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.1
On Gopal's worksheet on subtraction with regrouping, which comment from the teacher is most useful for his learning?
- A '6/10. You must practise subtraction with regrouping much more carefully from now on at home.'
- B 'Wrong! Do all these sums again neatly in your notebook and show me after class.'
- C 'Digits are lined up well. Now check the tens: what happens to 5 when you take a ten?'
- D 'Good effort, keep it up!' with a star at the top of the page and a smiley
Show answer
Correct answer: (C) 'Digits are lined up well. Now check the tens: what happens to 5 when you take a ten?'
Descriptive feedback tells the child what he did well and points to the exact step to rethink, so he knows what to do next. A mark, a scolding or general praise gives no such guidance; continuous assessment favours specific, qualitative feedback.
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Q.2
A Class 6 teacher says, 'Some children are born without a head for mathematics, so I concentrate on the bright ones.' According to NCF 2005, teachers should instead:
- A Group children permanently by ability so that the bright ones are never held back by others
- B Prepare only the top students for mathematics olympiads
- C Give easier question papers to the children they consider weak, so that all of them pass
- D Engage every child in class with the conviction that everyone can learn mathematics
Show answer
Correct answer: (D) Engage every child in class with the conviction that everyone can learn mathematics
NCF 2005's vision for school mathematics includes teachers engaging every child with the conviction that everyone can learn mathematics. The idea of an inborn 'maths brain' leads to neglect and fear in many children.
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Q.3
A Class 3 child writes 'three hundred five' as 3005 and 'two hundred forty' as 20040. This error reveals that the child:
- A Has not understood place value and is writing numbers as they are spoken
- B Does not know the number names, so cannot read the words correctly
- C Is careless in writing and needs more practice in speed and neat copying
- D Has mastered expanded form of numbers and is applying it correctly
Show answer
Correct answer: (A) Has not understood place value and is writing numbers as they are spoken
The child is writing each spoken part separately (300 then 5), which shows that the positional meaning of digits is not understood. Place-value materials such as Dienes blocks or an abacus are needed, not speed drills.
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Q.4
A student solves 52 - 27 = 35 and 73 - 48 = 35. The most likely reason for these errors is that the student:
- A Has forgotten the basic subtraction facts and is simply guessing the difference in each column of the sum
- B Subtracts the smaller digit from the larger in each column, not understanding regrouping (borrowing)
- C Is adding the digits instead of subtracting because he misreads the minus sign
- D Does not know how to write two-digit numbers and so reverses the tens and the ones digits in the answer
Show answer
Correct answer: (B) Subtracts the smaller digit from the larger in each column, not understanding regrouping (borrowing)
In both cases the child does 7 - 2 and 8 - 3 instead of regrouping a ten. This systematic error shows that the procedure of borrowing is not understood conceptually.
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Q.5
A Class 3 child writes 'six hundred four' as 64. The error mainly shows that the child:
- A Does not know the number name 'six hundred' and so drops it
- B Has confused the digits 6 and 4 while writing the number
- C Understands place value well but writes too fast in class
- D Does not use zero to show that the tens place is empty
Show answer
Correct answer: (D) Does not use zero to show that the tens place is empty
Without a 0 in the tens place, the 6 slides into the tens place and the number becomes sixty-four. Showing 604 on an abacus or place-value chart, where the tens rod is visibly empty, makes clear why 0 must be written.
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Q.6
Asked 'What is the difference between 9 and 5?', a Class 2 child replies, '9 is big and 5 is small.' This response mainly shows that:
- A Words like 'difference' have an everyday meaning that differs from their mathematical one
- B The child does not know how to subtract 5 from 9 and needs more subtraction practice with counters
- C The child is not paying attention in class and is giving a careless answer
- D Mathematical terms should not be used before Class 5, when children are able to understand them
Show answer
Correct answer: (A) Words like 'difference' have an everyday meaning that differs from their mathematical one
The child has used the everyday sense of 'difference' (how two things are unlike), not the mathematical sense (how much more one is than the other). Such words need to be built through use in context; the answer says nothing about subtraction skill.
