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.251
A Class 4 child adds fractions correctly with fraction strips but is confused when she meets 1/4 + 2/4 written in symbols. Following the concrete-pictorial-abstract approach, the teacher should:
- A Insist that she learn the rule 'add numerators, keep the denominator'
- B Return to the strips or a drawing and connect each step with the symbols
- C Give her more symbolic sums until the confusion disappears
- D Move on, since she has already shown understanding with the strips
Show answer
Correct answer: (B) Return to the strips or a drawing and connect each step with the symbols
The CPA approach is not a one-way ladder: when symbols are not yet meaningful, the teacher moves back to concrete or pictorial forms and links them explicitly to the symbols. A rule learnt without that link is easily misapplied.
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Q.252
A teacher notices that several students make the same error repeatedly in multi-digit multiplication. The teacher's first step should be to:
- A Give the whole class extra homework on multiplication so fluency improves
- B Analyse the pattern of the error to identify the underlying misconception
- C Re-teach the entire chapter from the beginning at a slower pace
- D Separate the weak students into a different section for extra drill
Show answer
Correct answer: (B) Analyse the pattern of the error to identify the underlying misconception
A repeated error is systematic, so the teacher should first diagnose the specific misconception and then plan targeted remedial teaching. Generic homework or re-teaching everything does not address the cause.
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Q.253
According to NCF 2005, at the secondary stage students become familiar with the characteristics of mathematical communication. Which of the following is NOT one of them?
- A Carefully defined terms and concepts, with no loose meanings
- B The use of special symbols to represent these terms and concepts precisely
- C Precisely stated propositions, and proofs that justify them through logical steps
- D Loose everyday wording, so each reader may interpret a statement in their own way
Show answer
Correct answer: (D) Loose everyday wording, so each reader may interpret a statement in their own way
For the secondary stage, NCF 2005 names carefully defined terms and concepts, the use of symbols to represent them, precisely stated propositions, and proofs justifying propositions; it also calls mathematical communication precise and unambiguous. A mathematical statement is meant to have one exact meaning, so wording open to personal interpretation is the opposite of these features.
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Q.254
Most students in a Class 6 group recognise shapes only by their overall appearance. Before asking them whether every square is a rectangle, the teacher should first:
- A Ask them to write formal two-column proofs about squares and rectangles using axioms
- B Give them the definitions of all quadrilaterals to memorise word for word
- C Give activities in which they fold, measure and describe the properties of shapes
- D Leave quadrilaterals out until the students are older and are able to reason abstractly
Show answer
Correct answer: (C) Give activities in which they fold, measure and describe the properties of shapes
Seeing relationships between classes of shapes (informal deduction) needs the analysis level first, where children discover properties by folding and measuring. Van Hiele levels are sequential, so jumping to proofs or memorised definitions does not work.
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Q.255
Which of the following practices is NOT in line with NEP 2020's approach to numeracy in the foundational stage?
- A Using toys, games and local materials such as pebbles for counting and comparing
- B Learning numbers through rhymes, stories and play-based activities in the mother tongue
- C Making Class 1 children copy long columns of numbers as daily written homework
- D Letting children explore shapes and patterns in their surroundings
Show answer
Correct answer: (C) Making Class 1 children copy long columns of numbers as daily written homework
NEP 2020 describes learning in the foundational stage as flexible, play-based, activity-based and inquiry-based. Mechanical copying of numbers as homework goes against this.
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Q.256
During group work on a data-handling task, a teacher notices that in one group a single child does everything while the others watch. Which step best addresses this?
- A Stop group work in that class altogether and return to individual seatwork
- B Give marks only to the child who did the work, so the others feel the need to try
- C Give each member a role, and say that anyone may be asked to explain the result
- D Make the group larger, so that more children are available to share all the work
Show answer
Correct answer: (C) Give each member a role, and say that anyone may be asked to explain the result
Assigning roles (reader, recorder, checker, presenter) and making every member accountable for explaining the group's work ensures that all children think and take part. Making groups larger usually makes it easier for some members to stay passive.
