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.101
A standard tangram is a square cut into seven pieces. Which of the following is NOT one of these pieces?
- A A large triangle
- B A square
- C A parallelogram
- D A trapezium
Show answer
Correct answer: (D) A trapezium
The seven tans are five triangles (two large, one medium, two small), one square and one parallelogram. There is no trapezium among them, although children can build one by combining pieces.
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Q.102
A teacher asks Class 5 children to extend the pattern 3, 7, 11, 15, ... and to explain how they would find the 20th term without writing all terms. The main purpose of this task is to develop:
- A Generalisation and early algebraic thinking
- B Speed in addition through repeated adding of 4
- C Memorisation of the multiplication table of 4
- D Recognition of prime and composite numbers
Show answer
Correct answer: (A) Generalisation and early algebraic thinking
Working with patterns and finding a rule for any term leads children to generalise, which is the foundation of algebraic thinking at the upper primary stage.
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Q.103
While groups work on finding all the rectangles with an area of 24 square units, the teacher should mainly:
- A Sit at the desk and check notebooks, so groups can work without disturbance
- B Tell each group the answers early, so that no time is lost in the period
- C Move among groups, listen, and ask 'How do you know you have found them all?'
- D Stop any group that is using a method different from the one she taught
Show answer
Correct answer: (C) Move among groups, listen, and ask 'How do you know you have found them all?'
During group work the teacher observes, assesses informally and scaffolds with probing questions, without taking the thinking away from the children. Giving answers or allowing only one method defeats the purpose of the task.
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Q.104
To show that the sum of any two odd numbers is even, a Class 5 child arranges counters in pairs: each odd number has one counter left over, and the two left-over counters make a pair. This is an example of:
- A Checking the rule on a few examples such as 3 + 5 and 7 + 9 only
- B A general argument from the structure of odd numbers
- C Memorising a rule given by the teacher and applying it to sums
- D Estimating the sum of two odd numbers by rounding them off
Show answer
Correct answer: (B) A general argument from the structure of odd numbers
The child explains why the result must always hold: every odd number is some pairs plus one, and the two extra ones pair up. This informal proof is stronger than checking 3 + 5 and 7 + 9, and NCF 2005 lists reasoning and proof among the processes mathematics should develop.
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Q.105
According to NCF 2005, 'mathematisation' of the child's thought processes means:
- A Making children memorise more formulae and standard procedures at an earlier age so they can solve textbook problems quickly
- B Converting every lesson, even in language and EVS, into numerical calculation and written sums
- C Teaching mathematics only through its applications in science, so that every topic has a practical use
- D Developing the child's ability to think clearly and logically, handle abstraction and pursue assumptions to logical conclusions
Show answer
Correct answer: (D) Developing the child's ability to think clearly and logically, handle abstraction and pursue assumptions to logical conclusions
NCF 2005 describes mathematisation as developing the child's inner resources to think and reason mathematically, to handle abstraction and to pursue assumptions to their logical conclusion.
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Q.106
A Class 4 student can correctly compute 45 - 18 but fails the problem 'Meena had 45 marbles. After giving some to Ravi she has 18 left. How many did she give?' The most likely difficulty is:
- A The student cannot subtract two-digit numbers when regrouping of tens is needed
- B The student has a specific learning disability in mathematics and needs to be referred to a special educator
- C The numbers in the problem are too large for a Class 4 child to handle mentally
- D The student cannot interpret the language and structure of the word problem to choose the operation
Show answer
Correct answer: (D) The student cannot interpret the language and structure of the word problem to choose the operation
The computation is already mastered, so the difficulty lies in comprehension: the problem has an unknown change, which is harder than 'had 45, gave 18, how many left'. Word problems need language work and modelling with objects.
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Q.107
To strengthen spatial thinking and visualisation in Class 6, which activity is most suitable?
- A Practising long division of four-digit numbers by two-digit numbers
- B Reciting the multiplication tables up to 20 in chorus every morning
- C Drawing different nets on squared paper, predicting which will fold into a cube, then checking
- D Copying the definitions and formulae of solid shapes from the textbook and learning them word for word
Show answer
Correct answer: (C) Drawing different nets on squared paper, predicting which will fold into a cube, then checking
Predicting whether a net folds into a cube requires turning and folding shapes in the mind, and then testing the prediction. Copying definitions or computation drills do not develop visualisation.
