CTET Paper 2 Maths & Science November 2012 (English-Hindi-Sanskrit) (Previous Year Paper)

A child-centered system of education is designed to develop the individual and social qualities of a student rather than providing generalized information or training by way of the prescribed subject matter. Child-centered education regards education as the fundamental right of every child. Every child is educated, no matter whatever is his social and economic background.

Important Points

According to John Dewey:-

''Learners interact with the teachers and the environment thus there is a collaboration effort on both sides to plan lessons, select content and do activities together.''

• In this system of education, the child should be allowed to learn from nature in his natural way without any interference, nothing should be taught to him until he is capable of understanding it. His natural interests like play and curiosity should form the basis of his education and more emphasis should be given to the child's sensory and natural development. This can be developed through activity-based learning. In a child-centred classroom, students are engaged in doing different types of activities.
• An example of a child-centred classroom might look like four students discussing a particular question in a book, another group of four students working on a dramatic production, and another group of students discussing a different aspect of the book. Finally, the whole group might come back together and share their work. So they all are engaged in different types of activities. In a child-centred classroom, there is movement, energy, flexibility in terms of what's happening in the classroom.

Hence, we conclude that Child-centred education was advocated by John Dewey.

Teaching-Strategy: It is a process, which is explicitly and systematically designed to, ensure that the learners accomplish the instructional objectives. The purpose of instruction is to improve performance. There are a variety of teaching methods that can be used by the teacher for teaching theory and skills in the classroom setting.

For the above situation, consider the following points:

• ​A child should not be treated differently just because he is a single parent child because it contradicts the concept of inclusive education.
• Assigning less assignment shows that the teacher is pitying the child and he has doubts about the child's ability.
• Providing a good environment is always appreciable, but it should be noted that if the teacher provides a good environment merely because a child has only a single parent, it again shows pity.
• So, the best strategy is to overlook this fact and treat him as a normal child because this will show that the teacher believes the child.

Hence, we conclude that while teaching a single parent-child, a teacher should ​overlook this fact and treat such a child at par with other children.

Gifted children- According to Torrance (1977), "The child who is gifted and talented shows an excellent performance in any area of human behavior that is important to society.

• The gifted child is essential exceptional.
• In comparison to children of his group, he is superior in some ability or group of abilities.
• A gifted child doesn't have to possess a very high IQ showing his superiority in general intelligence, over the other children of his age group.

Key Points

Characteristics of the gifted child:-

• They excel at expressing their views.
• They try to explore all the time.
• They engage them self best in any given work
• They learn any topic thoroughly.
• They have a strong sense of curiosity.

Important PointsAcceleration concerning gifted children:- Acceleration through which the gifted children may be allowed to complete the prescribed course of study in a shorter period. Many forms of acceleration are grade-skipping, early entrance to kindergarten or college.

• Acceleration means matching the curriculum to a student's abilities. For one student, that may mean grade skipping, for another, it may mean acceleration in a single subject, like math; for other students, enrichment-based activities in the classroom are all they need." (e.g., when a fifth-grade student takes a middle school math course).
• To facilitate intellectually bright child the teaching-learning strategy may be given extra promotion. In this way, the learning experiences should be so reached that gifted children find something new and challenging for them.

Hint

Acceleration method:-

• Double promotion for grade skipping.
• Provided in a research course.
• Provision for additional subjects while in the mainstream course.
• Admission at an earlier stage.

Hence, we can conclude that acceleration concerning gifted children means promoting such students to the next higher grade by skipping the present grade.

Giftedness refers to talent. The gifted students are essentially exceptional and generally show consistency in their performances and exhibit superiority in general intelligence. 

• A gifted child may or may not have a very high I.Q. and giftedness can be in one area and more than one area.
• They have great intellectual curiosity, creativity, imagination, and like to create and investigate.

The enrichment programs are the extra special opportunities provided to the learner who needs extra support to learn at a higher level to learn more and effectively other than the classroom activities. It is helpful to keep the learners engaged and interested in learning. It gives them extra challenges to learn and grow. 

Key Points

All the gifted students have some special needs to fulfil their curiosity and to enhance their creativity. The enrichment consists of giving the gifted child the opportunity to go deeper or to range more widely than the average child in his intellectual, social, and artistic experience. It can be done by:

• Emphasize the creative and other experimental work that will help the gifted students to learn and discover on their own.
• Co-operative planning and activity provide an opportunity for leadership training and experiences in social adjustment.
• The development of self-study habits by giving them special assignments that requires brainstorming and other cognitive skills.
• The stress should be given to independent work and originality to promote their creativity and bring out their talents into the light. So, they should be given independent projects to work on. 'Write an original play on given concepts' is one example related to this.
• They should be provided with rich and independent library services that will help them to read according to their pace, mood, needs, and interest. It will also garnish their knowledge and thought process in the long run.
• They should be encouraged to study a variety of books and reference materials and literature that will increase their vocabulary, curiosity, and the ability to generalize. They will also able to know and appreciate the things of which normal children are unaware.

Thus from the above-mentioned points, it is clear that 'write an original play on given concepts' is the most appropriate activity for gifted students.

Intelligence: Intelligence can be defined as the ability to grasp information, understand concepts, and solve problems. It should be noted that the Theory of Multiple Intelligence was proposed by Howard Gardner. 

Key Points According to him, the following are types of intelligence explained below:

Hence, a surgeon could be an end-stage of a child possessing bodily-kinesthetic intelligence.

Exceptional children are those who deviate from the normal population and need special education services to meet their needs. It includes children who are gifted, backward, creative, learning disabled, etc.

Key Points

• Gifted children refer to the children who perform tasks extraordinarily when compared with others of their peer group. They perform exceptionally well in any field important to human beings.
• They are independent in their judgments as they possess advanced logical and creative thinking.
• Gifted children are exceptionally curious and have a thirst for knowledge in order to satisfy their own curiosity. They are intrinsically motivated with high self-esteem.

A Gifted Child is the one who:

• has an IQ score of 140 or above
• has an ability that lies within the range of the upper two or three per cent of the population
• requires differentiated educational programs than the regular ones provided by the school to realize their true potential
• is capable of high-performance abilities in areas such as general intellectual ability, specific academic aptitude, leadership quality, etc.

Important Points

Characteristics of the gifted child:

• Easy retention of facts.
• High intellectual curiosity.
• Unusual alertness, even in infancy.
• High speed in processing information.
• Early development of a sense of time.
• Advanced logical and creative thinking.
• Excellent memory and novelty in expression.
• Curiosity, creativity, and independence in thought.

Thus from the above-mentioned points, it is clear that gifted students perform exceptionally well in any field important to human beings.

The concept of mixed age groups classrooms is an integral part of many of the alternative models of learning. In these multi-age groups, classrooms children develop a sense of being a family with their classmates where they have the freedom to experiment, take risks, and grow. 

• These mixed-aged groups explore, discover and learn together and, as a result, meaningful bonds form between our older students and their younger partners.
• The learning capacity and speed of each child are different, it is sometimes difficult for teachers to keep track of each student. The mixed age group (MAG) classrooms solve this problem efficiently, as the students help each other and approach the teacher as and when required.

Important Points

Stages of development:- Developmental influences cover a range of behaviors and transformations in a child's faculties and personalities. Social norms, institutions, customs, and laws also influence these stages. Knowledge of developmental stages is important for teachers teaching mixed-age class groups.

• It helps the teacher to identify the understanding and difficulty level of students.
• A sense of harmony exists in a class that has children of different age groups, as they co-exist by helping and learning from one another.
• Many psychologists have given child development theories; for example, Piaget's four-stage cognitive development theory helps understand the developmental stages of children.
• Piaget has identified 4 sequential stages through which every individual progresses in cognitive development. Each stage has an age span with distinctive learning capabilities. This would help frame the curriculum.

Hence, we can conclude that knowledge of developmental stages will be most significant for a teacher dealing with a class comprising students of mixed age groups.

RTE Act, 2009: The passing of the Right of Children to Free and Compulsory Education (RTE) Act 2009 marks a historic moment for the children of India. 

• RTE came into force on 1st April 2010. Under the provisions of this Act, every child in the age group of 6-14 years will be provided eight years of elementary education in an age-appropriate classroom in the vicinity of his/her neighbourhood.
• Teachers in current classrooms should design activities/teaching tasks that engage and challenges all the learners in a heterogeneous classroom.

Key Points

WHAT THE ACT SAYS:

• RTE Act, Section 3 (1) Every child aged 6 to 14 years shall have a right to free and compulsory education in a neighbourhood school until completion of elementary education.