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Q.257
A teacher draws a line marked only 0 at one end and 100 at the other, and asks children to mark where 50, 25 and 90 would be. This activity mainly develops:
- A Skill in measuring lengths accurately with a ruler in centimetres
- B Memory of the number names from one to a hundred in order
- C Speed in adding and subtracting two-digit numbers mentally
- D A sense of how big numbers are relative to 0 and 100
Show answer
Correct answer: (D) A sense of how big numbers are relative to 0 and 100
Placing numbers on an empty number line makes children reason about magnitude (50 is halfway, 25 is halfway to 50, 90 is close to 100), which is a core part of number sense. No measuring or recall of number names is involved.
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Q.258
A teacher prepares a rubric to assess a Class 5 data-handling project. A rubric is best described as:
- A A list of the correct answers to each question in the project, used as an answer key
- B A guide listing the criteria and describing work at each level of performance
- C A record of the dates on which each student submitted the project and its parts
- D A rank list of students from first to last based on their total project marks
Show answer
Correct answer: (B) A guide listing the criteria and describing work at each level of performance
A rubric sets out criteria (for example collecting data, organising it, drawing the graph, interpreting it) and describes levels such as beginning, developing and proficient. This makes marking transparent and tells children what to improve; an answer key or rank list does neither.
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Q.259
The NCERT Position Paper on Teaching of Mathematics identifies 'fear and failure' as a core problem. Which classroom practice is most likely to produce this fear?
- A Letting children discuss several ways of solving a problem in small groups
- B Using concrete materials like beads and sticks before introducing symbols
- C Emphasising speed, a single correct procedure and public comparison of marks
- D Encouraging children to estimate the answer before they calculate it exactly
Show answer
Correct answer: (C) Emphasising speed, a single correct procedure and public comparison of marks
Fear of mathematics is produced by emphasis on speed, the tyranny of one right procedure, and humiliation over marks. The other three practices are recommended by NCF 2005 to make mathematics enjoyable.
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Q.260
Which statement correctly describes the relationship between algorithms and understanding in NCF 2005's view of mathematics teaching?
- A Algorithms should be built on understanding; procedures taught without meaning lead to rote learning and fear
- B Standard algorithms must first be mastered through regular drill, and understanding will follow automatically later
- C Algorithms should never be taught at the primary stage, only at the upper primary stage
- D Children should learn only one algorithm for each operation, with no alternative strategies to confuse them at all
Show answer
Correct answer: (A) Algorithms should be built on understanding; procedures taught without meaning lead to rote learning and fear
NCF 2005 criticises the emphasis on procedure without understanding. Algorithms are useful but should emerge from and be connected to conceptual understanding, with children's own strategies respected.
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Q.261
A Class 4 teacher wants children to learn data handling meaningfully. Which sequence of activities is most appropriate?
- A Pose a question, collect data, organise it with tallies, represent it, interpret it
- B Draw a bar graph first, then decide which question the graph should answer
- C Copy a table from the textbook, draw its bar graph, then memorise the steps in order
- D Interpret a sample graph, collect data, pose a question, then represent what was found
Show answer
Correct answer: (A) Pose a question, collect data, organise it with tallies, represent it, interpret it
Data handling is an inquiry cycle that starts from a real question (for example, which game the class should play at recess). Starting from the question gives purpose to collecting, organising and representing data, and the interpretation answers the original question.
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Q.262
Ramu, who helps at his father's vegetable stall, quickly calculates the change for Rs 100 on a purchase of Rs 67, but struggles with the same subtraction written vertically in class. The teacher should:
- A Tell him that street methods are not allowed in school and he must use the column method
- B Make him practise the written algorithm fifty more times so that it becomes fully automatic
- C Conclude that he has a learning disability and refer him for special help
- D Build on his informal strategy, connect it to the written method and value it in class
Show answer
Correct answer: (D) Build on his informal strategy, connect it to the written method and value it in class
Children's informal or street mathematics is a resource. NCF 2005 asks teachers to connect school mathematics with the child's everyday experience instead of dismissing it.
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Q.263
Which of the following is NOT a good task for small-group work in a Class 4 mathematics class?
- A A routine sum such as 345 + 128 that each child can do alone in a minute
- B Finding all the ways to make Rs 20 using Rs 1, Rs 2, Rs 5 and Rs 10 coins
- C Collecting data on the class's favourite fruits and deciding how to show it
- D Deciding whether 'a number ending in 0 is always divisible by 5' is true, and why
Show answer
Correct answer: (A) A routine sum such as 345 + 128 that each child can do alone in a minute
Group work pays off when a task has several solutions, needs pooled effort or invites argument, so that members must share ideas. A routine single-answer sum gives nothing to discuss and is better done individually.
