LAC ; Solids

 

Parallel lines ; introduction ; 5

 

Decimal forms; First forms ; 4

 

Decimal forms; Converting a fraction into decimal ; 3

 

Different methods for teaching Ratios and Proportion

 Introduction

Ratio or proportion problems are important area of mathematics used in daily life. These concepts have a wide application in our surroundings. Ratio and proportions are used in Blueprints, Photographs, Maps, Construction of buildings, Engineering fields, Business, Science and Cooking. So taking this real life experience to classroom situation will enable the learner to get master in Ratio and proportion. Comparison of two quantities of same type is ratio, Proportion enable us to see that two or more ratios are equal.

The concept of ratio is closely related to fraction and division, that is why most of the introductory section of Ratio is starting with 'division of cake' . This problem is a common for all ratio chapters in Kerala syllabus text books.. But in real classroom we can't demonstrate the problem of cake because in a class students are eager to eat cake rather than learning the ratio behind it. So a teacher need to bring another methods to  make the concept of ratio and proportion clear.

This paper discuss some methods to teach ratio and proportion in class, and these methods are Ratio game using fraction, Box method using coins to understand the difference between ratio and proportion.

A. Ratio Game

Ratio game is a method of connecting fraction to ratio through a game board. This method is good for the introduction of ratio. This will makes the idea of ratio clear to students. So we can include this method as an introductory activity. This game can be converted according to our ideas. This game can be provided to 4 or ore students. So this is a group activity.

The main attraction of the game is the game board. It is a 4 *4 board, each box in the board contain  shaded pictures. This game can be played by 4 children. The board is placed between four children, each student is provided with four question paper. By reading the question paper students can place the colour coins in the corresponding box. Those who completes the four question paper will win the game.

Steps

1. 4*4 board

2. Question format 

• Find the ratio of 3 shaded part is to 5 unshaded part ?
• Which one one represents 2 is to 3 ?
• Find 3:6 from board 
• Which one represents 1:2 ?

This will helps the students to actively involve in a game, and also helps to understand the concept.

B. Coins to learn ratio and proportion

Ratio and proportion are relative to each other. But there is a difference between them. It may arise confusion among students. For avoiding this confusion and getting clear understanding about ratio and proportion we can use coins or balls to teach. Ratio is the comparison of two quantities. While proportion says that two or more ratio's are equal.

Steps

1. Consider the ratio 1:2 , we can arrange this using coins.

2. Now arrange the coins in 2:4 next to the first box.

3. By checking how many 1/2's are there in the second and third box.

On reducing , students can see that the ratio 1:2 is common in three boxes. So they are in proportion.

This method will enable the students to learn ratio and proportion in an effective way.

C. Bow and Arrow method

' Bow and arrow method ' can be used as an activity for learning ratio. A number of small shooting board will be attached on the wall with different questions written on paper attached to that. Students can take questions fro shooting board. If they know the answer they can place the arrow on the shooting board and they can explain the answers to others. Calculations should be done on the blackboard or paper.

This activity can be done in a group of 5 members. Maximum number of shooting boards should be placed on the wall. So the 5 members of a group able to do the problem quickly. The student who put maximum arrows on the boards will win.

The questions on this activity should be like:

1. The ratio of Apples to Oranges is 10:1. If there are 25 Oranges, how any Apples are there?
2. In a small business, 40 of the employees are men and 30 of the employees are women. What is the ratio of men to women?
3. Purple paint is made by mixing Red and Blue paint together in the ratio of 4:3.What fraction of the Purple paint is Red?

This activity will makes the class into an active one.

D. Box Method

Box method is another method of teaching ratio in class as the name indicates it uses box to do the problem. Any ratio or proportion problem is a comparison of at least two items. More than two objects could be involved. In any problem, by definition, there must be an unknown. For any ratio or proportion problem, we must have at least three other known quantities. So our first step should be to identify the unknown item. In a word problem, the missing quantities will usually appear in that last sentence of the problem.

Example : There are 2 rectangles, they are similar. The length and width of the rectangle are 5 and7. The length of 2nd rectangle is 10. What is the width of this rectangle?

Here for the last sentence the unknown is the width of the second rectangle. So we can name it 'X'.

We can arrange the details in this box. We have two rectangle we can call the Rectangle 1 and Rectangle 2, and can give that title to the box.

The length and width are provided in the question, so we can name the 2nd and 3rd row in the 1st column as length and width.

We have the measure of Rectangle 1. We can put the measurements in this columns.

By writing the length to width ratio, students can find the unknown X.

5/7 = 10/X

X = 14

this type of problem can be done easily without using any complicated equations. This method is follows in many ways in different books.

This Box Method is an effective tool for teaching students how to successfully solve ratio or proportion problems. It provides the additional detail and structure required for students to understand how to set these problems correctly.

