Q.

1. a) Give two real-life situations, with justification, in which a person would need to use the ability

to estimate the sum or difference of two fractions. (4)

b) Explain the differences in the following processes involved in the growth in mathematical

understanding. Also provide an example of each, pertaining to ‘data handling’.

i) known to unknown;

ii) particular to general. (8)

c) Illustrate how the E – L – P – S sequence can be applied to help children understand the concept

of ‘angle’. (4)

d) Is there any difference in the way you would plan a unit and a lesson? Explain your answer,

with examples in its support. (4)

2. a) Explain why the three pre-number concepts need to be developed by a learner for him/her to be

able to count. Your explanation needs to include specific examples. (6)

b) i) Outline a series of three activities (each requiring a different level of learner’s ability) to

help a learner develop an understanding of ‘place value’. (Note that giving a ‘series’

means that the links between the different activities must also be brought out.)

ii) How would you modify these activities if you were doing them with a class of 30

learners? (9)

c) There are broadly 5 different real-life situations which require multiplication. Give a word

problem each for these situations, in the context of children playing in a field. (5)

3. a) Children have several misconceptions regarding negative numbers. List four of them. Also, for

any one of these misconceptions, give a detailed strategy for helping the children correct it.

(6)

b) The diversity in any classroom has major implications for teaching mathematics. Explain this

statement, with examples from teaching algebra to support your explanation. (5) 4

c) Consider a classroom situation in which a teacher is introducing Class 6 children to operations

on negative numbers. In this context, explain the different levels at which mathematics and

language are related. (9)

4. a) Devise a game to help children improve their understanding of addition and subtraction of

fractions. Also give two distinct activities you would use for assessing the efficacy of this

game. (5)

b) Explain the following statements, giving examples from the context of operations on decimal

fractions (i.e., numbers like x y z r, where x, y, z, r are digits between 0 and 9):

i) Mathematics permeates every aspect of your life.

ii) In mathematics, truth is a matter of consistency and logic.

iii) Articulating reasons and constructing arguments helps children learn mathematical

processes. (10)

5. a) i) Explain the 5 levels of development in geometric understanding proposed by the Van

Hieles. Illustrate your explanation in the context of learning the concept of volume.

ii) Further, do you agree that children in Class 6 usually think at Level 2? Give reasons for

your answer. (12)

b) Can you think of a planar figure with exactly two axes of symmetry? Can this figure be a

triangle? Give reasons for your answers. (4)

c) Explain what inductive and deductive logic are, and illustrate them in the context of measuring

time. (4)

d) Give two reasons why children usually find mathematical notations confusing. Support your

answer with illustrations pertaining to representing and reading time. How would you help your

learners become comfortable with the notation?