Pedagogy

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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1. Q.201

   A Class 7 student argues, 'Every square is a rectangle because it has all the properties of a rectangle, but a rectangle need not be a square.' This reasoning corresponds to which Van Hiele level?

   1. A Informal deduction (abstraction)
   2. B Visualisation (recognising whole shapes)
   3. C Rigour (comparing axiom systems)
   4. D Analysis (descriptive)
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   Correct answer: (A) Informal deduction (abstraction)

   Relating classes of shapes by their properties (class inclusion) and giving informal arguments is the informal deduction level. At analysis level a child lists properties but does not see the relation between classes.

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2. Q.202

   Which of the following is NOT a pre-number concept that should be developed before formal counting?

   1. A Classification (sorting objects by attribute)
   2. B Seriation (ordering by size)
   3. C Addition of two-digit numbers
   4. D One-to-one correspondence (matching)
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   Correct answer: (C) Addition of two-digit numbers

   Pre-number concepts are classification, seriation, one-to-one correspondence and comparison. Addition of two-digit numbers comes well after number concept is established.

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3. Q.203

   In dynamic geometry software, Ritu makes a square by placing four points by eye, while Arjun constructs one using perpendicular lines and circles. When the vertices are dragged, Ritu's figure stops being a square but Arjun's stays a square. This mainly shows students that:

   1. A The software works properly only on Arjun's computer, which must be newer than Ritu's
   2. B Squares cannot be drawn correctly with software and must be drawn with ruler and compass
   3. C Dragging changes every figure, so it should be avoided when checking shapes
   4. D A constructed figure keeps its defining properties; one drawn by eye only looks right
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   Correct answer: (D) A constructed figure keeps its defining properties; one drawn by eye only looks right

   Arjun's square is built from its properties (perpendicular sides, equal lengths), so it survives the 'drag test'; Ritu's only resembles a square. This pushes students to think about which properties define a figure.

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4. Q.204

   'In a school there are 6 times as many students as teachers.' Using S for the number of students and T for the number of teachers, many Class 8 students write 6S = T. Which step best helps them check their equation?

   1. A Remind them to write the letters in the same order as the words appear in the sentence
   2. B Write the correct equation on the board and ask them to copy it into their notebooks
   3. C Try numbers, e.g. 2 teachers and 12 students, and see whether the equation holds
   4. D Ask them to solve the equation first for S and then for T
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   Correct answer: (C) Try numbers, e.g. 2 teachers and 12 students, and see whether the equation holds

   With 2 teachers and 12 students, 6S = T gives 72 = 2, which is false, while S = 6T gives 12 = 12. Matching the word order is a common cause of this error; testing with numbers makes students treat the letters as numbers of students and teachers, not as labels.

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5. Q.205

   In mathematics education, a task is called a 'problem' rather than an 'exercise' for a learner when:

   1. A It has large numbers or many steps of calculation which take a long time to finish
   2. B It appears in an examination paper and carries more marks than other questions
   3. C The learner has no ready-made procedure for it and must work out a way to solve it
   4. D It is taken from the end of a textbook chapter, after the solved examples
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   Correct answer: (C) The learner has no ready-made procedure for it and must work out a way to solve it

   An exercise practises a known procedure; a problem requires the learner to devise an approach, so the same task can be a problem for one child and an exercise for another. Large numbers do not make a task a problem.

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6. Q.206

   Children measure the same table and find that it is 10 hand spans long and 25 matchsticks long. A child says, 'The table is longer when we use matchsticks.' The idea the teacher should develop is that:

   1. A The smaller the unit, the more units are needed; the table has not changed
   2. B Matchsticks give the correct length of the table, and hand spans do not, as they vary
   3. C The child must have counted the hand spans or matchsticks wrongly and should recount
   4. D Lengths should never be measured with non-standard units like these in the classroom
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   Correct answer: (A) The smaller the unit, the more units are needed; the table has not changed

   A matchstick is shorter than a hand span, so more matchsticks fit along the same table. Understanding this inverse relationship between the size of the unit and the number of units is central to measurement and, later, to converting units.

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7. Q.207

   A Class 7 student writes 1 square metre = 100 square centimetres. The most helpful activity is to:

   1. A Ask her to memorise 1 m² = 10,000 cm² and write it ten times
   2. B Have her picture 1 m² as 100 rows of 100 one-centimetre squares
   3. C Tell her to multiply by 100 whenever she converts metres to centimetres
   4. D Give her a printed table of all conversions to keep in her notebook
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   Correct answer: (B) Have her picture 1 m² as 100 rows of 100 one-centimetre squares

   She has used the length conversion (1 m = 100 cm) for area. Visualising the square as 100 rows of 100 small squares shows why 1 m² = 10,000 cm²; a rule learnt without this picture is easily mixed up again.

