Module 9 - Activity 5: Reflect
A said ‘if the 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. Share your understanding in the blog.
let us consider length=10 and breadth=8
ReplyDeletearea = 10x8 = 80
according to the statement, 10+1 =11 and 8-1 = 7
new area = 11x7=77
so the area will decrease.
c is correct
Area of a rectangle = l x b
ReplyDeleteLet us take x to be the length of the rectangle
And, y to be the breadth of the rectangle
The area = xy
Now, according to the question area = (x+1) * (y-1)
=>xy - x + y - 1
=> (x+1) (y-1)
Hence the area remains same.
Ans. C is correct
ReplyDeleteLet the length and breadth be 5 and 2
ReplyDeleteso area = 10 sq units
IF length = 6 and breadth =1
area becomes 6 sq units
so area decreases on this situation
let length = 15 cm and breadth= 10cm
ReplyDeletearea=15 x 10 = 150 sq.cm
now, new length = 16cm and new breadth = 9 cm
new area = 16 x 9 = 144 sq. cm
Therefore area will decrease
to make the students draw the first figure then tell them to distribute it into small squares of 1cm X 1cm and then telling them to count all the squares. after this telling them to draw additional part of increasing length and decreasing breadth; also I'll make them divide the additional area in to 1cm X 1cm squares and let them count all the squares again. this will give them experience of what, why and how it will happen if the length increased and breadth decreases. then I'll teach them the equation by writing it on the board. this will help them understand better.
ReplyDeletealso will give couple of more experiencial examples to do at home by giving different measurements to different groups and make them share it next day.
ReplyDelete*experiential
ReplyDeleteTeach students drawing figure, using 1cm *1cm block count the area,after that change as per question, ask students, definitely the proper answer will come from them, now teacher can solve using numbers. Some examples, teacher have to give .
ReplyDeleteby using unit squares the area of both the measurements will be analysed as in second case the whole row has to be removed as breadth is decreasing the are will decrease will be brought into observation
ReplyDeleteto make the students draw the first figure then tell them to distribute it into small squares of 1cm X 1cm and then telling them to count all the squares. after this telling them to draw additional part of increasing length and decreasing breadth; also I'll make them divide the additional area in to 1cm X 1cm squares and let them count all the squares again. this will give them experience of what, why and how it will happen if the length increased and breadth decreases. then I'll teach them the equation by writing it on the board. this will help them understand better.
ReplyDeleteI would explain the concept again and revise area of rectangle. The teacher can make a model and explain to bring clarity. Then I would make the student draw the figure according to the sum given and solve it. Get a feedback if the child has understood the concept.Then give a few more similar sums to further clarify the doubt of the student.
ReplyDeleteBy Experimental Learning
ReplyDeletelet length is x
ReplyDeletewidth y
area= xy
new length x+1
width y-1
area= xy-x+y-1
here you can see from the area of the rectangle the length and 1 is subjected and only width is added so c is right
I will ask them to take paper and draw the rectangle and find its area and perimeter. Then again i will ask them o draw the new rectangle with the decreased 9 new measurement0 and find its area and perimeter. now they will be clear. I make my grade 4 students do this work.
ReplyDeleteThe best way to deal with this situation is to discuss the given situation properly by taking students responses.
ReplyDeleteHere students should be given authority to explain it in their own words how have they arrived to a solution. Teacher may guide/facilitate them if they say/ do something wrong.
I am sure students will take examples by reducing one side of a rectangle and increase other side of a rectangle and then come to a conclusion on there own.
Ans. C is correct
ReplyDeleteIn fact none of them is exactly right, as area in II case could be greater, less than or equal to the original area.
ReplyDeleteLet l be the original length, b be the original length
I Case: Area = lb sq units
II Case: Area = (lb - l + b - 1) sq units
Now if l > b, then II Area < I Area
But if l < b, then II Area > I Area
Stidents should be given a chance to demonstrate and justify their answers by showing the working and calculations of the Areas in all the three cases. This way they will learn by doing.
ReplyDeleteStudents should be asked to take different values of l and b , and check it by observation on their own . once they will reach the conclusion themselves , it will retain with them for a longer time .
