Other Math Answers

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

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.

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

The diversity in any classroom has major implications for teaching mathematics. Explain this
statement, with examples from teaching algebra to support your explanation.

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.

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.)

Is there any difference in the way you would plan a unit and a lesson? Explain your answer,
with examples in its support.

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.

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?

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.