KTET Paper 1: Mathematics Test - 8 - KTET MCQ

She uses this strategy to create a certain way of thinking and reasoning. In exploratory instruction, teacher teaches by planting questions, like seeds, that encourage students to investigate their own approaches to learning the material. The students create their own paths, instead of getting a ready-made path.

Rajan got confused with the basic operators when he was given word problems. He asked which one of the operators he had to perform. So, he lacks in understanding the number of operators. Either he is not familiar with the operators or he lacks the concept to understand how operators work.
Hence, the correct answer is "Rajan lacks understanding of number operations”.

Assessment refers to the collection of data and the gathering of evidence from different sources through different tools. It provides feedback on the performance of the student specifying his/ her strengths and areas for improvement which provides insights for taking appropriate steps for improving the learning.

Benjamin Bloom first framed the objective of educational taxonomy.

The teaching methods should be more reliable to the students at this stage. Mostly the teacher teaches the students by using the non-metric units to calculate the mathematics, these are also known as basic mathematical techniques. In this method, the students are used to measure the area or lengths with the help of their palm-size, with the length of the pencil they use or by taking some leaves to measure.

The mathematical manipulative tools are also a type of teaching-learning materials that are specifically used by the students to internalize the abstract mathematical concepts.

• The students used the manipulative tools by themselves to explore, investigate, and internalize the concepts to enhance their mathematical competency.
• These are the teaching tools or materials used to engage students in learning mathematics to provide direct and hands-on experience.

A square pyramid has a base of square and four triangles, which meet at one point. When we cut it horizontally, we get a rhombus.

By making a simple ratio of 4(1/3)
We get;
(3x4+1)/3 = 13/3
Now,
The number of degrees in 13/3 right angles
= (13/3) x 90º = 390º.

Mathematics is the study of geometrical figures, their co-relation, and their dependency on each other. It deals with quantity, measurement, and spatial relationships.

Rubrics is a guide listing specific criteria for grading or scoring academic papers, projects, or tests. It is a coherent set of criteria for students' work that includes descriptions of levels of performance quality on the criteria.
To assess the students' competency on solving word problems, based on addition and subtraction, rubrics of assessments are comprehension of problems, identification of operation to be performed, representation of problem mathematically, solution of problem and presentation of problem.

Questions are a great way to test the knowledge of a child. Generally speaking, a question refers to a sentence or phrase that asks for an answer. There can be different types of questions depending upon the need of learning and children.
Normally in mathematics pedagogy,  there are two types of questions as follows:
Closed-Ended Questions: refers to questions in which respondents have to present a set of pre-defined answers. Here answer options are limited and can be in the form of  ‘yes/no’ or a set of multiple options, or a rating scale. For example- Is India a country? The answer is Yes.

• What is the sum of 8 and 6? The answer is 14.
• Compute the sum of 8 and 6. The answer is 14
• What should be added to 8 to get 14? The answer is 6.
• In all the above cases, there can be only 1 answer(limited).

Open-ended questions: refers to questions in which respondents have the freedom to present a set of different answers. Here answer options are not limited. For example,

• Name two cities from India. The Answer can be the name of any two cities of India- including Delhi, Mumbai, Kolkata, Moradabad etc
• Partition 14 as the sum of two numbers. The answer can be
• 14=13+1
• 14=12+2
• 14=11+3 etc. Here, the answer is not limited to one.

There are 9000, four-digit numbers present in the Hindu-Arabic Numeration system. The series of those numbers start from 1000 and end at 9999 so the total no. of four-digit numbers = (9999−1000)+1= 8999+1 = 9000
Hence, the correct answer is 9000.

All these things come in the language of mathematics.

As 19009 = 1728 × 11 + 1
Therefore, on dividing 19009 by 11 we get the remainder 1.
Also, 9090 = 826 × 11 + 4
Similarly, on dividing 9090 by 11 we get the remainder 4.
Now, the product of the remainders = 1 × 4 = 4
Hence, the correct answer is 4.

Curriculum:-It includes the complete school environment, involving all the courses, activities, reading, and associations furnished to the pupils in school.
Principles of curriculum construction:

• Principle of Child Centredness
• Principle of Flexibility and Variety
• Principle of Correlation
• Principle of Creativity
• Principle of Integration
• Principle of Utility
• Principle of Community Service
• Principle of activity
• Principle of Values
• Principle of Totality

Thus by all these references, we can conclude that the Spiral approach does not belong to the “principles of curriculum construction.

This is the correct option. The wall is divided into 8 equal parts. The students will be able to know that if 1/2 litre is used to paint 1/8th of a wall, then 1/2 x 8 = 4 litre paint will be used to paint the complete wall.

“Start a discussion in the class on things in the child's environment which roll and slide. Help children to look at their shapes and see how some things roll and others slide.” This is more like an interactive session where the teacher is trying to draw the student’s attention towards some practical usages of learning concepts.
Depending on the structure and shape of the figure it will either slide or roll. If the surface of the figure is smooth and round it will roll and if the surface is bent and creates friction then it will slide. It is imperative for the teachers to draw the students’ attention towards the shapes and sizes, the basic knowledge about our day to day things surrounding us.
Hence, the correct answer is "It is imperative for the teachers to draw the children's attention to the things around them".

