Quiz-3: Mathematics and Pedagogy MCQ Question with Answer


Mathematics and Pedagogy MCQ Question with Answer


Directions (Q. 1–30): Answer the following questions by selecting the most appropriate option.

Q1. The length, breadth and height of a cuboid are 4 cm, 3 cm and 2 cm, respectively. What will be the lateral surface area of the cuboid?

(a) 28 cm2

(b) 14 cm2

(c) 24 cm3

(d) 12 cm2

Answer: (a)

Explanation: Lateral surface area of cuboid

= 2h (l + b)

= 2 × 2 (4 + 3)

= 4 × 7 = 28cm2

Q2. If F = number of faces, V = number of vertices and E = number of edges, which of the following is correct?

(a) 6F – 3V = E

(b) F + V = E

(c) F + V = E + 2

(d) F + V = E – 2

Answer: (c)

Explanation: The relation between V, F and E is: F + V = E + 2. This relationship is also called Euler’s formula.

Q3. Which of the following is an example of a two­ dimensional shape?

(a) Sphere

(b) Cone

(c) Line

(d) Square

Answer: (a)

Explanation: A shape that has two measures, i.e. length and breadth, is called a two-dimensional shape. Among the given options, the sphere is the only shape that has both length and breadth.

Q4. Which of the following points is on ∠ABC?

Math and Pedagogy_Quiz-3_q4

(a) P

(b) Q

(c) R

(d) Both Q and R

Answer: (a)

Explanation: ∠ABC is made by the line segments AB and BC, and point P is on the line segment AB. Therefore, P is on ∠ABC.

Q5. What is the difference in the place value and the face value of 1 in 9199?

(a) 101

(b) 100

(c) 99

(d) 91

Answer: (c)

Explanation: Place value of 1 in 9199 = 100

Face value of 1 in 9199 = 1

Hence, their difference = 100 – 1 = 99

Q6. Which of the following statements is correct?

(a) An even number is always a composite number.

(b) An odd number is always a prime number.

(c) A natural number is a positive integer.

(d) A prime and a composite number are always co­ primes.

Answer: (c)

Explanation: 2 is an even number, but it is a prime number. 9 is an odd number, but it is a composite number. A natural number is a positive integer. 3 is a prime number and 9 is a composite number, but they are not co-primes.

Q7. Two numbers are in the ratio of 5:6. If their HCF is 3, the two numbers are

(a) 75 and 108

(b) 18 and 15

(c) 15 and 18

(d) 5 and 6

Answer: (c)

Explanation: 15 and 18. Let two numbers which are in the ratio of 5:6 are 5x and 6x. HCF of 5x and 6x = x, i.e. x = 3 Therefore, two numbers are 15 and 18

Q8. The value of 7654 – 3456 – 2345 is

(a) 1111

(b) 6543

(c) 1853

(d) 13455

Answer: (c) 1853

Explanation: 7654 – 3456 – 2345

= 7654 – (3456 + 2345)

= 7654 – 5801 = 1853

Q9. The cost of a Parker pen is Rs. 50. What is the cost of 25 such pens?

(a) Rs. 125

(b) Rs. 1250

(c) Rs. 1025

(d) Rs. 1205

Answer: (b)

Explanation: Cost of 1 Parker pen = Rs. 50

Cost of 25 Parker pens = 25 × 50 = Rs. 1250

Q10. The sum of all the positive factors of 32 is…

(a) 64

(b) 120

(c) 60

(d) 63

Answer: (d)

Explanation: Positive factors of 32 are 1, 2, 4, 8, 16, and 32

Sum = 1 + 2 + 4 + 8 + 16 + 32 = 63

Q11. If a car covers 250 metres in 1 minute, how much distance will it cover in 35 minutes?

(a) 8.750 km

(b) 8.75 km

(c) 87500 cm

(d) 8750 km

Answer: (a)

Explanation: Distance covered by the car in 1 minute = 250 m

Distance covered by the car in 35 minutes = 35 × 250 = 8750 m

So, 8750 m = 8000 m + 750 m = 8 × 1000 m + 750 m = 8.750 km

Q12. 350g sugar can be kept in one bag. To keep 17.5kg sugar, how many bags will be required?

(a) 20

(b) 50

(c) 40

(d) 60

Answer: (b)

Explanation: To keep 350g sugar, 1 bag is required

To keep 1g sugar, 1/350

Bag will be required to keep 17500g sugar = $\frac{17500}{350}=50$

Bags will be required 50 bags

Q13. How many litres are there in 7.2 kilolitres?