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Q.7
In a Class 2 lesson, children play freely with bundles of ten sticks and loose sticks, but the teacher never asks them to explain or record what they did. Their understanding of tens and ones does not improve. The most likely reason is that:
- A Bundles of sticks are not a suitable material for place value, and only an abacus should be used
- B Children of Class 2 are too young to learn place value and should wait until they reach Class 4
- C Concrete materials help only when children reflect on their actions and link them to ideas and symbols
- D Concrete materials should be used only by the teacher for demonstration, never handled by the children
Show answer
Correct answer: (C) Concrete materials help only when children reflect on their actions and link them to ideas and symbols
Understanding comes from thinking about what the materials show, guided by questions, talk and recording, not from handling alone. Bundles of sticks are a standard material for place value; what is missing is reflection.
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Q.8
A Class 4 teacher plans lessons for children in Piaget's concrete operational stage. Which of the following is NOT typical of children at this stage?
- A Understanding that the number of objects stays the same when they are spread out or rearranged
- B Arranging sticks in order of length from shortest to longest (seriation)
- C Reasoning systematically about purely hypothetical statements with no concrete reference
- D Sorting objects by more than one attribute at a time, such as colour and shape
Show answer
Correct answer: (C) Reasoning systematically about purely hypothetical statements with no concrete reference
Systematic reasoning about hypothetical, abstract propositions marks Piaget's formal operational stage. Conservation, seriation and multiple classification are achievements of the concrete operational stage.
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Q.9
A child writes 5 x 0 = 5 and 7 x 0 = 7. Which misconception about zero does this reveal?
- A The child believes zero is the largest number since it makes numbers such as 10 and 100 bigger
- B The child thinks zero cannot be written as a digit, so it is ignored whenever it appears in a sum
- C The child believes any number divided by zero is itself
- D The child treats zero as 'nothing', so multiplying by it seems to leave the number unchanged
Show answer
Correct answer: (D) The child treats zero as 'nothing', so multiplying by it seems to leave the number unchanged
Children often think of zero as 'nothing happening', confusing it with the identity property of addition (5 + 0 = 5). The teacher should show 5 groups of zero objects to make the meaning concrete.
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Q.10
Match each problem with the strategy that suits it best.
P. I think of a number, multiply it by 3 and subtract 4 to get 20. What is it?
Q. Trees stand every 5 m along a 50 m road, from end to end. How many trees?
R. Hens and goats have 10 heads and 28 legs in all. How many goats?
i. Draw a diagram ii. Work backwards iii. Guess, check and improve
- A P-ii, Q-i, R-iii
- B P-i, Q-ii, R-iii
- C P-iii, Q-i, R-ii
- D P-ii, Q-iii, R-i
Show answer
Correct answer: (A) P-ii, Q-i, R-iii
Undoing the steps (20 + 4 = 24, 24 ÷ 3 = 8) is working backwards; a sketch of the road shows that 11 trees are needed, not 10; and trying a split of the 10 animals and adjusting it by the leg count gives 6 hens and 4 goats.
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Q.11
A Class 7 student simplifies 3a + 2b as 5ab and explains, '3 apples and 2 bananas make 5 fruits'. The misconception here is that the student:
- A Does not know the multiplication tables needed to combine the terms
- B Treats letters as labels for objects rather than as numbers (variables)
- C Has confused addition with subtraction while combining the two unlike terms
- D Is using the distributive property correctly to combine the unlike terms
Show answer
Correct answer: (B) Treats letters as labels for objects rather than as numbers (variables)
The 'fruit salad' approach treats letters as objects. In algebra a letter stands for a number, and 3a and 2b are unlike terms that cannot be combined. The teacher should emphasise variables as generalised numbers.
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Q.12
After a problem-solving task, pairs swap notebooks and check each other's solutions against criteria the class agreed on, writing one thing done well and one next step. This practice mainly develops:
- A Speed, as children finish checking their partner's work quickly and then move on
- B Competition, as each child tries to find more mistakes than the partner
- C Less marking for the teacher, which is the main purpose of the practice in large classes
- D Peer assessment: children apply quality criteria and learn from others' methods
Show answer
Correct answer: (D) Peer assessment: children apply quality criteria and learn from others' methods
In peer assessment children use shared criteria to judge work, which makes the criteria clear to them and shows them other methods; the 'one thing done well, one next step' format keeps the feedback constructive. Reducing the teacher's marking is at most a side benefit.
