In the 60-mark Mathematics & Science option of Paper-II, how many questions are on pedagogy?

20 — ten in mathematics and ten in science

10 — all of them in mathematics

20 — ten in mathematics and ten in science

None — pedagogy is only in the Child Development section

A Class VII pupil writes −3 − (−5) = −8. The rule the pupil is applying is:

Treating the minus of subtraction and the minus of the number as one minus, so both are counted as negative

Adding the two numbers and keeping the sign of the larger

Treating the minus of subtraction and the minus of the number as one minus, so both are counted as negative

Subtracting the smaller number from the larger

Several pupils write (a + b)² = a² + b². The most effective remedial step is to:

Have pupils draw a square of side (a + b), cut it into its four parts, and see where 2ab comes from

Make the class write the identity twenty times

Have pupils draw a square of side (a + b), cut it into its four parts, and see where 2ab comes from

Tell pupils that squaring never distributes and mark the error each time

Substitute a = 1 and b = 1 to show the two sides differ

The image formed by a plane mirror is:

Virtual, erect, of the same size, and as far behind the mirror as the object is in front

Real, inverted and smaller than the object

Virtual, erect, of the same size, and as far behind the mirror as the object is in front

Virtual, inverted and larger than the object

Real, erect and of the same size

A Class VI pupil says plants take their food from the soil through the roots. The teacher should:

Keep two identical potted plants, one in light and one in the dark, and let the class explain the difference

Correct the statement, write the definition of photosynthesis on the board, and move on

Keep two identical potted plants, one in light and one in the dark, and let the class explain the difference

Tell the pupil the answer is wrong and ask another pupil

Ignore it, since the pupil will read the correct account in the textbook

A school has no science laboratory and no apparatus grant. On the syllabus’s own terms, the teacher of Classes VI-VIII should:

Build the activities from low-cost and no-cost material — bottles, wire, bulbs, mirrors, syringes, the school ground

Teach the practical chapters from the textbook and note that the laboratory is unavailable

Build the activities from low-cost and no-cost material — bottles, wire, bulbs, mirrors, syringes, the school ground

Take the class to a neighbouring school’s laboratory once a year

Concentrate on the theory chapters, which carry more marks anyway

A Class VIII lesson requires heating a liquid in a test tube over a spirit lamp and adding concentrated acid. The soundest arrangement is:

The teacher demonstrates the heating and the acid step with the class at a safe distance, and the pupils record, predict and explain

Every pupil performs the whole experiment, since science must be done rather than watched

The teacher demonstrates the heating and the acid step with the class at a safe distance, and the pupils record, predict and explain

The experiment is dropped and the result is dictated as notes

The brightest pupil performs it while the others copy the observations

Mathematics & Science, Classes VI-VIII — Paper-II Subject Option

Paper-II gives 90 of its 150 marks to Child Development & Pedagogy and the two languages, and the remaining 60 to one subject option — this one, or Social Studies. The option is chosen on the application form, not in the hall, and it decides the last 60 questions of the paper. Two things about those 60 decide most scores. First, they are split evenly: 30 for mathematics and 30 for science, so a candidate strong in one and absent in the other is capped at half. Second, 20 of the 60 are pedagogy — ten in each subject — and they are the most predictable questions on the paper, because they repeat a small set of positions from NCF 2005 rather than testing content. This chapter takes the structure first, then upper-primary mathematics at the places it actually breaks, then the seven science themes NCERT organises Classes VI-VIII around, then the pedagogy the last twenty marks are for.

The 60 Marks, Split Four Ways

The subject option is not a choice between easy and hard; it is a choice about what you are eligible to teach. A candidate appointed on the Mathematics & Science option teaches those subjects in Classes VI to VIII, and the Social Studies option leads to a social science post. Both are 60 marks and both are graded the same way — one mark a question, no negative marking — so the arithmetic of qualifying does not change with the choice. What changes is the content, and, for this option, the fact that it is really two 30-mark subjects sharing a section.

How the 60 marks of the Mathematics & Science option are made up
Block	Questions	What it holds
Mathematics — content	20	Number system, algebra, geometry, mensuration, data handling.
Mathematics — pedagogy	10	Nature of mathematics, error analysis, the language problem, evaluation, remedial teaching.
Science — content	20	The seven NCERT themes — food, materials, the living world, moving things, how things work, natural phenomena, natural resources.
Science — pedagogy	10	Nature of science, process skills, activity and experiment, the laboratory, misconceptions, evaluation.