(a) 720

(b) 72

(c) 7200

(d) 72000

Answer: (c)

Explanation: We know 1 kl = 1000 l

So, 7.2 kl = 7.2 × 1000 = 7200 l

Q14. How many minutes are there in a week?

(a) 10080

(b) 1080

(c) 10800

(d) 168

Answer: (a)

Explanation: 1 week = 7 days = 7 × 24 hours = 7 × 24 × 60 minutes = 10080 minutes

Q15. Find the next term in 2, 3, 5, 7, 11, 13….

(a) 15

(b) 17

(c) 18

(d) 19

Answer: (b)

Explanation: 2, 3, 5, 7, 11, 13 are prime numbers. The prime number greater than 13 is 17.

Q16. Van Hiele’s ‘Levels of Geometric Thinking’, a student who can sort out rectangles from an assorted collection of shapes is at

(a) Level 2: Informal Deduction

(b) Level 3: Formal Deduction

(c) Level 0: Visualization

(d) Level 1: Analysis

Answer: (c)

Explanation: At Level 0: Visualisation, children can recognise geometrical figures by their shape or physical appearance and not by their parts or properties. They can identify similar-shaped figures, learn the vocabulary associated with geometry and identify the specified shape. By the end of this stage, children are able to group shapes or figures into classes because they seem to look ‘alike’.

Q17. The main goal of mathematics education is to

(a) help the students to understand mathematics

(b) develop useful capabilities

(c) develop children’s abilities for mathematization

(d) Formulate theorems of geometry and their proofs independently

Answer: (c)

Explanation: The main goal of mathematics education is to develop children’s abilities for mathematization. It means that children should learn to think about any situation using the language of mathematics and solve the problem by applying mathematical tools and techniques. Formulation of theorems of geometry is not at all a goal at the primary level. Helping students to understand mathematics and to develop their capabilities is a part of the main goal, i.e., mathematization.

Q18. A student identifies rectangles among four-sided figures on the basis of their properties (“It’s a rectangle because it has one set of opposite sides longer than the other set of opposite sides and opposite sides are parallel, and…”). According to Van Hiele’s ‘Levels of Geometric Thinking’, this student is at

(a) Level 2 – Informal deduction

(b) Level 3 – Formal deduction

(c) Level 0 – Visualisation

(d) Level 1 – Analysis

Answer: (d)

Explanation: At the analysis level, students identify figures as a class of shapes. They become proficient in describing the properties of two­ and three-dimensional shapes. Therefore, they benefit much from playing with geometric materials.

Q19. NCF 2005 talks about teaching ambitious, coherent and important mathematics. Here, what does ‘coherent’ mean?

(a) To achieve the higher aim rather than only the narrow aim.

(b) Linking mathematics with other subjects

(c) Providing activity oriented education

(d) Using ICT in the classroom

Answer: (b)

Explanation: Here, ‘coherent’ refers to the linking of mathematics with other subjects. This effort adds meaning to mathematical learning. Maths can be easily integrated with almost all the subjects.

Q20. “Students’ ability to come up with a formula is more important than being able to correctly use well-known formulae”. Which learning approach do you think is best suited for this?

(a) Contextual learning

(b) Constructivism

(c) Cooperative learning

(d) Mastery learning

Answer: (b)

Explanation: The given approach is a constructivist approach. Under constructivism, students construct their own knowledge by testing ideas and approaches based on their prior knowledge and experience. In contextual learning, the students plan and use their own experiences and process new knowledge with reference to their memory and everyday life experiences. In cooperative learning, students carry out activities in groups under the supervision and guidance of a teacher. They exchange ideas through discussions in order to solve a problem. In mastery learning, the whole curriculum content is broken down into small units and each unit is mastered one by one. The teacher makes sure that all students have mastered a unit taught before proceeding to the next unit.

Q21. A student was asked to express 5 m in cm. His answer was 50 cm. What type of error is it?

(a) Regrouping error

(b) Basic fact error

(c) Wrong algorithm

(d) Incorrect operation

Answer: (b)

Explanation: It is a basic fact error. The student does not know that 1 m = 100 cm.

Q22. What is the meaning of the term ‘tyranny of the right answer’?

(a) Putting the students under pressure to compare different methods of solving a problem

(b) Applying one algorithm that has been taught and getting that ‘one right answer

(c) Presenting too many ways to solve a problem and confusing the students

(d) Giving the students too much freedom to apply their mind

Answer: (b)

Explanation: Expecting all the students to understand the one algorithm taught in the class and getting that ‘one right answer’ is tyranny or cruelty to the students. Students think in multiple ways and have the potential to solve a problem in multiple ways. This potential of theirs should be encouraged. They should be let free to explore all the ways and then compare and decide as to which is the most appropriate one to solve the problem.

