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Following are some questions posed by the teacher in the mathematics classroom: A. What is the area of the rectangle whose one side is 5 cm and perimeter is 30 cm? B. Find a set of numbers whose median is 4. C. List all prime numbers between 0 - 8. D. Tell me anything mathematical information you know about rectangles.

Following are some questions posed by the teacher in the mathematics classroom: A. What is the area of the rectangle whose one side is 5 cm and perimeter is 30 cm? B. Find a set of numbers whose median is 4. C. List all prime numbers between 0 - 8. D. Tell me anything mathematical information you know about rectangles. Correct Answer A and C are closed ended and B and D are open ended questions

Generally, the questions asked by the teacher during the teaching-learning process can be broadly classified into two types:

Open-ended questions

  • These questions are also known as the divergent questions where the respondents are free to share, clarify and put their views. The students will elaborate their point of view and the teacher will be able to see the things from a student's perspective.
  • These questions are generally framed in a single statement that requires a longer response.

​Close-ended questions

  • These questions are also known as the convergent questions where the respondents answer in limited ways, like responding in ‘yes’ or ‘no’; underlining the replied among the predefined responses, putting the sign ‘correct’ or ‘incorrect’.
  • They provide limited insight but can be easily used to analyze quantitative data.

​ Key Points

What is the area of the rectangle whose one side is 5 cm and perimeter is 30 cm?
  • The perimeter of a rectangle (given 30 cm) is twice the sum of its length (l) and width (w).  Perimeter = 2 (l + b) 

          ⇒ 30 cm = 2 (5 + b) 

          ⇒ 30 cm = 10 + 2b

          ⇒ (30 - 10) cm = 2b 

          ⇒ 20cm = 2b ⇒  b = 10cm. 

  • The area of a rectangle is the space occupied by it which can be calculated by multiplying its length by its width.
  • That is 5 cm × 10 cm = 50 cm2.
  • This question has only one unique answer which makes it a close-ended question.
Find a set of numbers whose median is 4.
  • Median is used to represent the mid-point or the middle number/quantity in any series of quantities and numbers.
  • The students can find and tell numerous sets of numbers having a midpoint or median of 4.
  • They can also create a number set with a median of 4. Like, 2, 3, 7, 4, 9, 10,11. Here, 4 is in the middle of the given set. 
  • This question is an open-ended type of question.
List all prime numbers between 0 - 8.
  • Prime numbers are those numbers having only two factors which are 1 and themselves.
  • There are only limited prime numbers between 0 - 8. These are 2, 3, 5, and 7.
  • Other than these, nothing can be answered in response to this question which makes it a close-ended type of question.
Tell me anything mathematical information you know about rectangles.
  • Here, the students can tell many things regarding rectangle and its properties whichever comes to their mind first.
  • So, it is an open-ended question.

Thus, it is concluded that A and C are close-ended type questions whereas B and D are open-ended type questions.

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