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Q.13
Cuisenaire rods are coloured rods of lengths 1 to 10 units. Which of the following is their most appropriate use?
- A Exploring number relations like 3 + 4 = 7, factors and simple fractions by comparing lengths
- B Measuring the angles of a triangle by placing coloured rods along its three sides
- C Teaching the names and faces of three-dimensional solids such as the cube, cuboid, cone and cylinder
- D Recording data in a tally chart and drawing bar graphs from it
Show answer
Correct answer: (A) Exploring number relations like 3 + 4 = 7, factors and simple fractions by comparing lengths
Because each rod's length represents a number, placing rods end to end or side by side makes addition, subtraction, factors and fraction relationships visible without counting discrete objects.
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Q.14
Match each use of a letter with its role.
P. x + 7 = 15
Q. a + b = b + a
R. A = l × b, for the area of a rectangle
i. A specific unknown number to be found
ii. Variables that change together in a formula
iii. A generalised number in a property true for all numbers
- A P-iii, Q-i, R-ii
- B P-i, Q-ii, R-iii
- C P-i, Q-iii, R-ii
- D P-ii, Q-iii, R-i
Show answer
Correct answer: (C) P-i, Q-iii, R-ii
In x + 7 = 15 the letter stands for one particular number (8). In a + b = b + a the letters can be any numbers, stating a general property. In A = l × b the letters are variables: as l or b changes, A changes with them.
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Q.15
When algebra is introduced at the upper primary stage, the most appropriate way to present a variable such as 'n' is as:
- A A letter to be memorised along with one fixed value, as in a secret code where a = 1, b = 2 and so on
- B A generalised number taking different values, introduced through patterns like 'matchsticks for n squares'
- C An abbreviation for an object, such as n for notebooks, so that 3n is read as 'three notebooks'
- D A symbol that always stands for an unknown single value
Show answer
Correct answer: (B) A generalised number taking different values, introduced through patterns like 'matchsticks for n squares'
NCERT introduces variables through matchstick patterns and rules, where the letter represents a generalised number. Presenting it as an object label leads to the fruit-salad misconception.
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Q.16
A teacher writes 1, 2, 4, ... and asks for the next number. Asha says 8 (each number is doubled); Imran says 7 (add 1, then 2, then 3, ...). The teacher should:
- A Accept only 8, since doubling is the usual rule for such sequences in textbooks
- B Accept both, as each rule fits the terms, and discuss that a few terms alone do not fix a pattern
- C Mark both wrong, since a question in mathematics can have only one correct answer
- D Tell the class that such pattern questions are only guesswork and should be avoided in tests altogether
Show answer
Correct answer: (B) Accept both, as each rule fits the terms, and discuss that a few terms alone do not fix a pattern
Both rules produce 1, 2, 4, so both answers are correct for the rules stated. The mathematical point is that a pattern is fixed by its rule, not by a few terms, so children should state their rules and check them against every given term.
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Q.17
To teach decimals, a teacher takes the flat of the base-ten blocks as one whole. How should children show 1.23?
- A 1 flat, 2 longs and 3 small cubes
- B 1 small cube, 2 longs and 3 flats
- C 12 longs and 3 flats
- D 1 long, 2 flats and 3 small cubes
Show answer
Correct answer: (A) 1 flat, 2 longs and 3 small cubes
If a flat is 1, a long (one-tenth of a flat) is 0.1 and a small cube (one-hundredth) is 0.01, so 1.23 is 1 flat, 2 longs and 3 cubes. Redefining the whole in this way shows that the same base-ten exchange works to the right of the decimal point.
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Q.18
For teaching shapes in Classes 1 and 2, it is recommended to begin with three-dimensional objects (boxes, balls, cans) rather than two-dimensional figures. The reason is that:
- A Three-dimensional geometry is simpler mathematically, because solids have fewer properties to learn than plane figures
- B Two-dimensional shapes are not part of the primary syllabus until Class 4 or Class 5
- C Drawing two-dimensional figures accurately requires a compass and a ruler, which young children cannot yet handle
- D Children meet solid objects in their surroundings first, and flat shapes are abstracted from the faces of solids
Show answer
Correct answer: (D) Children meet solid objects in their surroundings first, and flat shapes are abstracted from the faces of solids
Children handle solid objects daily, so starting from solids and then tracing their faces to get circles, rectangles and triangles follows the path from concrete to abstract.