After the implementation of the RTE Act: 

• The onus is on teachers and school heads.
• Preparing them to embrace a new culture through appropriate programs.
• So, classrooms after the implementation of the RTE Act 2009 are age-wise more homogenous.
• Banning corporal punishment, no-detention policy, continuous and comprehensive evaluation, making schools and classrooms truly inclusive, and so on.
• Protect the rights of the children to learn as per the curriculum through quality education
• Not enrolled/drop-out children be admitted to an age-appropriate class after a period of Special Training.
• No child failed or expelled from school up to class VIII (corresponds to the age group 6-14).
• It lays down the norms and standards relating to, inter alia, Pupil Teacher Ratios (PTRs) buildings, and infrastructure, school working days, teacher working hours.

Thus from the above-mentioned points, it is clear that classrooms after the implementation of the RTE Act 2009 are age-wise more homogeneous.

Development refers to an increase in structure for better and enhanced functioning of organs. It includes all the qualitative changes in an individual over a period of time by the process of learning and maturation.

• It refers to the overall changes in an individual in various dimensions - physical, mental, social, emotional, and so on. It is a wide and continuous process, thus there are some principles that need to be followed for a better understanding of the concept.

Key Points

• Development proceeds from heteronomy to autonomy.
• Heteronomy means dependence on others, while autonomy means self-reliance. Young children are dependent on others for their care and welfare, but adolescents are capable of taking care of themselves. This shows the movement from heteronomy to autonomy. The systematic presentation of concepts is related to this principle.

Important Points 

Principles of development:

• The development follows a pattern.
• Development proceeds from general to specific (global to analytical).
• Development leads to integration.
• Development is continuous.
• Individuals differ with respect to the rate of development.
• Development occurs at different rates for different parts of the body.
• Development proceeds from ego-centrism to allocentric.
• Development is Predictable.

Thus from the above-mentioned points, it is clear that the systematic presentation of concepts may be related to the principle of development proceeds from heteronomy to autonomy.

Vygotsky’s Sociocultural Theory of Learning:

• Vygotsky was a Russian psychologist who believed that social interactions play a key role in development. According to him, learning occurs when children interact with people and the environment.
• He asserted that the cognitive development of children is enhanced through social interaction with other people, particularly those who are more skilled.
• He explains this with the concept of the Zone of Proximal Development (ZPD), which refers to a range of tasks that a child can achieve only with assistance from a more skilled adult or peer called the More Knowledgeable Other (MKO). Adult assistance is provided wherever necessary which is called Scaffolding.

Key Points

Scaffolding is a teaching method that enables a student to solve a problem, carry out a task, or achieve a goal through a gradual shedding of outside assistance. Scaffolding literally means the structure which is made to support the work crew while a building is constructed or repaired.

• Scaffolding is when adults adjust the support to extend the child's current level of performance

• Scaffolding refers to a technique that provides the right kind of support in the right amount at the right time to increase a child’s competence.

• In other words, it is a means by which a child's 'zone width' (or potential for new learning) can be assessed, i.e. scaffolding helps with providing support to learners in their initial phase of learning, which is in the right amount and gradually decreases as the learner progresses.

• As children are given assistance or shown how to perform certain tasks, they use this information as a guide on how to perform these tasks and eventually learn to perform them independently.

Thus from the above-mentioned points, it is clear that scaffolding in the context of learning theories refers to temporary support in learning by adults.

Language is human communication in spoken or written form consisting of the use of words in a structured and conventional way. Syntax and semantics are both words associated with the study of language, but as linguistic expressions, their meanings differ.

Important Points

• Every sentence has syntax and semantic. The syntax is the grammar rules of a language as in the case of English it is subject followed by a verb followed the agreement. and Semantic is what does the sentence really mean. The syntax is necessary for a sentence. To follow grammar rules is important but is not sufficient for semantic correctness.
• The syntax is related to the grammar of the sentence and semantics is related to the meaning of the sentence.
• A sentence that is syntactically correct, however, is not always semantically correct.
• The sentence 'Madam drives a bicycle’ is grammatically correct but the meaning of the sentence is not correct.
• The correct sentence is "Madam rides on a  bicycle".

Hence, it is concluded that the sentence 'Madam drives a bicycle’ is correct syntactically but semantically incorrect.

A group is the aggregation of human beings. A group may have a strong influence upon the individual in that the individual gladly accepts the activities of the group. Each and every human being has their own personal interests, attitudes, values, etc. As the group consists of a number of individuals with different backgrounds etc. there are differences in the characteristic features of the various groups.

Key Points

• In order to determine how students should be classified and what instruments can best be used for making the classification, we should have in mind the reasons why they ought to be classified.
• The chief basis of classification has grown out of the grading system, and this in turn has depended upon age as its basis.
• Classification may be done on the basis of intelligence tests or IQ.

Important Points

• IQ is an acronym for Intelligence Quotient.  The IQ is a measurement of your intelligence and is expressed in a number.
• An IQ test is an assessment that measures a range of cognitive abilities and provides a score that is intended to serve as a measure of an individual's intellectual abilities and potential.
• If the students are classified on the basis of IQ, it tends to decrease their self-esteem. It may be defined as how much you appreciate and like yourself regardless of the circumstances. Students feel bad about themselves who are considered to be in the lower group.
• Accommodates all children regardless of their physical, intellectual, social, emotional, linguistic, or other conditions is known as inclusive education.
• Inclusive education valuing all learners equally and encouraging them to learn.

Hence, it can be concluded that classification of students in different groups on the basis of their IQ tends to decrease  their self-esteem and decrease​ academic performance

Intelligence test has been classified based on a number of criteria such as based on the number of participants who can attempt the test, based on items used in the test and whether the test can be used across different cultures or not. 

• Every culture is unique in terms of its values, language, expectations, demands and environmental experiences. A child reared in America will be very different in many respects from a child brought up in an Indian sub-urban area. Due to this reason, in order to assess individual belonging to different cultures psychologists came up with tests which are free from any cultural biases. Some of the famous culture-fair tests are.

Key Points

• The Culture Fair Test (Cattell, 1940), Raven’s Progressive Matrices (Raven, 1938, 1986, 1995), The Leiter International Performance ScaleRevised (Roid &Miller, 1997) and Draw-a-Man Test (Goodenough, 1926). All these and other culturally faired tests are non-verbal in nature. Now we will discuss an example of culture-fair intelligence test-Draw-a-Man test.
• Raven’s Progressive Matrices (RPM) frees itself from the effects of language and speed. The test contains abstract figures that are considered not to favour any particular culture.

Thus from the above-mentioned points, it is clear that Raven’s progressive matrices test is an example of a culture-free IQ test.

Abraham Maslow, an American psychologist, was basically a 'Humanist' and he has propounded the Humanistic Theory of Motivation. He is best known for creating "Maslow's Hierarchy of Needs".

• Maslow sees human needs in the form of a hierarchy, starting in ascending order from the lowest to the highest needs and concludes that when one set of needs are satisfied then the need for another set arises.

Important Points

Five Levels of Maslow's "Hierarchy of Needs":

• Physiological Needs: These needs are related to the survival and maintenance of human life. It includes such things as food, clothing, shelter, air, water, and other basic necessities of life.
• Safety Needs: After satisfying the physiological needs, people want the assurance of maintaining a given economic level. It includes job security personal security, the security of the income, provision for old age, etc.
• Love / belonging Needs: We are interested in conversation, social interaction, exchange of feelings, companionship, recognition, belongingness, etc.
• Esteem Needs: People are able to satisfy their need to belong, they tend to want to be held in esteem both by themselves and by others.
• Self-actualization Needs: It is the final step under the need hierarchy. It is the desire to become what one is capable of becoming to maximize one's potential and to accomplish something.

Hint 

• This news may be understood best on the basis of physiological needs.

Thus from the above-mentioned points, it is clear that the news of a woman selling her child to obtain food' may be understood best on the basis of the Theory of hierarchical needs.

CCE refers to a school-based evaluation, which covers all aspects of school activities related to a child’s development. It emphasizes two-fold objectives such as continuity of evaluation and assessment of learning outcomes comprehensively. It covers all the domains of learning i.e. cognitive, affective, and psychomotor domains.

Important Points

• The theory of information processing is based on computer analogy.
• The theory uses a computer model to describe human learning.
• Information comes in, it gets processed, and then it gets stored and retrieved. So, it is not supported by the word comprehensive.

Key Points

The word ‘Comprehensive’ in the scheme Continuous and Comprehensive Evaluation is supported by the following:

• Theory of multiple intelligence
• J.P. Guilford’s theory of the structure of intellect
• L.L. Thurstone's theory of primary mental abilities

 Hint

• The term ‘continuous’ refers to regularity in assessment. The development of a child is a continuous process. Therefore, students’ development should be assessed continuously. Evaluation has to be completely integrated with the teaching and learning process.
• The second term associated with CCE is ‘comprehensive’. The term ‘comprehensive’ implies that evaluation of learners’ performance is carried out in both scholastic and co-scholastic areas.
• CCE is comprehensive as it takes care of the achievement of learners in various school subjects from science, mathematics, languages, social science, work education, and physical health activities as well as includes the assessment of co-scholastic abilities like attitude, values, life skills, interests, habits, etc
• CCE is comprehensive in terms of tools and techniques used for the evaluation of learners.
• CCE is comprehensive in nature as it is used for assessing various learning outcomes like knowing, understanding, applying, analyzing, evaluating, and creating.

