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.51
The heuristic method of teaching mathematics, associated with H. E. Armstrong, places the student in the position of:
- A A passive listener who notes down the teacher's solution and later revises it at home for tests
- B An examiner who checks others' work against the answer key
- C A copier of the textbook method who follows each solved example step by step in the notebook
- D A discoverer who investigates and finds the result on his own, with the teacher as guide
Show answer
Correct answer: (D) A discoverer who investigates and finds the result on his own, with the teacher as guide
Heuristic means 'I find'. In this method the teacher poses problems and guides, while the student discovers results through self-effort, developing self-reliance and a scientific attitude.
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Q.52
A student claims 0.25 is greater than 0.7 because 25 is greater than 7. The best remedial step is to:
- A Have the student place both on a number line marked in tenths and hundredths, or compare 0.25 and 0.70 on a hundred-grid
- B Tell the student to always pick the decimal with more digits after the point, since more digits mean more parts
- C Give a worksheet of fifty similar comparison questions, marking wrong answers in red until the rule becomes automatic
- D Ask the student to memorise the rule that shorter decimals are bigger and recite it before each test
Show answer
Correct answer: (A) Have the student place both on a number line marked in tenths and hundredths, or compare 0.25 and 0.70 on a hundred-grid
The error comes from ignoring place value in decimals. A number line or hundred-grid lets the child see that 0.7 = 0.70 is larger than 0.25; a memorised rule such as 'shorter is bigger' would itself be a new misconception.
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Q.53
Which of the following is NOT a good way to develop geometric reasoning in Classes 6 to 8?
- A Asking 'Will this always be true? Why?' after an activity
- B Letting students form conjectures from paper folding and then explain them
- C Asking students to explain the reason behind each step of a construction
- D Having students memorise theorems word for word, along with their figures
Show answer
Correct answer: (D) Having students memorise theorems word for word, along with their figures
Reasoning grows when students conjecture, question and explain; memorising statements and figures develops recall, not reasoning. The other three practices all ask students for reasons.
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Q.54
Which of the following is NOT one of the problems in school mathematics education listed in NCF 2005?
- A A sense of fear and failure regarding mathematics among most children
- B Mechanical, repetitive problems and evaluation with too much stress on computation
- C Teachers who lack confidence, preparation and support
- D Too much attention to spatial thinking and geometry in the curriculum
Show answer
Correct answer: (D) Too much attention to spatial thinking and geometry in the curriculum
NCF 2005 says the reverse: areas of mathematics such as spatial thinking are not developed enough in the curriculum. Fear and failure, mechanical and repetitive evaluation with too much emphasis on computation, and teachers who lack confidence, preparation and support are all on its list, which draws on the NCERT Position Paper on Teaching of Mathematics.
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Q.55
To teach the concept of one-fourth, a teacher uses a folded paper, a cut chapati, a measuring cup and a set of four marbles. This illustrates which principle of Zoltan Dienes?
- A Dynamic principle (play, structure, then practice)
- B Constructivity principle (building before analysis)
- C Mathematical variability principle
- D Perceptual variability (multiple embodiment) principle
Show answer
Correct answer: (D) Perceptual variability (multiple embodiment) principle
Perceptual variability means presenting the same concept through many different physical materials so that the child abstracts the common mathematical idea rather than the features of one material.
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Q.56
A child finds 48 + 36 by thinking '48 + 30 = 78, then 78 + 6 = 84' without writing anything. This is an example of:
- A A rote algorithm learnt by heart from the textbook
- B An error in place value while adding the tens
- C Deductive reasoning from a general rule of addition
- D Mental mathematics using decomposition of numbers
Show answer
Correct answer: (D) Mental mathematics using decomposition of numbers
Breaking 36 into 30 and 6 and adding in steps is a mental computation strategy based on understanding of place value. NCF 2005 values such mental mathematics and flexible strategies.
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Q.57
With two-colour counters (red = −1, yellow = +1; a red-yellow pair = 0), a teacher models 2 − (−3). She first puts out 2 yellow counters. What should she do next?