🎯 Where the cheap marks are

Twenty of these sixty marks are pedagogy, and pedagogy has a far smaller answerable universe than content does. Upper-primary science content can ask anything from stomata to fuses; the pedagogy questions come back, paper after paper, to the same handful of positions — science is a process and not a list, a child’s wrong answer is information, the activity comes before the definition, assessment should reach reasoning. A candidate who reads the last section of this chapter properly is close to twenty marks before touching a single formula.

Mathematics at Classes VI-VIII: Where It Breaks

Upper-primary mathematics is where arithmetic becomes algebra, and the transition has four named difficulties. Integers introduce a second meaning for the minus sign — it is now both an operation and a property of a number — and almost every integer error comes from conflating the two. Rational numbers ask a child to accept that between any two numbers there is another, which contradicts the counting picture built up over five years. Algebra asks that a letter stand for any number rather than for one unknown number to be found. And mensuration asks that area and perimeter be held apart, when the words for them in ordinary speech are not held apart at all.

The five content blocks, and the error each one is asked through
Block	What Classes VI-VIII cover	The characteristic error
Number system	Integers and their operations, factors and multiples, HCF and LCM, fractions and decimals, rational numbers, squares, cubes, roots, exponents.	−3 − (−5) computed as −8: the minus of subtraction and the minus of the number are added instead of cancelling.
Algebra	Variables and expressions, like and unlike terms, simple linear equations in one variable, identities, factorisation.	(a + b)² written as a² + b²: the square is treated as distributing over addition, which multiplication does and powers do not.
Geometry	Lines and angles, triangles and their properties, congruence, quadrilaterals, circles, construction, symmetry, solid shapes.	Reading a property off the drawing: a triangle that looks isosceles is called isosceles without the two sides being marked equal.
Mensuration	Perimeter and area of rectangle, square, triangle, parallelogram and circle; surface area and volume of cube, cuboid and cylinder.	Believing that doubling a side doubles the area, and that two shapes of equal perimeter have equal area.
Data handling	Collection and organisation of data, bar graph, pie chart, mean, median, mode, and elementary probability.	Using the mean where an extreme value makes the median the honest measure — and reading a bar graph without reading its scale.

⚠️ Four sums the paper sets as diagnoses

−3 − (−5) = 2, not −8 — subtracting a negative moves right on the number line. (a + b)² = a² + 2ab + b², and the missing 2ab is the two rectangles in the area model. A square of side 3 has perimeter 12 and area 9; of side 6, perimeter 24 and area 36 — the perimeter doubled and the area quadrupled. And 2/3 lies between 1/2 and 3/4, which is the fact a child who thinks in whole numbers cannot see. When a stem hands you a child’s wrong answer, work out which of these four rules produced it; the option that names that rule is the answer, and the option that says "careless" never is.

Science at Classes VI-VIII: The Seven Themes

NCERT does not divide upper-primary science into physics, chemistry and biology; it organises it into seven themes, and the paper asks it in the same shape. Knowing the themes matters for more than tidiness: a question that opens "In the theme Moving Things, People and Ideas..." is asking about motion, speed, force and pressure, and a candidate who has memorised chapter names rather than themes has to guess. The themes also explain the register. Upper-primary science asks what a thing does and how it is measured, not the molecular account of why — respiration is gas exchange and energy release, not the electron transport chain.