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Q.264
Which teaching-learning material is best suited for showing that 1/2, 2/4 and 4/8 are equivalent fractions?
- A An abacus with beads on vertical rods
- B Clock face
- C A set of dominoes with dot patterns
- D Fraction strips or paper folding
Show answer
Correct answer: (D) Fraction strips or paper folding
Fraction strips of equal length divided into 2, 4 and 8 parts let children line up 1/2, 2/4 and 4/8 and see they cover the same length; folding a paper strip repeatedly shows the same thing.
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Q.265
A Class 6 student says that a rectangle which is not a square has four lines of symmetry, including both diagonals. The most suitable way to address this is to:
- A Tell her a rectangle has two lines of symmetry and ask her to remember it for the test
- B Have her fold a paper rectangle along a diagonal and check whether the two halves match
- C Ask her to measure both diagonals and show that they are equal in length
- D Give her a worksheet on finding the lines of symmetry of capital letters
Show answer
Correct answer: (B) Have her fold a paper rectangle along a diagonal and check whether the two halves match
Folding along a diagonal shows that the two halves do not coincide, so a diagonal is not a line of symmetry of such a rectangle, while the folds through the midpoints of opposite sides do work. Equal diagonals are a different property and do not test symmetry.
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Q.266
A teacher poses a problem, gives each child a minute to think alone, asks pairs to compare their ideas, and then invites some pairs to share with the class. This strategy is called:
- A Drill and practice
- B Programmed instruction
- C Lecture-cum-demonstration
- D Think-pair-share
Show answer
Correct answer: (D) Think-pair-share
Think-pair-share gives every child time to think, a safe partner to try ideas with, and then a chance to speak to the whole class. It increases participation, especially of children who hesitate to answer in front of everyone.
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Q.267
Juice A is 2 glasses of concentrate mixed with 3 glasses of water; Juice B is 3 glasses of concentrate with 5 glasses of water. A student says B is stronger because it has more concentrate. Which approach best settles the question?
- A Compare the total amounts: B has 8 glasses in all against 5 for A, so B must be the stronger juice
- B Compare concentrate as a fraction of the drink: A is 2/5 = 0.4, B is 3/8 = 0.375, so A is stronger
- C Agree with the student, since 3 glasses of concentrate is more than 2 glasses
- D Say that taste is personal, so mathematics cannot decide which juice is stronger
Show answer
Correct answer: (B) Compare concentrate as a fraction of the drink: A is 2/5 = 0.4, B is 3/8 = 0.375, so A is stronger
Strength depends on the ratio of concentrate to the whole drink (or to water), not on the amount of concentrate alone. A has 2 parts in 5 (40%) and B has 3 parts in 8 (37.5%), so A is slightly stronger.
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Q.268
Class 8 students list all the properties of a rectangle they know. The teacher then asks, 'Which of these properties, on their own, are enough to be sure that a quadrilateral is a rectangle?' The main purpose of this question is to:
- A Move students from listing properties to seeing how one property implies another
- B Test whether students remember every property of a rectangle listed in the textbook
- C Reduce the number of properties students need to memorise for tests and examinations
- D Check how accurately students can measure sides and angles
Show answer
Correct answer: (A) Move students from listing properties to seeing how one property implies another
Seeing, for example, that a parallelogram with one right angle must have four right angles shows that properties are linked. This is the move from the analysis level towards informal deduction in the van Hiele model, and it is the basis of definitions and deduction.
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Q.269
After a student claims that 'every number divisible by 4 is also divisible by 2', the teacher asks her to write an explanation that would convince a classmate who was absent. This task mainly develops:
- A Handwriting and neat presentation of answers, so that the absent classmate is able to read them easily
- B Mathematical communication: a general argument, e.g. 4 = 2 × 2, so every multiple of 4 is one of 2
- C Memory of the divisibility rules for 2 and 4, which should be written out word for word in the explanation
- D Speed in finding multiples of 4
Show answer
Correct answer: (B) Mathematical communication: a general argument, e.g. 4 = 2 × 2, so every multiple of 4 is one of 2
Writing for a reader who was not present makes the student state each step explicitly and generally, going beyond listing examples. NCF 2005 counts mathematical communication and reasoning among the processes school mathematics should develop.