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Q.108
In a class the ratio of boys to girls is 3 : 2. A student says that 2/3 of the class are girls. Her error is that she:
- A Has reversed the ratio; girls are actually 3/2 of the class, not 2/3 as she says
- B Is correct, since a ratio and a fraction always mean exactly the same thing in mathematics
- C Has forgotten that boys must always be written first in any fraction made from this ratio
- D Treats a part-to-part ratio as a part-to-whole fraction; girls are 2 of every 5, i.e. 2/5
Show answer
Correct answer: (D) Treats a part-to-part ratio as a part-to-whole fraction; girls are 2 of every 5, i.e. 2/5
3 : 2 compares boys with girls, so in every group of 5 children, 2 are girls and the fraction of the class that is girls is 2/5. Telling part-part comparisons apart from part-whole ones is central to understanding ratio.
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Q.109
A Class 4 teacher asks children to estimate how many of their steps it will take to cross the classroom, write the estimate down, and then walk and count. The main purpose is to:
- A Find out who is the best guesser in the class and give that child a prize to motivate the others
- B Teach the conversion between metres and centimetres using footsteps
- C Use up the time left at the end of the period in a pleasant way
- D Develop estimation of measures by comparing estimates with actual results and refining them
Show answer
Correct answer: (D) Develop estimation of measures by comparing estimates with actual results and refining them
Estimating, checking and adjusting builds a feel for measures that children use in daily life. The goal is better judgement, not winning a guessing game.
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Q.110
According to Bloom's revised taxonomy, which of the following questions is at the 'create' level?
- A Write a word problem from daily life that can be solved by 24 divided by 6.
- B What is 24 divided by 6? Show your working.
- C State the formula for the area of a rectangle and name the unit in which area is measured.
- D Is 24 divisible by 6? Give a reason using the rule of divisibility.
Show answer
Correct answer: (A) Write a word problem from daily life that can be solved by 24 divided by 6.
Asking students to construct their own problem requires putting elements together into something new, which is the 'create' level. Computing 24 / 6 is 'apply' or 'remember', and stating a formula is 'remember'.
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Q.111
Consider these statements:
1. Under NEP 2020's 5+3+3+4 structure, the foundational stage covers ages 3 to 8: three years of preschool or Anganwadi plus Classes 1 and 2.
2. NIPUN Bharat covers children aged 3 to 9 years.
3. Under the same structure, the preparatory stage covers Classes 6 to 8.
Which are correct?
- A 2 and 3 only
- B 1 and 3 only
- C 1, 2 and 3
- D 1 and 2 only
Show answer
Correct answer: (D) 1 and 2 only
The foundational stage spans ages 3 to 8 (preschool or Anganwadi plus Classes 1 and 2), and NIPUN Bharat covers ages 3 to 9. Statement 3 is false: the preparatory stage covers Classes 3 to 5 (ages 8 to 11), and Classes 6 to 8 form the middle stage.
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Q.112
For teaching number recognition and addition to Class 1 children, the most appropriate approach is:
- A Lecture method with worked examples on the board
- B Play-way method using games, songs, dice and number cards
- C Deductive method starting from the properties of addition
- D Written drill of addition facts for 30 minutes daily
Show answer
Correct answer: (B) Play-way method using games, songs, dice and number cards
The play-way method suits young children, who learn through play and activity. Games with dice and number cards develop number sense while keeping mathematics enjoyable, as NCF 2005 recommends.
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Q.113
A student says that for x + y = 10, x = 3 and y = 7 is a solution, but x = 5 and y = 5 is not, 'because different letters must stand for different numbers'. The teacher should help him see that:
- A He is right: two different letters can never have the same value in one equation
- B x and y can only be whole numbers less than 10, and never fractions or decimals
- C Different letters can take the same value; they just need not be equal
- D In every equation with two letters, the letters must be equal to each other
Show answer
Correct answer: (C) Different letters can take the same value; they just need not be equal
Using two letters only means the values are not tied to each other; 5 + 5 = 10, so x = 5, y = 5 is a valid solution. The claim that x and y must be whole numbers below 10 is also false, since x = 12, y = −2 or x = 2.5, y = 7.5 also work.