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8. Q.208

   A school is planning a National Mathematics Day programme. Consider these statements:

   1. National Mathematics Day is observed in India on 22 December, the birth anniversary of Srinivasa Ramanujan.

   2. Ramanujan worked with the mathematician G. H. Hardy at the University of Cambridge.

   Which of these is/are correct?

   1. A Only 1
   2. B Only 2
   3. C Both 1 and 2
   4. D Neither 1 nor 2
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   Correct answer: (C) Both 1 and 2

   Ramanujan was born on 22 December 1887, and the day has been observed as National Mathematics Day since 2012. He went to Cambridge in 1914 and worked there with G. H. Hardy.

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9. Q.209

   A Class 8 student argues, 'Every square has four equal sides, so every figure with four equal sides is a square.' The teacher draws a rhombus that is not a square. The student's reasoning error is:

   1. A Confusing the perimeter of a figure with its area while comparing shapes
   2. B Making a mistake in measuring the sides of the figures with a ruler
   3. C Assuming that the converse of a true statement must also be true
   4. D Using inductive reasoning from too few examples
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   Correct answer: (C) Assuming that the converse of a true statement must also be true

   'If a figure is a square, it has four equal sides' is true, but its converse 'if a figure has four equal sides, it is a square' is false, as the rhombus shows. Telling a statement apart from its converse is a basic part of logical thinking in mathematics.

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10. Q.210

    After solving a problem, a student checks whether the answer is reasonable, solves it by another method, and asks whether the same approach would work for similar problems. In Polya's model, the student is:

    1. A Understanding the problem
    2. B Devising a plan
    3. C Looking back
    4. D Carrying out the plan
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    Correct answer: (C) Looking back

    Polya's fourth step, looking back, includes checking the result, trying another route and seeing whether the method can be used for other problems. It is often skipped, though it deepens learning.

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11. Q.211

    Which of the following is an example of meaningful drill and practice in mathematics, as opposed to mechanical drill?

    1. A Writing the table of 7 ten times in the notebook every day so that the table is fixed firmly in memory
    2. B Rolling two dice, multiplying the numbers, covering the product on a grid and discussing which products come up most
    3. C Repeating the addition facts aloud in chorus for twenty minutes every morning until every child can recite them all
    4. D Copying solved examples from the board and then doing twenty similar sums in which only the numbers are changed
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    Correct answer: (B) Rolling two dice, multiplying the numbers, covering the product on a grid and discussing which products come up most

    Practice is meaningful when it is embedded in a purposeful activity, involves thinking (which products are more likely) and comes after understanding. Copying and chorus repetition are mechanical and do not build understanding.

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12. Q.212

    For the question '0.5 + 0.3 = ?', a teacher writes the wrong options 0.08, 8 and 0.53, each matching an error children commonly make. The main advantage of building the options this way is that:

    1. A The wrong option chosen points to a specific misconception
    2. B The question becomes easier to guess, so weaker children also score some marks
    3. C Children learn to avoid these errors simply by reading the wrong options
    4. D The teacher needs no follow-up, as the test itself corrects the errors
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    Correct answer: (A) The wrong option chosen points to a specific misconception

    When the wrong options are built from known errors (0.08 treats tenths + tenths as hundredths, 8 ignores the decimal point, 0.53 writes the digits side by side), each wrong choice tells the teacher what the child is thinking, so remedial teaching can be targeted. Random wrong options only tell the teacher that the answer was wrong.

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13. Q.213

    A Class 7 student writes (−3) + (−4) = 7, explaining, 'Two minuses make a plus.' The most suitable response of the teacher is to:

    1. A Tell him the slogan applies only to multiplication and ask him to memorise it
    2. B Give him a chart of sign rules for all four operations to memorise
    3. C Use debts of Rs 3 and Rs 4, or moves on a number line, to show that the sum is −7
    4. D Accept the answer, as the rule of signs is the same for every operation
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    Correct answer: (C) Use debts of Rs 3 and Rs 4, or moves on a number line, to show that the sum is −7

    Two debts together make a bigger debt, and on a number line, starting at −3 and moving 4 steps to the left reaches −7. The error comes from stretching a memorised slogan, so the remedy is meaning, not another rule to learn.

