Module 9- Activity 5: Reflect
A said ‘if length of a rectangle is increased by 1 and breadth decreased by 1 the area enclosed by the rectangle remains the same’. B said ‘No, A is wrong as the new area will increase’. C said ‘No, A and B both are wrong, the new area will decrease’. How will you handle this situation?
Take a moment to reflect and post your comment in the comment box.
I as a teacher will handle this situation like the following way:
ReplyDeleteFirst I will ask trio that how they make their answers, I will ask A how can u say that the area will remain same and then I will note his reply. Then accordingly I will ask the same to B and C also and note their reply. By doing this I will come to know how they approached their conclusions. Then I will explain them what happens really when we change the dimensions of a rectangle.
I as a teacher will handle this situation like the following way:
DeleteFirst I will ask trio that how they make their answers, I will ask A how can u say that the area will remain same and then I will note his reply. Then accordingly I will ask the same to B and C also and note their replies. By doing this I will come to know their thought process. Then I will explain them what actually happens when we change the dimensions of a rectangle. As a teacher you have to encourage each of them.
To handle this situation, I would ask the children regarding their conclusion. Then I would explain all three situations through illustrations.
Deleteas a teacher iwill ask all of them one by one to tell the calculated area and note it then will compare it and make them understand it
DeleteWriting the solutions one by one , through Demonstration on the Blackboard with three different illustrations, correct fact is to be shown to the students.
DeleteWe can prove it by doing activities with rectangular card boards by changing the dimensions and calculating the area.
DeleteWriting the solutions one by one,through demonstration on the blackboard with three different illustrations,correct fact is to be shown to the students.
DeleteFirst i will show all the given answers by activity method - increase length and decrease the width of the paper of given area and let them think is it same or more or less than previous area. then i will explain on board by illustration
DeleteAs a teacher first I ask all the students reply patiently and write their responses on the board and at last I give my conclusion by explaining what exactly it takes place and make them understand and I also appreciate for their responses.
DeleteI will initiate the students to explain their thought process by how they have reached to this conclusion then as a teacher by giving examples I will explain them the concept of area of the rectangle by paper
Deletei will ask each student one by one how they answer den i'll explain them the concept by taking a paper.
DeleteAs a teacher first I ask all the students reply patiently and write their responses on the board and at last I give my conclusion by explaining what exactly it takes place and make them understand and I also appreciate for their responses.
ReplyDeleteBeing a teacher , I will handle this situation like the following way:
ReplyDeleteFirst I will ask trio that how they make their answers, I will ask A how can u say that the area will remain same and then I will note his reply. Then accordingly I will ask the same to B and C also and note their replies. By doing this I will come to know their thought process. Then I will explain them what actually happens when we change the dimensions of a rectangle. As a teacher you have to encourage each of them. By - Shatrughan Kumar Srivastava TGT SST JNV MORADABAD
Keeping all of them together, through Demonstration on the Blackboard with three different illustrations, correct fact is to be shown to them with the appreciation of the boy or the girl who is the owner of correct answer.
ReplyDeleteBeing a teacher I will handle this situation like the following way:
ReplyDelete1. First I will ask trio that how they make their answers, I will ask A how can u say that the area will remain same and then I will note his reply.
2. Then accordingly I will ask the same to B and C also and note their replies. By doing this I will come to know their thought process.
3. Then I will explain them what actually happens when we change the dimensions of a rectangle. As a teacher I have to encourage each of them.
Being a teacher , I will handle this situation like the following way:
ReplyDeleteFirst I will ask trio that how they make their answers, I will ask A how can u say that the area will remain same and then I will note his reply. Then accordingly I will ask the same to B and C also and note their replies. By doing this I will come to know their thought process. Then I will explain them what actually happens when we change the dimensions of a rectangle. As a teacher you have to encourage each of them. Rajkumar Singh Thakur
First I would like to take responses from the students and then I would like to conclude by clearing their doubts with a satisfactory end.
ReplyDeleteFirst I would ask the children to give reason for reaching their conclusion. Then I would explain all three situations through illustrations. Children would derive the correct answer through these illustrations.
ReplyDeleteAs a teacher first I ask all the students reply patiently and write their responses on the board and at last I give my conclusion by explaining what exactly it takes place and make them understand and I also appreciate for their responses.
ReplyDeleteCHRISTINE, MCPS MOTI NAGAR WEST
ReplyDeletei will give them a rectangle L&B & they will themselves arrive at the answer, to see whether their assumptions are correct or not. I can only facilitate them, they have to build. Later I'll explain how did this happen.
First I would ask the children to give reason for reaching their conclusion. Then I would explain all three situations through illustrations. Children would derive the correct answer through these illustrations.
ReplyDeleteFirst I would like to take responses from the students and then I would like to conclude by clearing their doubts with a satisfactory end.
ReplyDeleteFirst I would like to take responses from the students and then I would like to conclude by clearing their doubts with a satisfactory end.
ReplyDeleteI will call students to come and draw the rectangle on the board as it will help them to visualize and apply formula. After that I will explain on the board and appreciate them to try.
ReplyDeleteAs a facilitator I will ask the pupils to from an imaginary rectangle by asking them to line up and then will ask them to add one pupil in each dimension. They will themselves reflect that if one pupil is added to each length and breadth, will they occupy more area or not. This way they will give the solution themselves after reflecting at the outcome.
DeleteFirst I would like to take responses from the students and then l would like to conclude by clearing their doubts by satisfactory end
DeleteI will ask the student to to draw a rectangle with sample length of 10cm and width of 5cm. Now according to the question said by a the revised length will be 11 and the width will be 4. The original area will be 50 sq cm and the revised area of the rectangle will be 11 x 4 = 44 sq cm
ReplyDeleteHence the area has decreased from 50 to 44 sq cm.
Then I will ask to check the same with some other numbers
Like
If L= 5cm,B= 10cm Area= 50sq cm
Changed L =6cm ,B = 9cm Area= 54 sq cm
Now the area has increased after changing the length and breadth. Therefore it all depends on original Length and Breadth .