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Q.270
Two identical paper trapeziums, each with parallel sides a and b and height h, are joined (one turned upside down) to form a parallelogram. This helps students see that the area of one trapezium is:
- A (a + b) × h, the area of the parallelogram, which is the area of one trapezium
- B a × b × h
- C ½ × a × b
- D ½ × (a + b) × h, since the parallelogram has base a + b and height h
Show answer
Correct answer: (D) ½ × (a + b) × h, since the parallelogram has base a + b and height h
Placed together, the two trapeziums make a parallelogram whose base is a + b and whose height is h, and each trapezium is half of it. The formula is thus built from a known one rather than memorised.
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Q.271
Match each concept with the most suitable first experience for children:
A. Area B. Perimeter C. Angle D. Volume
(i) Walking along the boundary of the playground
(ii) Covering a table top with notebooks or tiles
(iii) Turning a door, or turning one's body to face a new direction
(iv) Filling a box with unit cubes
- A A-i, B-ii, C-iii, D-iv
- B A-ii, B-i, C-iii, D-iv
- C A-ii, B-i, C-iv, D-iii
- D A-iv, B-i, C-iii, D-ii
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Correct answer: (B) A-ii, B-i, C-iii, D-iv
Area is the amount of surface covered, perimeter the distance around a boundary, angle the amount of turn, and volume the space filled. Linking each measure to a bodily or hands-on experience gives it meaning before formulas are introduced.
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Q.272
Asked to find the value of 2a when a = 3, a Class 7 student writes 23. What does this error reveal?
- A She has substituted a wrong value for a in the expression before calculating it
- B She does not yet know the multiplication table of 2
- C She is right, since 2a stands for the two-digit number made of the digits 2 and a
- D She reads 2a as a two-digit numeral, as in place value, instead of 2 × a
Show answer
Correct answer: (D) She reads 2a as a two-digit numeral, as in place value, instead of 2 × a
In arithmetic, digits written side by side (23) show place value, but in algebra 2a means 2 × a, which is 6 here. The child carries the arithmetic convention into algebra, so the teacher should discuss the two conventions openly, e.g. by contrasting 2a with 23 and with 2 + a.
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Q.273
To find 3 − 7 on a number line, a student starts at 7, moves 3 steps to the left and gets 4. The teacher should:
- A Accept the answer, since subtraction, like addition, can be done in either order
- B Tell him 3 − 7 cannot be done, as a larger number can never be taken from a smaller one
- C Ask him to memorise that such a subtraction always gives 4, whichever number comes first
- D Help him start at 3 and move 7 steps left to reach −4, and compare this with 7 − 3 = 4
Show answer
Correct answer: (D) Help him start at 3 and move 7 steps left to reach −4, and compare this with 7 − 3 = 4
Subtraction is not commutative: 3 − 7 = −4 while 7 − 3 = 4. The rule that a larger number cannot be taken from a smaller one holds only for whole numbers and has to be revised once integers are introduced.
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Q.274
A diagnostic test shows that six children in Class 3 cannot regroup in addition (e.g. 38 + 25). The most suitable remedial plan is to:
- A Work with them in a small group, trading ten loose sticks for a bundle, then link it to writing
- B Make them copy several solved examples from the board until all the steps feel familiar to them
- C Ask them to memorise the rule 'carry one' and recite it aloud before attempting every sum
- D Give the whole class a short test every day until these six children show improvement
Show answer
Correct answer: (A) Work with them in a small group, trading ten loose sticks for a bundle, then link it to writing
Remedial teaching targets the diagnosed cause with a different, more concrete approach: physically exchanging ten ones for one ten shows what 'carrying' means. Copying examples or memorising 'carry one' repeats the rote approach that failed.