- A Add 3 zero pairs, then take away 3 red counters, leaving 5 yellow counters
- B Add 3 red counters, leaving 2 yellow and 3 red, so that the answer comes to −1
- C Take away the 2 yellow counters first, and then put down 3 red counters in their place
- D Stop here, since 3 red counters cannot be taken away from a set of yellow ones
Show answer
Correct answer: (A) Add 3 zero pairs, then take away 3 red counters, leaving 5 yellow counters
Adding zero pairs does not change the value (still 2) but supplies red counters to remove; taking away 3 reds leaves +5, so 2 − (−3) = 5 = 2 + 3. Adding 3 reds would model 2 + (−3), not subtraction.
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Q.58
In a Class 1 classroom, children first describe 'putting together' and 'taking away' in their home language, and only later meet the words 'addition' and 'subtraction' and the signs + and -. The main reason for this sequence is that:
- A Home language is needed only for children who are weak in mathematics and cannot follow the textbook language
- B Formal terms and symbols become meaningful when attached to ideas children already express in familiar language
- C Formal mathematical terms are not important at the primary stage and can be skipped until Class 6
- D It reduces the time needed to complete the textbook, since children already know the words
Show answer
Correct answer: (B) Formal terms and symbols become meaningful when attached to ideas children already express in familiar language
Children build meaning through the language they already use; symbols placed on top of that understanding make sense, while symbols given first are often memorised without meaning. The home language is a resource for all children, not only weak learners.
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Q.59
According to NCF 2005, the role of the mathematics textbook is best described as:
- A The complete curriculum, which must be covered page by page with every exercise done in the given order
- B The only valid source of exercises for assessment, so all test questions must come only from it
- C One of several resources, to be used flexibly with activities, local contexts and other materials
- D A reference book meant mainly for the teacher, from which children copy notes
Show answer
Correct answer: (C) One of several resources, to be used flexibly with activities, local contexts and other materials
NCF 2005 treats the textbook as a tool and not as the syllabus itself; teachers are expected to go beyond it using activities, local context and other learning materials.
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Q.60
To introduce the mean, a teacher has five students build towers of 2, 8, 3, 4 and 3 cubes, then move cubes between towers until all are the same height. This activity shows that the mean is:
- A The height that occurs most often among the towers: 3 cubes
- B The difference between the tallest and the shortest towers: 8 − 2 = 6 cubes
- C The height of the tallest tower: 8 cubes
- D The height each tower gets when all the cubes are shared out equally: 4 cubes
Show answer
Correct answer: (D) The height each tower gets when all the cubes are shared out equally: 4 cubes
Levelling the towers shares the total (20 cubes) equally among 5 towers, giving 4 each, which is exactly what 'add and divide' computes. The other options describe the mode, the range and the maximum.
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Q.61
A Class 4 teacher asks children to record daily temperature for a week during an EVS lesson and then draw a bar graph in the mathematics period. This is an example of:
- A Drill and practice of bar-graph drawing skills
- B Correlation of mathematics with other subjects
- C Summative assessment of the data handling unit
- D Deductive teaching, from general rule to example
Show answer
Correct answer: (B) Correlation of mathematics with other subjects
Linking data handling in mathematics with weather observation in EVS is correlation of mathematics with other curricular areas, which makes mathematics meaningful and connected.
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Q.62
Children make the bead pattern red, blue, blue, red, blue, blue, ... and then show the same pattern as clap, stamp, stamp, clap, stamp, stamp, ... This activity mainly helps them to:
- A Learn the names of colours and the actions of clapping and stamping
- B See the pattern's structure (ABB) apart from the objects, an early step to algebra
- C Develop their motor skills through clapping and stamping in rhythm
- D Memorise this particular sequence of red and blue beads so they can copy it later
Show answer
Correct answer: (B) See the pattern's structure (ABB) apart from the objects, an early step to algebra
Translating a pattern into another form shows that the child sees its repeating unit and structure, not just the particular beads. Describing many such patterns as 'ABB' is a first step towards generalisation and symbolic thinking.
