Understanding Ratios and Proportions

The assignment discusses common obstacles students encounter when learning about ratios and proportions in mathematics. It emphasizes the importance of relating these concepts to real-world examples and using visual aids to enhance understanding. The text suggests collaborative learning activities and analytical approaches to address student misconceptions and foster a positive learning environment.

Running head: METHOD OF CLASSROOM TEACHING OF RATIO-PROPORTION
Method of Classroom Teaching of Ratio-Proportion
Name of the Student:
Name of the University:
Author Note:

2METHOD OF CLASSROOM TEACHING OF RATIO-PROPORTION
Executive Summary:
This report represents the techniques and methods of teaching the chapter of mathematics
“Ratio and Proportion” to the students of a classroom through “Thinking Through a Lesson
Protocol”(TTLP). The format of the lesson plan is an integral part of teaching and learning
process. In the report, we are elaborately discussing the background information, relevant
information, reflection and summary of the teaching process of the chapter “Ratio and
Proportion” delivered to the 7th grade students.

3METHOD OF CLASSROOM TEACHING OF RATIO-PROPORTION
Table of Contents
Introduction:...............................................................................................................................4
Background Information:...........................................................................................................4
Aim of the teaching:...............................................................................................................4
Outcomes:..............................................................................................................................4
A method of assessment of students’ learning:......................................................................5
Other items and accessories:..................................................................................................5
Relevant Information:................................................................................................................5
Method of teaching:...............................................................................................................5
After finishing the lesson:......................................................................................................7
Expected outcome of the lesson:............................................................................................7
After the scheduled time of class:..........................................................................................8
Concluding the lesson:...........................................................................................................8
Conclusion:................................................................................................................................8
Reflections:............................................................................................................................8
Summary of the lesson:..........................................................................................................9
References:...............................................................................................................................10

4METHOD OF CLASSROOM TEACHING OF RATIO-PROPORTION
Introduction:
The objective of the report is to teach the idea of “ratio and Proportion” to the seventh
grade students of the school. The classroom contains 30 students of ages 10 or 11. Now,
among them, one student is handicapped in leg. Various learning charts are used and set of
questions is valued over answers in this classroom where an ambient atmosphere exists. It is
assumed, that students are aware of all the mathematical operations like addition, subtraction,
multiplication and division.
Teacher is aware of the condition of the class and his priority would be to teach this
topic playfully to the students. His approach must be helpful and collaborating towards the
entire class irrespective of their merit.
In the following, report describes particularly the effective method and technicality of
teaching the students. The report also appreciates the teacher to involve the students in
various extra curriculum activities at the time of teaching the chapter (Jalon and Arias, 2013).
Background Information:
Aim of the teaching:
This report incorporates the co-learning of many students along with teachers.
Students can practice to identify the objectives of instructions, improving mathematical
techniques and sequencing mathematical tasks. Teacher would also be able to develop
students’ competence effectively by chapter related extra curriculum activity, teaching
research activities and deepening the understanding of teaching (Lamon, 2013).

5METHOD OF CLASSROOM TEACHING OF RATIO-PROPORTION
Outcomes:
The students would be able to handle the mathematical ideas and decisive approach to
enter to the world of real numbers from whole numbers. In addition to the learning, the
students could apply this concept to the field of basic algebra. The knowledge of Ratio and
Proportion could influence them to relate several situations in real life.
A method of assessment of students’ learning:
Group participation and curriculum activities, observation and participation are the
crucial factors of the assessment. Teacher can invite the students to share their knowledge by
wall magazines, math journals of the class, observational games.
Other items and accessories:
An interactive whiteboard, wall hanging tables, math journals are truly essential to
deliver lesson to the students. Besides, teacher needs a computer lab to show the different
operations and attributes of ratio and proportion to the students after completion of topics.
Relevant Information:
Method of teaching:
In TTLP format, teacher’s standard of choice is TEKS where the teacher mainly
depends on classified textual format and documents. TEKS means Texas Essential
Knowledge and Skills. TEKS format mainly was introduced to bring the multicultural
education system in America (Casas, 2013).
Firstly, teacher can deliver a speech about any story related to proportion. Teacher
could invite first boy of the class and ask him to tell a number. Again, we could ask last boy
of the class to tell another number. Then, he or she would write those two numbers in the
white board and affix a proportional sign between them. Finally, teacher would inform

