension of acceleration will be = [LT-1]/[T][Acceleration] = [LT-2] = [M0LT-2]

5. Density of a body is defined as mass per unit volume, and its dimension

is given as:
Density = Mass / Volume
Dimension of mass = [M]Dimension of volume = [L3]

Dimension of density will be = [M] / [L3][Density] = [ML-3] or [ML-3T0]6. Force applied on a body is the product of acceleration and mass of
the body
Force = Mass × Acceleration
Dimension of Mass = [M]Dimension of Acceleration = [LT-2]Dimension of Force will be = [M] × [LT-2][Force] = [MLT-2]

1.3.3. Rules for writing dimensions of a physical quantity

We follow certain rules while expression a physical quantity in terms of
dimensions, they are as follows:
• Dimensions are always enclosed in [ ] brackets
• If the body is independent of any fundamental quantity, we take its
power to be 0
• When the dimensions are simplified we put all the fundamental
quantities with their respective power in single [ ] brackets, for example
as in velocity we write [L][T]-1 as [LT-1]• We always try to get derived quantities in terms of fundamental
quantities while writing a dimension.
• Laws of exponents are used while writing dimension of physical quantity
so basic requirement is a must thing.
• If the dimension is written as it is we take its power to be 1, which is an
understood thing.
• Plane angle and solid angle are dimensionless quantity that is they are
independent of fundamental quantities.
• Therefore, some of the examples of dimensions of physical quantities
include the following:
Force, [F] = [MLT-2]Velocity, [v] = [LT-1]Charge, (q) = [AT]

Specific heat, (s) = [L2T2K-1]Gas constant, [R] = [ML2T-2K-1 mol-1]

Benefits of Dimensions
Before writing dimensions of a physical quantity, it is must know a thing to
understand why do we need dimensions and what are benefits of writing a
physical quantity. Benefits of describing a physical quantity are as follows:
• Describing dimensions help in understanding the relation between
physical quantities and its dependence on base or fundamental
quantities, that is, how dimensions of a body rely on mass, time, length,
temperature and others.
• Dimensions are used in dimension analysis, where we use them to
convert and interchange units.
• Dimensions are used in predicting unknown formulae by just studying
how a certain body depends on base quantities and up to which extent.
• It makes measurement and study of physical quantities easier.
• We are able to identify or observe a quantity just because of its
dimensions.
• Dimensions define objects and their existence.

Limitations of Dimensions
Besides being a useful quantity, there are many limitations of dimensions,
which are as follows:
• Dimensions can’t be used for trigonometric and exponential functions.
• Dimensions never define exact form of a relation.
• We can’t find values of certain constants in physical relations with the
help of dimensions.
• A dimensionally correct equation may not be the correct equation
always.

Dimension Table
It consumes a lot of time while deriving dimensions of quantities. So in order
to save time, we learn some basic dimensions of certain quantities like
velocity, acceleration, and other related derived quantities.
For Example, suppose you’re asked to find dimensions of Force and you
remember dimension of acceleration is [LT-2], you can easily state that the
dimension of force as [MLT-2] as force is the product of mass and acceleration
of a body.
The table below depicts dimensions of several derived quantities which one
can use directly in problems of dimension analysis.

Application activity 1.3
1. i) What are four uses of dimensional analysis? Explain with one
example for each.
ii). What are three limitations of dimensional analysis in physics?
2. Show that 2
1 gt2 has the same dimensions of distance.
3. What are the missing words in the following statements?
a. The dimensions of velocity are ..................................... .
b. The dimensions of force are ..........................................
4. a) What does the term dimension mean in Physical quantities?
b) Given the formulas for the following derived quantities, calculate the
dimensions of each quantity.

iii.Momentum = mass x velocity
iv. Force = mass x acceleration
v. Work = force x displacement
21
Skills lab 1
Conduct a survey, collect and analyze data about when, where, and why
people use different measuring instruments or devices and physical laws.
To complete this project you must:
• Develop a survey sheet about physical quantities, measuring
instruments or devices, physical laws needed, appropriate SI units and
metric prefixes used in everyday life.
• Distribute your survey sheet to other student-teachers, family members
and neighbors.
• Compile and analyze your data.
• Create a report to display your findings in your sheet.
Plan it! To get started, think about the format and content of your survey
sheet. Brainstorm what kinds of questions you will ask. Develop a plan for
involving student-teachers in your class or other classes to gather more data.

End unit assessment 1
1. Differentiate a fundamental quantity and a derived quantity. Give one
example of each and its corresponding SI units.
2. Express the following in millimetres:
(a) 2.7 m (b) 26.9 cm (c) 356 μm.
3. What is the length of the glass rod shown in Figure below?

4. Use the knowledge and skills gained from the previous concepts to
complete the following sentences:
a) A quantity may be defined as any ............................ in nature
with which a number may be associated.
b) Physical quantities are classified into ................ and
..................... quantities.
c).................................are those quantities that are not defined
in terms of other quantities.
d) The value of a physical quantity is usually expressed as the
product of a .....................and a ........................
e) The SI units stands for ..............................................
5. Kaneza conducted an experiment on the growth of plants and
recorded the results in a table. He used four plants of the same type
and size and measured their growth after one month.
Table of results based on each plant type.