Hence, we can conclude that the word ‘Comprehensive’ in the scheme Continuous and Comprehensive Evaluation is supported by the following except theory of information processing.

Assessment plays a significant role in the teaching-learning process. Assessment of learning helps a teacher to design his/her teaching in a better way and to know the attainment level of learners in the subject content. 

• From the assessment, it is revealed that if the desired level of mastery has not been attained by learners, the teaching-learning process may be repeated and certain remediation may be provided to them.
• It helps students to know their progress in learning and learning difficulties in different subject areas.
• The quality in assessment decides the quality of learning.
• If you carry out the assessment effectively, learning will be enhanced otherwise learning will not match the expectation of the assessment.

Key Points 

Assessment for Learning-

• Assessment for learning influences learning by reinforcing the connections between assessment and instruction.
• Assessment is school-based and integral to teaching-learning
• Multiple evidence-based
• Assessing learning progress holistically
• Sensitive to individual learning needs
• Serves to observe changes in learning progress over time
• Helps teacher review and modify the teaching-learning

Assessment as Learning-

• A collaborative and participatory approach
• Helps children seek resources of knowledge
• Building skills of learning to learn among children

Assessment of Learning-

• Criteria-based comprehensive assessment
• Multiple evidence-based assessments
• Reporting without labelling or comparing children
• Sharing learning progress with the stakeholders.

Thus from the above-mentioned points, it is clear that assessment for learning influences learning by reinforcing the connections between assessment and instruction.

Gender refers to the socially constructed differences between men and women. It refers to the masculine and feminine qualities, behavior, roles, and responsibilities that society upholds. Gender can be changed / re-oriented. 

• Gender bias is the tendency to prefer one gender over another. It is a form of unconscious bias, or implicit bias, which occurs when one individual unconsciously attributes certain attitudes and stereotypes to another person or group of people. These described behaviors affect how the individual understands and engages with others.
• Gender Stereotyping refers to the relatively fixed and overgeneralized attitudes and behaviors that are considered normal and appropriate for a person in a particular culture based on his or her biological sex.
• It is an unfair idea that refers to a generalized view or characteristics that ought to be possessed by women and men.

 Key Points

• Gender stereotyping is defined as the overgeneralization of characteristics, differences, and attributes of a certain group based on their gender.
• The given fact shows the tendency of stereotyping masculine and feminine roles, which sadly exists in schools.
• Girls are generally given home-based tasks like washing clothes and utensils, cleaning, and cooking due to the stereotyped thinking of Indian society.

Hence, we can conclude that in science practicals, boys generally take control of apparatus and ask girls to record data or wash utensils. This tendency reflects that stereotyping of masculine and feminine roles takes place in schools also.

Additional InformationFollowing are few ways by which a teacher should be able to maintain gender equality in the classroom:-

• Be reflective and objective.
• Use gender-neutral language when appropriate.
• Use project-based learning.
• Provide equal opportunity to both boys and girls.
• Seat and group students intentionally.

However, by making efforts to break down traditional gender roles in the classroom, you can better prepare students to seek knowledge and participate more fully in discussions and other learning opportunities in many fields.

The teacher should provide a learning environment where learners actively create their meaning and develop their understanding through their active engagement in various contexts. The learning environment would impact the learner learning in both ways negative or positive.

Key Points

Role of Gender in learning

• Before entering school, children have a socially constructed idea of gender differences of equality and inequality. The school has its own social construction of gender differences. Depending on their socio-cultural background, teachers bring to school their ideas of gender stereotypes.
• The child's idea of gender stereotypes may or may not match with that of the school, teachers, and peer group. So how teachers and students construct gender in the classroom, impacts the learning environment. It could impact in both ways positive or negative. Like if the teacher encourages them to break gender stereotypes and zero biasedness based on gender in the class it will put positive impacts on learners while if the teacher and students promote gender biasedness and stereotypes it will impact learning in a negative way.
• The school practices Meaning and Scope may reinforce the child's idea of stereotypes or the child maybe required to adjust or sort out between differing views on gender equations. Although school is a formal environment of learning, it has all the characteristics of a society.
• Most of these societal characteristics are observable in manifested behaviors as these constitute the learning environment.

Additional Information

• Teachers play a significant role in determining the psychosocial environment for individual student's learning. Teachers can also set the physical environment for teaching-learning activities. Teacher behavior considerably affects the academic performance of individual students.
• Peer group behavior is another component in the efficacy of the learning environment for individual students. All these components constitute the psychosocial aspects of the learning environment.
• The physical environment is another factor that determines and limits the scope of the learning environment in a school.

Hence we can say that constructing gender in the classroom impacts the learning environment.

RTE 2009 (The Right of Children to Free and Compulsory Education Act or The Right to Education Act): The government on August 4, 2009, enacted and on April 1, 2010, brought into effect  RTE which gave provision:

Key Points

• The right of children to free and compulsory education till completion of elementary education in a neighbourhood school.
• It clarifies that ‘compulsory education’ means the obligation of the appropriate government to provide free elementary education and ensure compulsory admission, attendance and completion of elementary education to every child in the six to fourteen age group. ‘Free’ means that no child shall be liable to pay any kind of fee or charges or expenses which may prevent him or her from pursuing and completing elementary education.
• It makes provisions for a non-admitted child to be admitted to an age-appropriate class.
• It specifies the duties and responsibilities of appropriate Governments, local authority and parents in providing free and compulsory education and sharing of financial and other responsibilities between the Central and State Governments.
• It provides for rational deployment of teachers by ensuring that the specified pupil-teacher ratio is maintained for each school, rather than just as an average for the State or District or Block, thus ensuring that there is practically no urban-rural imbalance in teacher postings. It also prohibits the deployment of teachers for non-educational work, other than the decennial census, elections to the local authority, state legislatures, parliament, and disaster relief.
• It provides for the appointment of appropriately trained teachers, i.e. teachers with the requisite training and academic qualifications.
• For children in 6-14 age group, it prohibits (i) physical punishment and mental harassment, (ii) screening procedures for admission, (iii) capitation fees, (iv) private tuition by teachers, and (v) running of schools without recognition.
• It provides for the development of curriculum in consonance with the values enshrined in the Constitution and which would ensure the all-round development of the child, building on the child’s knowledge, potentiality and talent and making the child free from fear, trauma and anxiety through a system of child-friendly and child-centred learning.
• It provides for protection and monitoring of the child’s right to free and compulsory education and redressal of grievances by the National and State Commissions for Protection of Child Rights, which shall have the powers of a civil court.

Thus from the above-mentioned points, it is clear that the word ‘Compulsory’ in the ‘Right to Free and Compulsory Education 2009’ means, appropriate governments will ensure admission, attendance and completion of elementary education.

Lesson Planning: A lesson plan is the teacher's outline or road map of what students need to learn and how it will be done effectively during a specified time. It is a means of taking advanced decisions about the selection, sequencing, and execution of various activities to be performed in a classroom with a view to ensuring the learning of children.

Key PointsWhile planning a lesson, the following principles should be kept in mind:

• The planning should be flexible. It can be changed according to the needs of the teacher and the students.
• The teacher should have mastery in the topic from which the subject matter has been selected for a particular lesson.
• The teacher should plan well in advance. He/she should go fully period to the class.
• The teacher should be scientific in his treatment of learning.
• The teacher should use various teaching aids while presenting the topic. The presentation should be interesting.
• The plan should be prepared within the required limitations. It should not be too long.
• The teacher should provide ample opportunities to the students for the practical use of their knowledge.
• The teacher must know his/her pupils thoroughly and organize the materials in a psychological rather than merely a logical fashion

Important Points

• The objectives of teaching a particular lesson should be stated as per the competency to be developed amongst children. Thus, the objectives must be clear before teaching.
• Teachers should have a clear picture of the students, the syllabus, activities, language skills, language types, subject and content, and institution and its restrictions.
• Such knowledge guarantees that the materials can be appropriate for lesson objectives.
• A teacher should take into consideration the flexibility aspect while planning the lesson so that any changes can be incorporated during teaching.

​Hence, from the above-mentioned points, it is clear that the rigidity of planning principle is not involved in lesson planning.

Independent study is a process, a method, and a philosophy of education whereby a learner acquires knowledge by his or her own efforts and develops the ability for inquiry and critical evaluation.

Key Points

Self-regulation: Self-regulation of learners means the ability to monitor their own learning. It monitors not only academic learning or mental ability.

• Self-regulated learners are self-motivated, they are attempting to gain new skills, knowledge, and attitudes to improve their performance in any field.
• Self-regulated learning can be useful in improving family life and health, enjoying the arts and physical recreation, participating in a hobby, or simply increasing their intellectual capital.
• It involves self-awareness, self-motivation, and behavioural skill to implement that knowledge appropriately. The three steps in the process are
• Analyzing the task and planning the process
• Performing the task according to the plan
• Implementing self-evaluation of the task

Thus from the above-mentioned points, it is clear that ‘Self-regulation of learners’ means ability to monitor their own learning.