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Q.63
A student believes that two rectangles with the same perimeter must have the same area. The most effective activity to address this is:
- A Memorising the formulae for area and perimeter of a rectangle and practising them until they can be recalled instantly
- B Solving twenty numerical problems on perimeter, each followed by a matching problem on area
- C Watching the teacher derive the area formula on the blackboard and copying each step of the derivation into notebooks
- D Making different rectangles from one fixed loop of string on a geoboard or squared paper and counting squares inside
Show answer
Correct answer: (D) Making different rectangles from one fixed loop of string on a geoboard or squared paper and counting squares inside
Fixing the perimeter with a loop and comparing areas by counting squares lets the student discover that equal perimeter does not mean equal area. Formula memorisation does not address the conceptual confusion.
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Q.64
Consider these statements about integers:
1. Every negative integer is less than every positive integer.
2. The sum of two negative integers is always negative.
3. The product of two negative integers is always negative.
Which of these are correct?
- A 1 and 2 only
- B 1 and 3 only
- C 2 and 3 only
- D 1, 2 and 3
Show answer
Correct answer: (A) 1 and 2 only
Negative integers lie to the left of 0 and positive ones to the right, so statement 1 holds; adding two debts gives a bigger debt, so statement 2 holds. Statement 3 is false: (−2) × (−3) = 6, which is positive.
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Q.65
In Class 7, writing the distance from the Earth to the Sun as about 1.5 × 10⁸ km mainly helps students to:
- A Avoid learning place value for large numbers, since powers of 10 replace it
- B Find the exact distance without any approximation, to the nearest kilometre
- C Memorise the distances of all the planets from the Sun in a single standard form
- D Read, write and compare very large numbers compactly using powers of 10
Show answer
Correct answer: (D) Read, write and compare very large numbers compactly using powers of 10
Standard form shows the size of a number at a glance through the power of 10; 1.5 × 10⁸ km is 150,000,000 km. It rests on place value rather than replacing it, and the value given is an approximation.
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Q.66
A Class 1 teacher uses snakes and ladders, dice games and number-card games. Which of the following is NOT a valid reason for using such games?
- A Children practise counting on from any number in a meaningful context, many times over
- B Games remove the need for the teacher to plan or to discuss the mathematics afterwards
- C Children engage with numbers without fear of failure or of being marked wrong
- D Children talk about their moves and strategies with one another, which builds reasoning
Show answer
Correct answer: (B) Games remove the need for the teacher to plan or to discuss the mathematics afterwards
Games support counting, reasoning and a fearless attitude only when the teacher chooses them with a purpose and helps children reflect on the mathematics in them. Without planning and discussion, a game may stay just a game.
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Q.67
On a number line marked 0, 1 and 2, a Class 6 student marks 1/2 at the point labelled 1. This error shows that the student:
- A Cannot yet read the whole numbers marked on a number line
- B Has located 1/2 correctly, since 1 is halfway along the line
- C Confuses the numerator with the denominator of the fraction
- D Takes the whole segment 0 to 2 as the unit, not 0 to 1
Show answer
Correct answer: (D) Takes the whole segment 0 to 2 as the unit, not 0 to 1
On a number line the unit is the distance from 0 to 1, so 1/2 lies halfway between 0 and 1. The student has taken half of the whole line drawn, a part-whole habit carried over from shaded shapes; folding a strip that stands for 0 to 1 helps.
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Q.68
After children draw a bar graph of how they come to school, which question best develops interpretation and reasoning?
- A How many children come to school by bus, as shown in the graph?
- B Which bar in the graph is the tallest, and which one is the shortest?
- C Which colour did you use for each bar, and did you label the axes?
- D Why do so few children come by bicycle, and what could the school do?
Show answer
Correct answer: (D) Why do so few children come by bicycle, and what could the school do?