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Q.114
Consider these statements about estimation:
1. Estimation is a reasoned approximation, not a wild guess.
2. Estimation should be taught only after children master exact computation with large numbers.
3. Estimation helps children judge whether an answer is reasonable.
Which are correct?
- A 1 and 2 only
- B 2 and 3 only
- C 1, 2 and 3
- D 1 and 3 only
Show answer
Correct answer: (D) 1 and 3 only
Estimation uses number sense, such as rounding and benchmarks, to reach a sensible approximate value, and it serves as a check on answers. NCF 2005 asks for estimation and approximation in problem solving from the primary stage, not after exact computation is mastered.
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Q.115
Consider these statements about the mean:
1. The mean of a set of data must always be one of the values in the data.
2. The mean of whole-number data can be a fraction; for example, the mean of 2, 3 and 6 is 3 2/3.
Which of these is/are correct?
- A Only 2
- B Only 1
- C Both 1 and 2
- D Neither 1 nor 2
Show answer
Correct answer: (A) Only 2
The mean is the equal share of the total, so it need not be one of the data values or a whole number: (2 + 3 + 6) ÷ 3 = 11 ÷ 3 = 3 2/3. Statement 1 is a common misconception.
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Q.116
While teaching circles, a teacher mentions that Aryabhata gave π as about 3.1416 some 1,500 years ago. A student asks, 'So is π exactly 22/7 or exactly 3.1416?' The most accurate reply is:
- A Neither: both are approximations, as π cannot be written exactly as a fraction or finite decimal
- B π is exactly 22/7; Aryabhata's value was wrong, which is why all our textbooks use 22/7
- C π is exactly 3.1416, as Aryabhata found, and 22/7 is only a rough school value
- D π changes slightly from circle to circle, so any value close to 3 will do for all school sums
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Correct answer: (A) Neither: both are approximations, as π cannot be written exactly as a fraction or finite decimal
π = 3.14159... never ends or repeats; 22/7 (= 3.142857...) and 3.1416 are convenient approximations, and Aryabhata's is the closer one. The ratio of circumference to diameter is the same for every circle.
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Q.117
Students measure several pairs of vertically opposite angles and find them equal. The teacher then asks them to explain why this must always happen. Which explanation shows the kind of reasoning to encourage?
- A We measured four pairs with a protractor and found that they were all equal
- B ∠1 + ∠2 = 180° and ∠2 + ∠3 = 180° (linear pairs), so ∠1 = ∠3
- C They look equal in every figure we drew, however we drew the two lines
- D The textbook says that they are equal, and the textbook is always correct
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Correct answer: (B) ∠1 + ∠2 = 180° and ∠2 + ∠3 = 180° (linear pairs), so ∠1 = ∠3
The explanation uses a known fact (angles forming a linear pair add up to 180°) to show the result for any two intersecting lines. This informal deduction, beyond checking examples, is what upper primary geometry aims to build.
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Q.118
Dienes blocks (base-ten blocks) consisting of units, longs (tens), flats (hundreds) and cubes (thousands) are mainly used for teaching:
- A Angles and their measurement using a protractor
- B Place value and regrouping in addition and subtraction
- C Properties of triangles, quadrilaterals and other plane figures
- D Probability
Show answer
Correct answer: (B) Place value and regrouping in addition and subtraction
Base-ten blocks make the grouping of ten units into a ten and ten tens into a hundred physical, so children can see carrying and borrowing as exchange rather than as a rule.
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Q.119
A Class 5 child says, 'A rectangle has four right angles and its opposite sides are equal,' but insists that a square cannot be a rectangle. According to van Hiele, the child is at the level of:
- A Visualisation
- B Analysis
- C Informal deduction
- D Rigour
Show answer
Correct answer: (B) Analysis
At the analysis level, children describe shapes by their properties but do not yet see relationships between classes of shapes. Seeing a square as a special rectangle marks informal deduction.