The meaning of "progressive education" depends on the meaning assigned to the word 'progress'. Progress implies movement and movement involves changes in some direction.

Key Points

'Progressive education is that body of educational thought that nourished in the fertile mind of John Dewey. 

According to John Dewey, “Education is reconstruction or reorganisation of experience which adds to the meaning of experience and which increases the ability to direct the course of subsequent experiences.” This view implies that-

• the child already has acquired some experiences from his/her interaction with the environment

• education plays a role in reconstructing these experiences in the required direction in order to add meaning to those experiences

• ‘reconstruction of experience’ by themselves that results in knowledge which further helps in understanding subsequent knowledge through subsequent experiences.

• The values, ideals, goals, mores, traditions and culture of a society are inculcated in a child through education in order to make him/her an effective member of the society.

• Dewey School is shown to be an incredibly original and creative endeavour at rest, demonstrating most notably that Dewey's concept and its reality are not the same. In truth, the "schooling grammar" took its toll. Following some shaky beginnings, the LabSchool practice diverged significantly from Dewey's educational approach and only marginally from that of other contemporary progressive institutions.

Thus from the above-mentioned points, it is clear that the ‘Lab Schools’ advocated by John Dewey were examples of Progressive Schools.

Projects are developed generally in groups where students can learn various things such as working together, problem-solving, decision making, and investigating activities. Group activities enable students to discover deeper meaning in the content and improve thinking skills.

Important Points 

Facilitating social participation:-Group project activities give students a chance to interact with each other during the teaching-learning process, which enhances the sense of cooperation among them. Dewey believed that the school is a mini institution of society. Thus, schools should strive to create an environment that promotes social learning.

Key PointsAdvantyages of Group project activity

• It may involve a student or a small group of students.
• It provides an opportunity for the students to identify a problem, design a work plan,  address the problem, search for appropriate resources, carry out their plan, and draw conclusions based on data/information collected.
• It encourages children to work together and sharing their knowledge and ideas towards the same goal.
• It can help students develop a host of skills that are increasingly important in the professional world.
• It can reinforce skills that are relevant to both group and individual work.

hence, we can conclude that group project activity as prescribed by CBSE is a powerful means of facilitating social participation.

Motivation is defined as the reason, incentive, enthusiasm, or interest that causes a specific action or certain behaviour. Motivation is an important element of self-understanding and learning.

It is simply the reason for an action and that which gives purpose and direction to behaviour. There are two primary types of motivation namely, intrinsic motivation and extrinsic motivation. 

Key Points

Intrinsic Motivation: There is a high relationship between the activity to the goal. In such a situation, we say, the person is intrinsically motivated. Cognitivism holds the view that curiosity, interest, or a sense of accomplishment are sources of motivation that are intrinsic (internal) rather than responding to external forces.

• Intrinsic motivation is an inner drive that propels a person to pursue an activity**, not for external rewards**, but because the action itself is enjoyable.
• In other words, a person is motivated by the fun, challenge or satisfaction involved with an activity, not for an outside outcome, pressure or reward.
• An intrinsically motivated activity will always be rewarded due to the direct relationship between the activity and the goal. This secures a continuous motivation to do the activity.
• The element of joy experienced in doing the activity actually sustains the activity. The pursuit of our hobbies which give us pleasure are also examples of intrinsic motivation.
• Intrinsic motivation remains constant due to the high relationship between the activity and the goal.
• An intrinsically motivated person will work on a solution to a problem because the challenge of finding a solution provides a sense of pleasure. In neither case does the person work on the task because there is some reward involved, such as a prize, a payment, or in the case of students, a grade.
• Set challenges, Interest, and Purpose are some methods to increase intrinsic motivation.

Thus from the above-mentioned points, it is clear that for an intrinsically motivated student, rewards are not at all required. 

Hint

• Extrinsic motivation refers to a behaviour that is guided by earning rewards or avoiding punishment.
• External awards lead to temporary motivation.​

Achievement motivation (often termed as the need for motivation) is the desire to accomplish difficult tasks and to excel. Individuals differ greatly in the desire for achievement and the tendency to persist at challenging tasks is obvious. For some persons, accomplishing difficult tasks and meeting high standards of excellence are extremely important; whereas for others, just getting by is quite enough.

Important Points

The concept of achievement motivation was propounded by David​ McClelland. He aimed to explain how different types of motivation affect people's performance within a business setting. Achievement-based motivational theory and training models, and promoted improvements in employee assessment methods, advocating competency-based assessments and tests, arguing them to be better than traditional IQ and personality-based tests. 

Key Points 

McClelland has proposed that there are three major motives for personnel accomplishment. Each person has a tendency to be motivated by one of these needs. These motives are as follows:​

Need for Achievement:

• It is greatest for that individual who has a strong desire to excel.
• Their only focus is on success.
• They prefer work that has a moderate chance of success.
• Achievers prefer to work alone.

Need for Affiliation:

• They don't like high risk or uncertainties.
• They favour collaboration over competition.
• These people perform better in groups.
• They are very cooperative.
• They are concerned about 'being liked' and 'being accepted'.

Need for Power:

• They need Agreement and Compliance.
• They like to win arguments.
• They enjoy competition and winning.
• They enjoy status and recognition.
• They like to control others.
• They have the ability to influence people.

Thus from the above-mentioned points, it is clear that achievement motivation is the tendency to persist at challenging tasks.

Waiting time is the time teacher waits for the student to respond to the questions or coming to the classroom etc.

Important PointsGive students five to 15 seconds to formulate a response to a question for which they should know the answer. Not every learner processes thinking at the same speed. Quality should be measured in the content of the answer, not the speediness.

• Waiting for several seconds after asking a question so that students, particularly introverted ones, are able to gather their thoughts before responding is proven to expand participation and improve the quality of student responses.
• The time taken by the student varies according to the difficulty level of the question and the IQ of the student.
• A child with a high IQ  solves the question fast as compared to a low IQ student.

Hence, we can conclude that the ideal ‘Waiting Time’ for getting responses from students should be proportional to the difficulty level of the question.

Questions have long been used as a teaching tool by teachers and preceptors to assess students’ knowledge, promote comprehension, and stimulate critical thinking.

• Divergent questions that promote deep thinking, require analyzing and evaluate concepts.
• Lower-order, convergent questions that rely on factual recall of prior knowledge.

 . 

Important Points

• Being the Chairperson of a Board of School Education, to answer the question there are lots of possible solutions so it is a higher-order divergent question.

Key Points

Higher-Order Questions: Higher-order questions are those that the students cannot answer just by simple recollection or by reading the information “verbatim” from the text.

• Higher-order questions put advanced cognitive demand on students.
• They encourage students to think beyond literal questions.
• Higher-order divergent questions seek multiple perspectives and multiple possible answers to questions and problems.
• It is used to generate ideas with various possible solutions.
• Higher-order questions promote critical thinking skills because these types of questions expect students to apply, analyze, synthesize, and evaluate information instead of simply recalling facts.

Hint

• High order convergent question example, “What other tools could the main character have used to resolve the conflict?” is an example of a convergent question.
• Low order questions: A low order question has a limited number of acceptable answers. “How do you perform a transaction on the point of sale system?”

Hence, we can conclude that the above type of question is an example of higher-order divergent.

An ideal classroom is a positive place where a student can come to work toward specific goals set before them in the class objectives. The teacher is to be positive, organized, outgoing, confident, and compassionate. 

Important Points

• As a teacher, if the child says something then it's the teacher's responsibility to respond to the question of the child.
• Oh really, your mother rang up Principal ma’am last night. Did she seek an appointment with her? is the correct response given by the teacher.
• She should respond politely.

Hint

• Dear child, you are not using the correct form of verb, it should not be ringed, it should rather be rang and Why don’t you listen carefully? As I told you earlier, it should be rang, not ringed. These are not the correct options as the question is not about the grammar of the child. First, respond to the student politely.

Thus, it is concluded that A student says, "My mother ringed Principal mam last night." As a teacher your response should be Oh really, your mother rang up Principal ma’am last night. Did she seek an appointment with her?

Lawrence Kohlberg, an American psychologist, has propounded the 'Theory of Moral Development. He has systematically studied moral development in his theory that is categorized into 3 levels and 6 stages.

Key Points

Level 1: Pre-conventional Morality It consists of the first two levels of moral development. Here morality is judged based on the standards of adults and the consequence of an action.

Important Points

• Stage I (Obedience and Punishment Orientation) — An action is immoral if it is punished by the authority. Children in primary schools follow this stage. At this, children have the fear if they are not following the obedience principle get punished by the teachers or parents.
• Stage II (Individualism and Exchange) — This stage is self-interest driven and children understood that different individuals may have different viewpoints for the first time. An action is considered morally correct if it is in the best interest of the individual.  This stage is also followed by the children at the primary level.