Reading off a value or finding the tallest bar checks basic graph reading. Asking for reasons and suggestions makes children connect the data to their own context, draw inferences and justify them, which is a higher-level skill.
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Q.69
Which of the following is a growing pattern rather than a repeating pattern?
- A red, blue, red, blue, ...
- B 1, 3, 5, 7, 9, ...
- C △, ○, ○, △, ○, ○, ...
- D clap, clap, stamp, clap, clap, stamp, ...
Show answer
Correct answer: (B) 1, 3, 5, 7, 9, ...
In a repeating pattern a fixed unit (the core) repeats; in a growing pattern each term changes by a rule, here adding 2. Repeating patterns usually come first in the early classes, and growing patterns lead towards generalisation and early algebra.
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Q.70
Match each set of data with the most suitable graph.
P. How a family's monthly budget is divided among food, rent, travel and savings
Q. The number of students in each of Classes 6, 7 and 8
R. Heights of 40 students grouped as 140–145 cm, 145–150 cm, and so on
i. Bar graph
ii. Histogram
iii. Pie chart
- A P-i, Q-iii, R-ii
- B P-iii, Q-i, R-ii
- C P-iii, Q-ii, R-i
- D P-ii, Q-i, R-iii
Show answer
Correct answer: (B) P-iii, Q-i, R-ii
A pie chart shows the parts of one whole; a bar graph compares separate categories; a histogram shows data grouped in continuous class intervals, so its bars touch.
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Q.71
A teacher lets Class 8 students use calculators to write 1/7, 2/7, 3/7, ... as decimals and look for patterns in the repeating digits. Which statement about this use of calculators is most appropriate?
- A It is a good use: the calculator does the divisions, so attention goes to the pattern and explaining it
- B It is a good use, because students will no longer need to understand division by hand
- C It is a poor use, because calculators should never be used at all in the upper primary classes for any topic
- D It is a poor use, because calculators cannot show the decimal form of fractions like 1/7
Show answer
Correct answer: (A) It is a good use: the calculator does the divisions, so attention goes to the pattern and explaining it
The decimals of sevenths repeat the same six digits, 142857, in rotated order (1/7 = 0.142857..., 2/7 = 0.285714...). Handing the routine division to the calculator frees students to notice and explain this; it supports understanding instead of replacing it.
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Q.72
Zoltan Dienes held that learning a mathematical concept moves through cycles: free, unstructured play with materials first, then structured activities, and then practice and application. This is his:
- A Constructivity principle
- B Dynamic principle
- C Mathematical variability principle
- D Perceptual variability principle
Show answer
Correct answer: (B) Dynamic principle
Dienes' dynamic principle describes learning as moving from preliminary (play) activity to structured activity and then to practice, with play as the starting point. The constructivity principle is about construction coming before analysis.
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Q.73
A student believes that if each side of a square is doubled, its area also doubles. Which activity will best help her?
- A Reciting the formula 'area = side × side' several times aloud
- B Finding and comparing the perimeters of the 2 cm and 4 cm squares
- C Drawing 2 cm and 4 cm squares on squared paper and counting unit squares
- D Watching the teacher work out the areas of both squares on the board step by step
Show answer
Correct answer: (C) Drawing 2 cm and 4 cm squares on squared paper and counting unit squares
Counting shows 4 and 16 unit squares, so the area becomes four times, not two times. Comparing perimeters would only show doubling and could strengthen the misconception, because perimeter does double.
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Q.74
Consider the following statements:
1. Since mathematics deals with abstract ideas, concrete experiences have no role in learning it.
2. Abstraction in mathematics means drawing out a common structure from many concrete situations, e.g. the idea 'three' from three mangoes, three children and three claps.
Which of these is/are correct?
- A Only 1
- B Only 2
- C Both 1 and 2
- D Neither 1 nor 2
Show answer
Correct answer: (B) Only 2
Abstract ideas such as number are formed by noticing what many concrete situations have in common, so concrete experience is the route to abstraction, not irrelevant to it. Statement 1 is therefore false.