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14. Q.214

    A teacher builds a cuboid from unit cubes: each layer is 4 cubes long and 3 cubes wide, and there are 5 layers. She asks students to find the number of cubes without counting them one by one. The main idea being built is that:

    1. A Volume is the total length of all twelve edges of the cuboid, measured in unit lengths
    2. B Volume equals the area of the largest face of the cuboid, here 4 × 5 = 20 squares
    3. C Cubes must always be counted one by one to be sure of the total, as a check on any formula
    4. D Volume = cubes in one layer (4 × 3) × number of layers (5) = 60, leading to l × b × h
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    Correct answer: (D) Volume = cubes in one layer (4 × 3) × number of layers (5) = 60, leading to l × b × h

    Seeing the cuboid as layers, each a rectangle of 4 × 3 = 12 cubes, gives 12 × 5 = 60 cubes, so the formula l × b × h grows out of the structure of the solid rather than being memorised.

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15. Q.215

    To make the formula for the volume of a cylinder meaningful in Class 8, the most suitable activity is to:

    1. A Stack identical coins into a column and discuss that volume = base area × height, as for a cuboid
    2. B Write V = πr²h on the board and give practice sums at once, so that the formula is fixed in memory early
    3. C Wrap a sheet of paper around a cylinder to find its curved surface area, and call that its volume
    4. D Measure only the heights of several cylindrical objects and arrange them in order
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    Correct answer: (A) Stack identical coins into a column and discuss that volume = base area × height, as for a cuboid

    A stack of coins shows a cylinder as many equal circular layers, so its volume is the area of one layer times the height, the same idea as for a cuboid. Wrapping paper around it shows the curved surface area, which is a different quantity.

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16. Q.216

    NIPUN Bharat, the national mission for foundational literacy and numeracy launched by the Ministry of Education, stands for:

    1. A National Institute for Primary Understanding of Numbers
    2. B New Initiative for Primary Upliftment of Numeracy and Literacy in Government Schools
    3. C National Initiative for Primary Universal Numeracy and Reading Comprehension Skills
    4. D National Initiative for Proficiency in Reading with Understanding and Numeracy
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    Correct answer: (D) National Initiative for Proficiency in Reading with Understanding and Numeracy

    NIPUN stands for National Initiative for Proficiency in Reading with Understanding and Numeracy. It is the mission set up to achieve the foundational literacy and numeracy goal of NEP 2020.

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17. Q.217

    Each student in a Class 7 group draws a triangle with angles 50°, 60° and 70°. On comparing, they find triangles of the same shape but different sizes. This activity helps students see that:

    1. A The angle sum of a triangle depends on how big it is
    2. B Their protractors must be giving wrong readings
    3. C Triangles with equal angles always have equal sides
    4. D Equal angles alone do not make triangles congruent
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    Correct answer: (D) Equal angles alone do not make triangles congruent

    Fixing the three angles fixes the shape but not the size, so AAA is not a condition for congruence; by contrast, triangles built from the same three side lengths (SSS) all coincide. The students' own triangles make this visible.

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18. Q.218

    Asked to write the total cost of 3 pens at Rs x each and one notebook at Rs 20, a student writes 3x + 20, then rubs it out, saying, 'This is not an answer; an answer must be one number.' Her difficulty is that she:

    1. A Does not yet accept that an expression like 3x + 20 can be a complete answer
    2. B Does not know how to multiply 3 by x when the value of x is not given
    3. C Has added the cost of the notebook wrongly to the total cost of the three pens
    4. D Should have combined the two terms so as to write 23x as the single, final answer
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    Correct answer: (A) Does not yet accept that an expression like 3x + 20 can be a complete answer

    In arithmetic every answer is a single number, so students often feel an expression is unfinished and may even combine unlike terms into 23x. The teacher should show that 3x + 20 is a complete answer that gives the total cost for any price x.

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19. Q.219

    Which of the following classroom practices is most likely to reduce mathematics anxiety among students?

    1. A Announcing marks aloud in class so that students feel motivated to compete with one another for the top rank
    2. B Encouraging multiple methods, valuing effort and reasoning, and removing time pressure from routine work
    3. C Insisting that there is only one correct way to solve every problem, so that students are never confused
    4. D Frequent surprise tests with strict time limits to keep students alert and well prepared
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    Correct answer: (B) Encouraging multiple methods, valuing effort and reasoning, and removing time pressure from routine work

    Mathematics anxiety is fed by time pressure, fear of public failure and rigid 'one right way' teaching. Accepting different strategies and valuing reasoning builds confidence and reduces anxiety.