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Q.19
According to NEP 2020, the highest priority of the education system is to:
- A Introduce coding for all children from Class 1 as a compulsory school subject
- B Hold board examinations twice a year from Class 5 onwards in all schools
- C Achieve universal foundational literacy and numeracy in primary school
- D Make English the only medium of instruction from Class 1 in all government schools
Show answer
Correct answer: (C) Achieve universal foundational literacy and numeracy in primary school
NEP 2020 calls attaining foundational literacy and numeracy for all children an urgent national mission and the highest priority, with the target of achieving it in primary school by 2025. The other options are not what the policy says.
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Q.20
A Class 5 student multiplies 49 by 21 and writes 129 as the answer without noticing anything wrong. Which habit would best help her catch such errors herself?
- A Repeating the same calculation in exactly the same way to check whether she gets 129 again
- B Using a calculator for every multiplication so that no slip can occur
- C Estimating first (about 50 × 20 = 1,000) and comparing the estimate with her answer
- D Memorising the multiplication table of 49 up to 49 × 10
Show answer
Correct answer: (C) Estimating first (about 50 × 20 = 1,000) and comparing the estimate with her answer
An estimate of about 1,000 shows at once that 129 cannot be right. Estimation gives a sense of the size of an answer, which repeating the same steps cannot.
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Q.21
Consider these statements about the recommendations of the NCERT Position Paper on Teaching of Mathematics:
1. Assessment should test students' ability to mathematise rather than only their procedural knowledge.
2. Every student should be engaged with a sense of success, while conceptual challenges are offered to the emerging mathematician.
Which of these is/are correct?
- A Both 1 and 2
- B Only 1
- C Only 2
- D Neither 1 nor 2
Show answer
Correct answer: (A) Both 1 and 2
Both are among the paper's recommendations, along with shifting the focus from narrow to higher aims and enriching teachers with a variety of mathematical resources.
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Q.22
Before introducing fractions, a Class 3 teacher asks, 'How would you share 2 rotis equally among 4 friends?' and lets children try with paper circles. The main purpose is to:
- A Find which children already know the textbook definition of a fraction
- B Keep the class busy before the actual lesson starts
- C Teach the rule for dividing fractions
- D Build the new concept on children's informal experience of fair sharing
Show answer
Correct answer: (D) Build the new concept on children's informal experience of fair sharing
Children already share food fairly at home; starting from that experience lets them construct the idea of equal parts before meeting symbols. This is the constructivist principle of building on prior knowledge.
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Q.23
Match the material with the idea it best supports:
A. Place-value cards B. Ten-frame C. String of 100 beads in groups of ten D. Isometric dot paper
(i) Drawing three-dimensional shapes
(ii) Expanded form, e.g. 345 = 300 + 40 + 5
(iii) Seeing small numbers in relation to 5 and 10
(iv) Counting in tens and the order of numbers up to 100
- A A-iii, B-ii, C-iv, D-i
- B A-ii, B-iii, C-iv, D-i
- C A-ii, B-iv, C-i, D-iii
- D A-i, B-iii, C-iv, D-ii
Show answer
Correct answer: (B) A-ii, B-iii, C-iv, D-i
Place-value cards slide apart to show 300, 40 and 5; a ten-frame lets children see 8 as '5 and 3' or '2 less than 10'; a bead string grouped in tens supports counting in tens up to 100; isometric dot paper is used to draw solids.
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Q.24
A Class 3 child says a tall, thin bottle must hold more water than a short, wide jug because it is taller. The best way to address this is to:
- A Measure the heights of both containers with a ruler and compare them
- B Tell the child that the jug holds more, since it is wider
- C Fill the bottle with water and pour it into the jug to see which holds more
- D Ask the child to learn the rule that taller containers do not always hold more water
Show answer
Correct answer: (C) Fill the bottle with water and pour it into the jug to see which holds more
Capacity depends on height and width together, so height alone can mislead. Pouring from one container into the other is a direct comparison that lets the child test the claim, before non-standard and standard units are used.
