Pariksha SaathiPedagogy
CTET Maths Pedagogy MCQ with Answers
308 practice questions on Mathematics Pedagogy for CTET Paper I and Paper II (Mathematics), with answers; most also have an explanation or a worked solution. Try each one before you open its answer.
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Q.151
A teacher writes a short dated note: 'Asha (Class 2) today bundled ten sticks on her own while counting 34 sticks, without being told.' Such a record is called:
- A An anecdotal record
- B A rating scale
- C A standardised achievement test
- D A cumulative record
Show answer
Correct answer: (A) An anecdotal record
An anecdotal record is a brief, factual description of a significant incident in a child's learning, written soon after it happens. A rating scale grades a trait on fixed levels, and a cumulative record summarises a child's progress over several years.
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Q.152
Consider these statements about problem posing in mathematics:
1. Asking children to make their own problems helps the teacher see how they understand a concept.
2. Problem posing is suitable only for gifted students, after they have mastered all routine sums.
Which of these is/are correct?
- A Only 2
- B Both 1 and 2
- C Neither 1 nor 2
- D Only 1
Show answer
Correct answer: (D) Only 1
The problems children create reveal what they think an operation or concept means, which is useful to the teacher. Problem posing can be used with all children at every level, from simple story-making in the early classes onwards.
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Q.153
A Class 5 student divides 618 by 6 and writes the quotient as 13. What is the error?
- A He does not know the multiplication table of 6 beyond 6 × 3
- B He omits the zero in the quotient when 1 ten cannot be divided by 6
- C He has reversed the dividend and the divisor in the very first step of the sum
- D He has added the remainder of the first step to the quotient by mistake
Show answer
Correct answer: (B) He omits the zero in the quotient when 1 ten cannot be divided by 6
618 ÷ 6 = 103: after 6 ÷ 6 = 1, the 1 ten cannot be shared among 6, so a 0 must be written in the tens place of the quotient. Estimating first (618 ÷ 6 is about 100) would show that 13 is far too small.
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Q.154
A Class 6 teacher reads out, in simple words, a puzzle from Lilavati, the twelfth-century text by Bhaskara II, and asks students to solve it. The main value of this is that:
- A Lilavati contains formal proofs of all the theorems in the modern textbook, set out in the same order
- B Lilavati poses many problems as engaging verses and puzzles, part of a long tradition of word problems
- C It shows that the + and − signs used today were first invented in Lilavati and then spread from there
- D It removes the need for problems from the students' own surroundings, since these old puzzles are enough
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Correct answer: (B) Lilavati poses many problems as engaging verses and puzzles, part of a long tradition of word problems
Lilavati is well known for presenting arithmetic problems in poetic, puzzle-like form, which can make problem solving enjoyable and shows mathematics as part of India's cultural heritage. The modern + and − signs came much later, from Europe.
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Q.155
A Class 3 teacher spends almost the whole year on number operations and skips the chapters on shapes, patterns and data handling, calling them 'not real maths'. According to NCF 2005, this is inappropriate because:
- A Number operations are not part of the Class 3 syllabus and belong to higher classes
- B Data handling is more important than number at this stage and should take up most of the school year
- C Every chapter of the textbook must be finished page by page in the given order, whatever its content
- D Mathematics is not just arithmetic; shapes, space, patterns, measurement and data need due weight
Show answer
Correct answer: (D) Mathematics is not just arithmetic; shapes, space, patterns, measurement and data need due weight
NCF 2005 stresses that besides numbers and operations, due importance must be given to shapes, spatial understanding, patterns, measurement and data handling. The objection is to neglecting these areas, not to teaching numbers.
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Q.156
Which classroom task best serves the 'higher aim' of school mathematics described in NCF 2005?
- A Investigating whether the sum of any three consecutive numbers is always divisible by 3, and why
- B Completing 30 sums on multiplying three-digit numbers within one class period
- C Memorising the conversion table for units of length, from millimetre to kilometre
- D Copying the solved examples of the chapter into the notebook and learning each step by heart for the test
Show answer
Correct answer: (A) Investigating whether the sum of any three consecutive numbers is always divisible by 3, and why
The higher aim is to develop the child's ability to think and reason mathematically, pursue assumptions to their logical conclusion and handle abstraction; making and justifying a general claim does this. Computation drills serve at most the narrow aim of numeracy.