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20. Q.220

    A Class 6 student says that -3 is greater than -1 because 3 is greater than 1. The most suitable teaching-learning material to address this is:

    1. A A tangram set for making figures from seven geometric pieces
    2. B A geoboard with rubber bands for drawing shapes
    3. C A number line with zero in the middle, or a thermometer
    4. D Fraction strips showing halves, thirds, quarters and fifths
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    Correct answer: (C) A number line with zero in the middle, or a thermometer

    The number line shows that numbers to the left are smaller, so -3 lies to the left of -1 and is smaller. A thermometer offers a real-life context for the same idea.

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21. Q.221

    In a long worksheet, Child A writes 7 × 8 = 54 once but gets every other fact right. Child B writes 0.3 × 0.2 = 0.6, 0.4 × 0.2 = 0.8 and 0.5 × 0.3 = 1.5. Which conclusion is most appropriate?

    1. A Both children made errors in multiplication, so both need the same remedial plan
    2. B A's error looks like a slip; B's pattern shows a misconception
    3. C B is merely careless with decimal points and only needs to slow down
    4. D A has the deeper problem, because errors in basic facts are more serious
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    Correct answer: (B) A's error looks like a slip; B's pattern shows a misconception

    B multiplies the digits and always keeps one decimal place (the answers should be 0.06, 0.08 and 0.15), a systematic error that will recur until tenths × tenths = hundredths is understood. A single error among many correct facts is more likely a slip, so the two need different responses.

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22. Q.222

    Which of the following is NOT among the mathematical processes that NCF 2005 asks school mathematics to develop?

    1. A Memorisation of formulae without understanding
    2. B Visualisation and representation
    3. C Estimation and approximation
    4. D Reasoning, proof and mathematical communication
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    Correct answer: (A) Memorisation of formulae without understanding

    NCF 2005 lists processes such as problem solving, heuristics, estimation and approximation, optimisation, use of patterns, visualisation, representation, reasoning and proof, making connections and communication. Rote memorisation is what it argues against.

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23. Q.223

    The main purpose of a diagnostic test in mathematics is to:

    1. A Rank the students in the class so that the toppers can be rewarded
    2. B Decide each student's promotion to the next class on the basis of total marks obtained
    3. C Find the specific areas and causes of a student's difficulty so as to plan remedial teaching
    4. D Compare the school's average score with that of other schools in the district and state to fix its rank
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    Correct answer: (C) Find the specific areas and causes of a student's difficulty so as to plan remedial teaching

    A diagnostic test pinpoints exactly where and why a learner is going wrong (for example, regrouping across zero). It is followed by remedial teaching, not by ranking or grading.

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24. Q.224

    A Class 7 student writes 2³ = 6 and 5² = 10. This error shows that he:

    1. A Does not know the multiplication tables of 2 and 5, so the products come out wrong
    2. B Has swapped the base and the exponent, reading 2³ as 3² and 5² as 2⁵
    3. C Multiplies the base by the exponent, not the base by itself that many times
    4. D Has understood powers well but made a copying slip while writing down both answers
    Show answer

    Correct answer: (C) Multiplies the base by the exponent, not the base by itself that many times

    2³ means 2 × 2 × 2 = 8, not 2 × 3 = 6. Swapping base and exponent would give 3² = 9 and 2⁵ = 32, which does not match; writing powers in expanded form is the remedy.

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25. Q.225

    Which of the following is the correct description of remedial teaching in mathematics?

    1. A Teaching aimed at the specific misconception found by diagnosis, often with concrete materials and a new approach
    2. B Repeating the same lesson in exactly the same way for the whole class, but at a slower pace and with more drill
    3. C Giving extra homework with the same type of questions every day until the error stops appearing in notebooks
    4. D Punishing students for not learning the first time so that they pay more attention
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    Correct answer: (A) Teaching aimed at the specific misconception found by diagnosis, often with concrete materials and a new approach

    Remedial teaching follows diagnosis and attacks the root cause of the difficulty with a different, usually more concrete, approach. Simply repeating the lesson or adding homework does not remove the misconception.

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26. Q.226

    A Class 8 student writes (a + b)² = a² + b². Which activity best helps her see why this is wrong?

