Quiz-3: Mathematics and Pedagogy MCQ Question with Answer

Explanation: Lateral surface area of cuboid

= 2h (l + b)

= 2 × 2 (4 + 3)

= 4 × 7 = 28cm²

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

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.

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.

Explanation: Place value of 1 in 9199 = 100

Face value of 1 in 9199 = 1

Hence, their difference = 100 – 1 = 99

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.

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

Explanation: 7654 – 3456 – 2345

= 7654 – (3456 + 2345)

= 7654 – 5801 = 1853

Explanation: Cost of 1 Parker pen = Rs. 50

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

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

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

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

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

Explanation: We know 1 kl = 1000 l

So, 7.2 kl = 7.2 × 1000 = 7200 l

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

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

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’.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.