If L is more than B the area decreases and vice versa
I will ask the student to to draw a rectangle with sample length of 10cm and width of 5cm. Now according to the question said by a the revised length will be 11 and the width will be 4. The original area will be 50 sq cm and the revised area of the rectangle will be 11 x 4 = 44 sq cm
ReplyDeleteHence the area has decreased from 50 to 44 sq cm.
Then I will ask to check the same with some other numbers
Like
If L= 5cm,B= 10cm Area= 50sq cm
Changed L =6cm ,B = 9cm Area= 54 sq cm
Now the area has increased after changing the length and breadth. Therefore it all depends on original Length and Breadth .
If L is more than B the area decreases and vice versa
I will ask the student to to draw a rectangle with sample length of 10cm and width of 5cm. Now according to the question said by a the revised length will be 11 and the width will be 4. The original area will be 50 sq cm and the revised area of the rectangle will be 11 x 4 = 44 sq cm
ReplyDeleteHence the area has decreased from 50 to 44 sq cm.
Then I will ask to check the same with some other numbers
Like
If L= 5cm,B= 10cm Area= 50sq cm
Changed L =6cm ,B = 9cm Area= 54 sq cm
Now the area has increased after changing the length and breadth. Therefore it all depends on original Length and Breadth .
If L is more than B the area decreases and vice versa
First of all, I would ask the children to give their reason for reaching the conclusion. Thereafter, I would explain all the three situations through illustrations. Children would derive the correct answer through these illustrations.
ReplyDeleteDemonstrate the answers keeping all the options and explain which answer is correct
ReplyDeleteFirst I would ask the children to give reason for reaching their conclusion. Then I would explain all three situations through illustrations. Children would derive the correct answer through these illustrations.
ReplyDeleteAs a teacher i would ask the children to give the reason for their conclusion then i would tell them the correct answer with a satisfactory end.As the area is totally depended on the measurements we take.
ReplyDeleteDemonstrate the answers keeping all the options and explain which answer is correct. I think it is essential to know what is the process of thought of children
ReplyDeleteFirst I would ask the children to give reason for reaching their conclusion. Then I would explain all three situations through illustrations. Children would derive the correct answer through these illustrations.
ReplyDeleteAs a teacher 1st of all I would like to ask the answers from the students and if they have any doubt and which they are not understanding then I will clear their doubts by my explorations.
ReplyDeleteTeacher should ask students the reason of their results. Then she should explain all situations giving examples.
ReplyDeleteNeeri Bhagi
TGT Computer Science
Amity International School Mayur Vihar
I will ask all my students to give reason for their response and tell them which answer is true. For that I will ask them to consider some measurements and cut rectangles from paper and then practically, perform the experiment with it. Their conclusions will be proved right or wrong by the result of their experiment. This will also add an air of fun in the class. I will make the others understand that it's a good thing to answer in class and I will also tell them to not argue over answers and respect each other's response.
ReplyDeleteI will ask them question what is their answer and by them we will come to answer
ReplyDeleteFirst l would like to ask responses in this context from the students and then l would clearify their doubts
ReplyDeleteInitially I would like to take responses from the students and then I would like to conclude by clearing their doubts with a satisfactory end and will make sure that the concept is clear.
ReplyDeleteThe three students will be asked to draw the rectangles - original and with new dimensions - on paper and superimpose and check which rectangle has a greater area. Then they will be asked to compute the respective areas to verify.
ReplyDeleteThis can be taken further to keep increasing the length by 1 unit progressively and the breadth, decreasing by 1 unit and the students will observe that the area will keep getting reduced whereas the students will be asked to calculate areas in the opposite situation, when the length gets reduced by 1 unit while the breadth increases by 1 unit. The conclusion that as we get closer to a square, the area keeps increasing will be elicited from the students. Also, greater the disparity between the length and breadth, proportionately smaller will be the area.
i will ask A to solve the sum on the board first followed by B and C. All their perspective will be known to me after this. Now i can take an example and explain to them what exactly happens when the dimensions change in a rectangle.
ReplyDeleteKeeping all of them together, through Demonstration on the Blackboard with three different illustrations, correct fact is to be shown to them with the appreciation of the boy or the girl who is the owner of correct answer.
ReplyDeleteBeing a teacher, I would like each one of them to justify their answers with reasons. Peer discussion would be encouraged and at the end i would give the correct answer.
ReplyDeleteAs a teacher first I ask all the students reply patiently and write their responses on the board and at last I give my conclusion by explaining what exactly it takes place and make them understand and I also appreciate for their responses.
DeleteTeacher should ask students the reason of their results. Then she should explain all situations giving examples
ReplyDeleteAs a teacher first I ask all the students reply patiently and write their responses on the board and at last I give my conclusion by explaining what exactly it takes place and make them understand and I also appreciate for their responses.Peer discussion would be encouraged and at the end i would give the correct answer.
ReplyDeleteAs a teacher I can handle this situation by allowing each child to come and demonstrate how they reached to their conclusions.
ReplyDeleteChildren can be asked to draw rectangles and calculate area with different different dimensions and by experimenting on their own , they can generalize their observations.
First let the students calculate their answer and then let them compare it. Next the teacher can tell the correct answer and also explain the reason behind it.
ReplyDeleteAt first all three will give their responses and then as a teacher I will guide them to find the correct inference.
ReplyDeleteFind the correct answer and explain .
ReplyDeleteStep 1 – I will ask the students to draw a rectangle and label its dimensions as ‘l’ & ‘b’ respectively.
ReplyDeleteStep 2 – Then, I will ask students to write formula of area of rectangle, which is –
Area = Length × Breadth = l × b.
Step 3 – Then, I will ask students to give certain values that satisfy their statements.
Step 4 – After getting the responses, I will explain the students the pattern using their responses. Which are as follows –
Area of original rectangle = l × b,
Area of new rectangle = (l + 1) × (b – 1) = l × b + b – l – 1,
Case 1- For, Area to remain same,
Area of original rectangle = Area of new rectangle
=> l × b = l × b + b – l – 1
=> l + 1 = b,
For eg:- l = 4, b = 3.
Case 2- For, Area to decrease,
Area of original rectangle > Area of new rectangle
=> l × b > l × b + b – l – 1
=> l + 1 > b,
For eg:- l = 10, b = 5.