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Q.25
Each group in a class tosses a coin 10 times, and the number of heads varies from 3 to 8. When the results of all groups (300 tosses) are combined, the fraction of heads is close to 1/2. This mainly teaches that:
- A With more trials, experimental probability tends to come closer to the theoretical value
- B A small number of tosses always gives exactly half heads, if the coin is tossed fairly
- C The groups that got 3 heads must have used faulty or unevenly weighted coins
- D Probability experiments give no useful information, since results vary from group to group
Show answer
Correct answer: (A) With more trials, experimental probability tends to come closer to the theoretical value
Results of small experiments vary a lot by chance, but the relative frequency settles near 1/2 over many trials. This links the experimental and theoretical views of probability.
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Q.26
George Polya's four steps of problem solving, in the correct order, are:
- A Devise a plan, understand the problem, look back, carry out the plan
- B Understand the problem, carry out the plan, devise a plan, look back
- C Understand the problem, devise a plan, carry out the plan, look back
- D Look back, understand the problem, devise a plan, carry out the plan
Show answer
Correct answer: (C) Understand the problem, devise a plan, carry out the plan, look back
In 'How to Solve It' (1945) Polya gave the sequence: understand the problem, devise a plan, carry out the plan, and look back (check and reflect).
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Q.27
A child reasons, 'Ali is taller than Bina, and Bina is taller than Chetan, so Ali is taller than Chetan.' This logical ability, which Piaget associated with the concrete operational stage, is called:
- A Conservation
- B Centration
- C Transitivity
- D Object permanence
Show answer
Correct answer: (C) Transitivity
Transitivity is inferring the relation between two items from their relations with a third; seriation and the ordering of numbers and lengths depend on it. Conservation concerns a quantity staying the same despite changes in appearance.
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Q.28
Students type n = 1 to 50 in one column of a spreadsheet and the formula 3n + 1 in the next, then make a graph of the two columns. The main value of this activity is that students:
- A See the expression as a rule giving a value for every n, and examine many cases and the graph quickly
- B No longer need to learn how to substitute values into expressions, since the spreadsheet does it for them
- C Learn mainly how to format cells and choose colours in a spreadsheet, which is a useful computer skill
- D Find that 3n + 1 has only one correct value, which the spreadsheet shows in every row
Show answer
Correct answer: (A) See the expression as a rule giving a value for every n, and examine many cases and the graph quickly
A spreadsheet gives the value of 3n + 1 for every n at once, so the letter is seen as a variable and the expression as a relationship that can be tabulated and graphed. Students still need to understand substitution; the tool extends it.
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Q.29
In the context of NIPUN Bharat, 'foundational numeracy' refers mainly to a child's ability to:
- A Recite multiplication tables up to 20 quickly and without making any mistakes
- B Write numbers up to one lakh in words with correct spellings
- C Solve algebraic equations in one variable using standard textbook methods
- D Reason and apply simple number concepts to solve problems in daily life
Show answer
Correct answer: (D) Reason and apply simple number concepts to solve problems in daily life
Foundational numeracy is about understanding and using simple number concepts and reasoning in everyday situations, not about speed of recall. Algebra lies well beyond the foundational years.
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Q.30
Shown that 7 + 5 = 12, a child immediately says, 'Then 12 - 5 must be 7,' without counting. According to Piaget, the child is showing:
- A Centration on a single feature
- B Egocentrism
- C Reversibility of thought
- D Animism (life in non-living things)
Show answer
Correct answer: (C) Reversibility of thought
Reversibility is the ability to undo an operation mentally, here seeing subtraction as the inverse of addition; Piaget linked it to the concrete operational stage. Centration and egocentrism are limits of preoperational thought.
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Q.31
In the playground, a child holds the free end of a rope whose other end is tied to a peg, and walks around the peg keeping the rope tight while others mark the path with chalk. This mainly helps children understand that:
- A The circumference of a circle is always exactly three times its radius
- B A circle has exactly four lines of symmetry
- C The longer the rope, the smaller the circle that is drawn on the ground
- D Every point on a circle is at the same distance from its centre
Show answer
Correct answer: (D) Every point on a circle is at the same distance from its centre
The rope fixes the distance from the peg, so the path traced is a circle with the peg as centre and the rope as radius. The other statements are false: the circumference is about 2 × 3.14 times the radius, a circle has infinitely many lines of symmetry, and a longer rope gives a bigger circle.