The seven themes, and the facts each is asked through
Theme	What it holds, and what the paper takes from it
1. Food	Sources of food, nutrition in plants and animals, components of food. Photosynthesis needs chlorophyll, carbon dioxide, water and sunlight, and happens in the leaf; the gas enters through stomata. Deficiency: vitamin A — night blindness, vitamin C — scurvy, vitamin D — rickets, iodine — goitre, iron — anaemia, B₁ — beri-beri.
2. Materials	Materials of daily use, separation of substances, acids, bases and salts, physical and chemical change, synthetic fibres, metals and non-metals. Separation: winnowing, sieving, sedimentation, decantation, filtration, evaporation — salt from sea water is evaporation. Litmus turns red in acid and blue in base; turmeric turns red in base. Rusting is a chemical change; melting is physical.
3. The World of the Living	Cell structure and function, tissues, respiration, transport in plants and animals, reproduction, adolescence, microorganisms, crop production, ecosystems. The cell was discovered by Robert Hooke in 1665; every cell has a membrane, cytoplasm and nucleus, and a plant cell adds a cell wall. Photosynthesis stores energy, respiration releases it.
4. Moving Things, People and Ideas	Motion and measurement of distances, motion and time, force, friction and pressure. Speed = distance ÷ time, and a body covering equal distances in equal intervals is in uniform motion. Force changes the state of motion, the direction, or the shape. Friction opposes motion and is reduced by lubricants and ball bearings.
5. How Things Work	Electric current and circuits, magnets. A circuit must be closed for current to flow; the heating effect gives the filament and the fuse, and the magnetic effect gives the electromagnet. Like poles repel, unlike attract, and a freely suspended magnet points north-south.
6. Natural Phenomena	Light, sound, lightning, earthquakes. A plane mirror gives a virtual, erect image of the same size, as far behind the mirror as the object is in front, laterally inverted. Sound needs a medium; pitch follows frequency and loudness follows amplitude; the audible range is about 20 Hz to 20,000 Hz.
7. Natural Resources	Water, air, coal and petroleum, conservation of plants and animals, pollution, the greenhouse effect. Coal and petroleum are exhaustible and fossil-formed; sunlight and air are inexhaustible. Deforestation, ozone depletion and acid rain sit here, as does the difference between a national park and a wildlife sanctuary.

🧠 Physical or chemical, in one question

Ask whether a new substance was formed. Melting ice, dissolving sugar, tearing paper and boiling water make nothing new and are physical, however dramatic they look. Rusting, burning, cooking, curdling and the fizz of baking soda in lemon juice make a new substance and are chemical, however small they look. The one that catches candidates is dissolving — sugar in water is physical, because the sugar can be got back by evaporation.

The Twenty Pedagogy Marks

The pedagogy questions in this option are not content questions in disguise. They test one commitment, stated in NCF 2005 and repeated in the NCERT science and mathematics syllabuses: science is a way of finding out, not a body of findings, and it must be taught as one. Everything else follows. If science is a way of finding out, then the child must do the finding — hence activity before definition, observation before explanation, and the child’s own question as a legitimate starting point. If it is a way of finding out, then a wrong answer is a step in a process rather than a fault, so it must be diagnosed rather than corrected. And if it is a way of finding out, then an examination that asks only for recall is measuring the wrong thing.

The positions the pedagogy questions mark as correct
When the stem asks about	The marked answer
The aim of teaching science at upper primary	To develop the process skills and the scientific temper — observing, classifying, hypothesising, experimenting, inferring — not to prepare for competitive examinations and not to complete the textbook.
A child’s wrong idea — that plants take food from the soil, that heavier bodies fall faster	Treat it as a misconception with a reason behind it and design an activity whose result the misconception cannot explain. Not "tell the child the correct fact and move on".
The order of a lesson	Activity or demonstration, then observation, then the children’s own explanation, then the term. The definition-first lesson is the one every such question is set against.
No laboratory, or no apparatus	Improvise with low-cost and no-cost material — bottles, bulbs, wire, syringes, mirrors, the school ground. Absence of a laboratory is never a reason to teach science as text.
Evaluation	Continuous and comprehensive, reaching reasoning and process — predict the result, explain a graph, design a test, keep a record — rather than the recall of definitions.
Safety in an experiment	The teacher demonstrates what is hazardous and the children do what is safe. Safety is the one ground on which "the teacher shows rather than the child does" is the marked answer.

⚠️ The one exception to "let the child do it"

Almost every pedagogy question rewards the option in which the child observes, handles or explains, and the reflex of picking it works — until the activity involves concentrated acid, a spirit lamp, mains electricity or a heated glass tube. There the marked answer is teacher demonstration with the class at a safe distance, and the pupil-does option is the trap. Read the stem for a hazard before you apply the rule.