Additional Information

Level 2: Conventional Morality: This level consists of stages three and four. During this level, children start internalizing the value of society to judge morality.

• Stage III (Good Interpersonal Relationship) — The intention of the actor is more important in terms of judging moral values. If the intention is to gain the consensus of others or approval of the society then the actor will be judged morally right. At this stage, the children have the ideology of a good boy–good girl attitude.
• Stage IV (Maintaining the Social Order) — Judgment of morality is based on one’s duty, law, and social order. actively maintaining the current social system ensures positive human relationships and societal order.

Level 3: Post-Conventional Morality: The last level consist of stage five and six of moral development. According to Kohlberg, very few people can reach this level. Here, the individual perspective is given more importance over social rule and order. Individuals judge morality based on basic human rights and justice.

• Stage V (Social Contract and Individual Rights) – In this stage, the individual or child understands that different people and communities may hold different views and laws. Laws of society are not rigid edicts and should be changed with the change in the time and needs of society.
• Stage VI (Universal Principles) – Individuals judge the morality of the actor based on some universal principles that transcend beyond society’s rules and regulations.

Hence, we can conclude that children in primary schools follow obedience and punishment orientation and Individualism and Exchange​ stages as proposed by Lawrence Kohlberg.

Assessment in preschool should be formative, continuous, and flow from the experiences planned in the curriculum. It implies observing and documenting the development of the child, by interpreting the evidence from day-to-day experiences of the child to recognize and encourage strengths and addressing learning/developmental gaps.

\

Key Points

Anecdotal records:

• Anecdotal records are short and significant descriptions of the performance and behaviour of children in unexpected events, which would not be documented otherwise and are quite useful to observe day-to-day basis.
• Brief written notes based on observations of children—how and where children spend time, their social relationships, their use of language, modes of interaction, information about health and nutrition habits.
• An anecdotal record should be brief, concise, the objective report of an incident exactly happened.
• It gives an accurate description of events and a factual report with enough detail.

Additional Information

Uses of anecdotal records-  

• Anecdotal records are of special value in indicating social and emotional situations
• They give a realistic picture of students’ personality
• Anecdotal records are very useful in fields where formal measurements are very difficult
• A healthy teacher-pupil relationship is established when teachers are asked by the school organization to write down anecdotal reports.

Thus from the above-mentioned points, it is clear that 'it is subjective evidence of behaviour and therefore does not provide feedback for scholastic area' is not the feature of the anecdotal record.

Important Points

Given:

$\dfrac{3}{8},\dfrac{4}{5},\dfrac{31}{40},\dfrac{9}{20},\dfrac{7}{10}$

Range = $\left(\dfrac{1}{2} \right)$ to $\left(\dfrac{3}{4}\right)$ 

Calculations:

Taking the LCM of denominators of all the term,

LCM of (8, 5, 40, 20, 10, 4, 2) = 40

Fractions with 40 as denominators are,

$\dfrac{15}{40},\dfrac{32}{40},\dfrac{31}{40},\dfrac{18}{40},\dfrac{28}{40}$

Range with 40 as denominators are,

$\dfrac{20}{40}$ to $\dfrac{30}{40}$

The fraction that lies within the range is $\dfrac{28}{40}$

∴ The fraction that lies within the given range is $\dfrac{7}{10}$

Given:

• 20, $-\frac{3}{4}$, $\frac{1}{2}$, 10

Calculations:

Square of -20 = 400

Square of -3/4 = 9/16

Square of 1/2 = 1/4

Square of 10 = 100

Comparing the numbers and their squares,

⇒ - 20 < 400

⇒ -3/4 < 9/16

⇒ 1/2 > 1/4

⇒ 10 < 100

∴ Amongst the given numbers, only 1/2 is greater than its square

Given:

3 × 105 + 4 × 103 + 7 × 102 + 5

Calculations:

Solving the given expression,

⇒ 3 × 105 + 4 × 103 + 7 × 102 + 5

⇒ 300000 + 4000 + 700 + 5

⇒ 304705

∴ The value of the given expression is 304705

Given:

Sum of two numbers = 32

One of the two numbers = -36

Calculations:

Let the other number be N

⇒ N + (-36) = 32

⇒ N - 36 = 32

⇒ N = 32 + 36

⇒ N = 68

∴ The other number is 68

Given:

Population of a city = 30.3 million

Concept used:

1 million = 1000000

Calculations:

Population of the city = 30.3 × 1000000

⇒ 30300000

∴ The given number is same as 30300000

Given:

a3 = 1 + 7

33 = 1 + 7 + b

43 = 1 + 7 + c

Calculations:

Solving the given terms,

Solving for a,

⇒ a3 = 1 + 7

⇒ a3 = 8

⇒ a = 2

Solving for b,

⇒ 33 = 1 + 7 + b

⇒ 27 = 8 + b

⇒ b = 19

Solving for c,

⇒ 43 = 1 + 7 + c

⇒ 64 = 8 + c

⇒ c = 56

The sum of a, b and c = 2 + 19 + 56

⇒ 77

∴ The value of a + b + c is 77

Given:

210 - 1 

Calculations:

Solving the given term,

⇒ 210 - 1 

⇒ 1024 - 1

⇒ 1023

1023 is an odd number and thus can only be divisible by another odd number 

Option 1, 3, and 4 are even numbers thus 1023 is not divisible by these numbers

or, If the sum of the digits is divisible by 3 then the number is also divisible by 3

1 + 0 + 2 + 3 = 6 and 6 is divisible by 3

∴ 210 - 1 is divisible by 3

Given:

4, 20 and 28 

Calculations:

Expressing the given terms in prime factor form,

⇒ 4 = 2²

⇒ 20 = 2² × 5

⇒ 28 = 2² × 7

HCF = 2² = 4

LCM = 2² × 5 × 7= 140

Sum of HCF and LCM = 4 + 140 = 144

∴ The sum of HCF and LCM is 144

Given:

0.33 ÷ 0.11

Concept used:

A number can be expressed as a percent by multiplying the number by 100

Calculations:

Solving the given term,

⇒ 0.33 ÷ 0.11

⇒ 33 ÷ 11

⇒ 3

Expressing as a percent = 3 × 100

⇒ 300%

∴ The given term expressed as percent is 300%

Shortcut Trick

Sum of numbers = 5.02 + 5.18 + 5.12 + 5.007 + 5.018 = 25.345

Mean = 25.345 ÷ 5 = 5.069

Sorted Numbers: 5.007, 5.018, 5.02, 5.12, 5.18 → Median (3^rd term) = 5.02

Required Sum = 5.069 + 5.02 = 10.089

∴ The correct answer is 10.089.

Alternate Method

Given numbers: 5.02, 5.18, 5.12, 5.007, 5.018

Formula Used: Mean = (Sum of all observations) ÷ (Total number of observations); Median = Middle term when arranged in ascending order (for odd n).

Step 1: Calculate the Mean

⇒ Sum = 5.020 + 5.180 + 5.120 + 5.007 + 5.018

⇒ Sum = 25.345

⇒ Mean = 25.345 ÷ 5 = 5.069

Step 2: Find the Median

⇒ Arrange in ascending order: 5.007, 5.018, 5.02, 5.12, 5.18

⇒ Median = 3^rd term = 5.02

Step 3: Sum of Mean and Median

⇒ Result = 5.069 + 5.02 = 10.089

∴ The correct answer is 10.089.

Additional Information

Arithmetic Mean

The Mean is the average of a data set, calculated by dividing the total sum of values by the number of observations.

Median of Data

The Median is the middle value when data is sorted. For n terms, if n is odd, it is the ((n+1)/2)^th term; if n is even, it is the average of (n/2)^th and (n/2 + 1)^th terms.

Empirical Relationship

For moderately skewed distributions: Mode = 3 × Median − 2 × Mean.

Given:

Side of first square = x cm

Side of second square = (2x + 1) cm

Sum of their perimeter = 100 cm

Formula used:

Perimeter = 4 × Side of square

Area = (Side of square)²

Calculations:

Perimeter of first square = 4x

Perimeter of second square = 4 × (2x + 1) 

⇒ 8x + 4

Sum of their perimeters = 4x + (8x + 4)

⇒ 12x + 4 = 100

⇒ 12x = 96

⇒ x = 8

Side of first square = 8 cm

Side of second square = (2 × 8 + 1) = 17 cm

Area of the bigger square = 17 × 17

⇒ 289 cm²

∴ The area of the bigger square is 289 cm²

Concept used:

A figure has a line of symmetry if there is a line about which the figure may be folded so that the parts of the figure will coincide with each other.