Case 3- For, Area to increase,
Area of original rectangle < Area of new rectangle
=> l × b < l × b + b – l – 1
=> l + 1 < b,
For eg:- l = 5, b = 10.
Being a teacher,I will handle this situation like the following way:
ReplyDeleteFirst I will ask trio that how they make their answers, I will ask A how can u say that the area will remain same and then I will note his reply. Then accordingly,I will ask the same to B and C also and note their replies. By doing this I will come to know their thought process.Finally,I will explain them what actually happens when we change the dimensions of a rectangle.As a teacher you have to encourage them to try and solve the problems correctly.
Being a teacher , I will handle this situation like the following way:
ReplyDeleteI will ask students to create their own problem and justify their answers
As a teacher first I ask all the students reply patiently and write their responses on the board and at last I give my conclusion by explaining what exactly it takes place and make them understand and I also appreciate for their responses.
ReplyDeleteCheck with students about their approach towards the problem at hand. Then I would ask explain through illustrations what actually happens.
ReplyDeleteTo handle this situation, I would ask the children regarding their conclusion. Then I would explain all three situations through illustrations.
ReplyDeleteAs a teacher first i will ask how area is calculated and then ask everyone how he/ she calculated will write answer of every student on board and explain actual answer should be
ReplyDeleteAs a teacher I will ask all of them to draw a rectangle and find out the area in both situations.In conclusion they will get the correct answer. Hence ,C is correct .Therefore, area will decrease.
ReplyDeleteIt will be better if we ask them to draw rectangle and find out the area in both situations. After that the discussion will be done on the basis of the results.
ReplyDeleteI will ask the student to to draw a rectangle with sample length of 10cm and width of 5cm. Now according to the question said by a the revised length will be 11 and the width will be 4. The original area will be 50 sq cm and the revised area of the rectangle will be 11 x 4 = 44 sq cm
ReplyDeleteHence the area has decreased from 50 to 44 sq cm.
Then I will ask to check the same with some other numbers
Like
If L= 5cm,B= 10cm Area= 50sq cm
Changed L =6cm ,B = 9cm Area= 54 sq cm
Now the area has increased after changing the length and breadth. Therefore it all depends on original Length and Breadth .
If L is more than B the area decreases and vice versa
First I would ask the children to give reason for reaching their conclusion. Then I would explain all three situations through illustrations. Children would derive the correct answer through these illustrations.
ReplyDeleteयह बेहतर होगा यदि हम उन्हें आयत बनाने और दोनों स्थितियों में क्षेत्र का पता लगाने के लिए कहें। उसके बाद परिणामों के आधार पर चर्चा की जाएगी।
ReplyDeleteAs a teacher I will encourage A,B,C. and I will appreciate them for their response and I will ask them to explain their version how it would be correct then I will give them three rectangular shaped objects with different lengths and breadths and I will ask them to find out their areas later I will explain that it will be depending upon the length and breadth that they have taken when the length is more than breadth the area will decrease.
ReplyDeleteEXAMPLE ;The length of a rectangle is 5cm, breadth is 4cm the area of the rectangle is lxb=5cmx4cm=20cm. When length is increased by 1 the length becomes 6cm and breadth is decreased by 1 it becomes 3cm, area of a rectangle=6cmx3cm=18cm. so here the area of a rectangle is decreased.
When the length of a rectangle is lesser than it's breadth the area of a rectangle will increase Example ; If the length is 3cm and breadth is 7cm area of a rectangle =3cmx7cm=21cm when the length is increased by 1 it becomes 4cm , breadth is decreased by 1cm it becomes 6cm area of a rectangle =4cmx6cm=24cm. Here the area of a rectangle is increased.
coming to A if the length and breadth are inverse length is 4cm and breadth is 5cm if we change it same as the above the length becomes 5cm and breadth becomes 4cm so, the area of the rectangle = 4cmx 5cm =20 cm here the area of the rectangle is remains the same . so, every one is correct in their own view. Like this I will handle the situation.
I will ask the students regarding their conclusion. Then I will explain all three situations through illustrations.
ReplyDeleteFirst I would like to take responses from the students and then I would like to conclude by clearing their doubts with a satisfactory end.
ReplyDeleteFirst I will ask the children that how they come to this conclusion. I will ask A how can u say that the area will remain same and then I will note his reply. Then accordingly, I will ask the same to B and C also and note their replies. By doing this I will come to know their thought process. Finally,I will explain them what actually happens when we change the dimensions of a rectangle. As a teacher I will try to encourage them to try and solve the problems correctly. The doubts of all the children should be cleared properly.
ReplyDeleteFirst I will ask the children that how they come to this conclusion. I will ask A how can u say that the area will remain same and then I will note his reply. Then accordingly, I will ask the same to B and C also and note their replies. By doing this I will come to know their thought process. Finally,I will explain them what actually happens when we change the dimensions of a rectangle. As a teacher I will try to encourage them to try and solve the problems correctly. The doubts of all the children should be cleared properly.
ReplyDeleteकुल मान कम हो जाएगा क्योंकि चौड़ाई घटने से लम्बाई की इकाइयों में अनुपातिक कमी हो जाती हैं और क्षेत्रफल मे कमी हो जाती है।
ReplyDeleteI will say to all the students to reply patiently and write their responses by explaining through demonstration method. I will clear to students about all aspects of mathematics, e.g. the role of the angles, length of the lines etc.
ReplyDeleteWill do it by deductive reasoning, taking various examples and then finally conclude it along with children
ReplyDeleteAs a teacher first I ask all the students reply patiently and write their responses on the board and at last I give my conclusion by explaining what exactly it takes place and make them understand and I also appreciate for their responses.
ReplyDeleteAs a teacher first I ask all the students reply patiently and write their responses on the board and at last I give my conclusion by explaining what exactly it takes place and make them understand and I also appreciate for their responses.
ReplyDeleteBeing a teacher I will handle this situation like the following way:
ReplyDelete1. First I will ask trio that how they make their answers, I will ask A how can u say that the area will remain same and then I will note his reply.
2. Then accordingly I will ask the same to B and C also and note their replies. By doing this I will come to know their thought process.
3. Then I will explain them what actually happens when we change the dimensions of a rectangle. As a teacher I have to encourage each of them.