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Q.32
For 'If 12 pencils cost Rs 30, what do 18 pencils cost?', students build a ratio table: 12 → 30, 6 → 15, 18 → 45. The main advantage of this strategy is that it:
- A Avoids multiplication and division altogether, so that students only need to add
- B Works only when the numbers happen to be multiples of 6, as they are in this particular question
- C Removes any need to understand what the question is actually asking, since the table does the thinking
- D Keeps both quantities in the same ratio while building the answer by easy steps like halving and adding
Show answer
Correct answer: (D) Keeps both quantities in the same ratio while building the answer by easy steps like halving and adding
Halving both quantities (6 → 15) and adding rows (12 + 6 → 30 + 15) keeps the ratio fixed, so the answer, Rs 45, is reached by reasoning students can follow. It still uses multiplication and division, but in steps the students choose themselves.
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Q.33
In the constructivist 5E model of lesson planning, the phase in which students handle materials and investigate the concept before the teacher gives a formal explanation is:
- A Evaluate
- B Elaborate
- C Explore
- D Engage
Show answer
Correct answer: (C) Explore
The 5E phases are engage (arouse curiosity), explore (hands-on investigation), explain (concepts and terms are clarified), elaborate (apply to new situations) and evaluate. Exploration comes before formal explanation.
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Q.34
A child counts six pencils as 'one, two, three, four, five, six' and, when asked how many pencils there are, answers 'six'. This shows understanding of which counting principle?
- A Order irrelevance principle
- B Cardinality principle
- C Abstraction principle
- D Stable order principle
Show answer
Correct answer: (B) Cardinality principle
The cardinality principle says that the last number named in counting represents the total number of objects in the set. Stable order refers to saying the number names in a fixed sequence.
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Q.35
A teacher displays an anonymous wrong solution and asks, 'What might this student have been thinking, and how could we fix it?' This practice mainly helps to:
- A Warn the class about the marks lost by students who make careless mistakes in tests
- B Save the teacher's time, as one solution is corrected for the whole class
- C Show the class that only the method given in the textbook leads to the answer
- D Make mistakes a normal part of learning, reducing fear and deepening understanding
Show answer
Correct answer: (D) Make mistakes a normal part of learning, reducing fear and deepening understanding
Discussing an error without naming anyone treats it as a source of learning rather than shame, so children are less afraid of being wrong. Analysing why the error seems sensible also deepens everyone's understanding of the concept.
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Q.36
A teacher tells children, 'If you see the word more in a question, add.' A child then solves 'Rina has 12 toffees. She has 4 more than Sohan. How many does Sohan have?' as 12 + 4 = 16. What does this show?
- A The child has not memorised the key-word rule properly and should practise it on many more such questions
- B Key-word shortcuts can mislead; children must understand the situation, e.g. by drawing or acting it out
- C Word problems are beyond the level of primary children and should be introduced only from Class 6 onwards
- D The child cannot add a two-digit and a one-digit number without making mistakes
Show answer
Correct answer: (B) Key-word shortcuts can mislead; children must understand the situation, e.g. by drawing or acting it out
Here 'more' appears but Sohan has fewer, so the answer is 12 - 4 = 8. Teaching key words as rules replaces understanding with guessing; modelling the situation helps children choose the operation.
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Q.37
A recipe for 4 people needs 6 cups of rice. Asked how much is needed for 6 people, a student says 8 cups: 'two more people, so two more cups'. The student is:
- A Using additive reasoning where proportional (multiplicative) reasoning is needed
- B Unable to add whole numbers correctly, so the total number of cups comes out wrong
- C Using the unitary method correctly by finding the rice needed for one person first
- D Showing a full understanding of ratio, as the difference between people and cups stays the same
Show answer
Correct answer: (A) Using additive reasoning where proportional (multiplicative) reasoning is needed
In a proportion the ratio, not the difference, stays constant: 6 cups for 4 people is 1.5 cups per person, so 6 people need 9 cups. Moving from additive to multiplicative comparison is a key step in learning ratio.
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Q.38
A student writes her working as 25 + 15 = 40 ÷ 2 = 20. Her final answer, 20, is what the question asked for. What should the teacher point out?