    1. A Ask her to recite (a + b)² = a² + 2ab + b² aloud again and again until she can remember it firmly
    2. B Build a square of side a + b from paper pieces: it contains a², b² and two rectangles of area ab
    3. C Give her ten more expansions of the same kind to practise at home
    4. D Tell her the result she wrote is true only when a and b are equal, so she must check that first
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    Correct answer: (B) Build a square of side a + b from paper pieces: it contains a², b² and two rectangles of area ab

    The area model shows the square of side a + b split into a², b² and two ab rectangles, so (a + b)² = a² + 2ab + b². A numerical check agrees: (2 + 3)² = 25, but 2² + 3² = 13.

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27. Q.227

    Which of the following is the most suitable first activity for introducing data handling in Class 3?

    1. A Calculating the mean of twenty numbers collected from the class register
    2. B Drawing a pie chart with a protractor to show the different ways children travel to school daily
    3. C Collecting favourite fruits of the class, recording them with tally marks and drawing a pictograph
    4. D Reading a double bar graph from the newspaper and answering questions on the trends it shows
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    Correct answer: (C) Collecting favourite fruits of the class, recording them with tally marks and drawing a pictograph

    Data handling at primary level begins with collecting real data from the children's own lives, organising it with tally marks and representing it with pictographs, before bar graphs and later measures like the mean.

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28. Q.228

    A shirt costing Rs 500 has its price raised by 10%, and then the new price is reduced by 10%. Most students say the final price is Rs 500. The best response of the teacher is to:

    1. A Tell them the answer is Rs 495 and move on to the next question
    2. B Agree with them, since a rise of 10% and a fall of 10% always cancel each other out exactly
    3. C Have them work out 500 → 550 → 495 and discuss why the second 10% is of a larger amount
    4. D Give them a rule that two successive changes of the same percentage always lower the price
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    Correct answer: (C) Have them work out 500 → 550 → 495 and discuss why the second 10% is of a larger amount

    Each percentage is taken of a different base: 10% of 500 is 50, but 10% of 550 is 55, so the final price is 495. Working it through shows that a percentage has meaning only relative to its base.

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29. Q.229

    A Class 8 teacher asks students to show how the cost of tickets at Rs 20 each depends on the number of tickets: in words, as a table, as a graph and as an equation (C = 20n). The main purpose is to:

    1. A Give students more written work to complete at home on the same small topic
    2. B Check whether students can draw neat graphs with correctly labelled axes
    3. C Help students move between representations showing the same relationship in different ways
    4. D Show that an equation is the only proper and complete way to express a relationship in mathematics
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    Correct answer: (C) Help students move between representations showing the same relationship in different ways

    Words, tables, graphs and equations each bring out something different about the same relationship (the table shows values, the graph the steady rise, the equation the rule). NCF 2005 lists representation among the processes school mathematics should develop, and translating between forms deepens understanding.

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30. Q.230

    Before giving the formula 2(lb + bh + hl), a teacher has students open out an empty cardboard box and find the area of each face. The main purpose is to show that:

    1. A The surface area and volume of a box are the same thing, measured in different units
    2. B Every box becomes a cube when it is opened out flat
    3. C The formula works only if the cardboard is cut neatly along every edge
    4. D Surface area is the total area of the faces, which form three pairs of equal rectangles
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    Correct answer: (D) Surface area is the total area of the faces, which form three pairs of equal rectangles

    Opening the box shows six rectangular faces in three equal pairs (l × b, b × h, h × l), so the formula is simply their total. This keeps surface area, a measure of covering, distinct from volume, a measure of filling.

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31. Q.231

    Which of the following tasks would best challenge the misconception that 'division always makes a number smaller'?

    1. A Dividing 24 by 6 by sharing 24 counters equally among six children
    2. B Dividing 100 by 10 on a number line by making backward jumps of ten each
    3. C Dividing 36 by 4 using repeated subtraction of 4 until nothing is left over
    4. D Asking how many half-litre bottles 6 litres can fill (6 divided by 1/2)
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    Correct answer: (D) Asking how many half-litre bottles 6 litres can fill (6 divided by 1/2)

    6 divided by 1/2 equals 12, which is larger than 6, so the child sees that dividing by a number less than 1 gives a bigger result. The other examples all divide by whole numbers and reinforce the misconception.

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32. Q.232

    A Class 7 student simplifies a + a + a as a³. Which response of the teacher best addresses this?

    1. A Tell her to memorise the rule 'add the letters, multiply the numbers' for such sums
    2. B Give her twenty more expressions of the same kind to simplify
    3. C Compare a + a + a and a × a × a for a = 2 (6 and 8), and link a + a + a to 3a
    4. D Accept the answer, since the letter a appears three times in both, so they are equal
    Show answer

    Correct answer: (C) Compare a + a + a and a × a × a for a = 2 (6 and 8), and link a + a + a to 3a

    Repeated addition of a gives 3a, while repeated multiplication gives a³; substituting a number shows they differ (2 + 2 + 2 = 6 but 2 × 2 × 2 = 8). A memorised rule or more practice does not touch the confusion between the two operations.

