Can we integrate "integration" in
our daily lives?
I hope that you all are well and enjoying good times. Let me
introduce myself. I'm an academic coordinator at Shahwilayat Public
School in Karachi, Pakistan. I'm also teaching additional mathematics
to o-levels. Nowadays I'm working in an on-line iearn course. One of
my course coordinators has asked me to be part of this segment too, so
I'm sending my project template for a start. I welcome your
Designing a Problem-Base
Teacher: Abeer Rizvi
Can we integrate "integration" in our daily lives?
Project this will contribute to:
integration is a new concept for the students at this level
and they are a bit reluctant to investigate the actual depth
and breadth of the topic. However, the condition is reverse
in this case as this project of mine will make it very clear
that they have come across the integration in their daily
life while learning many of the concepts in physics and
advance physics. It will enable students develop an
awareness and understanding of the different huge mysteries
of daily life are being resolved by the help of integration.
As the project is going to uncover many different
daily life phenomena so I'll be a mentor throughout.
Observers, Analyzers, Facilitators and Researchers,
Time Frame for the Unit:
Approximately needs 4 -5 weeks.
Meet the Problem:
Well, the thing which is going to give my students
a hook surely are my unit questions:
Do you think that "rate of change" is what life all about?
Where can we relate "integration" in our daily lives?
This will motivate them enough to start this project as
they are already quite into to
Investigate the application of integration in daily life.
Know/Need to Know:
My comments for the KNK are:
Know (K) Need to Know (NK)
concept of "rate of change" i.e "differentiation".
up all the small changes gives the new concept of "integretion".
concepts of physics for example, work, Kinetic energy, Potential
energy, Thermal expansion, Rockets thrust, impulse and collisions,
Rotational inertia, Fluid motion, Thermodynamics.
relate and investigate all these
scientific concepts already learnt in their previous grades
and to learn how they have been derived using the "integration".
all are frequent users of computers and internet resources.
will need guidance in the keywords for browsing the internet
are familiar with the softwares like word,power point and
will need mentoring in organizing and designing their projects
using all these softwares.
around the sites they know to handle the data provided at
need thorough monitoring and understanding of "what is copyrights?"
and "what is fairuse?"
the researchers and analyzers, how can we investigate the
daily life examples in such a way so that we can relate
them with the concept of integration and also how the queries
of our previous years which were left unanswered by writing
"beyond the scope of the book" can be answered by applying
Information Gathering & Sharing:
For gathering the information the students
will be utilizing:
Different reference books
Different CD's of physics
Browsing different sites (key words -- guided by the teacher)
sessions with their mathematics and physics teachers
For sharing the information they will:
Word documents for soft board presentations
Power point presentations
Generating Possible Solutions and Determining a Fit:
As I have mentioned earlier this project is not touching
some particular problem, but it is uncovering many previous
concepts on which the whole physics is based.
the end the students will be able to relate the following
physics concepts with integration:
Kinetic energy, Potential energy, Thermal expansion, Rockets
thrust, impulse and collisions, Rotational inertia, Fluid
motion, Thermodynamics and some more depending upon the
1. Students will gain an understanding what is the area
under a curve.
2. Be able to develop and understand the "rate of change".
3. Also be able to develop the understand that how these
all rates of changes can all be summed up to determine the
area under the curve.
4. Understand the integration as a reverse process of differentiation.
5. Investigate different types of integrals i.e indefinite
and definite integrals.
6. Students will relate the integration procedures with
different daily life examples.
7. Students will use collaboration skills to convey ideas
and create presentations.
8. .Students will use research skills; basic and intermediate
computer skills, navigate resources including, an internet
browser, word processing software, CD ROMs, and presentation
9. Using right key words for browsing the internet.
10. Students will observe copyright rules.
Students will develop and promote Higher-Level Thinking
skills that is they will be able to recognize, comprehend,
apply, analyze, schematize, and assess/ evaluate
the different situations provided from time to time by the
Students will be able to design intelligent reflection forms
to get the feed back from other group mates.
goal of the project is to enable students by systematic
study to acquire the knowledge, skill, and judgment to continue
to learn for themselves; to participate intelligently, justly,
and responsibly in civic life and to avail themselves resources
like internet sites, libraries, multimedia information sources
wherever they may live or travel. It lets the students to
learn to apply the mathematics in their daily lives.
Curriculum areas covered:
1. Area under the curve.
2. Studying the area under the curve.
3. Rates of changes.
5. Integration as a reverse process of differentiation.
6. Relating integration with the daily life examples.
7. Different techniques of integration.
8. Definite integration and indefinite integration.
Working with the mathematical calculations of:
Work, Kinetic energy, Potential energy, Thermal expansion,
Rockets thrust, impulse and collisions, Rotational inertia,
Fluid motion, Thermodynamics and some more depending upon
the time frame.
Working with the softwares
1. Power point
Embedded Instruction Activities to Meet the Outcomes:
activities are necessary to give students the knowledge
and skills they need to solve the problem and achieve the
1. Area under the curve.
2. Studying the area under the curve.
3. Rates of changes.
1. Integration as a reverse of differentiation.
2. Integration related to mathematical calculations of different
concepts in physics.
Different groups will work on different fields of physics
like Mechanics, Waves,
Oscillations, fluids, Thermodynamics and Eletromagnetism,
designing documents, forms, templates, soft board material
and class presentations.
Rules for integration
Definite and indefinite integrals
Resources of internet, CD Roms etc.
Solutions to some unique problems of integration.
Sessions with Physics teacher
The groups will be assessed on the basis of how:
Each group will use resources to present its research work
i.e soft boards, class presentations.
2. They will also design forms to collect reflections from
other groups of the class.
3. The students will develop a plan of action to determine
how to get the research completed.
4. The group should be able to summarise the unit.
5. They should also be able to design a Tool kit which should
include "terms to understand, Symbols to recognize, Limitations
to keep in mind.
After completing the research,the way the students will
create PowerPoint presentations with partners over their
area of expertise.
7. Students will present PowerPoint presentations to the
8. They will also design rubrics.
9. Usage of publisher software will give them some extra
1. Students will be interviewed about their developed
2. Individual class presentation to be given.
3. MCQ's, quizzes, word problems, conceptual numericals
will be given to assess them.
4. Students will also be required to design observation
charts during the class presentation of other class mates.
5. Every day participation in the respective group.
as far as I am concerned, debriefing the unit again will
help the students to have a contented feeling of completing
a task. I am sure that with this project the approach of
the students will totally be changed as that will be more
motivated and investigating towards very complex learnings.
The best thing about this project is that the student will
always be ready to uncover the depth and the breadth of
the topic and can relate different fields at all stages.
project can easily be expanded as the concept of integration
is also useful in different types of motion e.g Projectile,
Vertical, Horizontal, angular, sliding and molecular motions
The whole picture will come up as a summation of all the
areas covered of different curriculums and thus developing
much better higher level thinking skills.
Other Concern and/or Notes:
my practice that I always train my students to make their
time schedules for the whole week, their weekend and then
their assessment too.
I'm going to keep a check in their project work that they
do work keeping a written organizer with them and working
thing which is also very important as I have mentioned above
that they should be able to design a checklist for their
project as they will be designing a Tool kit at the end
of the project.