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Q.157
Which statement about the Van Hiele levels of geometric thinking is correct?
- A Progress through the levels depends mainly on the child's age, as in Piaget's stages of development
- B The levels are sequential, and progress depends more on instruction and experience than on age
- C A child can skip the analysis level and go directly to deduction if the teacher gives proofs early
- D The levels apply only to three-dimensional geometry, not to plane figures
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Correct answer: (B) The levels are sequential, and progress depends more on instruction and experience than on age
Van Hiele held that the levels are hierarchical and sequential and that advancement depends on appropriate instruction rather than biological maturation, which is why teaching should match the child's current level.
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Q.158
A student writes 3 m 5 cm as 3.5 m. What has the student not understood?
- A That 5 cm is 5 hundredths of a metre, so it is 3.05 m
- B That a metre is longer than a centimetre, so cm cannot be added to m
- C How to add the numbers 3 and 5 when they are written with a point
- D That lengths in metres and centimetres can never be written as decimals
Show answer
Correct answer: (A) That 5 cm is 5 hundredths of a metre, so it is 3.05 m
3.5 m would be 3 m 50 cm. The student has joined the two numbers with a point without considering that centimetres are hundredths of a metre; a metre scale marked in centimetres and a place-value chart help.
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Q.159
A student says, 'Tomorrow it will either rain or not rain, so the probability of rain is 1/2.' The teacher should help her see that:
- A Two possible outcomes need not be equally likely; 1/2 applies only when they are
- B She is right, since there are exactly two outcomes and each must have an equal share
- C Probability can be found only for coins and dice, not for events like the weather
- D The probability of rain must be 0, since the future is unknown and cannot be predicted
Show answer
Correct answer: (A) Two possible outcomes need not be equally likely; 1/2 applies only when they are
Counting outcomes gives a probability only when the outcomes are equally likely, as with a fair coin. Rain depends on season and weather, so its chance must be judged from data, not from the number of outcomes.
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Q.160
A mathematics laboratory in a school is mainly intended to:
- A Replace the mathematics textbook completely with charts, kits and ready-made models
- B Prepare selected students for mathematics olympiads only, by special coaching in advanced problem solving
- C Give students a space to verify and discover mathematical ideas through activities, models and manipulatives
- D Conduct written examinations in a separate room fitted with charts and models of formulae
Show answer
Correct answer: (C) Give students a space to verify and discover mathematical ideas through activities, models and manipulatives
A mathematics laboratory supports learning by doing: students handle manipulatives, make models and perform activities that make abstract concepts concrete. A mathematics club similarly fosters interest through puzzles, projects and exhibitions.
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Q.161
For teaching the angle-sum property of a triangle in Class 7, which sequence is generally recommended?
- A Students explore several triangles to find the rule, then justify it logically and apply it
- B The teacher states the rule and students then apply it to many textbook exercises for practice
- C Students only measure triangles; no justification is needed at this stage of school
- D Students memorise the proof first and then measure triangles to confirm what they have learnt
Show answer
Correct answer: (A) Students explore several triangles to find the rule, then justify it logically and apply it
In the inductive phase students discover the rule from examples, and in the deductive phase they establish why it holds and apply it; combining the two (the inducto-deductive approach) is generally preferred. Either alone leaves understanding or certainty incomplete.
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Q.162
Before giving the formula area = length × breadth, a teacher asks children to cover rectangles with unit squares and notice that the squares form rows and columns. The purpose is to:
- A Keep children busy and engaged until the real lesson on the area formula begins
- B Check whether children can count large collections of unit squares accurately and fast
- C Show children that length × breadth works only for squares and never for rectangles
- D Let the formula grow out of rows × columns, so it is understood, not just memorised
Show answer
Correct answer: (D) Let the formula grow out of rows × columns, so it is understood, not just memorised
When children see that 3 rows of 5 squares make 15, length × breadth becomes a short way of counting the squares. A formula built on this structure is easier to apply and to recall correctly.