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33. Q.233

    Using an abacus, a child adds 1 to 999. Each time a rod gets ten beads, she removes them and puts one bead on the next rod to the left, until 1000 is shown. This mainly helps her understand that:

    1. A Ten in any place is exchanged for one in the next place to the left
    2. B Zero has no value of its own, so it can simply be left out of a number
    3. C A larger number always needs more beads than a smaller number on the abacus
    4. D Each rod of an abacus can hold any number of beads at a time
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    Correct answer: (A) Ten in any place is exchanged for one in the next place to the left

    The chain of exchanges (10 ones for 1 ten, 10 tens for 1 hundred, 10 hundreds for 1 thousand) shows the base-ten rule that governs every place. It also shows that 1000 uses fewer beads than 999, so value comes from position, not from the number of beads.

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34. Q.234

    A Class 8 student writes 2⁻³ = −8. Which reasoning best helps her correct this?

    1. A A negative exponent makes the value negative, so −8 is correct and needs no change
    2. B 2⁻³ means 2 × (−3), so the answer should be −6
    3. C Negative exponents have no meaning, so the question itself is wrongly set
    4. D 2² ÷ 2⁵ = (2 × 2) ÷ (2 × 2 × 2 × 2 × 2) = 1/2³, and the law gives 2⁻³, so 2⁻³ = 1/8
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    Correct answer: (D) 2² ÷ 2⁵ = (2 × 2) ÷ (2 × 2 × 2 × 2 × 2) = 1/2³, and the law gives 2⁻³, so 2⁻³ = 1/8

    Dividing powers by cancelling factors gives 1/2³ = 1/8, and the law aᵐ ÷ aⁿ = aᵐ⁻ⁿ gives 2⁻³, so the two must be equal. A negative exponent indicates a reciprocal, not a negative number.

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35. Q.235

    Told to 'subtract 3 from 8', a Class 2 child writes 3 - 8. This error mainly arises because:

    1. A The child does not yet know the subtraction fact 8 - 3 = 5 and so cannot tell which number comes first
    2. B The word order in 'subtract 3 from 8' differs from the order in which the symbols are written
    3. C The child has a visual-perceptual disability that makes him see and write numbers in reverse order
    4. D The child is careless and needs more speed practice with subtraction facts
    Show answer

    Correct answer: (B) The word order in 'subtract 3 from 8' differs from the order in which the symbols are written

    The spoken instruction names 3 first, but the number sentence starts with 8; translating between everyday language and mathematical symbols is a skill that has to be taught. Nothing in the error suggests the child lacks the fact itself.

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36. Q.236

    Ravi gets most 'how many more' word problems wrong. To find out why, the most informative step for the teacher is to:

    1. A Count how many such problems he got wrong this month and record the number in a register
    2. B Compare his marks in word problems with the class average for the term
    3. C Ask his parents whether he is careless or inattentive while doing homework at home
    4. D Ask Ravi to solve a few aloud, explaining each step, while the teacher listens
    Show answer

    Correct answer: (D) Ask Ravi to solve a few aloud, explaining each step, while the teacher listens

    A one-to-one interview in which the child thinks aloud reveals how he reads the problem and chooses an operation, which written answers cannot show. Counting errors or comparing marks only confirms that a problem exists.

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37. Q.237

    According to NCF 2005, the use of mathematical games, puzzles and stories at the primary stage mainly helps children to:

    1. A Finish the syllabus faster than with regular chalk-and-talk teaching in class
    2. B Prepare for competitive examinations by learning short-cut tricks and speed
    3. C Develop a positive attitude and connect mathematics with everyday thinking
    4. D Do away with the need for any assessment of their learning
    Show answer

    Correct answer: (C) Develop a positive attitude and connect mathematics with everyday thinking

    NCF 2005 says games, puzzles and stories help develop a positive attitude and make connections between mathematics and everyday thinking. They are about engagement and meaning, not speed or exam preparation.