Rashmi Raj
ReplyDeleteI will again read the question to the students. I would ask the children to give reason for reaching their conclusion and then conclude by clearing their doubts with a satisfactory end and will make sure that the concept is clear.
Premendra Bahadur Singh
ReplyDeleteAs a teacher 1st of all I would like to ask the answers from the students and if they have any doubt and which they are not understanding then I will clear their doubts by my explorations
Daiho Chiipfoza, JNV Roing: First of all, I would ask the children to give their reason for reaching the conclusion. Thereafter, I would explain all the three situations through illustrations. Children would derive the correct answer through these illustrations.
ReplyDeleteI will first ask the three children how they had arrived at the conclusion regarding the increase or decrease in area . Then with the help of illustrations and an activity with paper or cardboard rectangles of different sizes , the responses can be verified and reasoned out practically.
ReplyDeleteI will handle the situation , firstly see and ask all the three students how they have reached their respective conclusions and then explain the correct answer by proper reasoning and examples
ReplyDeleteFirst I would ask the children to give reason for reaching their conclusion. Then I would explain all three situations through illustrations. Children would derive the correct answer through these illustrations.
ReplyDeleteThe best way would be to give them hands on experience by giving rectangular objects and then tell them to turnwise come and show the solution using it .This way possibility is that they shall themselves reach the correct solution as they are able to visualize the concept better or else the teacher or other students can then guide them on where they are going wrong.
ReplyDeleteAs a teacher we can handle the situation by expression of area of rectangular objects by pictorial representation to draw the right fact. By this way students may reach at the right discison.
ReplyDeleteAs a teacher,I will ask students to show their solutions on board by taking values of length and breadth,and drawing inferences afterwards whether their answers are right or wrong.
ReplyDeleteAs a teacher I will handle this situation like the following way:-
ReplyDeleteFirstly, I will ask all of them that how they make their answers and ask them to note their reply.
Secondly, I will cross their responses by giving various examples.
Finally, I will explain them and clear their doubts. As a teacher I encourage each of them for their responses and respect their thoughts.
I will take the responses from all three students and then give them a set of dimensions and ask them to find the area of rectangle as given in the equation.
ReplyDeleteI will ask the students to draw a rectangle with sample length of 11cm and width of 6cm. Now according to the question said by the revised length will be 12cm and the width will be 5cm. The original area will be 66 sq cm and the revised area of the rectangle will be 12cm x 5cm = 60 sq cm
Hence the area has decreased from 66 to 60 sq cm.
Then I will ask to check the same with some other numbers
Like
If L= 5cm,B= 10cm Area= 50sq cm
Changed L =6cm ,B = 9cm Area= 54 sq cm
Now the area has increased after changing the length and breadth. Therefore it all depends on original Length and Breadth .
If L is more than B the area decreases and vice versa
Monalisa Majumdar (Bhavan's NSCB Vidyaniketan)
ReplyDeleteBeing a teacher, I would like each one of them to justify their answers with reasons. Peer discussion would be encouraged and at the end i would give the correct answer and clear the doubt.
Explaination of the concept through demonstration..n motivating the child who gives the answer.
ReplyDeleteFirst would ask reaching thair concelasion.themi lwould derive the correct.answer.through .
DeleteFirst I would like to take responses from the students and then I would like to conclude by clearing their doubts with a satisfactory end
ReplyDeleteFirst of all as a teacher i would try to know whether the students have any knowledge of what they are saying or they are just saying it illogically. i'll ask them to explain their answers and after that i'll explain all the three situations with illustrations and by taking one or two examples.
ReplyDeleteAs a teacher, first I will elicit 1.The concept involved.
ReplyDelete2. Formula needed.
I will give them activity using paper cutting. I will give them some measurements of length and breadth. Find the area. I will ask them to increase 1 unit length and decrease 1 unit breadth. Find the area. Children will come out with solutions. I will ask them to generalise.
I as a teacher will handle this situation like the following way:
ReplyDeleteFirst I will ask trio that how they make their answers, I will ask A how can u say that the area will remain same and then I will note his reply. Then accordingly I will ask the same to B and C also and note their replies. By doing this I will come to know their thought process. Then I will explain them what actually happens when we change the dimensions of a rectangle. As a teacher you have to encourage each of them.
I will first take the answers of the students and find out their knowledge regarding the topic. Then clarify the concept to them. Give different examples, discuss different situations and encourage them to think and answer.
DeleteSanta Basu
ReplyDeleteFirst I will take responses from the children. Then their doubts will be cleared by me and I will appreciate them for trying.
As a teacher , I will ask the trio to take a small example and make them understand to satisfy their result , after that I will explain how to do. Sums doing with handy example will help them to understand.
ReplyDeleteBeing a teacher, I would like each one of them to justify their answers with reasons. Peer discussion would be encouraged and at the end i would give the correct answer.
ReplyDeleteI will handle this situation like the following way:-
Firstly, I will ask all of them that how they make their answers and ask them to note their reply.
Secondly, I will cross their responses by giving various examples.
Finally, I will explain them and clear their doubts. As a teacher I encourage each of them for their responses and respect their thoughts.
This problem can be solved by illustration with an example. Ask them to recall how to find the area of a rectangle. the formulae involved. Then using examples explain the concept .
ReplyDeleteAs a teacher, i would let all 3 give the reply and then clear the doubts by explaining the correct answer n the concept.
ReplyDeleteAs a teacher first I ask all the students reply patiently and write their responses on the board and at last I give my conclusion by explaining what exactly it takes place and make them understand and I also appreciate for their responses.
ReplyDeleteAs a teacher I will handle this situation by allowing each child to come and demonstrate how they reached to their conclusion. I will ask all my students to give reason for their response. Then I would give them some figures to apply the formula of deriving the area of the rectangle (Area = LX B), thus arriving to some concrete answer. I will also cut rectangles from paper and then practically, perform the experiment with it. The conclusion will be proved right or wrong by the result of their experiment. Thus at the end we will come to the correct answer. This will add an air of fun in the class. I will make others understand that it's a good thing to answer in class and respect each other's response.