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Q.120
While counting toys a child says 'one, two, three, five, six, seven'. Which counting principle has the child violated?
- A Cardinality principle
- B Abstraction principle
- C One-to-one correspondence principle
- D Stable order principle
Show answer
Correct answer: (D) Stable order principle
The stable order principle requires the number names to be said in the same fixed order every time. Skipping 'four' breaks this sequence.
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Q.121
On finding that 8 x 0.5 = 4, a Class 6 student insists the answer must be wrong because 'multiplication always makes the number bigger'. This belief is:
- A Correct for all real numbers, because multiplication is just repeated addition of equal groups
- B An over-generalisation from whole numbers, which breaks down for multipliers less than 1
- C A sign that the student cannot multiply and needs to relearn the tables
- D Correct for decimals but wrong for fractions, which follow different rules of multiplication
Show answer
Correct answer: (B) An over-generalisation from whole numbers, which breaks down for multipliers less than 1
With whole numbers greater than 1, multiplication does increase the number, so children over-generalise. Multiplying by a number between 0 and 1 gives a smaller result; area models and 'half of 8' language help correct this.
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Q.122
Consider these statements about technology in mathematics teaching:
1. Virtual manipulatives, such as on-screen fraction bars, can support learning when linked to discussion and symbols.
2. Technology is useful in mathematics mainly for drill and practice of computation.
3. Graphs drawn by software still need to be read and interpreted by students.
Which of these are correct?
- A 1 and 2 only
- B 2 and 3 only
- C 1, 2 and 3
- D 1 and 3 only
Show answer
Correct answer: (D) 1 and 3 only
Like physical materials, virtual ones help when students reflect on them and link them to symbols, and a software graph is useful only if students interpret it. Limiting technology to computational drill misses its main value: exploration and visualisation.
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Q.123
A Class 5 teacher asks children to write in a 'maths diary' how they solved a problem, what confused them and what they would try next time. The main purpose is to:
- A Help children reflect on and communicate their mathematical thinking in their own words
- B Improve children's handwriting through regular writing in a notebook
- C Collect marks for the term-end examination from the entries each child makes
- D Make sure every child copies the teacher's solution correctly into the diary for later revision
Show answer
Correct answer: (A) Help children reflect on and communicate their mathematical thinking in their own words
Writing about their methods makes children organise and explain their reasoning, and it shows the teacher how they think. It develops mathematical communication and reflection, not handwriting or copying.
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Q.124
Which of the following contexts is LEAST suitable for introducing negative integers in Class 6?
- A Counting the number of students present in the class each day
- B Temperatures above and below 0 °C in a hill town on a winter morning
- C Heights above and below sea level
- D Floors above and below the ground floor of a building, shown in a lift
Show answer
Correct answer: (A) Counting the number of students present in the class each day
Negative numbers make sense where there are two opposite directions from a zero point, as with temperature, sea level or floors. A count of students present can never be negative, so it gives no reason to need negative numbers.
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Q.125
A geoboard with rubber bands is most useful for helping children explore:
- A Multiplication tables
- B Reading of a clock and telling time to the minute
- C Decimal place value and rounding of decimals
- D Shapes, their properties, area and perimeter
Show answer
Correct answer: (D) Shapes, their properties, area and perimeter
On a geoboard children stretch rubber bands around pegs to make polygons, compare shapes, and count unit squares for area and unit lengths for perimeter.
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Q.126
Consider the following statements about assessment in NEP 2020:
1. NEP 2020 wants school assessment to remain mainly summative and focused on testing memorisation.
2. NEP 2020 recommends a holistic, 360-degree progress card that includes self-assessment and peer assessment along with teacher assessment.
Which of the statements is/are correct?
- A Only 1
- B Only 2
- C Both 1 and 2
- D Neither 1 nor 2
Show answer
Correct answer: (B) Only 2
NEP 2020 calls for a shift from summative, rote-based testing to regular, formative, competency-based assessment that tests higher-order skills. It also recommends a holistic, multidimensional progress card that includes self-assessment and peer assessment.
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Q.127
Which of the following is NOT a characteristic of the nature of mathematics?