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Q.163
A child correctly names a square when its sides are horizontal and vertical, but calls the same square 'a diamond, not a square' when it is turned. The most suitable teaching response is to:
- A Tell the child that diamonds are also squares and simply move on to the next topic quickly
- B Show squares in many orientations and sizes and let children check the sides and angles
- C Draw squares only with horizontal bases on the board so that the child is never confused again
- D Make the child memorise the definition of a square and repeat it aloud
Show answer
Correct answer: (B) Show squares in many orientations and sizes and let children check the sides and angles
A child at the visual level judges shapes by their typical look, so a turned square seems different. Varied orientations together with checking properties help the child move from appearance to properties.
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Q.164
On one pan of a balance a teacher puts a closed bag with some marbles and 3 loose marbles; on the other pan, 7 loose marbles. The pans balance. Children then remove 3 marbles from each pan. This activity best builds the understanding that:
- A A letter in an equation always stands for the number 3 shown beside it
- B Heavier objects are always larger in size than lighter objects
- C Doing the same to both sides keeps an equation balanced: x + 3 = 7, so x = 4
- D Subtraction always makes any number smaller, so the bag must be lighter
Show answer
Correct answer: (C) Doing the same to both sides keeps an equation balanced: x + 3 = 7, so x = 4
The balance models the equation x + 3 = 7: taking the same amount from both pans keeps them level and leaves the bag balancing 4 marbles. It gives meaning to 'doing the same to both sides' instead of the rote rule 'change the side, change the sign'.
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Q.165
A student claims, 'All prime numbers are odd.' The teacher simply asks, 'What about 2?' Which feature of mathematical reasoning does the teacher's question bring out?
- A A single counter-example is enough to show that a general statement is false
- B A general statement is true if it holds for most of the cases checked
- C Mathematical statements depend on the opinion of the person making them
- D Every general statement in mathematics needs at least ten examples to be accepted
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Correct answer: (A) A single counter-example is enough to show that a general statement is false
In mathematics a general claim must hold in every case, so one counter-example (2 is prime and even) is enough to disprove it. Agreement with many cases never makes a general statement true.
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Q.166
A Class 8 teacher says: 'Think of a number, double it, add 10, halve the result, then subtract the number you started with. Your answer is 5.' Asking students to explain why this always works mainly helps them to:
- A See how a letter proves it for all numbers: (2n + 10) ÷ 2 − n = 5
- B Practise doubling and halving quickly, which is the main aim of the game
- C Check the trick with many different numbers until they are fully convinced
- D Memorise that the answer to every such puzzle is always 5
Show answer
Correct answer: (A) See how a letter proves it for all numbers: (2n + 10) ÷ 2 − n = 5
Trying many numbers only suggests the result; writing the steps with n shows that n cancels out, so the answer is 5 for every number. This shows the power of algebra as generalised arithmetic.
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Q.167
Two rows of five buttons each are shown to a child. When one row is spread out, the child says that the spread-out row has more buttons. According to Piaget, the child:
- A Has reached the formal operational stage
- B Has a counting disability
- C Has not yet attained conservation of number
- D Understands one-to-one correspondence fully
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Correct answer: (C) Has not yet attained conservation of number
Conservation of number means understanding that quantity stays the same when arrangement changes. A child who judges by length of the row has not yet conserved number, typical of the pre-operational stage.
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Q.168
To develop the area of a circle, a Class 7 teacher cuts a paper circle into many equal sectors and arranges them, pointing alternately up and down, into a shape close to a rectangle. This 'rectangle' has:
- A Length about half the circumference (πr) and breadth the radius (r), so the area is about πr²
- B Length equal to the full circumference (2πr) and breadth equal to the radius, so area is 2πr²
- C Length equal to the diameter and breadth equal to the radius, so area is 2r²
- D Length and breadth both equal to the radius
Show answer
Correct answer: (A) Length about half the circumference (πr) and breadth the radius (r), so the area is about πr²
Half the arcs form each long side, so each long side is half of 2πr, that is πr, and the short side is the radius. The more sectors there are, the closer the shape is to a rectangle, which is why the area of a circle is πr × r = πr².
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Q.169
For a parallelogram with sides 8 cm and 5 cm, and height 4 cm on the 8 cm side, a student writes area = 8 × 5 = 40 cm². Which activity best addresses this?