Q23. Which suggestion should be avoided in the textbook of mathematics for primary classes?

(a) Textbooks should use language that a child would normally speak and understand.

(b) Too many pictures should be avoided and maximum space should be given to practice sums.

(c) The texts and visuals should be sensitive to concerns of gender and equality.

(d) Mathematical concepts should be used in tandem with concepts of other subjects to build a deeper understanding of mathematics.

Answer: (b)

Explanation: Being at the concrete operational stage, the students of primary classes need a lot of visuals and other concrete objects to understand the concepts in a better way. Moreover, pictures should be used as background fillers to convey the idea that mathematics can be fun.

Q24. The curriculum (NCF 2005) at the primary stage is not in favour of

(a) Giving due place to non-number areas of mathematics such as space, visual patterns and data handling

(b) Development of number sense including number patterns

(c) Teaching children very big numbers to enhance the child’s cognitive capacity

(d) Building a stronger conceptual base for fractions and decimals

Answer: (c)

Explanation: NCF 2005 does not advocate ‘overloading the child’s cognitive capacity which can be better used for mastering the logical skills at the earlier stages.

Q25. At the primary level, the use of tangram, dot games, patterns, etc. helps students

(a) Enhance spatial understanding ability

(b) Develop the sense of comparing numbers

(c) Strengthen calculation skills

(d) Understand basic operations

Answer: (a)

Explanation: The use of manipulative such as tangrams, dot games, patterns, etc. helps students develop their spatial sense in mathematics, which further helps them to improve their skills in geometry and reasoning­ related problems. It has been proved by researchers that students who find difficulty in using symbolic mathematical notations, sometimes, do very well in visual/spatial activities. These activities do not strengthen calculation skills nor do they help to understand basic operations. The sense of comparing numbers also does not develop with tangrams.

Q26. Tangrams are not useful in developing

(a) Visual-spatial skills

(b) Concept of place value

(c) An understanding of geometry vocabulary

(d) An understanding of relationships between different shapes

Answer: (b)

Explanation: The concept of place value cannot be developed with the help of tangrams. Tangrams are pieces or blocks that when combined together form some shape. They are also known as dissection puzzles. Understanding the concept of place value involves the knowledge of numbers, which cannot be achieved through tangrams.

Q27. Which manipulative would you select to teach the concepts of area and perimeter to class IV students?

(a) Abacus

(b) Geoboard

(c) Fraction discs

(d) Base ten blocks

Answer: (b)

Explanation: Geoboard is a board, usually of plastic, with some nails driven in it. A rubber band is placed on the nails in different ways to teach students different geometrical shapes and related concepts like the area and perimeter of shapes. The other three given options are used to teach other mathematical concepts, but not geometry.

Q28. Ravi is able to tell the correct number of objects in a small collection. He is at the

(a) Operational phase

(b) Emergent phase

(c) Quantifying phase

(d) Partition phase

Answer: (b)

Explanation: At the emergent phase, students are able to compare quantities of objects in small collections using the terms ‘bigger, ‘smaller’ and ‘the same’. They can distinguish spoken numbers from spoken words and numerals from other written symbols. They can count and tell the correct number of objects in a small collection.

Q29. Sheenu can perform simple additions/subtractions (e.g. 2 + 3 or 4 – 2) that are given as word problems in a story through role play. He is at

(a) Matching phase

(b) Emergent phase

(c) Quantifying phase

(d) Partition phase

Answer: (a)

Explanation: Students, at the matching stage, are able to recall the sequence of number names at least up to double digits. They know how to count a collection, understand that it is the last number said which gives the count, match one collection with the other through one-to-one pairing, compare two collections one-to-one and use this technique to decide which is bigger and how much bigger than the other. They can solve simple number problems given in a story form, which requires them to add some, take away some, or combine two amounts by imagining or role-playing the situation and counting the resulting quantity.

Q30. Which one of the following is not a mathematical process?

(a) Measurement

(b) Visualisation

(c) Estimation

(d) Memorisation

Answer: (d)

Explanation: The faster way to master mathematics is by working out problems because it is a subject that is less theoretical and is rather based on numbers and calculations. Memorisation can help only in learning mathematical formulae, but the rest requires practice and active thinking. According to NCF 2005, mathematical processes include problem-solving, use of heuristics, estimation and approximation, optimisation, use of patterns, visualisation, representation, reasoning and proof, making connections and mathematical communication.

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