- A It is hierarchical: later concepts such as decimals depend on earlier ones like place value
- B It uses precise symbols and terms whose meanings are agreed and fixed
- C Its results are established by repeated empirical observation rather than by proof
- D It is abstract and deals with ideas such as number and shape rather than physical objects
Show answer
Correct answer: (C) Its results are established by repeated empirical observation rather than by proof
Mathematics is deductive: results are proved logically from definitions and axioms, not verified by experiment. Being hierarchical, symbolic, precise and abstract are all accepted characteristics.
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Q.128
A Class 6 student says the area of a leaf cannot be found 'because there is no formula for a leaf'. The teacher should:
- A Agree, since area can be found only for regular shapes that have formulas, such as rectangles and circles
- B Ask her to measure the leaf's length and breadth and multiply them, as for a rectangle
- C Have students trace the leaf on squared paper and estimate its area by counting full and part squares
- D Tell her to find the perimeter of the leaf with a thread instead, since its area cannot be found at all
Show answer
Correct answer: (C) Have students trace the leaf on squared paper and estimate its area by counting full and part squares
Area is the amount of surface covered, which can be estimated for any shape by counting unit squares (for instance, counting squares more than half covered as one and ignoring those less than half covered). Formulas are shortcuts for regular shapes, not the meaning of area.
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Q.129
On a geoboard, children make a rectangle that covers 6 unit squares, then stretch a band along its diagonal and find that each triangle covers 3 squares. This activity leads children towards the idea that:
- A A triangle's perimeter is always half the perimeter of the rectangle drawn around it
- B A triangle always has more area than a rectangle with the same base and height
- C A right triangle's area is half that of the rectangle on the same base and height
- D All triangles that can be made on a geoboard have the same area
Show answer
Correct answer: (C) A right triangle's area is half that of the rectangle on the same base and height
The diagonal splits the rectangle into two equal right triangles, so each has half its area; this prepares the formula 1/2 × base × height. A triangle never has more area than the rectangle that encloses it, and its perimeter is not half the rectangle's.
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Q.130
A student adds 1/2 + 1/3 and writes 2/5. What does this error most likely indicate?
- A The student cannot add single-digit numbers reliably and so gets both the numerator and the denominator wrong
- B The student has understood equivalent fractions and correctly rewritten both fractions in fifths before adding them
- C The student adds numerators and denominators as separate whole numbers, not seeing that fractions need a common unit
- D The student has made a random slip of attention that will disappear with more practice of similar sums
Show answer
Correct answer: (C) The student adds numerators and denominators as separate whole numbers, not seeing that fractions need a common unit
Adding numerators and denominators separately is a systematic error arising from whole-number thinking. Using fraction strips to show that halves and thirds must be converted to sixths before adding addresses the root cause.
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Q.131
A Class 3 teacher sets up a 'class shop' with empty packets, price tags and play money, and children take turns as buyers and sellers. The main mathematical value of this activity is that children:
- A Memorise the prices of common household items sold in the local market
- B Learn how to run a business when they grow up, including keeping its accounts
- C Use addition, subtraction and estimation with money in a real-life context
- D Stay busy in a pleasant way while the teacher sits and checks notebooks at the desk
Show answer
Correct answer: (C) Use addition, subtraction and estimation with money in a real-life context
Buying and selling makes children add totals, work out change and judge whether money is enough, so the operations gain meaning from a familiar context. Memorising prices is not the purpose.
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Q.132
A teacher's rubric gives separate scores for 'understanding the problem', 'choice of strategy', 'accuracy of calculation' and 'explanation'. Compared with a rubric that gives one overall score, the main advantage of this analytic rubric is that it:
- A Shows in which aspects each child is strong or needs help
- B Takes much less time to mark, since the teacher looks only at the final answer
- C Removes the need for teacher judgement, because every criterion is scored by a key
- D Ranks the children more quickly and fairly on a single overall scale
Show answer
Correct answer: (A) Shows in which aspects each child is strong or needs help
An analytic rubric scores each criterion separately, so it gives diagnostic feedback on each part of the work. A holistic rubric (one overall score) is quicker to use but does not show where exactly the child needs help.