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Q.75
During a class discussion, instead of saying whether an answer is right, the teacher asks, 'Do you agree with Ravi? Why or why not?' and invites students to respond to one another. This practice mainly helps to:
- A Save the teacher from having to know and check the correct answers to all the questions that come up in class
- B Build a classroom where students explain, question and justify, so reasoning, not the teacher, decides
- C End the discussion quickly once most students agree, so that the lesson can move on
- D Find out which students are not paying attention in the discussion, so that their marks can be cut for it
Show answer
Correct answer: (B) Build a classroom where students explain, question and justify, so reasoning, not the teacher, decides
When students must give reasons for agreeing or disagreeing, they listen to each other and learn that a mathematical claim is settled by argument. The teacher still guides the discussion towards correct mathematics; majority agreement is not the test.
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Q.76
A fair coin shows heads five times in a row. Most students say tails is now more likely on the sixth toss. The teacher should:
- A Agree, since tails is now 'due' after so many heads, and the results must balance out over the next few tosses
- B Help them see the coin has no memory, so tails is still 1/2, and let them test it with many trials
- C Say heads is now more likely because the coin is 'on a streak', and such streaks usually go on for a while
- D Say that probability cannot be discussed for coins, as each toss is a matter of luck
Show answer
Correct answer: (B) Help them see the coin has no memory, so tails is still 1/2, and let them test it with many trials
Each toss of a fair coin is independent of earlier tosses, so the probability of tails stays 1/2. Collecting class data on what follows a run of heads lets students test their intuition.
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Q.77
In the Herbartian approach to lesson planning, the correct order of the five formal steps is:
- A Presentation, preparation, generalisation, association (comparison), application
- B Preparation, association (comparison), presentation, application, generalisation
- C Generalisation, preparation, presentation, association (comparison), application
- D Preparation, presentation, association (comparison), generalisation, application
Show answer
Correct answer: (D) Preparation, presentation, association (comparison), generalisation, application
Herbart's steps are preparation (introduction), presentation of new material, association or comparison with known ideas, generalisation of the rule, and application. Recapitulation is often added as a sixth step.
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Q.78
NCF 2005 distinguishes between the 'narrow aim' and the 'higher aim' of school mathematics. The narrow aim refers to:
- A Preparing students to score well in competitive and entrance examinations
- B Developing useful capabilities, particularly numeracy, for daily life
- C Producing professional mathematicians and researchers for the nation
- D Completing the prescribed textbook and the syllabus within the session
Show answer
Correct answer: (B) Developing useful capabilities, particularly numeracy, for daily life
The narrow aim is to develop useful capabilities, especially number-related skills (numeracy), needed in daily life; the higher aim is to develop the child's resources to think and reason mathematically.
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Q.79
Match each mental calculation with the strategy it uses.
P. 25 × 16 = 50 × 8 = 400
Q. 99 + 47 = 100 + 47 - 1 = 146
R. 8 + 7 = 7 + 7 + 1 = 15
i. Using a near double ii. Compensation iii. Doubling and halving
- A P-ii, Q-iii, R-i
- B P-iii, Q-i, R-ii
- C P-iii, Q-ii, R-i
- D P-i, Q-ii, R-iii
Show answer
Correct answer: (C) P-iii, Q-ii, R-i
Halving one factor and doubling the other keeps the product the same; rounding 99 up to 100 and then taking away 1 is compensation; using the known double 7 + 7 is a near-double strategy.
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Q.80
A teacher lets students compute 2 x 3, 3 x 2, 4 x 5, 5 x 4 and several more pairs, and then asks them to state what they notice. Students arrive at 'order does not matter in multiplication'. The method used is:
- A Deductive method
- B Lecture method
- C Synthetic method
- D Inductive method
Show answer
Correct answer: (D) Inductive method
In the inductive method students examine many particular examples and generalise to a rule (here, the commutative property). Deduction would start with the stated rule and apply it to examples.