- A Tell her that the correct formula is base × height and ask her to learn it by heart before the next class
- B Give her ten more parallelogram sums for practice, with the base and slant side marked
- C Cut and rearrange a paper parallelogram into a rectangle and compare its sides with the base and height
- D Ask her to measure the slanting side more carefully with a ruler, since a small error there changes the area
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Correct answer: (C) Cut and rearrange a paper parallelogram into a rectangle and compare its sides with the base and height
The rectangle formed has length equal to the base (8 cm) and width equal to the height (4 cm), so the area is 32 cm². The slanting side (5 cm) is longer than the height, so 8 × 5 overestimates the area; seeing this makes base × height meaningful.
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Q.170
A tangram, a square cut into seven pieces that can be rearranged into many figures, is primarily useful for developing:
- A Number facts up to 20, through the quick recall of addition and subtraction facts in timed games
- B Skills of data handling such as collecting data, tally marks, pictographs and simple bar graphs
- C Spatial sense, visualisation and the idea that area stays the same when pieces are rearranged
- D Understanding of decimals and their place value up to hundredths
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Correct answer: (C) Spatial sense, visualisation and the idea that area stays the same when pieces are rearranged
Rearranging tangram pieces develops spatial sense and shows that the same pieces (same total area) can form many different shapes, supporting the idea of conservation of area.
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Q.171
A teacher folds a paper isosceles triangle so that its two equal sides lie on each other, and the two base angles fit exactly. Why is this useful at the upper primary stage?
- A It informally justifies, through the line of symmetry, why the base angles must be equal
- B It is a formal proof that makes any deductive proof of this result unnecessary at later stages
- C It shows that the base angles of every triangle are equal, whatever the lengths of its sides
- D It mainly develops skill in folding paper neatly
Show answer
Correct answer: (A) It informally justifies, through the line of symmetry, why the base angles must be equal
The fold is a line of symmetry, so one base angle lands exactly on the other, giving a visual reason for the property. It is a step towards deductive proof, not a substitute for it, and it holds only for isosceles triangles.
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Q.172
Consider these statements about algebra in Classes 6 to 8:
1. Within one expression or equation, the same letter stands for the same number everywhere; in x + x = 10, both x's are 5.
2. In an equation such as 3x + 2 = 14, x can take any value we like.
Which of these is/are correct?
- A Only 1
- B Only 2
- C Both 1 and 2
- D Neither 1 nor 2
Show answer
Correct answer: (A) Only 1
A letter keeps one value throughout a single expression or equation, so x + x = 10 gives x = 5. Statement 2 is false: an equation holds only for particular values, here x = 4, since 3 × 4 + 2 = 14.
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Q.173
Match each activity with Bruner's mode of representation.
P. Four children act as birds on a tree and one 'flies away'
Q. Children draw four birds and cross one out
R. Children write 4 - 1 = 3
i. Symbolic ii. Enactive iii. Iconic
- A P-iii, Q-ii, R-i
- B P-ii, Q-i, R-iii
- C P-i, Q-iii, R-ii
- D P-ii, Q-iii, R-i
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Correct answer: (D) P-ii, Q-iii, R-i
Enactive representation is through action, iconic through pictures or images, and symbolic through numerals and signs. They correspond to the concrete, pictorial and abstract stages of the CPA approach.
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Q.174
Before giving a ruler to Class 2 children, a teacher asks them to measure the length of the table with hand spans and pencils. The purpose of this is to:
- A Help children feel the need for a standard unit after finding that non-standard units give different results
- B Save money on buying rulers, since hand spans and pencils are always available
- C Teach the metric system directly, by having children convert each hand span into centimetres and metres
- D Test whether the children can already read the numbers on a scale before rulers are given out to the whole class
Show answer
Correct answer: (A) Help children feel the need for a standard unit after finding that non-standard units give different results
Measuring with non-standard units such as hand spans leads to different answers for different children, which creates the need for a standard unit. This is the recommended sequence for teaching measurement.
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Q.175
Which of the following is NOT a sound reason for bringing the history of mathematics into the classroom?