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Q.133
While introducing integers, a teacher tells the class that Brahmagupta, in the seventh century, called positive numbers 'fortunes' and negative numbers 'debts'. The best use of this fact in class is to:
- A Ask students to memorise the year and title of Brahmagupta's work, since it may come in the test
- B Show that mathematical ideas grew from human needs, and use fortune–debt to make sign rules meaningful
- C Replace all number-line work with stories from history, which children find more interesting
- D Show that negative numbers are only about money and debts, and have no other use in mathematics or daily life
Show answer
Correct answer: (B) Show that mathematical ideas grew from human needs, and use fortune–debt to make sign rules meaningful
Thinking of a negative number as a debt makes results such as 'taking away a debt leaves you better off' sensible, which helps with rules like 0 − (−3) = 3. History used this way adds meaning and context; memorising dates does not.
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Q.134
A child divides a rectangle into three parts of clearly different sizes, shades one part and writes 1/3. The child has not understood that:
- A The parts must be equal for each to be one-third
- B Fractions should be shown with circles, not with rectangles
- C The shaded part of a figure must always be the one on the left
- D In a fraction the numerator must always be larger than the denominator
Show answer
Correct answer: (A) The parts must be equal for each to be one-third
One-third means one of three equal parts of the whole. Fair-sharing tasks (sharing a roti equally among three) and folding paper into equal parts build this idea before symbols are used.
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Q.135
A Class 8 class plans and runs a one-day school fair, preparing a budget, pricing items, measuring the stall area and calculating profit. The method of teaching mathematics being used is the:
- A Project method, associated with W. H. Kilpatrick
- B Lecture-cum-demonstration method, led by the teacher
- C Analytic method, moving from the unknown to the known
- D Drill method, based on Thorndike's law of exercise
Show answer
Correct answer: (A) Project method, associated with W. H. Kilpatrick
The project method, developed by Kilpatrick on Dewey's ideas, uses a purposeful, real-life task carried out by students in a social setting, integrating many mathematical ideas.
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Q.136
In which of the following situations is an estimate NOT sufficient, so that an exact calculation is needed?
- A Deciding whether Rs 500 is enough for a list of groceries
- B Judging roughly how long a 12 km cycle ride will take
- C Writing the amount to be paid on a shop's bill
- D Checking whether a calculator answer is of the right size
Show answer
Correct answer: (C) Writing the amount to be paid on a shop's bill
A bill records the actual amount owed, so it must be exact. In the other situations an estimate is enough to decide, plan or check.
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Q.137
Students construct a 60° angle: an arc with centre O cuts the arm at A, and an arc of the same radius with centre A cuts the first arc at B. Asked why angle AOB must be 60°, which justification should the teacher look for?
- A It reads 60° on the protractor when we measure it, which proves it for every case
- B OA, OB and AB all equal the radius, so triangle OAB is equilateral and each angle is 60°
- C A compass always produces angles of 60°
- D Any arc drawn with a compass cuts off an angle of 60° at the centre of the circle
Show answer
Correct answer: (B) OA, OB and AB all equal the radius, so triangle OAB is equilateral and each angle is 60°
The justification links the construction to known facts: three equal sides make an equilateral triangle, whose angles are equal, so each is 180° ÷ 3 = 60°. Asking 'why does this work?' turns a construction from a recipe into reasoning.
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Q.138
A child says, 'This is a square because it looks like a square', and cannot say anything about its sides or angles. According to Van Hiele, the child is at the level of:
- A Deduction
- B Analysis
- C Visualisation
- D Informal deduction
Show answer
Correct answer: (C) Visualisation
At the visualisation level children recognise shapes by their overall appearance, not by properties. At the analysis level they can list properties, and at informal deduction they relate properties and classes of shapes.
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Q.139
According to NCF 2005, at the primary stage, helping children develop a positive attitude towards and a liking for mathematics is:
- A Less important than speed and accuracy in computation, which must always come first
- B A concern only after the basic algorithms have been fully mastered through regular practice
- C Needed only for children who are already afraid of mathematics and avoid it
- D As important as, if not more important than, the concepts and skills they acquire
Show answer
Correct answer: (D) As important as, if not more important than, the concepts and skills they acquire
NCF 2005 says this directly about the primary stage. It also lists a sense of fear and failure, which makes a majority of children give up on mathematics early, among the main problems of school mathematics. Attitude is treated as a goal in its own right, not an afterthought.