ReplyDeleteARCHANA KUMARI FUTURE BHUBANESWAR SCHOOL It will be better if we ask them to draw rectangle and find out the area in both . After that the discussion will be done on the basis of the results. It will be better if we ask them to draw rectangle and find out the area in both situations. After that the discussion will be done on the basis of the results.
ReplyDeleteFirst I would like to take responses from the students and then I would like to conclude by clearing their doubts with a satisfactory end.
ReplyDeleteAs a teacher first I ask all the students reply patiently and write their responses on the board and at last I give my conclusion by explaining what exactly it takes place and make them understand and I also appreciate for their responses.
ReplyDeleteThis problem can be solved by illustrations with an example ask them to recall how to find the area of a rectangle the formula involved then using examples explain the concept easily
ReplyDeleteFirst reason of their answers will be asked then the three situations will be explained on blackboard
ReplyDeleteAs a teacher first I will encourage three of them for their responses then I will ask them their reasons behind their answers as they will come up with their aswers along the process I will explain them through pictorial unit as well as through formula that Area of rectangle is {L*B }. By this peoper process they will be able to understand basic process by themselves.
ReplyDeleteI WOULD LIKE TO ACCEPT THE RESPONSE OF EACH CHILD AND THEN GIVE THE EXPLANATION WITH THE HELP OF DIAGRAM AND FORMULA.
ReplyDeleteAs a teacher first I will ask all the students to reply patiently and write their responses on a sheet and after hearing them out at last I will give my conclusion by explaining what exactly it takes place and make them understand and I will also appreciate them for their responses.
ReplyDeleteI will listen to all the three responses and finally explain the concept to them and give them an example to work out and understand that as the length increases , the area would decrease.
ReplyDeleteChildren will be asked to draw rectangles and calculate area with different different dimensions and by experimenting on their own , they will generalize their observations.
ReplyDeleteI will ask them to reply first though it isr or wrong, and at last I will explain them what exactly the answer is and will also appreciate them for their responses.
ReplyDeleteFirst I would ask the children to give reason for reaching their conclusion. Then I would explain all three situations through illustrations. Children would derive the correct answer through these illustrations.
ReplyDeleteI as a teacher will handle this situation like the following way:
ReplyDeleteFirst I will ask trio that how they make their answers, I will ask A how can u say that the area will remain same and then I will note his reply. Then accordingly I will ask the same to B and C also and note their replies. By doing this I will come to know their thought process. Then I will explain them what actually happens when we change the dimensions of a rectangle. As a teacher you have to encourage each of them
The situation will be handled by hands on learning. All the students would be asked to demonstrate their answer by actually drawing and finding the area of rectangles in both situation. learning by doing always works.
ReplyDeleteI will ask to all three student to explain their answer with the help of example... then will come to conclusion with all explanation..definitely student will learn when the area will remain same when it will increase and when it will decrease.
ReplyDeleteI will ask the children to illustrates their answers in their notebooks and put their answers forward logically.
ReplyDeleteI as a teacher will handle this situation like the following way:
ReplyDeleteFirst I will ask trio that how they make their answers, I will ask A how can u say that the area will remain same and then I will note his reply. Then accordingly I will ask the same to B and C also and note their reply. By doing this I will come to know how they approached their conclusions. Then I will explain them what happens really when we change the dimensions of a rectangle
After reasoning out as to how they arrived at the answers, i would illustrate as to what happens when the dimensions change and how area is calculated.
ReplyDeleteFirst I would ask for reaching thair conlasion.them l would derive the correct.answer . Through.
DeleteStudents will be asked to give their answers logically and then it can be explained to them with illustrations.
ReplyDeleteSabita Rout
ReplyDeleteFUTURE BHUBANESWAR SCHOOL
As a teacher, first I would like to ask the children how they calculate the area with given units. After listening to them I will make them understand by drawing the rectangle on the board.
1.suppose the length is 5cm and breadth is 3cm.Then the area will be length breadth=5x3=15sq.cm
if the length increased by 1 then it will be 6cm and breadth will be 1 less and it is 2cm,then the area will be 6x2=12sq.cm
so the area depends upon the original measure of length and breadth. This way we can explain.
Sabita Rout
ReplyDeleteFUTURE BHUBANESWAR SCHOOL
As a teacher, first I would like to ask the children how they calculate the area with given units. After listening to them I will make them understand by drawing the rectangle on the board.
1.suppose the length is 5cm and breadth is 3cm.Then the area will be length breadth=5x3=15sq.cm
if the length increased by 1 then it will be 6cm and breadth will be 1 less and it is 2cm, then the area will be 6x2=12sq.cm
so the area depends upon the original measure of length and breadth. This way we can explain.
I will ask trio that how they make their answers, I will ask A how can u say that the area will remain same and then I will note his reply. Then accordingly I will ask the same to B and C also and note their reply. By doing this I will come to know how they approached their conclusions. Then I will explain them what happens really when we change the dimensions of a rectangle.
ReplyDeleteI would divide the board in three column and being the facilitator i world ask three children to solve the given question together on the board and give reason for reaching their conclusion. Then I would explain all three situations through illustrations. All the children would be appreciated for attempting the question and would be facilitated how to derive the correct answer through these illustrations.
ReplyDeleteThe best way would be to give them hands on experience by giving rectangular objects and then tell them to turnwise come and show the solution using it .This way possibility is that they shall themselves reach the correct solution as they are able to visualize the concept better or else the teacher or other students can then guide them on where they are going wrong.
ReplyDeleteI would divide the board in three column and ask them to draw the diagram of rectangle ,being the facilitator i world ask three children to solve the given question together on the board and give reason for reaching their conclusion. Then I would explain all three situations through illustrations. All the children would be appreciated for attempting the question and would be facilitated how to derive the correct answer through these illustrations.
DeleteWill solve the problem using variables and then explain the reasoning of each student.
ReplyDeleteBeing a teacher , I will handle this situation like the following way:
ReplyDeleteFirst I will ask trio that how they make their answers, I will ask A how can u say that the area will remain same and then I will note his reply. Then accordingly I will ask the same to B and C also and note their replies. By doing this I will come to know their thought process. Then I will explain them what actually happens when we change the dimensions of a rectangle. As a teacher you have to encourage each of them.