- A To show that mathematics is a human activity that developed across many cultures, including India's
- B To give context, such as why a place-value system with zero made calculation easier
- C To show that ideas were refined over time, so questioning and correcting are part of mathematics
- D To give students lists of mathematicians' names and dates to memorise for tests
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Correct answer: (D) To give students lists of mathematicians' names and dates to memorise for tests
History helps when it gives meaning, context and a sense of mathematics as a living human activity. Turning it into names and dates to memorise adds rote load without building understanding.
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Q.176
Three bars of chikki are shared equally among four children, and the class finds that each child gets 3/4 of a bar. This problem mainly helps students see a fraction as:
- A Only a part of a single whole object, such as one bar cut into pieces
- B A comparison of two parts of the same whole, such as boys and girls
- C A number that must always be converted to a decimal before use
- D The result of dividing one whole number by another: 3 ÷ 4 = 3/4
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Correct answer: (D) The result of dividing one whole number by another: 3 ÷ 4 = 3/4
Sharing 3 bars among 4 gives each child 3/4 of a bar, so 3 ÷ 4 = 3/4. This is the quotient (division) meaning of a fraction, which goes beyond the part-of-one-whole meaning met in the early classes.
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Q.177
Continuous and Comprehensive Evaluation (CCE) in mathematics implies that:
- A Only the final written examination is counted, even though unit tests are held throughout the year for practice
- B Assessment is ongoing and covers reasoning, communication, attitudes and processes, not only written answers
- C Formal written tests are conducted every day and all their marks are added up to give the final result
- D Marks are replaced by no assessment at all, since under the no-detention idea every child is promoted automatically
Show answer
Correct answer: (B) Assessment is ongoing and covers reasoning, communication, attitudes and processes, not only written answers
'Continuous' means assessment is ongoing and integrated with teaching; 'comprehensive' means it covers all aspects of learning, including processes and attitudes, through varied tools such as observation, projects and oral work.
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Q.178
Using a string of 7 beads, a Class 1 child shows 7 as 5 and 2, then as 4 and 3, then as 6 and 1. This activity mainly develops:
- A Part-whole understanding of number (composing and decomposing it)
- B Seriation of objects by their size, from the smallest to the largest
- C Rote counting of number names in the correct sequence
- D Measurement of the length of objects using non-standard units such as beads on a string
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Correct answer: (A) Part-whole understanding of number (composing and decomposing it)
Seeing one number as made of different pairs of parts is part-whole thinking, the basis of addition and subtraction facts and of mental strategies. It goes beyond reciting number names.
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Q.179
To help reduce mathematics anxiety, which message from the teacher to parents is most appropriate?
- A Involve your child in everyday maths like shopping and cooking, and praise effort
- B Tell your child that you too were weak in maths, so there is no need to worry about it
- C Make your child practise a hundred sums every day to build speed and accuracy in exams
- D Compare your child's marks with those of other children to keep up motivation
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Correct answer: (A) Involve your child in everyday maths like shopping and cooking, and praise effort
Everyday use of mathematics at home shows it as useful and ordinary, and praising effort and reasoning builds confidence. Telling a child that weakness in maths runs in the family passes on a fixed, negative belief.
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Q.180
To make sense of (−3) × (−2), a teacher writes 3 × (−2) = −6, 2 × (−2) = −4, 1 × (−2) = −2, 0 × (−2) = 0 and asks students to continue the pattern. The main value of this approach is that students:
- A Memorise the slogan 'minus into minus is plus' more quickly and reliably
- B Avoid the need to understand multiplication of integers
- C See each product grow by 2, so (−1) × (−2) = 2 and (−3) × (−2) = 6
- D Learn that products of integers follow no fixed rule at all
Show answer
Correct answer: (C) See each product grow by 2, so (−1) × (−2) = 2 and (−3) × (−2) = 6
As the first factor decreases by 1, the product increases by 2; continuing the pattern gives 2, 4, 6, so the sign rule appears as a consequence of keeping the pattern consistent rather than as an arbitrary slogan.
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Q.181
Which activity best helps Class 4 children get a feel for how large 1,000 is?
- A Writing the numeral 1,000 and its number name ten times each, neatly, in the notebook
- B Learning by heart that 1,000 = 10 × 100 and 1,000 = 100 × 10
- C Collecting 1,000 bottle caps as a class, in bags of ten and boxes of a hundred
- D Reading aloud all the numbers from 900 to 1,000 in chorus, led by the class monitor
Show answer
Correct answer: (C) Collecting 1,000 bottle caps as a class, in bags of ten and boxes of a hundred
Physically collecting and grouping a thousand objects gives children an image of the quantity and of its structure (10 hundreds, 100 tens). Writing, reciting or memorising facts about 1,000 can be done with no sense of its size.