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38. Q.238

    After two weeks of remedial work on comparing decimals, Sana correctly answers the same five questions she had earlier got wrong. Before concluding that her misconception is gone, the teacher should:

    1. A Declare the remedial work complete, since all five answers are now correct
    2. B Give her the same five questions every day for a week to make the learning firm
    3. C Give new items in another form, such as placing 0.4 and 0.38 on a number line
    4. D Move her to the next chapter and give her a certificate to boost her confidence
    Show answer

    Correct answer: (C) Give new items in another form, such as placing 0.4 and 0.38 on a number line

    Correct answers to repeated questions may be remembered rather than understood. New items in a different form, which a child holding the misconception would get wrong (0.38 looks bigger than 0.4), show whether understanding has really changed.

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39. Q.239

    Which teaching-learning material is most suitable for showing that adding a negative integer means moving in the opposite direction, as in 5 + (-3) = 2?

    1. A Number line
    2. B Tangram
    3. C Fraction strips
    4. D Geoboard
    Show answer

    Correct answer: (A) Number line

    On a number line, adding a positive number is a move to the right and adding a negative number is a move to the left, which makes integer operations visible. The other materials deal with shapes or fractions.

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40. Q.240

    Which of the following is most likely a sign of mathematics anxiety rather than a gap in knowledge?

    1. A A child who solves sums well when relaxed goes blank in class tests
    2. B A child cannot yet count beyond 20 even with objects in front of her
    3. C A child makes exactly the same regrouping error in every subtraction sum
    4. D A child often writes 6 as 9 when copying numbers from the board
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    Correct answer: (A) A child who solves sums well when relaxed goes blank in class tests

    When a child can do the work in a relaxed setting but not under test pressure, the problem is anxiety interfering with thinking, not missing knowledge. A consistent regrouping error points instead to a misconception, and counting only to 20 to a learning gap.

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41. Q.241

    Match each situation with the relationship between its two quantities.

    P. Litres of milk bought and their cost, at a fixed price per litre

    Q. Speed of a bus and the time it takes for a fixed journey

    R. A child's age and her height

    i. Neither direct nor inverse proportion

    ii. Inverse proportion

    iii. Direct proportion

    1. A P-ii, Q-iii, R-i
    2. B P-iii, Q-i, R-ii
    3. C P-i, Q-ii, R-iii
    4. D P-iii, Q-ii, R-i
    Show answer

    Correct answer: (D) P-iii, Q-ii, R-i

    At a fixed price, cost ÷ litres stays constant (direct). For a fixed distance, speed × time stays constant (inverse). Height increases with age but not in a fixed ratio, since a 20-year-old is not twice as tall as a 10-year-old (neither).

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42. Q.242

    Arrange these steps in the correct order for helping a child with a persistent difficulty in division:

    (i) Remedial teaching using a different approach

    (ii) Re-assessing to check progress

    (iii) Identifying the child through regular class work

    (iv) Diagnosing the specific cause of the difficulty

    1. A (iv), (iii), (i), (ii)
    2. B (iii), (i), (iv), (ii)
    3. C (iii), (iv), (i), (ii)
    4. D (i), (iii), (iv), (ii)
    Show answer

    Correct answer: (C) (iii), (iv), (i), (ii)

    The teacher first notices who is struggling, then diagnoses exactly where and why, then plans remedial teaching for that cause, and finally re-assesses to see whether the difficulty is resolved. Remedial teaching before diagnosis is guesswork.

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43. Q.243

    Which question best assesses a Class 4 child's understanding of fractions rather than recall?

    1. A In the fraction 3/4, which number is the numerator and which is the denominator?
    2. B Write 'three-fourths' in figures, and write 3/4 in words.
    3. C Read aloud the fractions 2/5, 3/8 and 7/10 written on the board.
    4. D Is 3/4 of a roti more or less than half of it? Draw to explain.
    Show answer

    Correct answer: (D) Is 3/4 of a roti more or less than half of it? Draw to explain.

    Comparing 3/4 with 1/2 and justifying it with a drawing requires the child to reason about the size of fractions. The other questions test only naming and notation, which a child can answer without understanding.

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44. Q.244

    Mathematics is often described as the study of patterns and relationships. Which classroom task best reflects this view?

    1. A Memorising the squares of the numbers from 1 to 20 for quick recall in tests
    2. B Copying the steps of long division from the board and then practising ten such sums at home
    3. C Writing the textbook definition of 'pattern' five times so that it is remembered word for word
    4. D Investigating whether the digits of every multiple of 9 add up to a multiple of 9, and why
    Show answer

    Correct answer: (D) Investigating whether the digits of every multiple of 9 add up to a multiple of 9, and why

    Seeing mathematics as the study of patterns means noticing regularities, asking why they hold and testing them. Memorising squares or copying steps involves no search for a pattern or relationship.