As Maths teacher I would ask the three children to sit together and write their hypothesis. Then I would ask each of them to prove their statement by taking values and increasing and decreasing them as per their statements. They would experiment to reach the correct conclusion this way.
ReplyDeleteThe best way would be to give them hands on experience by giving rectangular objects and then tell them to turnwise come and show the solution using it .This way possibility is that they shall themselves reach the correct solution as they are able to visualize the concept better or else the teacher or other students can then guide them on where they are going wrong.
ReplyDeleteREPLY
I will all three of them to explain how they have come to the conclusions.Then I will explain my conclusion.
ReplyDeleteFirst I will take the responses of different students and see whether any one of them can come out with the correct response. Then I will give the correct solution which will clear their doubts.
ReplyDeleteAs a teacher atfirst I'll ask the students about the reasons behind their conclusion and then if any child answers perfectly then I'll request her or him to explain. Then I'll explain the whole lastly.
ReplyDeleteI would ask the children to give reason for reaching their conclusion. Then I would explain all three situations through illustrations. Children would derive the correct answer through these illustrations. They would experiment to reach the correct conclusion this way.
DeleteI would handle the situation by asking the children to clarify the reasons for their answers. I would also explain all these situation through various demonstrations. This way they will understand the reason behind the correct answers.
ReplyDeleteRita Sinha, The Pinnacle School, New Delhi
ReplyDeleteAccording to A, the area remains the same.
According to B, the Area will increase and according to C, the new Area will decrease.
So, I will ask each child to work out the area of their individual rectangles giving them the following measurements:
Take a rectangle with length 3 inches and breadth of 2 inches. Work out the Area of this rectangle.
(Area of this rectangle = L x B =3 x 2 =6 sq. inches.)
Next, I will ask them to increase the length by 1 and decrease the breadth by 1.
then Area of the new rectangle = Lx B=4 x 1= 4 sq. inches.
Hence, we can see that the area has reduced.
So, A and B are proven wrong.
Therefore, in this case C is correct.
The three children will be asked to draw two rectangles each to prove their point.
So practically and theoretically the children will arrive at a conclusion that C is right.
UPASALA KAVITA
ReplyDeleteI will first take the answers of the students and find out their knowledge regarding the topic. Then clarify the concept to them. Give different examples, discuss different situations and encourage them to think and answer.
Being a teacher, I will first talk to the students as how they have arrived at the answers. Then, I will try to explain them by giving real life examples like measuring the area of a tile or a brick that we usually find at our home by measuring the length and breadth and applying the formula to find the area of a rectangle. Now by applying the same concept for the given calculations, students will find the area and will compare the difference.
ReplyDeleteAs a teacher, I will encourage all the three children “A, B and C” and will appreciate all three of them for their responses. I will ask them first to explain their justification for their stance.
ReplyDeleteThen, I will give them three rectangles with different lengths and breadths and would make the following illustration on the blackboard for all three of them to observe.
Example 1.
If we take a rectangle with length = 3 cm and breadth = 7 cm;
Area of the rectangle = Length × breadth.
Hence, area of of the rectangle = 21sq.cm
Now, if we increase the length by 1, the new length now is 4 cm and decreasing the breadth by 1 makes the new breadth as 6 cm. The new area of the rectangle = 24 sq.cm.
We observe that here, the area of the rectangle has increased.
Example 2.
If we take another rectangle with length = 5 cm and breadth = 3 cm;
Area of the rectangle = Length × breadth.
Hence, area of of the rectangle = 15 sq.cm
Now, if we increase the length by 1, the new length now is 6 cm and decreasing the breadth by 1 makes the new breadth as 2 cm. The new area of the rectangle = 12 sq.cm.
We observe that here, the area of the rectangle has decreased.
Example 3.
If we take a rectangle where length and breadth are inverse.
Say length = 4 cm and breadth = 5 cm
Area of the rectangle = Length × breadth.
Hence, area of of the rectangle = 20 sq.cm
Now, if we increase the length by 1, the new length now is 5 cm and decreasing the breadth by 1 makes the new breadth as 4 cm. The new area of the rectangle is 20 sq.cm.
We observe that here, the area of the rectangle remains the same.
Hence, from the three examples above, we find out that :
A. When length is lesser than its breadth, the area of the rectangle increases. Hence, B is correct.
B. When length is greater than its breadth, the area of the rectangle decreases. Hence, C is correct.
C. When length and breadth of a rectangle is inverse, it remains the same. Hence, A is correct.
Hence, all three of you A, B and C are correct.
Jhimki Kar
Future Bhubaneswar School
As a teacher I would let students respond to the question . I would summarise the students' responses , solve the question with logics and explain the answer . I would also appreciate the students for their responses .
ReplyDeleteSABARI GHOSH DAS, IVWS,KOLKATA
ReplyDeleteFirst I will ask the answer then I will clarify the doubts
Being a teacher I will handle this situation like the following way:
ReplyDelete1. First I will ask trio that how they make their answers, I will ask A how can u say that the area will remain same and then I will note his reply.
2. Then accordingly I will ask the same to B and C also and note their replies. By doing this I will come to know their thought process.
3. Then I will explain them what actually happens when we change the dimensions of a rectangle. As a teacher I have to encourage each of them.
-Gopal Kumar
The best way according to me is to make the student understand this concept by using pictorial representation or inductive method.
ReplyDeleteLet us take a simple example:
Given, the length and breadth of a given rectangle are 4cm and 3cm respectively.The area of this rectangle will be 4cm x 3cm = 12 sq cm.
Now according to given situation, length has to be increased by 1 unit.Thus length= 5cm ;breadth has to be decreased by 1 unit.Thus breadth= 2cm.Hence the new area will be 5cmx 2cm=10sq cm
We find that 12 sqcm>10 sq cm.This means the new area will decrease.
At this stage ,students will be asked to check the same by using different length and breadth.
And finally conclusion will be drawn that if length is increased by 1 unit and breadth is decreased by 1 unit,the new area will decrease.
Chhatron ko parimaap evem kshetrafal kids abdharna pahle samjhayenge phir sawal par le jayenge. Is tarah chhatra samajh jayenge.