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Q.182
A Class 6 student writes 7 ÷ 0 = 0. The best way for the teacher to address this is to:
- A Ask: which number times 0 gives 7? As none does, 7 ÷ 0 is not defined
- B Tell her the answer is 7, since dividing by nothing leaves the number unchanged
- C Tell her to memorise 'any number divided by 0 is not defined' and move on
- D Skip it for now, as division by zero is too abstract an idea for Class 6
Show answer
Correct answer: (A) Ask: which number times 0 gives 7? As none does, 7 ÷ 0 is not defined
Linking division to multiplication lets the student reason that no number times 0 gives 7, so division by zero is not defined. Memorising the result without reasoning, or giving a wrong answer like 7, leaves the misconception in place.
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Q.183
Fractions are introduced in early primary classes as halves and quarters of real objects, revisited in later primary classes with equivalent fractions, and taken up again in upper primary with operations. This arrangement reflects Bruner's idea of a:
- A Spiral curriculum
- B Programmed learning sequence
- C Mastery learning model
- D Linear, once-only syllabus
Show answer
Correct answer: (A) Spiral curriculum
Bruner proposed a spiral curriculum in which key ideas are revisited at increasing levels of depth and abstraction. Mastery learning (Bloom) and programmed learning (Skinner) are different models.
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Q.184
Jerome Bruner described three modes of representing knowledge. In the correct order of development they are:
- A Symbolic, iconic, enactive
- B Enactive, iconic, symbolic
- C Iconic, enactive, symbolic
- D Enactive, symbolic, iconic
Show answer
Correct answer: (B) Enactive, iconic, symbolic
Bruner's modes are enactive (action with objects), iconic (images and pictures) and symbolic (language and mathematical symbols), in that order of development.
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Q.185
A child says angle P is bigger than angle Q because P has longer arms, though Q is clearly wider. The best activity is to:
- A Measure the arms of both angles with a ruler and compare their lengths
- B Place a cut-out of one angle over the other to compare the openings
- C Ask the child to draw longer arms on angle Q so that it looks bigger
- D Tell the child to ignore the drawing and memorise the definition of an angle
Show answer
Correct answer: (B) Place a cut-out of one angle over the other to compare the openings
The size of an angle is the amount of turn between its arms, not the length of the arms. Laying one angle over the other, or turning a paper angle tester, focuses attention on the opening; measuring arm lengths reinforces the misconception.
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Q.186
A Class 5 student says 1/5 is greater than 1/3 because 5 is greater than 3. This error shows that the student is:
- A Confusing numerator with denominator and so reading each fraction upside down
- B Unable to read fractions written in the a/b form used in the textbook
- C Applying whole-number reasoning to fractions without understanding what the denominator means
- D Correct, as a larger denominator always gives a larger fraction when numerators are equal
Show answer
Correct answer: (C) Applying whole-number reasoning to fractions without understanding what the denominator means
The child is transferring the whole-number rule 'bigger number means bigger value' to fractions. Fraction strips or paper folding help the child see that dividing into more parts makes each part smaller.
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Q.187
Asked for the area of a rectangle 5 cm long and 3 cm wide, a child writes '16 cm'. The most suitable remedial activity is to:
- A Repeat the formula for area and ask her to write it at the top of every new sum
- B Have her cover the rectangle with 1 cm squares, and separately trace its boundary
- C Give her twenty more area sums on rectangles of different sizes
- D Ask her to learn by heart that area is in cm² and perimeter in cm
Show answer
Correct answer: (B) Have her cover the rectangle with 1 cm squares, and separately trace its boundary
16 cm is the perimeter (5 + 3 + 5 + 3), so area and perimeter are being confused. Covering the surface with unit squares (15 square cm) and tracing the boundary show that area measures the space inside and perimeter the length around it.