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Q.275
Bruner held that any subject can be taught effectively in some intellectually honest form to any child at any stage of development. For mathematics, this implies that:
- A Algebraic symbols should be taught in Class 1 in the same form as in Class 8, only a little more slowly
- B A child's stage of development has no effect on how a topic should be taught, only on how fast
- C Young children can meet an idea like fractions by sharing real objects, long before formal symbols
- D Difficult topics should wait until children reach the formal operational stage at about eleven years of age
Show answer
Correct answer: (C) Young children can meet an idea like fractions by sharing real objects, long before formal symbols
Bruner's point is that a topic can be presented in a form suited to the learner's mode of thinking (enactive, iconic or symbolic) and deepened later. It does not mean teaching the same formal content at every age.
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Q.276
A Class 7 student says a big triangle drawn on the board must have a larger sum of angles than a small triangle in her notebook. Which activity best addresses this?
- A Measure the sides of both triangles with a ruler and compare their perimeters
- B Tear off the corners of different-sized triangles and place them together on a line
- C State the angle sum property and ask her to write it ten times in her notebook
- D Draw an even bigger triangle on the board and measure its largest angle with a protractor
Show answer
Correct answer: (B) Tear off the corners of different-sized triangles and place them together on a line
For every triangle the three torn corners together form a straight angle (180°), whatever its size, so the student discovers for herself that the angle sum does not depend on the lengths of the sides.
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Q.277
A student converts 2 hours 30 minutes to 2.30 hours. The teacher should help him see that:
- A His answer is correct, because the 30 minutes are written after the point
- B An hour has 60 minutes, so 30 minutes is 0.5 hour: 2.5 hours
- C A day has 24 hours, so hours must be written as whole numbers
- D Time should always be written in minutes only, never in hours
Show answer
Correct answer: (B) An hour has 60 minutes, so 30 minutes is 0.5 hour: 2.5 hours
The student has applied base-ten decimal notation to minutes; 0.30 hour would be 18 minutes. Using a clock face to show that 30 minutes is half of 60 minutes connects the units correctly.
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Q.278
NEP 2020 gives increased emphasis to mathematics and computational thinking from the foundational stage onwards. Which method does it specifically mention for this?
- A Daily timed tests on multiplication tables to build speed and accuracy
- B Separate mathematics tuition classes after school hours for the children who lag behind
- C Regular use of puzzles and games that make mathematical thinking more enjoyable
- D Memorising formulae through repetition and regular written practice
Show answer
Correct answer: (C) Regular use of puzzles and games that make mathematical thinking more enjoyable
NEP 2020 says mathematics and computational thinking will be emphasised through innovative methods, including the regular use of puzzles and games that make mathematical thinking more enjoyable and engaging. Timed tests and rote repetition are not what it proposes.
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Q.279
A Class 1 child counts on her fingers to find 4 + 3. The most appropriate response of the teacher is to:
- A Forbid finger counting because it is a bad habit that will slow her down in higher classes
- B Tell her to memorise all addition facts up to 20 at home before coming to class, so that she need not count
- C Accept it as a natural strategy and gradually help her move to mental strategies like counting on from 4
- D Reduce her marks for not using the correct method so that she stops depending on her fingers
Show answer
Correct answer: (C) Accept it as a natural strategy and gradually help her move to mental strategies like counting on from 4
Finger counting is a natural stage in developing number sense. The teacher should accept it and gradually support the child in moving towards more efficient strategies rather than banning it.
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Q.280
Asked to write 'add 3 to x, and then multiply the result by 2', a student writes 2x + 3. Which activity best helps her see the error?
- A Tell her always to write the number before the letter, as textbooks do in 2x
- B Tell her that brackets can be left out in algebra whenever the meaning is clear
- C Try x = 5: (5 + 3) × 2 = 16 but 2 × 5 + 3 = 13, then discuss why brackets are needed
- D Give her the rule that multiplication is always written first in any algebraic expression
Show answer
Correct answer: (C) Try x = 5: (5 + 3) × 2 = 16 but 2 × 5 + 3 = 13, then discuss why brackets are needed
Testing with a number shows the two expressions give different results, so the order of operations in the words must be shown with brackets: 2(x + 3), which equals 2x + 6, not 2x + 3.
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Q.281
A student measures an angle that is clearly acute and writes 130°. What is the most likely cause, and the best advice?