ReplyDeleteFirst I would like to take responses from the students and then I would like to conclude by clearing their doubts with a satisfactory end.
ReplyDeleteAs a teacher first I ask all the students reply patiently and write their responses on the board and at last I give my conclusion by explaining what exactly it takes place and make them understand and I also appreciate for their responses.
ReplyDeleteFirst l would like to ask responses in this context from the students and then l would clearify their doubts
ReplyDeleteAs a teacher first of all I will ask A,B and C how they have got their answers. And then I will take any variable for Length and breadth and explain how area is decreased by giving 2,3 examples.
ReplyDeleteपहले छात्रों को उनके उत्तर की गणना करने दें और फिर उनकी तुलना करने दें। आगे शिक्षक सही उत्तर बता सकता है और इसके पीछे का कारण भी बता सकता है।
ReplyDeleteFirst, I will ask each student to explain how they arrived at their answer. Then I will demonstrate practically what is the correct way to do it.
ReplyDeleteI would take the responses from all the three students and request reasoning for their conclusion.
ReplyDeleteThen, through demonstrations of their theories, i would help them visually understand what happens in all the three use cases. This way, they will understand the concept via illustration.
The correct way to do this would be to draw a rectangle of size LxB and vary their dimensions for a concrete learning
As a teacher I'll guide them first then take the three responses
ReplyDeleteIf the answers are inappropriate then I'll make the concepts clear
Writing the solutions one by one , through Demonstration on the Blackboard with three different illustrations, correct fact is to be shown to the students.
ReplyDeleteThe concept of place value is not clear
ReplyDeleteI would divide the board in three column and ask them to draw the diagram of rectangle ,being the facilitator i world ask three children to solve the given question together on the board and give reason for reaching their conclusion. Then I would explain all three situations through illustrations. All the children would be appreciated for attempting the question and would be facilitated how to derive the correct answer through these illustrations.
ReplyDeleteIf the length of a rectangle is increased by 1 and breadth decreased by 1 near area will be formed . We should go with B.
ReplyDeleteWriting the solutions one by one , through Demonstration on the Blackboard with three different illustrations, correct fact is to be shown to the students.
ReplyDeleteWith the help of paper and pencil we explain above situation.. In easy language
ReplyDeleteAll answers given will be illustrated by activity method - increase the length and decrease the breadth of the paper of given area and let them think whether it is same or more or less than previous area. Then an explanation will be given on board by illustration
ReplyDeleteAs a teacher I will encourage three of them and I will appreciate them for their response. I will ask them to explain their understanding of the problem. Then, I will give them three rectangular shaped objects with different lengths and breadths and I will ask them to find out their areas later I will explain that it will be depending upon the length and breadth that they have taken when the length is more than breadth the area will decrease.
ReplyDeleteWill ask the students as to why do they think answer will be the same, then give them a rectangle on the board with L 10 and B 9 and vice a versa and calculate Area through formula, for them to understand.
ReplyDeleteTo solve these type of problems, I think it would be a good idea to initiate a discussion with the students and ask them to justify their thinking with the help of concrete examples. They will be able to arrive at a correct answer on their own once they start justifying their thinnking.
ReplyDeleteBeing a teacher,I will handle this situation like the following way:
ReplyDeleteFirst I will ask trio that how they make their answers, I will ask A how can u say that the area will remain same and then I will note his reply. Then accordingly,I will ask the same to B and C also and note their replies. By doing this I will come to know their thought process.Finally,I will explain them what actually happens when we change the dimensions of a rectangle.As a teacher you have to encourage them to try and solve the problems correctly.
I will explain all three situations on blackboard and demonstrate through concrete objects
ReplyDeleteWill see their calculations behind their answer s first. Then facilitate them an idea to imagine a number for length and another less than that of length as breadth of the rectangle and calculate the area and see the result. Will help them if they does any mistakes in Calculating the area
ReplyDeleteAs a teacher I will try to understand their way of thinking and their approach about how they are trying to solve and clarify with them in their approach.
ReplyDeleteChildren can use use cutouts or draw the figures and do the calculations themselves to solve the problems.
ReplyDelete1.Ask the three students how to calculate the area of a rectangle.
ReplyDelete2. Give them the length as 4 cm and breadth as 3 cm.
3. Now tell them to increase the length by 1 cm and decrease the breadth by 1 cm.
4. Now find the area.
Teacher can give them rectangular objects and can ask them to calculate the areas of the same. Later teacher can ask to increase and decrease the length and the breadth respectively and then compute new areas. Then students will compare their answers.
ReplyDeleteOR
Teacher can use board to draw and explain
OR
Teacher can ask them to cut rectangles of given dimensions and compute areas for comparison.
I will initiate the students to explain their thought process by how they have reached to this conclusion then as a teacher by giving examples I will explain them the concept of area of the rectangle by paper folding and cutting activity.
ReplyDeleteI as a teacher will handle this situation like the following way:
ReplyDeleteFirst I will ask each of them to explain that how they make their answers.. By doing this I will come to know how they approached their conclusions and their thought process . Then I will explain them what happens really when we change the dimensions of a rectangle , using graph sheets. Ask them to draw a rectangle with a given dimension and find the area by counting unit squares enclosed by the rectangle. Then ask them to highlight the rectangular region in which length increased by one unit and breadth decreased by one unit.then find the area of the new rectangle by counting the unit squares enclosed by the new rectangle. Ask the students to repeat with few such examples . This will help the children to visualize as well as generalize this concept.
As a teacher, I will encourage all the three children “A, B and C” and will appreciate all three of them for their responses. I will ask them first to explain their justification for their stance.
ReplyDeleteThen, I will give them three rectangles with different lengths and breadths and would make the following illustration on the blackboard for all three of them to observe.
Example 1.
If we take a rectangle with length = 3 cm and breadth = 7 cm;
Area of the rectangle = Length × breadth.
Hence, area of of the rectangle = 21sq.cm
Now, if we increase the length by 1, the new length now is 4 cm and decreasing the breadth by 1 makes the new breadth as 6 cm. The new area of the rectangle = 24 sq.cm.
We observe that here, the area of the rectangle has increased.
Example 2.