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Q.188
To introduce percentage, a Class 7 teacher shades 35 small squares of a 10 × 10 grid and writes 35%. This mainly helps students understand that:
- A A percentage can never be greater than 100, whatever the situation
- B 35% is the same as 0.035
- C Per cent means 'per hundred', so 35% is 35/100 of the whole
- D Percentages are used only for examination marks and nothing else
Show answer
Correct answer: (C) Per cent means 'per hundred', so 35% is 35/100 of the whole
The 100-square grid shows the whole as 100 equal parts, so 35% = 35/100 = 0.35. Percentages above 100 are meaningful (a price can rise to 150% of its old value), and 0.035 would be 3.5%.
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Q.189
Asked to fill the blank in 37 + 56 = 36 + __, a child says, '36 is one less than 37, so the blank must be one more than 56, that is 57,' without adding. This shows:
- A Relational thinking about the equals sign, which supports early algebra
- B Weakness in two-digit addition, so the child avoids adding the numbers
- C Rote use of a shortcut rule learnt by heart without understanding
- D Confusion about place value in two-digit numbers like 37 and 56
Show answer
Correct answer: (A) Relational thinking about the equals sign, which supports early algebra
The child treats both sides as equal quantities and reasons about how they are related, instead of first computing 93. Such relational thinking is a foundation for working with equations later, and teachers should invite children to explain it.
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Q.190
In a hill town the temperature was −4 °C at 6 a.m. and 5 °C at noon. Asked for the rise in temperature, a student answers 1 °C. The teacher should ask her to:
- A Find the change by adding the two readings, 5 + (−4), and then write the result as the rise in °C
- B Mark both readings on a thermometer or vertical number line and count the degrees between them
- C Recalculate 5 − 4 more carefully
- D Ignore the minus sign, since the question is only about the size of the change in temperature
Show answer
Correct answer: (B) Mark both readings on a thermometer or vertical number line and count the degrees between them
Counting on the scale gives 4 degrees up to 0 °C and 5 more up to 5 °C, a rise of 9 °C, which equals 5 − (−4). The answer 1 comes from ignoring the sign of −4, and adding the readings gives the same wrong result.
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Q.191
Meena has a small chapati and Rohit a large one. Meena says, 'Half of my chapati is the same amount as half of yours, because half is half.' The idea the teacher should bring out is that:
- A Half means any one of two pieces, whether or not they are equal
- B A fraction is always smaller than any whole number, so both halves are small
- C Fractions should be taught with shapes, not with food items like chapatis
- D The size of a fraction depends on the size of the whole
Show answer
Correct answer: (D) The size of a fraction depends on the size of the whole
1/2 of a small chapati is less than 1/2 of a large one; a fraction is always a fraction of a particular whole. Comparing fractions only makes sense when the wholes are the same.
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Q.192
Looking at the dots on a die, a Class 1 child says 'five' at once, without counting them one by one. This ability is called:
- A Subitising
- B Seriation
- C Rote counting
- D Conservation of number
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Correct answer: (A) Subitising
Subitising is recognising the number in a small group at a glance, especially in familiar arrangements such as dice patterns. It supports number sense and counting on, whereas seriation is ordering by size.
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Q.193
Without using the square-root key, students use a calculator to find a number whose square is close to 50: 7² = 49, 7.1² = 50.41, 7.05² = 49.7025, ... The activity mainly develops:
- A Speed in pressing calculator keys correctly without looking at them
- B Estimating and refining: narrowing in, step by step, on a number whose square is close to 50
- C The belief that square roots can always be found exactly, if one only tries enough decimal places
- D Memory of the squares of the numbers from 1 to 10, which are used again and again at each step here
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Correct answer: (B) Estimating and refining: narrowing in, step by step, on a number whose square is close to 50
Since 49 < 50 < 50.41, √50 lies between 7 and 7.1, and further trials narrow it down (it is about 7.07). The calculator does the squaring so that students can concentrate on the guess-check-improve reasoning.
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Q.194
A Class 6 teacher wants to develop problem-solving ability. Which approach is most suitable?
- A Solve one example on the board, then give twenty similar sums so that students copy the method
- B Pose a problem, let students try their own strategies in groups, then compare and discuss the methods
- C Give the formula first and ask students to apply it to all the textbook exercises in order
- D Let only the fastest students answer aloud so the lesson moves quickly and the syllabus is finished
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Correct answer: (B) Pose a problem, let students try their own strategies in groups, then compare and discuss the methods
Problem-solving ability grows when students face a problem without a given method, try strategies and reflect on different solutions. Imitating a worked example builds procedure-following, not problem solving.