Conclusion

Practicing is one way to secure Knowledge. Once there, understanding can begin to develop, Each higher level of understanding typically results from new information automatically stores in brain. When we learn a new skill, initially we simply follow the rules in mechanical fashion. Then, with practice, we gradually become better, and as our performance improves, our understanding grows. The  method discussed in this section will be helpful for students for learning Ratio and Proportion.

Reference

Some research papers and you tube videos helped me a lot in writing this article. The details are given below

1. www.mathplanet.com/education
2. James sullivan [2009]The 'Box Method' for teaching Ratio/proportion problems.
3. Teacher ACER -  https://youtu.be/DJV7h7YzpHA 
4. Ratios and Proportions manipulative Activity-https://youtu.be/18x6BOC3fQA 

Pairs of equations ; Solving equations with different variables ; 2

 

Experience as a mathematics teacher during internship

 Experience as a mathematics teacher during internship

Introduction

Internship programme and Induction programme are the essential part of B.ed. The four week programme , induction gives a view of the student teachers. During internship we will get a full experience regarding the events in the school.Internship programme helps a student teacher to gain confidence,experience in the proffessional development.Intrenship programme is a 3 month training programme assigned by the university.During this three month the student teacher has to do several works related to the course.This works helps the student teacher to understand students in a better way.This report is based on internship programme during the year 2020-2021.

New developments

Due to the covid-19 pandemic situation, we didn't get the real school experience.We expected that we will get atleast one month in school but that doesn't happen.During the starting of third semester our university gave permission to conduct online internship for student teachers.So this online internship was a new experience to every one. We need to change ourselves for that . According to the instructions from our teachers we need to develop teaching manuals ,worksheets, activity cards ,charts and should be uploaded in google classroom.This was a new development during this period.

Online school

During the 3rd week of August , we got our school for internship programme.After all formalities i got Cardinal HS Thrikkakara.I got the permission to enter into their whatsapp group.The school created the Whatsapp group for each class.So it was easy for them to handle the class.Each group contains the students in that class, teachers, PTA representatives, principal.Teachers are the admin of the group.9B Class was assigned for me. Ms.Mini T J was their class teacher .She is teaching malayalam. Ms.Jenny E A Was the Mathematics teacher in this class and she is the instructur during the programme.The whatsapp  group was created in such a way that only teachers can send the details .If the teachers need response then they can allow permission in the group.Before joining the group she gave me neccessory informations and instructions.

Kite victers

Ms.Jenny told me that 'the schoolfollows kite victers channel classess.So you have to prepare the notes as well as the works according to these classess''. In our college also our teachers said to us that we need to prapare the teaching manual according to the victers channel classes.They have a certain time table.Each day the classteacher will upload the timetable in our whatsapp group.In one day 2 or 3 subjects of 9th standard will upload in the channel.so in one week we will get 2 or 3 classess of mathematics.It only have 20 to 30 minutes duration.Usully the class statrs at the time around 4 or 6 pm.Repeatition of the same class will be availlable on sunday and saturday.The class is available on youtube also.So student teachers have to share the youtube link on their group and should give neccesory instructions also.

Online mathematics

Among students mathematics is a difficult subject to learn.Real classroom experience reduce this difficulty to its maximum. In online platform a teacher should be vigilent all time.Kite victers presents the class in an effective way. Students have the oppertunity to watch the class again and again.But students are not all the same.Some students take the initiative to watch the class but most of them may not even watch the class.I have prepared videos related to some topics in mathematics.Sometimes this video will be helpful for students.Activity cards.worksheet are provided through whatsapp group.So after reading and doing they can ask the doubts, questions.Students have faced difficulty in the chapter 'New numbers',the concept as well as the topic was new to students so they had lots of doubts reharding this chapter.Some of them asked me to make a video related to certain topics in new numbers.Video creation and uploading in group was a difficuly task.So i made video about 3 to 8 minutes.Helping notes will be given to them so they can refer and ask questions.As a teacher i need to check their notes and works.there are 54 students in my class so it become difficult to check their works online . Then as a solution i have alloted time for certain roll numbers to upload their works.Aroud 40 to 45 response will get for each work form students.After correcting their works neccessory information will be given through voice message.Students have the permission to call the teachers and ask their doubts.Different kinds of applications, sites were used during this period.Google sheets,google slides,slideshare,bambooze are some of them.Google sheets helped me to check their progress in learning.Geogebra is used in the victers classess so i also used the geogebra in the class of 'circles'. These applications helps to make the class more effective.Students actively participated in the doubt clearing sections.I asked their suggestions about the class ,that helped me to make class more effective.Exams are also conducted through online.Notification reagarding exam should gave before one week of exam.