Scope of connecting knowledge to life outside the school: 

• Market: Most of the students might have gone to a market with their parents. They must have observed and participated in the way of buying and selling of goods and also the approach of the buyer and seller. You should take the advantage of real situations and utilizing the experience of the students in the calculation of profit & loss, preparation of bills, process of weighting, counting of money, amount and price etc.
• Real-life: A frog climbs 30 meters on a pole in a day and slides back 20 meters in a night. If the pole is 70 meters high, then how many days the frog will take to climb to the top of the pole? Most of our students of upper primary classes may calculate the answer as 7. One student told the answer is 5 as the frog climbs 40 meters in 4 days and in the fifth day it reached on the top i.e. 70 meters. Students get opportunities to work in a natural setting, they work according to their own perceptions. So their real-life experience must take into consideration.
• Garden: Students prepare plots in home, schools and also in playing with peers. During that time they may not know counting, measurement, construction of angles, different types of geometrical figures, areas, different lines, average etc. but they may do it using their perception. You may share the experience of the students in these activities and it will be amazing to find out that they have already acquired a lot of mathematical concepts which requires slight refinement for acquiring formal knowledge and understanding of the concepts.  
• Making designs: Students covered their notebooks, paint pictures, decorate their houses, plants trees in garden, design their playing kits etc. Teacher must observe the process of making design and utilized it in the classroom.
• Festival: We celebrate many festivals in our homes as well as in our schools. Students heartily involved on the Independence day, Republic day, Teacher’s day, Children’s day, Saraswati puja, Ganesh puja, Id, Christmas etc. They involve themselves in different activities to make these special occasions memorable. They go to the market to buy various materials, decorate the school, distribute sweets, calculate expenditure etc. at that time they also learn mathematics.
• Playground: Students are playing Kabaddi, football, cricket, volleyball, basketball and also many indoor games. They frame their rules of their own, prepare playground in a group. Students construct Circles, Rectangles, Squares, triangles etc. In their playground without knowing the rules of construction. They count individual and group scores through their own strategies.

Hence, we conclude that both statements are examples that can help the students in connecting their knowledge with the life outside the school.

B. F. Skinner propounded the theory of Operant Conditioning.

From the given information:
The given time hours = 4 hours 59 minutes
The before time = 2:58 pm
Convert the twelve hours format into twenty-four hours format:
⇒ 2:58 pm = 12 + 2:58 = 14:58
Now, The required time
= 14:58−4:59
= 9:59 am
Therefore, it is 9.59 am before 2 :58 pm

• Mathematics is the study of numbers, shapes, quantities, and patterns.
• Mathematics is the ‘queen of all sciences and its presence is there in all the subjects.
• It acts as the basis and structure of other subjects.
• Proof of a Mathematical Statement consists of a sequence of statements, each statement being justified with a definition or an axiom or a proposition that is previously established by the method of deduction using only the allowed logical rules.
• Thus, each proof is a chain of deductive arguments each of which has its premises and conclusions.

Proof by contradiction: 

• It is also called reductio ad absurdum (a Latin phrase) because it relies on reducing a given assumption to an absurdity.
• Here, we start with the assumption that the given statement is false.
• By rules of logic, we arrive at a conclusion contradicting the assumption and hence it is inferred that the assumption is wrong and hence the given statement is true.
• In this method, to prove q is true, we start by assuming that q is false (i.e., ~ q is true).
• Then, by a logical argument we arrive at a situation where a statement is true as well as false, i.e., we reach a contradiction r ∧ ~ r for some statement that is always false.
• This can only happen when ~ q is false also.
• Therefore, q must be true.
• To prove 'A line passing through the midpoints of two sides of a triangle is parallel to the third side' for this we assume that the statement is false and end up with the conclusion that the statement is true.

​Thus, from the above-mentioned points, it is clear that this type of proof is proof by contradiction.

We know that
345271 = 1 mod (10)
Therefore,
(345271)⁷⁹³⁹⁹ ≡ (1)⁷⁹³⁹⁹ mod (10)
≡ 1 mod (10)
Hence, the remainder is 1.

HOTS questions are able to make students trained to think creatively about any topic or concept. So, it demands knowledge and some degree of cognitive efforts.

A concept map provides a concrete record of the connections perceived by the students, and thus it indicates how the student’s knowledge is organized and interconnected.

The concept of areas of plane figures can be introduced to the students of Class V by measuring the area of any figure with the help of different objects like palm, leaf, pencil etc.

Solve by thinking and reasoning is very much important. Until and unless students don't have such ability then it is not worth keeping mathematics as a subject in the course curriculum. Teachers must not give students the formulae sets to solve the problems rather they must help them to answer the problem by thinking and finding out the reason themselves so that they have the capability to handle everything easily.
Hence, the correct answer is, 'Giving students set formulae to solve the numerical questions,'

Mathematics is a subject matter of complex abstractions and mainly deals with patterns, shapes, sizes, figures, and data analysis. It is based on practical usability in all aspects of life.

• The concepts for which the proof or verification is done by experimentation or activities are better understood by learners and are retained in their brains for a longer period of time. 

Arithmetic, Algebra, Trigonometry and Coordinate Geometry are the different branches of mathematics. 'Quadratic Equations' is the sub branch of Algebra. So, Algebra and Quadratic Equations represent the same branch.

Multidisciplinary is something that combines many fields. For a Class IV student, if a teacher has given to draw the flag of India and identify the number of lines of symmetry in the flag, then this student must aware of the design, colors and symbol in the flag of India and also should be aware of the concept of symmetry to find the number of lines in symmetry in the flag. Thus, it is referred as a Multidisciplinary Problem.
Hence, the correct answer is, 'Draw the flag of India and identify the number of lines of symmetry in the flag.'

The synthesis method in teaching is an approach that encourages students to combine various pieces of information to form a new concept, or to draw new conclusions.