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Q.195
A teacher shows the picture of a fruit shop with prices and asks children to make their own questions that can be answered from it. This activity is called:
- A Summative assessment
- B Drill and practice
- C Problem posing
- D Deductive proof
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Correct answer: (C) Problem posing
Problem posing asks children to create problems rather than only solve them. It is a higher-order, creative activity recommended by NCF 2005 to develop mathematical communication and understanding.
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Q.196
Consider these statements about the van Hiele levels:
1. At the analysis level, students write formal proofs using axioms and theorems.
2. At the deduction level, students understand the role of axioms, definitions and theorems and can construct proofs.
3. At the rigour level, students can compare different axiomatic systems, such as Euclidean and non-Euclidean geometry.
Which are correct?
- A 1 and 2 only
- B 1 and 3 only
- C 2 and 3 only
- D 1, 2 and 3
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Correct answer: (C) 2 and 3 only
Formal proof belongs to the deduction level, and comparing axiomatic systems to rigour. At the analysis level students only describe shapes by their properties.
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Q.197
A teacher wants to assess students' problem-solving process, not just the final answer. The most suitable tool is:
- A A multiple-choice test with one correct option for each problem, scored quickly by a machine or an answer key
- B A speed test of 50 sums in 10 minutes, with one mark for each correct final answer and no partial credit
- C A true-or-false quiz on the steps of standard methods
- D A rubric that credits understanding the problem, choosing a strategy, carrying it out and checking the result
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Correct answer: (D) A rubric that credits understanding the problem, choosing a strategy, carrying it out and checking the result
A rubric with criteria for each stage of problem solving allows the teacher to assess the process. Multiple-choice and speed tests capture only the final answer.
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Q.198
A student works out 23 × 14 as 23 × 4 = 92 and 23 × 1 = 23, adds them and gets 115. What is the misconception?
- A He does not know the multiplication table of 4 beyond 4 × 5
- B He treats the 1 in 14 as 1 instead of 1 ten
- C He has made a mistake while adding the two partial products
- D He should have used repeated addition, as the algorithm is too hard
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Correct answer: (B) He treats the 1 in 14 as 1 instead of 1 ten
23 × 14 = 23 × 4 + 23 × 10 = 92 + 230 = 322. Writing 14 as 10 + 4 and using an area (grid) model makes the place value of each partial product visible.
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Q.199
Before teaching any rule for comparing fractions with different denominators, a Class 5 teacher has children lay strips for 2/3 and 3/4 under a strip for one whole. The main advantage of this is that:
- A It is quicker than any written method for every pair of fractions, however large
- B Children will never need a written rule for comparing fractions
- C It proves that the fraction with the larger numerator is always the larger fraction
- D Children see which is larger and build a sense of fraction size for later rules
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Correct answer: (D) Children see which is larger and build a sense of fraction size for later rules
Seeing that 3/4 covers more of the whole than 2/3 gives children an image of fraction size, so a later method (such as equivalent fractions with a common denominator) makes sense and can be checked. Strips are not quicker for every pair, and the larger numerator does not always mean the larger fraction.
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Q.200
A child places a pencil along a ruler from the 0 mark to the 7 mark, counts the numbers 0, 1, 2, ..., 7 aloud and says the pencil is 8 cm long. The child:
- A Has measured correctly, as the pencil reaches the eighth mark
- B Does not yet know the numbers up to 8 in the correct order
- C Counts the marks instead of the unit spaces between them
- D Has confused centimetres with millimetres on the ruler
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Correct answer: (C) Counts the marks instead of the unit spaces between them
Length is the number of unit spaces covered, not the number of marks; from 0 to 7 there are 7 one-centimetre spaces. Laying unit pieces end to end, or measuring with a 'broken' ruler that does not start at 0, makes this clear.
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How these questions were made
Authored by an AI assistant (Claude) from its own general knowledge of stable, well-established facts (no live lookup) - not reviewed by a subject-matter expert; verify against an official source before relying on any fact.