21.

Read the approaches used by the two teachers to teach solving oflinear equation, say 2x - 6 = 10

Teacher A	Teacher B
Steps (a)Take 6 on other (b) Change the sign of 6 and add to 10 (c) Get 2x = 16 (d)Take 2 on the other side and divide (e) Get x = 8	Steps (i) Equation always mentain equality. So, same operation with same number can be performed on both sides to maintain equality (ii) HENCE, 2X - 6 + 6 = 10 + 6 = 2X = 16 (iii) $\frac{2\mathrm{x}}{2} = \frac{16}{2} \Rightarrow \mathrm{x} = 8$

It can be observed that

• teacher A focuses on conceptual knowledge while teacher B focuses on procedural knowledge

• teachers A and B focus on instrumental
  understanding

• teacher A emphasizes on instrumental understanding while teacher B emphasizes on
  relational understanding

• teacher A emphasizes on relational understanding while teacher B emphasizes on instrumental understanding

$\mathrm{A} \mathrm{student} \mathrm{writes} \frac{10 \mathrm{cm}}{12 \mathrm{cm}} = \frac{5}{6}\mathrm{cm}$

$\frac{15 \mathrm{cm}}{15 \mathrm{m}} = 1000\mathrm{m}. \mathrm{This} \mathrm{student}$

• can reduce fractions to lowest term correctly and can write the units properly

• has concept of units, conversion of units, fractions but missed the concept that ratio does not have units

• always commits clerical error of writing unit with ratio

• has clear concept of units and their conversion

$$\begin{gathered} \mathrm{If} {\mathrm{a}}^3 = 1 + 7, 3^3 = 1 + 7 + \mathrm{b} \mathrm{and} 4^3 = 1 + 7 + \mathrm{c}, \mathrm{where} \mathrm{a}, \mathrm{b} \mathrm{and} \mathrm{c} \mathrm{are} \mathrm{different} \mathrm{positive} \\ \mathrm{integers}, \mathrm{then} \mathrm{the} \mathrm{value} \mathrm{of} \mathrm{a} + \mathrm{b} + \mathrm{c} \mathrm{is} \end{gathered}$$

• 77

• 79

• 58

• 68

We call a number perfect if it is the sum of all its positive divisors, except itself. e.g., 28 is a perfect number because 28 = 1 + 2 + 4 + 7 + 14. Which of the following numbers is a perfect number?

• 9

• 6

• 13

• 10

Which of the following numbers is a perfect square?

• 548543251

• 548543241

• 548543213

• 548543215

A fraction is equivalent to $\frac{5}{8}$. Its denominator 8 and numerator add upto 91. What is the difference between the denominator and numerator of this fraction ?

• 19

• 21

• 3

• 13

A polyhedron has 6 faces and 8 vertices. How many edges does it have ?

• 14

• 15

• 10

• 12

If

$$\begin{gathered} 1957 \\ - \mathrm{\alpha }9 \\ \mathrm{\_\_\_\_\_\_} \\ 18\mathrm{b}8 \end{gathered}$$

the sum of the digits a and b is

• 13

• 12

• 15

• 14

The mean of median and mode of the data 7, 6, 7,9, 8, 8, 10, 8 is

• 8.5

• 9

• 5.5

• 8

A teacher conducted a debate in the class on the following topic

"Zero is the most significant number.''

She encouraged every child to express his/her view on the topic. The teacher is

• using her Mathematics class as life-skill class to develop value of argument among the children

• inducing problem-solving skill among the children

• making her classroom more communicative and reflective

• passing her time as students are not in mood of studying