Detailed solution:

In the figure given below:

It can be observed that the given figure can be folded 6 times so that the parts of the figure will coincide with each other

∴ The given figure has 6 lines of symmetry

Given:

Circumference of circle = 3 cm

Formula used:

Circumference of circle = 2 π R

Area of circle = π R²

Where,

R = Radius of circle

Calculations:

Let the radius of the circle be R

⇒ 2 × π × R = 3

$⇒ R = \frac{3}{2π}$

Area of circle = $\pi \times \frac{3}{2\pi} \times \frac{3}{2\pi}$

$\Rightarrow \frac{9}{4\pi}$

∴ The area of the circle is $\frac{9}{4\pi }$

Given:

Area of rectangle = A cm²

Length = l cm

Formula used:

Perimeter of rectangle = 2 × (Length + Breadth)

Area of rectangle = Length × Breadth 

Calculations:

Let the breadth of rectangle be b

⇒ l × b = A

⇒ b = A/l

Perimeter = 2 × [l + (A/l)]

$\Rightarrow 2l + \dfrac{2A}{l}$

∴ The perimeter of the rectangle is $2l+\dfrac{2A}{l}$

Given:

Speed for 1^st km= 30 km/h

Speed for 2^nd km = 40 km/h

Formula used:

Time taken = Distance / Speed

Average speed = Total distance covered / Total time taken

Calculations:

Let the time taken for first and second kilometer be t₁ and t₂

Time taken for first kilometer

⇒ t₁ = 1/30 hour

Time taken for the second kilometer

⇒ t₂ = 1/40 hour

Average speed = $\frac{1 +1}{\frac{1}{30} + \frac{1}{40}}$

$⇒ \frac {2}{\frac{40 + 30}{30 \times 40}}$

$⇒ \frac{2 \times 1200}{70}$

$\Rightarrow \frac{240}{7}$

$\Rightarrow 34 \frac{2}{7}$

∴ The average speed of the car for the 2 km is ​$34 \frac{2}{7}$

Given:

Volume of cube = 125 cm³

Formula used:

Volume of cube = (Side of cube)³

Area of one of its face = (Side of cube)²

Calculations:

Let the side of cube be 'a'

Volume of cube = a³

⇒ a³ = 125 

⇒ a = 5 cm

Area of its one face = a²

⇒ 5 × 5

⇒ 25 cm²

∴ The area of its one face is 25 cm²

Given:

∠BAD = 62° 

∠BDC = 119° 

∠CBD = 18° 

Concept used:

Sum of all the angles made at a straight line is 180°  

Sum of all the angles of a triangle makes 180° 

Calculations:

Let the ∠ABD be x

Sum of angles at a straight line = 180° 

⇒ ∠BDC + ∠BDA = 180° 

⇒ ∠BDA = 180° - 119°    

⇒ ∠BDA = 61° 

Sum of all the angles of ΔABD,

⇒ ∠BAD + ∠BDA + ∠ABD = 180° 

⇒  62° + 61° + ∠ABD = 180° 

⇒ ∠ABD = 180° - 123° 

⇒ ∠ABD = 57° 

∴ The value of ∠ABD is 57°

Given:

PQ = TR 

PR = TQ

Concept used:

SSS congruence rule → If all three sides of one triangle are equal to the corresponding sides of another triangle, then the two triangles are congruent

Detailed solution:

Comparing the equal sides of the two triangles,

PQ = TR

PR = TQ

QR = QR

∴ Δ PQR ≅ Δ TRQ

Given:

x2 + 7x + 10

x2 - 3x - 10 

Calculations:

Factorising the first equation,

⇒ x2 + 7x + 10 = 0

⇒ x2 + 2x + 5x + 10 = 0

⇒ x(x + 2) + 5(x + 2) = 0

⇒ (x + 5)(x + 2) = 0

Factorising the second equation,

⇒ x2 - 3x - 10 = 0

⇒ x2 - 5x + 2x - 10 = 0

⇒ x(x - 5) + 2(x - 5) = 0

⇒ (x - 5)(x + 2) = 0

Comparing the factors of both the equations, we get

Common factor = (x + 2) 

∴ The common factor of both the equations is (x + 2) 

Alternate Method

Alternatively, we can directly check options

Checking option 3, both equations give 0 at x = -2

Additional Information

If (x - n) is a factor of ax² + bx + c

Then at x = n, ax² + bx + c = 0

Given:

Sum of two positive numbers = 63

One number = 2 × Other number

Calculations:

Let the number be x

2 × Other number = x

⇒ Other number = x/2

Sum of the numbers = x + (x/2)

⇒ x + (x/2) = 63

⇒ x/2 = 63 - x

⇒ 2/x = 1/(63 - x)

⇒ 2 = x/(63 - x)

∴ The equation is $\dfrac{x}{63-x}=2$

Evaluation is an integral part of the teaching-learning process and not apart from it. One of the important functions of evaluation is to provide feedback to students and teachers, which may help in the improvement of the teaching-learning process.

• Written tests whether objective or essay type provides information about the product of a task but do not provide adequate information about the process of learning in terms of student's performance on the learning tasks or about the performance itself.
• The function of teachers is to help students learn by imparting knowledge to them and by setting up a situation in which students can and will learn effectively. So, it is important for the teachers to make the learning environment comfortable

 Important PointsIn the class test that followed after the unit, the teacher asked about the problems on the construction of quadrilateral.No one in the class was able to perform well in the test. The reason may be:-

• There is a gap between the instructions given in class and the assessment conducted.
• If the majority of the students did not understand the concept effectively and responded badly in their test, it means the teacher would not be able to teach the related concept.
• The teacher taught the properties of quadrilaterals but tried to assess construction-related problems that were not taught by him.

Hence, we can conclude that the reason may be there is a gap between instructions given in the class and the assessment conducted.

Teaching is a complex, multifaceted activity, often requiring us as instructors to juggle multiple tasks and goals simultaneously and flexibly.

• Effective teaching involves acquiring relevant knowledge about students and using that knowledge to inform our course design and classroom teaching.
• It involves aligning the three major components of instruction: learning objectives, assessments, and instructional activities.

Important Points“How does a square form a parallelogram? Explain.” Here, the teacher is providing an opportunity to students to explain the question so that they can think and reflect.

• Different students will come with multiple responses.
• Teachers reflect on their practice to grow and improve.
• Students will use their knowledge to explain the question.
• The concept will be more if students will reflect on it

Hence, we can conclude that the objective of the teacher is giving an opportunity to students to think and reflect.

We want to show that if we add two odd numbers, the sum is always an even number. The only way to achieve that is to express an odd number in its general form. Then, we add the two odd numbers written in general form to get a sum of an even number expressed in a general form as well.

Key Points Effective teachers are those who explained well the concepts in the class with various examples.

• Here, all the students are quoting the same examples as 5 +7=12, they have just memorized the concept.
• The students have a problem of understanding the logical proof of the question.
• If the teacher proved this statement then this problem would not come.

Hence, we can conclude that It is observed that to a problem like ‘Show that the sum of any two odd numbers is an even number’, most of the students replied by quoting one example, say, 5 + 7 =12. Students answered this question inappropriately as students have not learned the logical proof for the statement in the class.

Assessment is a process of collecting relevant information on student learning. It is one of the crucial components of the teaching-learning process. Assessment does more than just measuring learning. The Assessment Strategies that can be used to encourage interdisciplinary Mathematics are stated below.

• The assessment strategies to test the interest and aptitude of the learner in mathematics are checklist, portfolio, project method, and class participation.

Key Points

Portfolio Assessment is a purposeful collection of work products and evidence used by teachers or students in a systematic way to identify student's strengths and weaknesses.

• The portfolio is a wonderful resource culminating in a collection of student work, thoughts, and reflections. It is the source to provide a summary of the school year.
• It is a powerful tool that allows students to monitor their academic performance of the student.
• Portfolio assessment can help teachers and students to detect and remedy weaknesses and misunderstandings which can increase student's performance.
• Portfolio of Mathematics students can have a collection of work that student has done, which can include homework, test, class notes, quizzes, assignments, worksheets, mathematics lab record, mathematical model, mathematical vocabulary, research,  student-generated problems, etc.
• It serves as a guide for future learning by illustrating students present level of achievement.
• It supports the assessment, evaluation and communication of student learning.​

Hence it is clear that a portfolio of mathematics students can have records of assignments, worksheets, math lab activity records, write-up of any mathematics model, mathematical posters and cards, any new type of problem attempted or generalizations made, etc.

Mensuration is the branch of mathematics that studies the measurement of geometric figures and their parameters like length, volume, shape, surface area, lateral surface area, etc. 

Key PointsThe objective "Learners will be able to understand the application of mathematics" is inappropriate because

• compared to the content it is a very vast objective as it talks about understanding and application of mathematics rather than just mensuration.
• the concept is mensuration and the objectives are also should be specified according to it.
• including the whole mathematics in the objective makes it inappropriate.
• "learners will be able to understand the application of mensuration" would have been the correct one.

Hence "Learners will be able to understand the application of mathematics" this objective is inappropriate, as the objective is vague and not well defined.