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Q.140
A teacher regularly says, 'Boys are naturally better at mathematics, girls should focus on languages.' Which statement about this is correct?
- A It is a scientifically established fact about differences between boys' and girls' brains, so it is acceptable to state
- B It is harmless because young children rarely notice such remarks or take them seriously when choosing subjects
- C It motivates girls to try harder in order to prove the teacher wrong, so it does some good
- D It is a gender stereotype that lowers girls' confidence and participation in mathematics, and must be actively countered
Show answer
Correct answer: (D) It is a gender stereotype that lowers girls' confidence and participation in mathematics, and must be actively countered
Differences in mathematics performance are not innate but shaped by expectations. NCF 2005 asks teachers to challenge such stereotypes and ensure equal participation of girls in mathematics.
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Q.141
Match each mathematician with a contribution.
P. Aryabhata
Q. Bhaskara II
R. Srinivasa Ramanujan
S. Baudhayana
i. Lilavati, a text on arithmetic and geometry
ii. A rule in the Sulba Sutra: the square on the diagonal of a rectangle equals the sum of the squares on its two sides
iii. The value of π as about 3.1416, in the Aryabhatiya
iv. Work in number theory; the number 1729 is linked with his name
- A P-iii, Q-i, R-iv, S-ii
- B P-ii, Q-i, R-iv, S-iii
- C P-iii, Q-iv, R-i, S-ii
- D P-i, Q-iii, R-iv, S-ii
Show answer
Correct answer: (A) P-iii, Q-i, R-iv, S-ii
Aryabhata's Aryabhatiya (5th century CE) gives π ≈ 3.1416; Bhaskara II wrote Lilavati (12th century); Baudhayana's Sulba Sutra (about 800 BCE) states the rule now called the Baudhayana–Pythagoras theorem; Ramanujan (1887–1920) worked in number theory, and 1729 is called the Hardy–Ramanujan number.
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Q.142
Students measure the circumference and diameter of several circular objects (bangles, lids, coins) and find that the ratio is always a little more than 3. This activity is an example of which method?
- A Lecture-cum-demonstration method
- B Deductive method of teaching
- C Laboratory method
- D Synthetic method
Show answer
Correct answer: (C) Laboratory method
The laboratory method uses hands-on measurement and experimentation with real objects so that students arrive at a mathematical result (here, an approximation of pi) by their own activity.
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Q.143
Children from weaving families in a Class 5 group point out repeating designs and lines of symmetry in the cloth their parents weave, and the teacher uses these to teach symmetry. This best reflects which guiding principle of NCF 2005?
- A Connecting knowledge to life outside the school
- B Introducing vocational training at the primary stage
- C Teaching mathematics only through art and craft
- D Reducing the content of the mathematics syllabus
Show answer
Correct answer: (A) Connecting knowledge to life outside the school
Connecting knowledge to life outside the school is one of the guiding principles of NCF 2005, and designs from children's homes make symmetry meaningful. The craft is a context here, not a replacement for mathematics or vocational training.
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Q.144
Consider the following statements about mathematics anxiety:
1. Giving extra sums as a punishment for misbehaviour can make children link mathematics with fear.
2. Mathematics anxiety affects only children who score low marks.
Which of the statements is/are correct?
- A Only 1
- B Only 2
- C Both 1 and 2
- D Neither 1 nor 2
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Correct answer: (A) Only 1
Using mathematics as a punishment attaches negative feelings to the subject. Anxiety is not limited to low scorers: children who understand mathematics well can also freeze under pressure, so it should not be read simply as low ability.
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Q.145
A teacher uses the history of mathematics to motivate students, telling them about the Indian mathematician whose seventh-century work Brahmasphutasiddhanta gave rules for operations with zero and negative numbers. This mathematician is:
- A Srinivasa Ramanujan
- B Brahmagupta
- C Bhaskara II
- D Varahamihira
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Correct answer: (B) Brahmagupta
Brahmagupta (7th century CE) set out rules for arithmetic with zero and negative numbers in the Brahmasphutasiddhanta. Aryabhata is associated with place value and an approximation of pi, and Ramanujan with 20th-century number theory.