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Q.81
Asked to fill the blank in 8 + 4 = __ + 5, most children in a class write 12. This error reveals that they:
- A Read the equals sign as 'the answer comes next', not as a symbol of balance or equivalence
- B Do not know that 8 + 4 is 12 and are guessing the missing number
- C Cannot add three numbers together, so they stop after adding the first two numbers
- D Have understood the commutative property of addition and are applying it correctly to both sides
Show answer
Correct answer: (A) Read the equals sign as 'the answer comes next', not as a symbol of balance or equivalence
Children often see '=' as an instruction to compute, not as 'is the same as'. The correct answer is 7, and a pan balance helps children see both sides as equal quantities.
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Q.82
To teach the concept of a parallelogram, a teacher shows parallelograms of different sizes, side lengths, angles and orientations, while the property 'opposite sides parallel' stays the same in all. This applies Dienes':
- A Mathematical variability principle
- B Perceptual variability (multiple embodiment) principle
- C Dynamic principle
- D Constructivity principle
Show answer
Correct answer: (A) Mathematical variability principle
Mathematical variability means varying the irrelevant features of a concept while the essential one stays constant, so that the learner can generalise. Perceptual variability, by contrast, presents the same concept through different materials.
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Q.83
Asked to construct triangles with sides 5 cm, 6 cm, 7 cm and with sides 3 cm, 4 cm, 8 cm, students find that the second cannot be drawn. The teacher should use this to:
- A Have them investigate when three lengths make a triangle: any two sides together exceed the third
- B Tell them they must have used the compass wrongly in the second case and should carefully draw it again
- C Skip the second case, since it is not one of the textbook exercises and will not come in the test
- D Conclude that no triangle can ever have a side of 8 cm, as it is too long to draw
Show answer
Correct answer: (A) Have them investigate when three lengths make a triangle: any two sides together exceed the third
Since 3 + 4 = 7 is less than 8, the arcs never meet. Using this 'failure' as the start of an investigation lets students discover the triangle inequality themselves instead of being told it.
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Q.84
Which of the following is NOT a benefit of regular mental mathematics in the primary classes?
- A It builds number sense and flexibility with numbers
- B It removes the need for children to understand place value
- C It helps children estimate and check written answers
- D It encourages children to share and compare different strategies
Show answer
Correct answer: (B) It removes the need for children to understand place value
Mental strategies such as splitting a number into tens and ones depend on place value; they strengthen it rather than replace it. Number sense, estimation and discussion of strategies are real benefits.
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Q.85
Consider these statements about mathematics at the pre-primary stage in NCF 2005:
1. Learning should occur through play rather than through didactic communication.
2. Formal written algorithms for all four operations should be introduced at this stage.
Which of these is/are correct?
- A Only 2
- B Both 1 and 2
- C Neither 1 nor 2
- D Only 1
Show answer
Correct answer: (D) Only 1
NCF 2005 says that at the pre-primary stage all learning occurs through play, with simple comparisons, classification and the link between counting and quantity. Written algorithms belong to much later stages.
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Q.86
Consider the following statements about teaching data handling:
1. In a pictograph, the key tells how many objects one symbol stands for, and children must use it to read the graph.
2. In a bar graph, all bars should be of equal width, and the height of a bar shows the frequency.
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: (C) Both 1 and 2
A child who reads four ball symbols as '4 children' when one symbol stands for 5 has ignored the key. In a bar graph only the height carries information, so bars of unequal width would mislead the reader.
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Q.87
Which of the following statements best reflects the vision of mathematics education in NCF 2005?
- A Children learn to enjoy mathematics, talk about and communicate it, and pose and solve meaningful problems
- B Children master the standard algorithm for each operation through repeated drill before attempting any application
- C Children learn mathematics mainly to score well in examinations
- D Children cover the full syllabus by memorising formulae and definitions so that no topic is left out
Show answer
Correct answer: (A) Children learn to enjoy mathematics, talk about and communicate it, and pose and solve meaningful problems
NCF 2005 envisions children enjoying mathematics rather than fearing it, learning important mathematics, communicating about it and posing and solving meaningful problems. It explicitly argues against rote memorisation.