- A The protractor is faulty; she should borrow another one and measure again
- B She read the wrong scale; she should estimate first and read from the 0 on the base arm
- C She does not know what an angle is, so angles must be retaught from the start
- D Her eye was not level with the protractor, so she misread the marks by a few degrees each time
Show answer
Correct answer: (B) She read the wrong scale; she should estimate first and read from the 0 on the base arm
A protractor has two scales, and 130° is what the other scale shows for a 50° angle. Estimating first (an acute angle is less than 90°) and counting from the 0 on the arm along the base line prevents this error.
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Q.282
A teacher plans to teach decimals only after children are comfortable with fractions and place value. This decision is based on which characteristic of mathematics?
- A Its symbolic (representational) nature
- B Its precision and exactness
- C Its aesthetic (pattern-based) nature
- D Its hierarchical (sequential) nature
Show answer
Correct answer: (D) Its hierarchical (sequential) nature
Mathematics is hierarchical: each concept builds on earlier ones, so decimals (tenths, hundredths) require prior understanding of fractions and place value.
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Q.283
Which statement about the deductive method of teaching mathematics is correct?
- A It begins from particular examples and leads the learner step by step to discover the general rule or formula
- B It is the best method for introducing a new concept to young children, because it is quick, exact and complete
- C It states the rule first and applies it to examples; it saves time but does not by itself build understanding
- D It is the same as the heuristic method, because both rely on the learner discovering the rule
Show answer
Correct answer: (C) It states the rule first and applies it to examples; it saves time but does not by itself build understanding
The deductive method proceeds from the general rule to particular cases. It is quick and useful for practice and for older students, but it should follow inductive discovery, not replace it, when introducing new concepts.
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Q.284
A teacher gives Class 4: 'A bus has 40 seats. 25 passengers get on at the first stop. The driver is 45 years old. How many seats are empty?' Including the driver's age is meant to:
- A Make the problem longer so that it takes more time and keeps the whole class busy for longer
- B Help children pick out relevant information instead of operating on every number given
- C Test whether children remember the driver's age when they are asked about it suddenly later
- D Introduce problems on ages, which will be taught in the next chapter
Show answer
Correct answer: (B) Help children pick out relevant information instead of operating on every number given
Children who mechanically combine all the numbers in a problem show that they are not reasoning about the situation. Problems with extra (or missing) information train them to decide what is relevant.
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Q.285
For the number of matchsticks needed to make a row of n squares, three groups write 3n + 1, 4 + 3(n − 1) and 4n − (n − 1). The best response of the teacher is to:
- A Accept only 3n + 1, since it is the form given in the textbook answer key
- B Ask each group to explain its rule from the picture, then show all three simplify to 3n + 1
- C Tell the class that only one of the three can be right, and let them vote to decide which one it is
- D Accept the first two but reject 4n − (n − 1), as it uses subtraction inside brackets
Show answer
Correct answer: (B) Ask each group to explain its rule from the picture, then show all three simplify to 3n + 1
Each expression records a different way of seeing the same pattern (4 sticks for the first square and 3 for each new one, or 4 per square minus the n − 1 shared sticks), and all equal 3n + 1. Comparing them builds the idea of equivalent expressions and of justifying a rule from the structure.
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Q.286
To help students accept that 2⁰ = 1, the most meaningful approach is to:
- A Use the pattern 2³ = 8, 2² = 4, 2¹ = 2, dividing by 2 at each step, so 2⁰ = 1
- B Show 2⁰ on a calculator and ask students to simply accept the result it gives
- C State that any non-zero number to the power 0 is 1, and then give plenty of practice sums
- D Explain that the power 0 means the number is not multiplied at all, so it stays 2
Show answer
Correct answer: (A) Use the pattern 2³ = 8, 2² = 4, 2¹ = 2, dividing by 2 at each step, so 2⁰ = 1
Moving down the pattern divides by 2 each time, so continuing it gives 2⁰ = 2 ÷ 2 = 1; the same follows from 2³ ÷ 2³ = 2⁰, which also equals 1. The rule then makes sense instead of being an arbitrary fact.
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Q.287
A child writes 47 + 38 = 715 and 56 + 27 = 713. What does this error show?