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Q.146
An advertisement shows a bar graph of sales: Brand A 100, Brand B 110. The vertical axis starts at 90, so B's bar looks twice as tall as A's. Asking students to discuss this graph mainly develops:
- A Skill in drawing bars of equal width with equal gaps between them
- B Memory of the sales figures of the two brands for later questions
- C Critical reading of graphs, as a 10% difference is made to look like a 100% difference
- D The habit of always starting the vertical axis at a high value like 90, so differences show clearly
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Correct answer: (C) Critical reading of graphs, as a 10% difference is made to look like a 100% difference
Measured from 90, the bars are 10 and 20 units tall, so B looks twice A although it is only 10% more. Interpreting and questioning representations of data is a key part of data handling.
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Q.147
A student adds 4.2 and 1.35 by writing them one below the other and gets 1.77. What is the most likely cause?
- A She does not know the addition fact 2 + 5 and guesses the digits
- B She multiplies the two decimals instead of adding them
- C She lines up the last digits instead of the decimal points
- D She added correctly but copied the question wrongly from the board
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Correct answer: (C) She lines up the last digits instead of the decimal points
Lining up 42 under 135 from the right treats 2 tenths as 2 hundredths (the correct sum is 5.55). Writing 4.2 as 4.20 and using a place-value chart with ones, tenths and hundredths columns helps her align digits of the same place value.
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Q.148
Match each stage with the emphasis NCF 2005 gives mathematics at that stage.
P. Pre-primary Q. Primary R. Upper primary S. Secondary
i. Structure of mathematics as a discipline; proofs
ii. Comparison and classification along one dimension at a time; shapes and symmetries
iii. Algebraic notation; systematic study of space and shapes
iv. Concrete-to-abstract progression; estimation and approximation
- A P-iv, Q-ii, R-iii, S-i
- B P-ii, Q-iii, R-iv, S-i
- C P-ii, Q-iv, R-i, S-iii
- D P-ii, Q-iv, R-iii, S-i
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Correct answer: (D) P-ii, Q-iv, R-iii, S-i
NCF 2005 places simple comparisons and classification along one dimension at a time, and identifying shapes and symmetries, at the pre-primary stage; an explicit progression from concrete to abstract and stress on estimation and approximation in solving problems at the primary stage; algebraic notation and the systematic study of space and shapes at the upper primary stage; and the structure of mathematics as a discipline, with justifications and proofs, at the secondary stage.
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Q.149
According to the van Hiele model, a common reason why many students fail to follow geometry proofs in secondary classes is that:
- A They are too young to learn any geometry before the age of sixteen
- B Geometry is too abstract for most students ever to learn, however it is taught to them
- C They lack good drawing instruments such as a compass, protractor and set squares at home
- D Teaching is pitched at a higher level of thinking than the level students have reached
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Correct answer: (D) Teaching is pitched at a higher level of thinking than the level students have reached
Van Hiele observed that teacher and students may in effect speak at different levels; proofs at the deduction level mean little to students still at the visual or analysis level. Instruction has to be matched to the level the students have reached.
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Q.150
A Class 2 teacher working towards foundational numeracy goals finds that some children can recite numbers to 100 but cannot say which of 38 and 83 is greater. The most appropriate next step is to:
- A Use bundles and loose sticks or place-value cards in games to build the meaning of tens and ones
- B Make them write the numbers from 1 to 100 every day until they are fluent
- C Move on to three-digit numbers to keep pace with the syllabus, and come back to this during revision
- D Tell them that the number with the bigger last digit is always greater, as a quick rule to remember
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Correct answer: (A) Use bundles and loose sticks or place-value cards in games to build the meaning of tens and ones
Comparing 38 and 83 needs the understanding that the 8 in 83 stands for eight tens, which recitation does not give. Concrete grouping into tens and ones, used playfully, builds the meaning that foundational numeracy aims for.
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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.