6METHOD OF CLASSROOM TEACHING OF RATIO-PROPORTION
students that it is the standard form of proportion. Lastly, teacher could define that what ratio
is.
At the next step, he would tell students to reduce some proportions to their reduced
form. Suppose a student tells a number 6. He should put the next number 8 and write it as 6:8.
Then, he could advice them to reduce the value to 3:4 with the concept of greatest common
divisor. He would not discuss the previous chapters but revise the knowledge in other way.
The general idea to develop is that these two quantities change at the same rate. Then, he can
write two ratios in divisible form. It is a new approach to write proportion. They would get a
chance to improve and revise the cross-multiplying.
Teacher could have another approach to divide students in many groups. They are
randomly given a task to observe two variable tables, where these two variables’ columns are
filled with related data that are proportionally allocated like hours and distance covered by a
train, number of pens and the cost of pens, dollars and meters in the taxi-fare (Ekawati,Lin
and Yang, 2015). After studying tables and equivalent rates, the students would get prepared
to tackle word problems on Ratio and Proportion. Teacher should choose simple ones at first,
and let students think in the hope that they might well come up with an answer by their own.
The next step is to provide the knowledge of proportion and the true relation between
proportion and ratio. He would tell the students that the main difference is units. Ratio is unit-
free whereas the proportion could be dependent upon units. Teacher should provide the
relevant preliminary definitions on ratio and proportion.
He can justify our teaching in the way that real life aspects of “Ratio and Proportion”
are applicable to our teaching. Suppose, a teacher could tell that he went to market to buy 1
kg of potato at rupees 10, next day again 2 kg of potato at rupees 20. The teacher could ask

7METHOD OF CLASSROOM TEACHING OF RATIO-PROPORTION
the student that what it is going to be the total cost price tomorrow if he would buy 5
kilograms of potato.
If the concept of proportion is more or less clear to all the students, then they can
think about inverse proportion. He would provide the idea of increment of one variable with
the increment or decrement of another variable. As an example, he can cite the time and the
number of workers problem. Teachers should form balanced groups (in terms of abilities) and
advice the students to find different ideas about this topic from the mathematics textbook
(Carrillo et al., 2013). The teacher should make sure that the student is able to solve the basic
problems on Ratio and proportion and understand what is actually happening to the topic.
After the group work of the students, the teacher should provide an independent activity to
each student to express their response and ideas (Assessment, 2013).
After finishing the lesson:
The teacher can spend this time playing math quiz with the students on the interactive
whiteboard and award the students with appreciation. Teacher can ask some inherent
questions from the discussion to the students as well (Boyle and Kaiser, 2017). Teachers
should relate facts from student’s day-to-day life; comprehend and conceptualize the specific
topic “Ratio and Proportion” discussed.
Expected outcome of the lesson:
The teacher should get evidence that the students have learned properly at the end of
the day. He or she could playfully call the students to the white-board to solve some easy
sums. He or she would continuously guide the student to solve it. As he or she is the
mathematics teacher of the class, teacher should be aware of different IQ level of different
students. Teacher should be more caring toward the student who is comparatively behind