Key takeaways

The option is 60 marks in four blocks — mathematics content 20, mathematics pedagogy 10, science content 20, science pedagogy 10. Mathematics and science are 30 each, so neither can be abandoned, and 20 of the 60 are pedagogy.
Four errors carry most of the mathematics questions: the two meanings of the minus sign, (a + b)² read as a² + b², the belief that doubling a side doubles the area, and whole-number thinking applied to rational numbers. Name the rule that produced the wrong answer — never "carelessness".
Upper-primary science is organised as seven themes, not as three subjects: Food, Materials, The World of the Living, Moving Things People and Ideas, How Things Work, Natural Phenomena, and Natural Resources. Physical change makes no new substance; chemical change does.
The pedagogy marks rest on one commitment — science is a way of finding out. So activity precedes definition, a misconception is diagnosed rather than corrected, absence of a laboratory is met with low-cost improvisation, and evaluation reaches process. The single exception is a hazardous experiment, which the teacher demonstrates.

Practice questions (8)

Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.

In the 60-mark Mathematics & Science option of Paper-II, how many questions are on pedagogy?
1. 10 — all of them in mathematics
2. 20 — ten in mathematics and ten in science
3. 30 — half the option
4. None — pedagogy is only in the Child Development section
Show answer
Answer: B — 20 — ten in mathematics and ten in science
The option is built as two 30-mark subjects, and each is split 20 content and 10 pedagogy, which puts 20 of the 60 on pedagogy. Ten-in-mathematics-only is the shape of one subject mistaken for the whole option. Thirty would be half the option and overstates it, though it is the most tempting wrong answer because pedagogy feels heavier than it is. And the last option is the belief that costs candidates most: pedagogy is a named part of every subject section on both papers, not a separate Child Development block, which is why a candidate who prepares only content is capped at forty of these sixty marks.
A Class VII pupil writes −3 − (−5) = −8. The rule the pupil is applying is:
1. Adding the two numbers and keeping the sign of the larger
2. Treating the minus of subtraction and the minus of the number as one minus, so both are counted as negative
3. Subtracting the smaller number from the larger
4. Ignoring the brackets
Show answer
Answer: B — Treating the minus of subtraction and the minus of the number as one minus, so both are counted as negative
The correct value is 2, because subtracting a negative moves right on the number line. To get −8 the pupil has collapsed two different minus signs into one: the operator between the numbers and the sign belonging to 5, so both are read as "negative" and the magnitudes are added. Naming that is the diagnosis, and it points at the number line as the remedy. "Adding and keeping the larger sign" describes what the answer looks like but not the fault — it is the correct rule for −3 + (−5) and so misses that the operator was the thing misread. Subtracting smaller from larger would give 2 or −2, not −8. Ignoring the brackets gives −3 − 5 = −8 numerically, which is why it is the near-miss, but the brackets here carry no operation to ignore; the sign inside them is the whole difficulty.
Several pupils write (a + b)² = a² + b². The most effective remedial step is to:
1. Make the class write the identity twenty times
2. Have pupils draw a square of side (a + b), cut it into its four parts, and see where 2ab comes from
3. Tell pupils that squaring never distributes and mark the error each time
4. Substitute a = 1 and b = 1 to show the two sides differ
Show answer
Answer: B — Have pupils draw a square of side (a + b), cut it into its four parts, and see where 2ab comes from
The area model is the remedy because it explains rather than contradicts: a square of side (a + b) visibly contains a square of a², a square of b², and two rectangles of ab, so the missing term stops being an arbitrary rule and becomes something the pupil has seen. Twenty repetitions of the identity practise a string of symbols and leave the belief that produced the error intact. Telling the class that squaring does not distribute is correct and useless, because the error comes from a false analogy with multiplication over addition and nothing in the telling touches that analogy. Substituting 1 and 1 does prove the two sides differ and is worth doing, which is what makes it the strong distractor — but a counter-example shows the statement is false without showing what is true, and pupils who accept it often reproduce the same error a fortnight later.
The side of a square field is doubled. Its perimeter and area become, respectively:
1. Double and double
2. Double and four times
3. Four times and double
4. Four times and four times
Show answer
Answer: B — Double and four times
Perimeter is 4s, which is linear in the side, so doubling s doubles it; area is s², which is quadratic, so doubling s multiplies it by four. Side 3 gives perimeter 12 and area 9; side 6 gives perimeter 24 and area 36. "Double and double" is the commonest answer in a Class VII class and the one the question exists to catch, because it applies one rule to both measures. "Four times and double" swaps the two, and is chosen by candidates who remember that something goes up fourfold but not which. "Four times and four times" treats both as areas. Teaching this on squared paper rather than by formula is what makes it stick, and the same misconception explains why pupils believe two rectangles of equal perimeter must have equal area.