- A She does not know the addition facts, so her sums of the ones are all wrong
- B She writes the full column sum instead of regrouping ten ones as one ten
- C She subtracts in the tens column instead of adding the two digits written there
- D She reverses the digits of the answer while copying it into the box
Show answer
Correct answer: (B) She writes the full column sum instead of regrouping ten ones as one ten
7 + 8 = 15 and 4 + 3 = 7 are both right, but 15 ones are written as '15' instead of 5 ones with 1 ten carried to the tens column. Exchanging ten loose sticks for a bundle, or ten unit cubes for a long, makes regrouping meaningful.
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Q.288
Under the NIPUN Bharat Mission, every child is expected to attain foundational literacy and numeracy by the end of:
- A Grade 3
- B Grade 5
- C Grade 2
- D Grade 8
Show answer
Correct answer: (A) Grade 3
NIPUN Bharat aims that every child attains foundational literacy and numeracy by the end of Grade 3, with 2026-27 as the target year.
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Q.289
Students write their own definition of a 'polygon' and test it against figures drawn by classmates, such as a circle, an open zigzag line and a star shape, revising it each time it fails. This activity mainly develops:
- A Speed in copying the textbook definition into the notebook
- B Skill in drawing neat figures
- C Precise use of mathematical language, refining a definition to include all polygons and exclude others
- D The idea that each student may hold a different, but equally correct, meaning of the word 'polygon' in mathematics
Show answer
Correct answer: (C) Precise use of mathematical language, refining a definition to include all polygons and exclude others
Testing a definition against examples and non-examples shows why mathematical terms must be stated carefully. Students arrive at something like 'a simple closed figure made of line segments' through their own reasoning rather than by copying it.
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Q.290
A teacher places three 1/2 fraction strips end to end beside a strip for one whole. This helps children see that:
- A All fractions are less than one, so three halves is not a fraction
- B 1/2 is greater than 1, because three halves are longer than the whole
- C Halves can be added only when they come from different wholes
- D A fraction can be more than one whole: 3/2 = 1 1/2
Show answer
Correct answer: (D) A fraction can be more than one whole: 3/2 = 1 1/2
Three halves cover one whole strip and half of another, so 3/2 = 1 1/2. This challenges the common belief that a fraction is always a part smaller than one whole, and introduces improper fractions and mixed fractions meaningfully.
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Q.291
For the area of a circle of diameter 14 cm (taking π = 22/7), a student writes 22/7 × 14 × 14 = 616 cm². What has she most likely done?
- A Used the formula for the circumference of the circle instead of the formula for its area
- B Used the diameter in place of the radius; with r = 7 cm the area is 154 cm²
- C Made a slip in multiplying, since 22/7 × 14 × 14 actually comes to 308 cm²
- D Worked correctly, since the area formula for a circle uses the diameter, not the radius
Show answer
Correct answer: (B) Used the diameter in place of the radius; with r = 7 cm the area is 154 cm²
πr² needs the radius, 7 cm: 22/7 × 7 × 7 = 154 cm². Using the diameter gives four times the area (616 = 4 × 154); her multiplication itself is correct.
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Q.292
Students measure the angles of five triangles and get angle sums of 179°, 181°, 180°, 178° and 180°. Which conclusion is most accurate?
- A The angle sum varies from one triangle to another, depending on its shape and size
- B These measurements prove that the angle sum is exactly 180° for every possible triangle
- C The activity is useless, because the measurements are not all equal and therefore prove nothing at all
- D The results suggest a sum of 180°, but measuring alone cannot show it exactly for every triangle
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Correct answer: (D) The results suggest a sum of 180°, but measuring alone cannot show it exactly for every triangle
Measurement involves error and covers only a few cases, so it supports a conjecture but cannot prove it; certainty needs a deductive argument. The activity is still valuable for forming the conjecture.
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Q.293
A student says an obtuse-angled triangle has no height on one of its shorter sides, 'because a height must be drawn inside the triangle'. The teacher should:
- A Agree, since the height of a triangle always lies inside it, whatever the type of triangle
- B Extend that side and show that the perpendicular from the opposite vertex can fall outside
- C Tell her to use only acute-angled triangles when finding areas, to avoid this difficulty
- D Ask her to use the length of another side as the height, since any side can serve as one
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Correct answer: (B) Extend that side and show that the perpendicular from the opposite vertex can fall outside
A height is the perpendicular distance from a vertex to the line containing the opposite side, and in an obtuse-angled triangle it can lie outside. The belief comes from seeing only 'typical' acute triangles standing on a horizontal base.