Earlier, a subject-centred curriculum used to be followed which was also known as ‘Traditional Curriculum’ and we have moved away from this after the implementation of NCF-2005. The previous approach to curriculum laid more emphasis on content in comparison to learners and the teaching process. The needs and interests of the child had no place in this curriculum. Children were expected to learn and memorise facts, concepts, processes, skills etc, and reproduce them at the time of examination. 

NCF 2005 recommends that the main goal of mathematics education is the development of children's ability in mathematization. Basically, it means that children should learn to think about any situation using the language of mathematics. They can use the tools and techniques of mathematics in real life. 

Note that:

• The paradigm shift from ‘behaviourism’ to ‘constructivism’ as advocated by NCF-2005, has to be seen as the recent trend in the teaching-learning process at school in our country.
• This trend or shift has been the outcome of criticism, doubts, and questions about the validity of the subject-centred approach to curriculum development, dominated by textbook contents that existed at that time.
• It is imperative that teachers should have a clear understanding of the various approaches and the trends in the development of curriculum.
• The four major components in any educational process are curriculum, teachers, students and the contexts.

Hence, it can be concluded that the present NCERT textbooks on Mathematics are written keeping in mind the recommendations of the National Curriculum Framework - 2005.

Mathematics is a systematized, organized, and exact branch of  Science. It plays an important role in accelerating the social, economical, and technological growth of a nation. It helps in solving problems of life that need enumeration and calculation.

Key Points 

• Specific objectives are short-term immediate goals or purposes that may be achieved through the classroom instructional/educational process. Thus we may call such an objective an educational objective/instructional objective.
• Bloom (1956) had organized various educational objectives in a hierarchical order and we call it Bloom’s Taxonomy of Educational Objectives. The educational objectives falling in each domain are hierarchically placed in ascending order of complexity.
• Cognitive Domain: Cognitive means ‘knowledge’. The levels falling under the cognitive domain are as follows:
• Remembering: identifying the steps to solve, factor, evaluate, etc.
• Understanding: describe what we are looking for and why – zeros, vertex, intersection, etc.
• Apply: solve an equation or draw a graph.
• Analyze: compare, contrast, and classify different functions.
• Synthesis: Synthesis refers to the ability to put parts together to form a new whole.
• Evaluation: Evaluation is concerned with the ability to judge the value of material for a given purpose.

Important Points

• Application: The learner can apply different facts, concepts, theories, laws, or principles in a new situation. Application subsumes both knowledge and understanding. Example: applying knowledge of calculating the area of the rectangle to find the area of own house of the learner.
• To solve the algebraic equation $\dfrac{x+1}{2x+3}=\dfrac{3}{8}$knowledge and understanding of algorithms are required.

Hence, it is concluded that the application cognitive skill of Bloom’s Taxonomy is emphasized in this question.

Additional Information 

• Affective Domain: It deals with the emotional aspects of the learner. The various emotional states of an individual like different feelings, motivation, interest, attitude, values, appreciation, etc fall under an affective domain. Similar to the cognitive domain, the learning objectives of the affective domain are hierarchically ordered i.e. from simple to complex.
• Psychomotor Domain: Psychomotor domain includes the ability to use body parts to accomplish tasks, neuromuscular movements, and types of body actions. The psychomotor skills can be observed while playing, typing, stitching, etc. Psychomotor skills are developed through practice and are measured in terms of speed, precision, accuracy, etc

Concept map: Concepts maps include graphical and diagrammatical representations to illustrate the meaningful acquisition of various sub-topics of a concept. 

• A concept map is a visual organizer that can enrich students' understanding of a new concept. Using a graphic organizer, students think about the concept in several ways.
• It helps the learners to draw an outline of the topic/concept or to briefly explain the concept or to link any two concepts of any subject by summarizing it.
• The arrangement of concepts is done in a hierarchical order from top to bottom, placing the most general concept at the top and moving downward.

 Important Points

• Concept maps provide a complete picture of the concepts to be learned along with their relationship with each other.
• It is a general method that can be used to help any individual or group to describe their ideas about some topic in a pictorial form.
• It enhances the spatial ability of the learners and they can visualize the complete unit as a whole.
• Teachers can use concept maps as a pre-reading strategy by inviting students to share what they already know about a particular concept.
• It can develop logical thinking and study skills which are part of cognitive skills as it compels the students to shows the degree of inclusiveness of the concepts i.e., to which extent or how much in-depth knowledge of a concept is to be included.

Hence, we can conclude that with this activity in class, the teacher is using a concept map to enhance the spatial ability of the learner so that she/he can see the complete unit as a whole.

This is a question of a word problem. Word problems in mathematics are those questions that are given in the form of statements, which, after comprehension, are solved using mathematical operations. Word problems help to develop the ability to convert real-life problems into mathematical problems and find out a solution. 

Important Points

• “The organizers of an essay completion decide that a winner gets a prize of Rs. 100 and a participant who does not win gets a prize of Rs. 25. The total prize money distributed is Rs, 3,000. Find the number of winners, if the total number of participants is 63.”
• Through this discussion, the students will be writing thoughts on social issues that can be developed as a regular habit, and the opportunities to make their thoughts public can be availed through participation in an essay competition.

Key Points Apart from checking the mathematical concept, the teacher can inculcate the value of social issues among students.

• Poverty, unemployment, unequal opportunity, racism, and malnutrition are examples of social issues.
• By writing about social issues, creates awareness among students.
• It can be developed as a regular habit.
• It improves critical and higher-level thinking skills.
• When students write in essay competitions, they learn to express their ideas.

Thus, from the above-mentioned points**,** it is clear that apart from checking the mathematical concept, the teacher inculcates the value writing of thoughts on social issues can be developed as a regular habit, and the opportunities to make your thoughts public can be availed through participation in essay competition that amongst students, during the discussions.

The question can be referred to as a problem or difficulty that need to be discussed or dealt with by thinking and recalling the concept. It can be either open-ended or close-ended questions.

Key PointsOpen Ended Question:

• Open-Ended Question allows to give free form answer or respondent can answer in open text format based on complete knowledge and understanding.
• Open-Ended Questions can not be answered in "yes" or "no" responses. They can never be a one-word answer.
• Open-Ended Questions may not have limited responses. It may refer to a problem that may have more than one correct answer and more than one strategy to obtain the answer.
• Example: What are the properties and types of Quadrilateral?
• In the given problem, option (2) is referred to as an open-ended question. It can have multiple responses depending on the learner.

Close Ended Questions:

• Close Ended Questions leaves limited responses.
• It can be answered by selecting a limited number of options means using "single word", "rating scale", etc.
• It can be answered with short or fixed responses.
• Example: What is the square of 6?​
• In the given problem, options (1), (3), (4) are referred to as close-ended problems. It has a single response in the form of an answer. It does not have multiple answers.

Hence, we can conclude that option (2)," Write any 5 numbers whose cube is more than 64." is an open-ended problem.

Concept:

Homogenous and Heterogeneous mixture

**Explanation:**​

• Iodised table salt is a heterogeneous mixture.
• Iodisation of salt is basically the physical process of mixing the iodine compound with common salt.
• The composition of consistent particles in the iodized salt is not uniform or homogenous.
• Hence, even though the components are not identified by the naked eyes, Iodised table salt is not a homogenous mixture.

So, the correct option is Iodised table salt.

Explanation:

• Magnetic separation is the process of separating such a heterogeneous mixture in which one of the components is a magnetic substance and another one is not.
• Magnetic substances are simply those which get attracted by a magnet. For example Iron
• A mixture of sulphur and iron can be separated by the process of magnetic separation as iron is magnetic and sulphur is not.
• When a magnet will be brought near the mixture of iron filings and sulphur powder, the magnet will attract iron fillings and sulphur will remain as it is.
• Thus, both components get separated.
• Now, iron fillings get attracted equally to both poles as both poles will have equal magnetic strength.

So, the correct option is only the iron filings get attracted equally to both poles of the magnet.

Additional Information

• A magnet consists of two poles, the North pole and the south pole.
• The like poles attract each other and unlike poles repel each other.
• Poles of the magnet have higher strength as compared to other parts.

The correct answer is the Convex lens.

Key Points

An image is formed when a ray of light coming from a point intersects at another point. 

Spherical mirror

• The mirror having curved reflecting surfaces is called a spherical mirror.
• There are two types of spherical mirrors: Concave and convex.
• A concave mirror has a reflecting surface curved inwards and the convex mirror has a reflecting surface curved outward.
• The concave mirror can form a real image when the object is kept at certain locations.
• The convex mirror cannot form a real image.

Spherical lens

• A transparent medium bounded by the spherical surface is the lens.
• A concave lens has both surfaces curved inward and a convex lens have both surfaces curved outwards.
• A convex lens can form a real image. when the object is kept at certain distances.
• A concave lens cannot form real images.