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45. Q.245

    A student draws all the diagonals from one vertex of a pentagon, gets 3 triangles and concludes that its angles add up to 540°. She then predicts the sums for a hexagon and a decagon. This activity mainly develops:

    1. A Skill in measuring angles accurately with a protractor, which must be used to check each sum
    2. B Generalising from structure: an n-gon splits into n − 2 triangles, so its angle sum is (n − 2) × 180°
    3. C Memory of the angle sum of each polygon separately, as given in a table at the end of the textbook chapter
    4. D Speed in multiplying numbers by 180
    Show answer

    Correct answer: (B) Generalising from structure: an n-gon splits into n − 2 triangles, so its angle sum is (n − 2) × 180°

    The reasoning (3 triangles × 180° = 540°) explains the result and extends to any polygon: a hexagon gives 4 × 180° = 720° and a decagon 8 × 180° = 1440°. The rule is built from a reason, not memorised case by case.

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46. Q.246

    A child cannot solve a two-step word problem alone but solves it when the teacher asks guiding questions such as 'What do we need to find first?'. In Vygotsky's terms, the teacher is working in the child's:

    1. A Zone of proximal development, through scaffolding
    2. B Concrete operational stage, through hands-on tasks
    3. C Zone of actual development, through self-correction
    4. D Iconic mode of representation, through pictures
    Show answer

    Correct answer: (A) Zone of proximal development, through scaffolding

    The zone of proximal development is the gap between what a child can do alone and what the child can do with guidance; the teacher's guiding questions are scaffolding within that zone.

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47. Q.247

    A student says 2.5 × 10 = 2.50 because 'to multiply by 10 we put a zero at the end'. The best response of the teacher is to:

    1. A Accept the answer, since adding a zero is the rule for multiplying by 10
    2. B Give her a new rule to memorise, 'move the point one place right', without reasons
    3. C Show on a place-value chart that each digit becomes ten times as large
    4. D Mark it wrong and give her ten more such sums so that she practises
    Show answer

    Correct answer: (C) Show on a place-value chart that each digit becomes ten times as large

    The 'add a zero' shortcut works for whole numbers only because each digit moves one place left; 2.50 equals 2.5, so nothing has changed. Seeing 2 ones become 2 tens and 5 tenths become 5 ones (25) gives a reason that works for all numbers.

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48. Q.248

    A 4-year-old recites the numbers from 1 to 20 fluently, but when asked to give 6 blocks she hands over a random handful. What does this show?

    1. A She has fully understood numbers up to 20 and is only being playful when handing over the blocks
    2. B Reciting number names by rote is not understanding number; counting must be linked to quantity
    3. C She has a memory problem that needs to be assessed by a specialist before any teaching continues
    4. D She should now be taught to recite numbers up to 100, since she has fully mastered 1 to 20
    Show answer

    Correct answer: (B) Reciting number names by rote is not understanding number; counting must be linked to quantity

    NCF 2005 cautions against rote learning of the number sequence at the pre-primary stage and asks that children link counting with quantity using small sets. The child knows the sequence but not yet how it tells 'how many'.

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49. Q.249

    A student reasons: 'All multiples of 10 end in 0. 370 is a multiple of 10. So 370 ends in 0.' This is an example of:

    1. A Deductive reasoning, from a general rule to a particular case
    2. B Inductive reasoning, from particular cases towards a general rule
    3. C Reasoning by analogy
    4. D Trial and error
    Show answer

    Correct answer: (A) Deductive reasoning, from a general rule to a particular case

    Applying an accepted general statement to a particular case to reach a certain conclusion is deduction. Induction runs the other way, from several cases to a general rule.

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50. Q.250

    Students fold a sheet of paper in half again and again and record the number of layers: 2, 4, 8, 16, ... The activity mainly helps them to:

    1. A See that the number of layers increases by 2 with each fold, just as in the multiplication table of 2
    2. B Link repeated doubling with powers of 2 and see how fast they grow (ten folds: 2¹⁰ = 1,024 layers)
    3. C Learn the multiplication table of 2 up to 2 × 10 by reading out the number of layers after each fold
    4. D Practise folding paper neatly into equal halves, a skill needed later for symmetry work
    Show answer

    Correct answer: (B) Link repeated doubling with powers of 2 and see how fast they grow (ten folds: 2¹⁰ = 1,024 layers)

    After n folds there are 2ⁿ layers, because each fold doubles the layers, so the growth is multiplicative, not additive (2, 4, 8, not 2, 4, 6). The activity gives powers a concrete meaning.

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