The image formed by a plane mirror is:
1. Real, inverted and smaller than the object
2. Virtual, erect, of the same size, and as far behind the mirror as the object is in front
3. Virtual, inverted and larger than the object
4. Real, erect and of the same size
Show answer
Answer: B — Virtual, erect, of the same size, and as far behind the mirror as the object is in front
A plane mirror gives a virtual, erect image of the same size, at the same distance behind the mirror as the object is in front, and laterally inverted — left and right exchanged, which is why AMBULANCE is painted reversed on the front of the vehicle. Real and inverted describes what a concave mirror or a convex lens can do, not a plane one, and it is chosen by candidates carrying the ray diagrams of curved mirrors into this question. Virtual and inverted is not a combination a plane mirror produces at all, since virtual images from a plane mirror are always erect. "Real, erect and same size" gets two of the three right and fails on the one that matters: the image cannot be caught on a screen, and that is exactly what virtual means. Lateral inversion is not the same as being upside down, and the paper tests that difference.
A Class VI pupil says plants take their food from the soil through the roots. The teacher should:
1. Correct the statement, write the definition of photosynthesis on the board, and move on
2. Keep two identical potted plants, one in light and one in the dark, and let the class explain the difference
3. Tell the pupil the answer is wrong and ask another pupil
4. Ignore it, since the pupil will read the correct account in the textbook
Show answer
Answer: B — Keep two identical potted plants, one in light and one in the dark, and let the class explain the difference
The pupil holds a misconception with an honest reason behind it — water and minerals do come from the soil through the roots — so it will not be dislodged by a correction that never engages it. Two identical plants differing only in light give a result the misconception cannot explain, which is what makes an activity remedial rather than merely enjoyable, and the class does the explaining. Writing the definition on the board is the definition-first lesson every pedagogy question is set against; the pupil can recite it and keep the old belief underneath. Passing the question to another pupil is worse than a correction, because it teaches the class that a wrong answer is a social risk. And leaving it to the textbook abandons the one moment when the misconception was visible and addressable.
A school has no science laboratory and no apparatus grant. On the syllabus’s own terms, the teacher of Classes VI-VIII should:
1. Teach the practical chapters from the textbook and note that the laboratory is unavailable
2. Build the activities from low-cost and no-cost material — bottles, wire, bulbs, mirrors, syringes, the school ground
3. Take the class to a neighbouring school’s laboratory once a year
4. Concentrate on the theory chapters, which carry more marks anyway
Show answer
Answer: B — Build the activities from low-cost and no-cost material — bottles, wire, bulbs, mirrors, syringes, the school ground
The syllabus treats the absence of a laboratory as a constraint on the apparatus rather than on the method: a bottle, a bicycle valve tube and a bowl of water make a demonstration of air pressure, and the school ground makes a lesson on speed. Improvisation is the marked answer because process skills, not equipment, are what the section is for. Teaching the practical chapters as text and recording the shortage is the honest-sounding option and it is the one the framework rejects — it converts a resource problem into a change of subject. An annual visit to another laboratory is better than nothing and still leaves fifty-nine weeks of text, so it cannot be the primary answer. And retreating to theory because it carries more marks makes examination weightage the aim of teaching, which is the position both the mathematics and the science pedagogy sections are written against.
A Class VIII lesson requires heating a liquid in a test tube over a spirit lamp and adding concentrated acid. The soundest arrangement is:
1. Every pupil performs the whole experiment, since science must be done rather than watched
2. The teacher demonstrates the heating and the acid step with the class at a safe distance, and the pupils record, predict and explain
3. The experiment is dropped and the result is dictated as notes
4. The brightest pupil performs it while the others copy the observations
Show answer
Answer: B — The teacher demonstrates the heating and the acid step with the class at a safe distance, and the pupils record, predict and explain
Safety is the one ground on which teacher demonstration outranks pupil handling, and the arrangement keeps the pedagogy intact: the children still predict, observe, record and explain, so every process skill except manipulation is exercised while the hazard stays with the adult. The first option applies the usual rule — let the child do it — without reading the stem for a hazard, and it is the trap this question is built on. Dropping the experiment and dictating the result removes the observation as well as the risk, and is the definition-first lesson in its worst form. Letting one pupil perform while the rest copy is unsafe for that pupil and passive for the rest, and copying another child’s observations is not observation at all.