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Q.88
Which of the following is NOT one of Zoltan Dienes' principles of mathematics learning?
- A Dynamic principle
- B Law of effect
- C Perceptual variability principle
- D Constructivity principle
Show answer
Correct answer: (B) Law of effect
Dienes proposed four principles: dynamic, constructivity, mathematical variability and perceptual variability. The law of effect belongs to Thorndike's connectionism.
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Q.89
The main drawback of the synthetic method of teaching proofs in mathematics is that:
- A It takes too much classroom time because students must discover every step of the proof themselves
- B It presents the proof as a finished product, so students may not understand why each step is taken
- C It cannot be used for geometry and works only for algebraic identities
- D It requires expensive laboratory equipment and models for every proof
Show answer
Correct answer: (B) It presents the proof as a finished product, so students may not understand why each step is taken
The synthetic method is short and logical but moves from the known to the unknown without showing how the steps were found, so it should be combined with the analytic method, which supplies the 'why'.
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Q.90
While proving a geometry theorem, a teacher starts from what is to be proved and keeps asking 'what must be true for this to hold?' until the given facts are reached. This is the:
- A Analytic method
- B Synthetic method
- C Inductive method
- D Project method
Show answer
Correct answer: (A) Analytic method
The analytic method breaks the problem down, moving from the unknown (conclusion) back to the known (hypothesis). The synthetic method goes the opposite way, from the given facts to the conclusion.
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Q.91
Match each situation with the most suitable measure.
P. The shoe size a shop sells most often
Q. A typical monthly income when one person earns far more than the rest
R. The average marks of a class in which all marks lie between 40 and 70
i. Mode
ii. Median
iii. Mean
- A P-iii, Q-ii, R-i
- B P-i, Q-iii, R-ii
- C P-i, Q-ii, R-iii
- D P-ii, Q-i, R-iii
Show answer
Correct answer: (C) P-i, Q-ii, R-iii
The mode gives the most frequent value, which is what a shopkeeper needs. One very large income pulls the mean up, so the median describes a typical income better. When values are spread without extremes, the mean uses all the data and is suitable.
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Q.92
From a constructivist viewpoint, errors made by children in mathematics should be seen as:
- A Windows into the child's thinking that help the teacher plan the next step
- B Signs that the child is not suited to mathematics and needs an easier stream
- C Results of carelessness that will disappear with more drill and regular practice
- D Reasons to reduce marks so that the child becomes careful next time
Show answer
Correct answer: (A) Windows into the child's thinking that help the teacher plan the next step
Most errors are systematic and reveal the child's current understanding or misconception. Analysing them (error analysis) is a diagnostic tool, which is more useful than penalising or drilling.
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Q.93
In a survey of 60 students, 15 chose cricket as their favourite game. A student draws the cricket sector of a pie chart with an angle of 15°. The teacher should help him see that:
- A He should draw 15 small sectors, one for each of the students who chose cricket
- B The angle should be 15 × 10 = 150°, giving ten degrees to each student who chose cricket
- C A pie chart cannot be used for data about favourite games; it suits only money or time data
- D The sector must be the fraction of 360° that cricket is of the whole: 15/60 × 360° = 90°
Show answer
Correct answer: (D) The sector must be the fraction of 360° that cricket is of the whole: 15/60 × 360° = 90°
A pie chart shows each category as a fraction of the whole circle. Cricket is 15 out of 60, a quarter of the students, so it needs a quarter of 360°, which is 90°; each student is worth 360° ÷ 60 = 6°, not 1° or 10°.
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Q.94
According to Piaget, children of primary classes (about 7 to 11 years) are in the concrete operational stage. The main implication for teaching mathematics is that:
- A New concepts should be introduced through concrete objects and real situations before symbols
- B Children can reason about abstract algebraic variables without any support from objects or pictures
- C Teaching should rely mainly on clear verbal explanation of rules, followed by written practice
- D Children cannot learn any logical operation at this age, so only rote counting is possible
Show answer
Correct answer: (A) New concepts should be introduced through concrete objects and real situations before symbols
In the concrete operational stage children reason logically about concrete objects but not yet about abstract propositions, so mathematics should be introduced through manipulatives and real situations.