- A Nothing, since the final answer is correct and the marks are given only for the answer
- B Each '=' must join equal quantities; 25 + 15 = 40 ÷ 2 is false, so steps should be separate statements
- C She should not show her working at all, only the answer, so that no such errors appear
- D She should use a calculator to avoid such mistakes in future, and write down only what the calculator shows
Show answer
Correct answer: (B) Each '=' must join equal quantities; 25 + 15 = 40 ÷ 2 is false, so steps should be separate statements
Read as written, the line claims that 25 + 15 equals 40 ÷ 2, that is 40 = 20, which is false. Writing 25 + 15 = 40 and then 40 ÷ 2 = 20 keeps every statement true; precise use of symbols is part of mathematical communication.
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Q.39
Looking at two lines drawn on the board, a Class 7 student says, 'They are parallel because they look parallel.' The most suitable response of the teacher is to ask:
- A 'Are you sure? Look at them again carefully, and tell me if you still think so.'
- B 'Who agrees with her? Raise your hands.'
- C 'Can you copy the definition of parallel lines into your notebook and learn it by heart for tomorrow?'
- D 'How could we check? Say, by measuring the gap at two places, or the angles a transversal makes'
Show answer
Correct answer: (D) 'How could we check? Say, by measuring the gap at two places, or the angles a transversal makes'
The question moves the student from judging by appearance to testing a property: parallel lines stay the same distance apart, and a transversal makes equal corresponding angles with them. Looking again, voting or copying a definition keeps the judgement visual or rote.
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Q.40
A child correctly counts out 26 sticks. When asked to circle the sticks that the '2' in 26 stands for, she circles 2 sticks. This shows that she:
- A Thinks the digit 2 means two, not two tens
- B Has fully understood place value, since she counted all 26 correctly
- C Cannot yet count beyond 20 without making mistakes
- D Has confused the digits 2 and 6 because they look similar
Show answer
Correct answer: (A) Thinks the digit 2 means two, not two tens
The '2' stands for 2 tens, that is 20 sticks. Correct counting and writing can hide this gap; regrouping the sticks into bundles of ten and connecting the bundles to the tens digit builds the meaning of place value.
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Q.41
The recommended sequence for teaching measurement of length at the primary level is:
- A Standard units, non-standard units, direct comparison
- B Direct comparison, non-standard units, standard units
- C Non-standard units, standard units, direct comparison
- D Standard units, direct comparison, non-standard units
Show answer
Correct answer: (B) Direct comparison, non-standard units, standard units
Children first compare objects directly (longer or shorter), then measure with non-standard units (hand spans, sticks), and finally use standard units (centimetre, metre) when the need for uniformity is felt.
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Q.42
In the concrete-pictorial-abstract (CPA) approach to teaching multiplication, the correct sequence of activities is:
- A Write 3 x 4 = 12; draw 3 groups of 4 dots; make 3 groups of 4 pebbles
- B Make 3 groups of 4 pebbles; draw 3 groups of 4 dots; write 3 x 4 = 12
- C Draw 3 groups of 4 dots; write 3 x 4 = 12; make 3 groups of 4 pebbles
- D Write 3 x 4 = 12; make 3 groups of 4 pebbles; draw 3 groups of 4 dots
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Correct answer: (B) Make 3 groups of 4 pebbles; draw 3 groups of 4 dots; write 3 x 4 = 12
CPA moves from handling concrete objects, to pictorial representation, and finally to abstract symbols, matching Bruner's enactive-iconic-symbolic sequence.
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Q.43
A teacher includes this item in a test: 'The answer is 24. Write as many questions as you can that have this answer.' The main reason for using such an item is that it:
- A Is quicker and easier to mark than a question that has only one correct answer
- B Tests mainly whether the child remembers the multiplication tables up to 12
- C Shows how well a child understands the operations, and allows many correct answers
- D Helps the teacher rank children by how many questions they can write in a fixed time
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Correct answer: (C) Shows how well a child understands the operations, and allows many correct answers
An open-ended item lets children respond at their own level (12 + 12, 30 − 6, 4 × 6, 48 ÷ 2, half of 48), so the teacher sees how flexibly they understand operations. Marking it actually needs more judgement, not less.