8METHOD OF CLASSROOM TEACHING OF RATIO-PROPORTION
others. If the student succeeds to solve any hard problem of “Proportion”, teacher would
request others to clap to encourage that student.
After the scheduled time of class:
The teacher should spend this time responding to any clarifications from students after
scheduled time of the class. He or she can also provide a one-minute individual activity and
award whoever performs according to the teacher’s expectations. The students with the help
of teachers should stick the charts and wall magazines that they have prepared during the
lesson on the classroom notice board. In addition, the teacher should explain the expected
outcomes of the chapter to the students (Furlong, 2013).
Concluding the lesson:
The teacher could take the help of reasoning and communication with the students in
each segments of curriculum. After that, the teacher should carry out a class activity by
asking students some problems. For example, “I am thinking two numbers that are divisible
by 3, their proportion is 5:7. What are these two numbers?”
Summarization of the whole topic could be helpful to all the students as they can
remind the forgotten points. The teacher can let the students express their views and feelings
towards the topic. Finally, each student can express their doubts and queries and other
students would try to solve it before they leave the classroom.
Conclusion:
Reflections:
One of the biggest obstacle that students face about “Ratio and proportions” is the
notion that assuming proportion and inverse proportion are confusing to remind and easy to
forget (Boudreaux,Kanim and Brahmia, 2015). Many students find that these are not relating

9METHOD OF CLASSROOM TEACHING OF RATIO-PROPORTION
to anything they have read in past. The duty of teacher is to relate or formulate those
annoying things that are making students scary. If students are not finding any segment
reasonably and logically correct, teacher would guide them analytically. Sometimes, he or
she can take the help of algebraic expressions and variables like x or y. Teacher jointly with
classroom can arrange a group discussion where all of them can participate and one student
can answer or debate with others. It is a new scientific process of learning and overcoming
the obstacles. Students are the assets of the class. Therefore, their soulful participation in the
process of learning could create a healthy learning atmosphere.
Summary of the lesson:
The summary of the lesson elaborately justifies the credibility of the teacher if and
only if students’ performance spreads out from their core as outcome. Students could perform
better in their assignments and exams, if their misconceptions wipes out with the heartiest
attempt of teacher. Teacher would help the students with patience although they are not being
able to solve the simplest sums. The chapter surly is going to improve the logical and
reasoning power of the students along with the math solving ability. If students find interest
in the chapter, it is sure that teaching and learning process is successful.

10METHOD OF CLASSROOM TEACHING OF RATIO-PROPORTION
References:
Assessment, W. S. B. P. (2013). Conceptual Framework.
Boudreaux, A., Kanim, S., & Brahmia, S. (2015). Student facility with ratio and proportion:
Mapping the reasoning space in introductory physics. arXiv preprint
arXiv:1511.08960.
Boyle, J.D. and Kaiser, S.B., 2017. Collaborative Planning as a Process. Mathematics
Teaching in the Middle School, 22(7), pp.406-419.
Carrillo, J., Climent, N., Contreras, L. C., & Muñoz-Catalán, M. D. C. (2013). Determining
specialised knowledge for mathematics teaching. In Proceedings of the CERME (Vol.
8, pp. 2985-2994).
Casas, M., 2013. Designing an AntiRacist Curriculum For Middle School Students in Texas
via The Texas Essential Knowledge and Skills (TEKS) and Latino/Latina Critical
Pedagogy. Journal of Border Educational Research, 7(1).
Díaz-Aguado Jalón, M. J., & Martínez Arias, R. (2013). Peer bullying and disruption-
coercion escalations in student-teacher relationship. Psicothema, 25(2).
Ekawati, R., Lin, F. L., & Yang, K. L. (2015). DEVELOPING AN INSTRUMENT FOR
MEASURING TEACHERS’MATHEMATICS CONTENT KNOWLEDGE ON
RATIO AND PROPORTION: A CASE OF INDONESIAN PRIMARY
TEACHERS. International Journal of Science and Mathematics Education, 13(1), 1-
24.

11METHOD OF CLASSROOM TEACHING OF RATIO-PROPORTION
Furlong, C. (2013). The teacher I wish to be: Exploring the influence of life histories on
student teacher idealised identities. European Journal of Teacher Education, 36(1),
68-83.
Lamon, S. J. (2013). More! Teaching Fractions and Ratios for Understanding: In-depth
Discussion and Reasoning Activities. Routledge.