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Q.95
A Class 2 child believes that a large ball of cotton wool must be heavier than a stone the size of a lemon, because it is bigger. The best way to address this is to:
- A Tell the child clearly that the stone is heavier, and correct her answer
- B Show a picture of a weighing machine and read out the weight of each object
- C Ask the child to memorise the rule that size does not decide weight
- D Let children compare them on a pan balance and talk about size and weight
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Correct answer: (D) Let children compare them on a pan balance and talk about size and weight
Direct comparison on a balance lets the child test her prediction and see that a larger object can be lighter. Experiencing the result is more convincing than being told, and it separates the attribute 'weight' from 'size'.
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Q.96
In a discussion, children share different ways of finding 25 × 12: '25 × 10 + 25 × 2', '25 × 4 = 100, so 100 × 3', and '12 × 100 ÷ 4'. The main value of this discussion is that it:
- A Confuses children, who should first master one standard method thoroughly
- B Builds flexibility and number sense as children compare and justify strategies
- C Wastes time that would be better spent on written practice of the standard algorithm
- D Helps the teacher show the class that her own method is the quickest one
Show answer
Correct answer: (B) Builds flexibility and number sense as children compare and justify strategies
All three methods give 300. Comparing them shows how numbers can be broken up and recombined using place value and the properties of multiplication, and asking children to justify methods develops reasoning and communication.
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Q.97
A student writes 2³ × 2⁴ = 2¹². Which approach best helps her?
- A Tell her the rule 'add the powers' and give twenty practice sums to fix it in memory
- B Tell her to multiply the bases as well as the powers, which gives 4¹² as the answer
- C Write both in expanded form: (2 × 2 × 2) × (2 × 2 × 2 × 2) has seven 2s, so it is 2⁷
- D Accept the answer, since 3 × 4 = 12 and powers are always multiplied
Show answer
Correct answer: (C) Write both in expanded form: (2 × 2 × 2) × (2 × 2 × 2 × 2) has seven 2s, so it is 2⁷
Counting the factors in expanded form shows why exponents are added when powers of the same base are multiplied: 8 × 16 = 128 = 2⁷, whereas 2¹² = 4096. The law then comes from meaning, not memory.
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Q.98
A child believes every four-sided figure is a 'square'. After measuring and comparing several figures, she changes her idea and separates squares from other quadrilaterals. In Piaget's terms, this change is:
- A Accommodation
- B Assimilation
- C Conservation of number
- D Centration
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Correct answer: (A) Accommodation
Accommodation is modifying an existing schema when new experience does not fit it. Assimilation would mean fitting the new figures into her old idea without changing it.
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Q.99
According to Dienes' constructivity principle, in planning mathematical activities:
- A Every concept must be shown through at least four different materials so that it can be fully abstracted
- B Construction before analysis: children build a concept through experience before analysing it logically
- C Children should first learn the formal definition of a concept and then construct their own examples of it
- D Only the teacher should construct models while children observe and note down the steps
Show answer
Correct answer: (B) Construction before analysis: children build a concept through experience before analysing it logically
Dienes argued that children first construct mathematical ideas through activity and only later can analyse them logically, so formal definitions should not come first. Showing a concept through several materials is the perceptual variability principle.
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Q.100
Consider the following statements about teaching-learning materials in mathematics:
1. Low-cost local materials such as seeds, sticks, bangles and bottle caps can be used effectively for counting, grouping and patterns.
2. Children should handle the materials themselves, not only watch the teacher demonstrate with them.
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: (C) Both 1 and 2
Mathematics materials need not be expensive kits; everyday objects work well and connect learning to the child's surroundings. Learning comes from children's own actions on materials, so a demonstration alone is far less effective.
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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.