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Q.44
Before teaching a systematic method for solving 4x + 5 = 25, a teacher has students try x = 1, 2, 3, ... in a table and check both sides each time. The main purpose is to help them understand:
- A That trial and error is always the fastest and best way to solve any equation
- B What a solution is: the value of x that makes both sides equal, here x = 5
- C That equations can be solved by guessing alone, without any reasoning at all
- D The multiplication table of 4 up to 4 × 10, needed for checking each row
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Correct answer: (B) What a solution is: the value of x that makes both sides equal, here x = 5
Trying values shows that a solution is the value that balances the equation (4 × 5 + 5 = 25). The slowness of trial for harder equations then motivates a systematic method.
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Q.45
Which of the following is an open-ended mathematics problem?
- A Find the perimeter of a rectangle whose length is 8 cm and breadth is 5 cm.
- B Draw as many different rectangles as you can whose perimeter is 24 cm.
- C What is 12 multiplied by 7?
- D Convert 3/4 into a decimal.
Show answer
Correct answer: (B) Draw as many different rectangles as you can whose perimeter is 24 cm.
An open-ended problem has more than one correct answer or solution path. Many rectangles have perimeter 24 cm, so students can explore, compare and generalise; the other items have a single fixed answer.
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Q.46
Which of the following problems best connects mathematics with the lives of Class 5 children?
- A Plan a class picnic for 30 children with Rs 1,500: what to buy and how much each item can cost
- B A train travels at 72 km per hour. How far will it go in 5 hours if it does not stop anywhere on the way?
- C Find 3/7 of 49 and check your answer by multiplying.
- D Simplify 12 + 8 × 2 - 6 using the correct order of operations.
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Correct answer: (A) Plan a class picnic for 30 children with Rs 1,500: what to buy and how much each item can cost
Planning a real class event on a fixed budget asks children to make decisions, estimate and compute in a situation they care about. The other items are routine exercises with little connection to children's own lives.
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Q.47
A teacher forms small mixed-ability groups for an activity on fractions. In terms of Vygotsky's ideas, the main benefit is that:
- A Weaker children can copy the answers of abler ones and so finish the task well on time
- B The teacher no longer needs to plan the activity, as the groups manage themselves fully
- C Abler children learn faster when they do not have to wait for the teacher's help
- D Abler peers scaffold others within their ZPD, and explaining deepens their own grasp
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Correct answer: (D) Abler peers scaffold others within their ZPD, and explaining deepens their own grasp
For Vygotsky, learning happens through social interaction with a more knowledgeable other, who may be a classmate. In mixed groups peers scaffold each other, and the child who explains has to organise and justify her own thinking.
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Q.48
A Class 8 student claims that '−x is always a negative number'. Which question from the teacher would best challenge this belief?
- A For x = 5, is −x negative?
- B Is −5 less than 0?
- C If x = −5, what is −x?
- D What is x − x?
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Correct answer: (C) If x = −5, what is −x?
If x = −5, then −x = 5, which is positive; −x means 'the opposite of x', not 'a negative number'. Checking x = 5 or asking about −5 only confirms the student's belief.
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Q.49
Which of the following is an example of formative assessment in mathematics?
- A The annual written examination held at the end of the year, whose marks decide promotion to the next class
- B A board examination in Class 10 that certifies each student's achievement
- C A term-end test used only to assign grades and rank students on the report card
- D A teacher observing group work on fractions and asking questions to decide what to teach next
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Correct answer: (D) A teacher observing group work on fractions and asking questions to decide what to teach next
Formative assessment is continuous and is used to give feedback and shape further teaching. End-of-term or annual examinations used for grading are summative.
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Q.50
A student writes: 'If 4 workers build a wall in 12 days, 8 workers will take 24 days.' The best way for the teacher to help is to:
- A Ask whether more workers need more or less time: twice the workers need half the time, 6 days
- B Tell him always to multiply when one quantity is doubled, as in the unitary method
- C Accept the answer, since it uses the unitary method correctly and the working is neat and complete
- D Give him the inverse-proportion formula to memorise, without any discussion of the actual situation
Show answer
Correct answer: (A) Ask whether more workers need more or less time: twice the workers need half the time, 6 days
Here the quantities are in inverse proportion: workers × days stays the same (4 × 12 = 48 = 8 × 6). Making students reason about the situation before calculating stops them from applying direct proportion blindly.
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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.