ReplyDeleteIt will depend on the dimensions of Length and Breadth. For example: L= 2 cm and Breadth = 3 cm and if we increase Length then L = 2+1=3 cm and If we decrease Breadth then B=3-1 = 2 cm then area of rectangle in both the cases is coming same. But in Second Case: If we take L= 2 cm and Breadth = 4 cm and if we increase Length then L = 2+1=3 cm and If we decrease Breadth then B=4-1 = 3 cm then area of rectangle is increasing. Or may be if we take Length as 8 cm and Breadth as 10 cm so area will decrease. So it all depends on the dimensions of the rectangle.
ReplyDeleteThis comment has been removed by the author.
ReplyDeletestudents should be given a chance to demonstrate and justify their answers
ReplyDeleteExperiential learning would help the students understand the concept better rather than just using formula and numbers. Students can try/witness with a simple grid paper, geo-boards or Lego blocks. Moving from Concrete to abstract knowledge.
ReplyDeleteif length=10 and breadth=8
ReplyDeletearea
= 10x8 = 80
according to the statement,
10+1 =11 and 8-1 = 7
new area
= 11x7=77
then area will decrease.
correct =c
Experimental learning will help the students.All the students divided into some groups and told to use papers of different sizes and calculate the area before and after according to the question.
ReplyDeletec is correct. We can give an example of a rectangle with dimensions 4 cm and 3cm and then its area is 12 sq.cm if we decrease its length and breadth both by 1 cm, then area will decrease since then new area will be product of 3 and 2= 6. so, the area will decrease in such a situation. we can cut two rectangles of the example i have taken and compare the amount of surface enclosed by the rectangles for an illustration too.
ReplyDeletec is correct. We can give an example of a rectangle with dimensions 4 cm and 3cm and then its area is 12 sq.cm if we decrease its length and breadth both by 1 cm, then area will decrease since then new area will be product of 3 and 2= 6. so, the area will decrease in such a situation. we can cut two rectangles of the example i have taken and compare the amount of surface enclosed by the rectangles for an illustration too.
ReplyDeleteThis situation is to be explained with a rectangle divided into squares of 1 cm each.
ReplyDeleteSay l = 8 cm and breadth = 5 cm then , total number of squares gives the area . so area is 40 sq cm.
Now lets increase length and decrease breadth by 1 cm .
l = 9cm and breadth = 4 cm . here total number of squares are 36. Area = 36 sq units.
The number of squares are decreased as one row is removed. so area is decreased.
- E. indira
For primary students Experiential learning would help the students understand the concept better rather than just using formula and numbers. Students can try/witness with a simple grid paper, geo-boards or Lego blocks. Moving from Concrete to abstract knowledge.
ReplyDeleteFor upper primary students,
l= length=10 and b= breadth=8
Length is not equal to breadth, which is a rectangle
area of the rectangle = 10x8 = 80
according to the statement,
L=10+1 =11 and B= 8-1 = 7
new area=LxB
= 11x7=77
then the area will decrease. from 80 square units to 77 square units
Decreased area= 80 -77= 3 square units
correct =c
There are two ways of handling this situation :
ReplyDelete1. take examples of rectangles with known length and width and then increase and decrease the length and width and then compere the values of areas.
2. show with the help f activity , by taking squared sheet and then mark rectangles in that and let the students see for themselves what happened to the area with the changes length and width.
Ans. C is correct
ReplyDeleteAnswer:
ReplyDeletec is right
Step-by-step explanation:
let length is x
width y
area= xy
new length x+1
width y-1
area= xy-x+y-1
here you can see from the area of the rectangle the length and 1 is subjected and only width is added so c is right
We can use a rectangle shaped squared paper to explain this to students by shading/colouring the squares according to the l and b given.
ReplyDeleteLet the length and breadth be 5 and 2
ReplyDeleteso area = 10 sq units
IF length = 6 and breadth =1
area becomes 6 sq units
so area decreases on this situation
Explain the concept by giving an example
ReplyDeleteEg - l = 10 cm b = 2 cm
Area= lx b = 10x 2 = 20cm
Now suppose l is increased by 1 cm and becomes 11 cm
and b is decreased by 1 cm and becomes 1 cm
Area= lx b= 11 x 1= 1cm
Therefore the area of the rectangle has decreased.
c is correct
ReplyDelete