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Q.294
The NCERT Position Paper on Teaching of Mathematics says the school mathematics curriculum disappoints the majority who fear mathematics, and also:
- A Parents, by giving too little homework
- B The talented minority, by offering them no challenges
- C Teachers of other subjects, by taking up their periods
- D Children who prefer the arts, by being a compulsory subject
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Correct answer: (B) The talented minority, by offering them no challenges
The position paper notes that the curriculum fails both the non-participating majority, who give up out of fear, and the talented minority, who find nothing challenging. Its recommendations therefore include offering conceptual challenges to the emerging mathematician.
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Q.295
To teach 'one-fourth of 12 marbles' in Class 4, which activity is most suitable?
- A Asking children to imagine each marble cut into four equal pieces
- B Shading one-fourth of a circle drawn on the board, then writing 12 next to it
- C Sharing the 12 marbles equally into 4 groups and counting the marbles in one group
- D Writing the rule 'divide by the denominator, multiply by the numerator' to memorise
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Correct answer: (C) Sharing the 12 marbles equally into 4 groups and counting the marbles in one group
A fraction of a collection is found by making equal groups: one of the 4 equal groups of 12 marbles is 3 marbles. Children who know fractions only as parts of one shape may wrongly think one-fourth means cutting each object.
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Q.296
A child writes 63 − 29 = 44 and 81 − 37 = 54. Which is the most likely cause?
- A She subtracts the smaller digit from the larger digit in each column of the sum
- B She adds the digits in the ones column instead of subtracting them
- C She regroups but does not reduce the tens digit of the first number by one
- D She does not yet know the subtraction facts up to 10 and guesses the ones
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Correct answer: (C) She regroups but does not reduce the tens digit of the first number by one
13 − 9 = 4 and 11 − 7 = 4 are correct, but the tens are worked as 6 − 2 and 8 − 3 instead of 5 − 2 and 7 − 3 (correct answers 34 and 44). Smaller-from-larger would give 46 and 56. With base-ten blocks the child must physically break a long, so the tens visibly go down by one.
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Q.297
Which of the following questions most requires logical reasoning rather than recall?
- A What is 7 × 8? Write the answer in the box.
- B Can a triangle have two right angles? Explain why or why not.
- C Name a shape that has three sides and draw it neatly in your notebook.
- D Write the numeral for forty-two, exactly as dictated by the teacher.
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Correct answer: (B) Can a triangle have two right angles? Explain why or why not.
Answering it needs reasoning: two right angles already add up to 180°, leaving nothing for the third angle, so the two sides would never meet. The others can be answered from memory.
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Q.298
The model of five levels of geometric thinking (visualisation, analysis, informal deduction, deduction and rigour) was proposed by:
- A Pierre van Hiele and Dina van Hiele-Geldof
- B Jean Piaget, Barbel Inhelder and Alina Szeminska
- C Zoltan Dienes
- D George Polya
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Correct answer: (A) Pierre van Hiele and Dina van Hiele-Geldof
The Dutch educators Pierre van Hiele and Dina van Hiele-Geldof proposed these levels from their work with school students. Dienes is known for principles of mathematics learning and Polya for problem solving.
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Q.299
A child is shown 8 red and 3 yellow wooden beads. Asked, 'Are there more red beads or more wooden beads?', she says, 'More red beads.' According to Piaget, she has not yet developed:
- A Object permanence
- B Conservation of volume
- C Hypothetical-deductive reasoning
- D Class inclusion
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Correct answer: (D) Class inclusion
Class inclusion is understanding that a subclass (red beads) is part of a larger class (wooden beads), so the whole cannot be smaller than a part. Piaget placed this in the concrete operational stage, and part-whole reasoning in number rests on it.
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Q.300
The study of mathematical ideas embedded in the practices of a cultural group, such as rangoli patterns, traditional measuring units or weaving designs, is called:
- A Ethnomathematics
- B Pure (theoretical) mathematics
- C Applied statistics
- D Axiomatic (formal deductive) mathematics
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Correct answer: (A) Ethnomathematics
Ethnomathematics refers to the mathematics practised within cultural groups. Bringing such community mathematics into class connects school learning with children's lives.
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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.