If we take another rectangle with length = 5 cm and breadth = 3 cm;
Area of the rectangle = Length × breadth.
Hence, area of of the rectangle = 15 sq.cm
Now, if we increase the length by 1, the new length now is 6 cm and decreasing the breadth by 1 makes the new breadth as 2 cm. The new area of the rectangle = 12 sq.cm.
We observe that here, the area of the rectangle has decreased.
Example 3.
If we take a rectangle where length and breadth are inverse.
Say length = 4 cm and breadth = 5 cm
Area of the rectangle = Length × breadth.
Hence, area of of the rectangle = 20 sq.cm
Now, if we increase the length by 1, the new length now is 5 cm and decreasing the breadth by 1 makes the new breadth as 4 cm. The new area of the rectangle is 20 sq.cm.
We observe that here, the area of the rectangle remains the same.
Hence, from the three examples above, we find out that :
A. When length is lesser than its breadth, the area of the rectangle increases. Hence, B is correct.
B. When length is greater than its breadth, the area of the rectangle decreases. Hence, C is correct.
C. When length and breadth of a rectangle is inverse, it remains the same. Hence, A is correct.
Hence, all three of you A, B and C are correct.
SHILPI AGARWAL
FUTURE BHUBANESWAR SCHOOL
I will ask children to take paper of some size and then again take another paper with increase in length and breadth by 1cm and then place first paper on second check which one is greater. From observation students can say area will increase or decrease after increasing length and breadth.
ReplyDeleteThe teacher should first listen to the three conclusions given by the students. Then ask them the explanation to how they came to this conclusion. Then show the correct answer through an illustration and also explain through the same illustration where the students went wrong. This will make them understand their mistakes and also understand how to think in different ways to come to a conclusion.
ReplyDeleteA teacher can ask 3 of them to solve and see or give a string and ask them to do hands on by marking the perimeter. Then provoke them in discussion and understand each others points to come to a conclusion.
ReplyDeleteAs a teacher, I will encourage all the three children to give reason for their respons. I will explain their mistake by actually cutting paper of the given size and ask them to judge .Fact will remove thier misunderstanding.
ReplyDeleteWe can prove it by doing activities with rectangular card boards by changing the dimensions and calculating the area. This will clear thri misunderstanding.
ReplyDeleteI as a teacher would ask or encourage them to use variables , algebraic expression and equation.
ReplyDeleteThen I will help them to reach to a relation/equation which can be used to relate the two dimensions under which the areas in two cases be same.
And, then I will try to explain to them that all three of them are correct, provided the dimensions of rectangle are taken accordingly.
The teacher will first listen to what the three students had to say and why they thought so with proper reasons then the teacher can clarify their misconceptions with algebraic expressions or with paper cuttings by changing the dimensions of the rectangle.
ReplyDeleteWe can prove it by doing activities with rectangular card boards by changing the dimensions and calculating the area.
ReplyDeleteWe can prove it by doing activities with rectangular card boards by changing the dimensions and calculating the area.
ReplyDeleteThis misconception is quite obvious among students. So, I think we can address this by giving them multiple generalisation/examples.
ReplyDeleteThe best way to find out solution to the problem is to make all the three students justify their answers by showing it.
ReplyDeleteAsking the students to justify their answers and reflect on the same again by giving assistance until come out from right answer.
ReplyDeleteThe students will be asked to calculate and write the response . The calculations will be explained and thereby prove to the students about the correct answer. With specific examples ,by taking actual values and doing the calculations , the students can be explained about the real situation
ReplyDeleteAs a teacher first I ask all the students reply patiently and write their responses on the board and at last I give my conclusion by explaining what exactly it takes place and make them understand and I also appreciate for their responses.
ReplyDeleteAs a teacher I can handle this situation by allowing each child to come and demonstrate how they reached to their conclusions.
ReplyDeleteChildren can be asked to draw rectangles and calculate area with different different dimensions and by experimenting on their own , they can generalize their observations.
I will explain the children in the following manner:
ReplyDeleteL= Length
B= Breadth
Area of Rectangle= Length x Breadth
By following the steps,
After changes:
Length=L+1, Breadth= B-1
Area=(L+1)(B-1)
=L(B-1)+(B-1)
=LB-L+B-1
=LB-(L-B+1)
Where 'LB' is our old area so, the new area is old area minus (L-B+1).
So new area < old area
I would like to ask the students about their take on the problems, how they come to such conclusions and then will clear their doubts.
ReplyDeleteAnswer will be demonstrated to the students by explaining on blackboard that on changing the length by one and breadth by one(decreasing) area will remain same .
ReplyDeleteKeeping all of them together correct fact is to be shown
ReplyDeleteI would ask all the three students to explain how they reached their answer. It is possible that the students who are giving wrong answer would automatically understand the correct way during the discussion or find another way to come to the correct solution.
ReplyDeleteI will clear the confusion by taking the rectangular cut outs of different dimensions and explain them the effect in area with the increase and decrease in dimensions.
ReplyDeleteFirst I would like to take responses from the students and then I would like to conclude by clearing their doubts with a satisfactory illustrations.
ReplyDeleteRupa Banerjee
ERHS,Asansol
First I would like to take responses from the students and then I would like to conclude by clearing their doubts with a satisfactory illustrations.
ReplyDeleteRupa Banerjee
ERHS,Asansol
It can be explained by using ice-cream stick.
ReplyDeleteAs a teacher I will ask all of them to draw a rectangle and find out the area in both situations.In conclusion they will get the correct answer. Hence ,C is correct .Therefore, area will decrease.
ReplyDeleteThe best way to handle this situation is to give the example and ask them to solve and come to the conclusion.
ReplyDeleteImagine, l-5 and b-4 so, the area of rectangle =lxb=5x4=20
now as the situation given in the question length increases by 1 and breadth decreases by 1,
Hence new length and breadth are as follows;
l-6, b-3 so, lxb=6x3=18
This is how the students can come to the conclusion that the area will decrease in that given situation in the question.
First have to encourage three of them for their responses then have to ask them their reasons behind their answers as they will come up with their aswers along the process have to explain them through pictorial unit as well as through formula that Area of rectangle is {L*B }. By this process have to understand basic process by themselves.
ReplyDelete