Explain the difference in the processes of abstraction and generalisation. Give two detailed examples, one related to gender issues and one related to ‘data handling’, as a part of your explanation.

Sanjit claims that if you toss a coin continuously, you can’t get 5 trails in a row, but you can only get at most 2 tails in a row. How would you help her understand that this not correct?

Write 30 in base 2 and base 5.

What is divisibility rule for 11 in the decimal system? Explain this with two distinct examples. Further, what is the logic behind the rule?

Which of the following statements are true? Give reasons for yours answers. Marks are only for appropriate reasons. 
a) Errors made while learning are a reflection of lack of practice and concentration on
the part of the learners.
b) There are about one-third learners in any class who are not capable of learning mathematics.
c) A good classroom must have pin-drop silence.
d) Knowledge is best acquired by memorisation.
e) A circle has more lines of symmetry than a square. 

What is ‘mode’ of a set of data? Give an example, with justification, of data gathered in a real-life situation with more than one mode.

What are three key aspects that define a model of learning? Explain these using the programming model. Why is this model considered inappropriate for teaching and learning?

Give an activity, with justification, to help develop the understanding of ‘variable’ for a Class VI child. This activity must have at least four qualities to be found in a good activity. Your answer must clearly specify how the activity has these qualities.

Manju claims, “By the time children reach class IX, most prefer science to mathematics.” What data is needed to test Manju’s statement? How would you gather it, record it, and analyse it to draw conclusions?

Give a series of three activities, requiring different ability levels, to generate mathematical thinking in 30 children of Class IV. Explain why the activities are in a series.

Give an example of an axiom. What is the difference between an axiom and a theorem?

Explain what a schema is. Further, explain the processes involved in elaborating a schema, through an example pertaining to a child of Class IV learning the concept of ‘angle’.

Give three main difference between a map and a picture of a place. Give one situation with justification, in which a picture is a better representation of the situation than a map.

What is meant by
i) Rotation symmetry
ii) Glide symmetry 

What are the four stages of the scaffolding process? Illustrate these stages in the context of development of a number sense in young children.

Use the principle of Mathematical induction to prove 2 > 2 n for all n > .1

Write the numbers 0.00099, 0.03, 0.001, 0.6, 14, 1.005, 7 in descending order. What is the algorithm you used for doing this?

In what way does playing with tangrams help in developing spatial understanding? Explain with an example of children from Class III playing with tangrams.

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