Prove that the sum of the first n even numbers is an even number. Is the kind of logic used in proving this is inductive, deductive or both? Justify your answer.

Here is a think of a number game: ‘Think of a number, then double it, add six to the sum, divide the sum by half and then subtract 3 from it the number’. Did you receive the same number you had started with? Why? Justify.

What is an equation? Does all the equation involve a variable. Give an example of an equation with a variable in it and which does not have a variable in it.

What could be the logic behind the following subtraction done by a child:

Does this shows that the child has not understood the process of subtraction of numbers? Give reasons for your answer. How will you help her to correct her mistake.

Illustrate the use of each of the following in learning the concept of “fraction”.

i) an outdoor activity

ii) newspapers and magazines

How would you convince a child that any number multiplied by 0 is 0, using a teaching aid.

Evaluation at every step, through immediate feedback, should form part of teaching – learning process. Explain this statement in the context of each, teaching and learning of place-value. Further give three distinct multiple assessment techniques for evaluation in the context given.

Suggest two activities of different kinds that would help children arrive at a formula that relates centimeters to meters.

‘Mathematics is hierarchical in nature’. Justify this statement with help of an example.

Suman plays basketball. State two different mathematical concepts she used for this. Justify your answer.

Explain the relationship of arithmetic and algebra with the help of a suitable example.

Give an example each, with justification, of a situation in which a child uses deductive reasoning.

i) While playing

ii) In Mathematics.

Explain how mathematics is a language. Further give two distinct activities to help assess how comfortable a child is with her language.

Represent pictorially

i) .17 and .07

ii) 

Rinku, 8 years old has her birthday in December and Sonal (6 years old) has her birthday in April. Rinku says Sonal is older than her. What is the misconception Rinku has? Derive a detailed strategy to help Rinku overcome this misconception

What is an open-ended question? Give two examples of such questions, one pertaining to single digit addition and one to multiplication.

Enlist two situations each from our daily life in which we use

i) Geometry

ii) Integers

iii) Algebra

Jaya solved the division problem as shown below:

i) What is the mistake she committed?

ii) What is the probable reason for her mistake?

iii) Devise a strategy to overcome her misconception.

Explain why use of concrete material and hands on experiences, in teaching learning of mathematics at primary level are more effective. Illustrate with the help of one example each.

कारण सहित उत्तर देते हुए बताइए कि निम्नलिखित समस्याओं के लिए आप किस प्रकार के निदर्शन का प्रयोग करेंगे। इन समस्याओं के चार अनिवार्य तथ्य भी बताइए।

i) एक बीमा कंपनी की आर्थिक व्यवहार्यता (viability) जोखिमों का निर्धारण करने और जोखिम को संरक्षित रखने के लिए, लिए गए प्रीमियम संबंधी निर्णय पर मुख्यत निर्भर करती है। यदि प्रीमियम कम हो, तो अर्चा वसूल की गयी धनराशि से अधिक हो सकता है और ऐसी स्थिति में कंपनी दिवालिया हो सकती है। इसके विपरीत यदि प्रीसियन अधिक हो तो ग्राहकों की संख्या में कमी आती जाएगी जो कि कंपनी के लाभ को प्रभावित करेगी। विभिन्न जोखिमों के लिए प्रीमियम संबंधी निर्णय लेने में बीमा कंपनी की सहायता करना जिससे कि आर्थिक व्यवहार्यता सुनिश्चित बनी रहे और लाभ अधिकतम होता रहे।

ii) एक नदी के किनारों पर स्थित कंपनियां, जो रासायनिक पदार्थों का उत्पादन करती हैं, अपने अपशेष पदार्थों को लगातार नदी में फेंक कर निपटाती है जिसके कारण नदी अत्यधिक प्रदूषित होती जाती है। ऐसी स्थिति में स्थानीय अधिकारियों ने इस संबंध में नया कानून लागू किया है कि यदि नही प्रदूषण एक निश्चित सांदण सीमा से अधिक हो जाता है तो ऐसा करने वाली कंपनियों को जुर्माने के रूप में भारी धनराशि का भुगतान करना होगा। अपशेष को निपटाने के संबंध में एक ऐसी नीति मालूम करना जिससे कि यह सुनिश्चित किया जा सके कि प्रदूषण का स्तर कभी भी नियत की गई सीमाओं से अधिक न हो पाए।