Explanation:

• Only real images can be obtained on the screen.
• To obtain the real image on the screen, we can use either a convex lens or a concave mirror.
• In the given options only the convex lens can form real image.
• A real image can be obtained on a wall just like a screen.

So, the correct option is convex lens. 

Additional Information

 The image formation by the convex lens is shown below diagram. 

The real image is formed in most of cases.

Concept:

• Speed: Total distance traveled by the total time taken is called speed.
• Speed measures how fast the body is moving.

$\rm speed = \dfrac{distance}{time}$

• Average speed: It is defined as the total distance traveled by the total time taken.
• Odometer: It is the device that is used to measure the distance traveled by a vehicle.
• Average speed: The total distance traveled by the total time taken will give the average speed.

$\rm Average \ speed = \dfrac{total \ distance}{total \ time}$

• Conversion of speed from km / hr to m /s

1 km = 1000 m

1 hr = 3600 second

So,1 km / 1 hr = 1000 m / 3600 second = $\frac{5}{18} \ m / s$

Calculation:

The initial reading of the odometer = 6640 km (at 8.00)

Final reading of the odometer = 6712 km (at 10.00)

Distance travelled d = 6712 km - 6640 km = 72 km

Time taken = 10;00 - 8:00 = 2 hr

So, average speed = (total distance) / (total time) = 72 km / 2 hr = 36 km / hr

Now, this has to be converted into m /s by multiplying it with $\frac{5}{18} \ m / s$

So,  

$36 \ km /hr = 36 \times \frac{5}{18} m /s = 10\ m /s$

So, the correct option is 10 m / s.

Mistake Points

Students may write answer in km/hr instead of m /s . Questions should be always read properly.

Concept:

Force

• Force is any push or pulls which causes a change in speed, the status of rest or motion, the direction of motion, or shape of any object.
• Force is a vector quantity that means both its magnitude and direction is considered.
• No change in speed, direction, or status of rest or motion will be made unit an unbalanced force (net force is not zero) is applied.
• In there is no change in speed, which means no force is applied.
• The SI unit of force is Newton.

Velocity

• Speed is defined as the total distance traveled by the total time taken.
• If the direction of motion is considered along with speed, it becomes velocity.
• If velocity is constant, that means both speed and direction are constant.
• There is no change in either speed or direction.
• Velocity is also a vector quantity.

Explanation:

• The object is moving on a frictionless or smooth surface that means no frictional force is acting on it.
• The velocity is constant, which means neither speed or direction is changing.
• Since there is no change in speed or direction in order to move with constant velocity, we can say that the net force applied is zero.

So, the correct option is 0 newton. 

By the second law of motion, the force is given as

F = ma

m is mass, a is acceleration

a = Δv / Δt

Δv = 0, which means velocity is not changing.

a = 0

⇒ F = m (0) = 0

So, the net force is zero Newton. 

Additional Information

Laws of Motion given by Newton are as follows:

Concept:

Digestion: 

• ​it is the complex process of turning the food we eat into nutrients, which the body uses for energy, growth and cell repair needed to survive.
• It also involves creating water to be excreted.

Human Digestive system:​

• Human Digestive system consists of the alimentary canal which can be further divided into various components. a) The buccal cavity b) food pipe or oesophagus c) stomach d) small intestine e) large intestine ending in the rectum f) the anus

Mouth or Buccal cavity:

• Food is taken into the body through the mouth. The process of taking food into the body is called ingestion.
• our mouth has the salivary glands which secrete saliva.
• When we chew the food, saliva secreted from the salivary gland and mixes with food.
• Food becomes moisten by getting mixed with saliva.
• Partial digestion of food starts here.

Food pipe:

• ​The swallowed food then passes into the food pipe or oesophagus.
• Food is pushed down by the movement of the wall of the food pipe.

The stomach: 

• The stomach is a thick-walled bag. Its shape is like a flattened U and it is the widest part of the alimentary canal.
• The inner lining of the stomach secretes mucous, hydrochloric acid, and digestive juices.
• The mucous protects the lining of the stomach.
• The acid kills many bacteria that enter along with the food and makes the medium in the stomach acidic, which helps digestive juices to break down the proteins into simpler substances.

The Small Intestine:

• It is highly coiled and is about 6-8 meters long. It receives secretions from the liver and the pancreas.
• The digested food can now pass into the blood vessels in the wall of the intestine. This process is called absorption.
• The inner walls of the small intestine have thousands of finger-like outgrowths.
• These are called villi. (It increases the surface area of absorption of the digested food).

Large intestine: 

• ​It is wider and shorter than the small intestine.
• It is about 1.5 meters in length.
• Its function is to absorb water and some salts from the undigested food material.

Conclusion:

So, the correct sequence through which food goes under the complete process of digestion is

Mouth → oesophagus → stomach → small intestine → large intestine

The correct answer is conversion of pyruvate to lactic acid.

Concept:

• The breaking of the C-C bonds of complex compounds through oxidation within the cells, leading to the release of a considerable amount of energy is called respiration.
• The compounds that are oxidized during this process are known as respiratory substrates.
• Along with the energy carbon dioxide and metabolic water is also released as a by-product in respiration.

Explanation:

• The first step of respiration is the breakdown of glucose, a six-carbon molecule, into a three-carbon molecule called pyruvate.
• This process takes place in the cytoplasm.
• Further, the pyruvate may be converted into ethanol and carbon dioxide. This process takes place in yeast during fermentation. Since this process takes place in the absence of air (oxygen), it is called anaerobic respiration.
• Breakdown of pyruvate using oxygen takes place in the mitochondria. This process breaks up the three-carbon pyruvate molecule to give three molecules of carbon dioxide. The other product is water. Since this process takes place in the presence of air (oxygen), it is called aerobic respiration.
• The release of energy in this aerobic process is a lot greater than in the anaerobic process.
• Sometimes, when there is a lack of oxygen in the muscle cells, another pathway for the breakdown of pyruvate is taken.
• Here the pyruvate is converted into lactic acid which is also a three-carbon molecule.
• This build-up of lactic acid in our muscles during sudden activities like exercise causes cramps.

This process can be easily understood by the diagram below.

Concept:

• The alimentary canal is basically a long tube extending from the mouth to the anus.
• It consists of different parts. Various regions are specialised to perform different functions.
• The main organs of the alimentary canal are:

1. The Mouth: It is the first part of our digestive system. Food is ingested through the mouth.
2. Buccal cavity: It comprises the palate, tongue and teeth.
3. Pharynx: It is the common passage for food and air. Epiglottis prevents the entry of food into the windpipe
4. Oesophagus: It is a muscular tube through which a small bolus of food passes from the mouth to the stomach.
5. Stomach: It is a muscular bag, positioned at the upper left part of the abdominal cavity.
6. Intestine:

• Small intestine: Consists of three parts, Duodenum, Jejunum, and Ileum.
• Large intestine: Consists of three parts, Caecum, Colon, and Rectum.

Explanation:

The Oesophagus, large intestine, rectum do not carry out any digestive function.

• The oesophagus or the food pipe is a long tube that carries the food from the mouth to the stomach. It is not involved in any digestive process.
• The Large intestine has no role in digesting the food, it only absorbs water from the undigested food.
• The rectum temporarily stores the faecal material that is to be excreted out of the body via the anus, hence it also has no role in digestion.

Additional Information

Digestive function of the mouth (buccal cavity) - 

• Digestion of food begins in the mouth (buccal cavity) itself.
• A fluid called saliva is secreted by the salivary glands in the buccal cavity.
• Saliva contains the enzyme salivary amylase or ptyalin, which performs the digestion of Carbohydrates (starch).
• About 30 per cent of starch gets hydrolyzed into a disaccharide – maltose in the mouth itself by this enzyme.

Digestive function of the small intestine -

• The small intestine is the site of the complete digestion of carbohydrates, proteins and fats.
• It receives the secretions of the liver and pancreas for this purpose.

The correct answer is Small intestine.

Key Points 

• Hepatic cells secrete bile that passes through the hepatic ducts and is stored in the gall bladder.

• The cystic duct from the gall bladder joins the hepatic duct from the liver forming the common bile duct.

• The bile duct and the pancreatic duct open together into the duodenum as the common hepato-pancreatic duct is guarded by a sphincter called the sphincter of Oddi.

• As the duodenum is part of the small intestine.

• So, the correct answer is option 3.

Concept:

• Digestion: 
• ​it is the complex process of turning the food we eat into nutrients, which the body uses for energy, growth and cell repair needed to survive.
• It also involves creating water to be excreted.
• Human Digestive system:​
• Human Digestive system consists of the alimentary canal which can be further divided into various components. a) The buccal cavity b) food pipe or oesophagus c) stomach d) small intestine e) large intestine ending in the rectum f) the anus

Explanation:

• The components of food such as carbohydrates are complex substances. These complex substances cannot be utilized as such. So they are broken down into simpler substances. The breakdown of complex components of food into simpler substances is called digestion.
• The food is digested by the body in the following steps: Ingestion⇒digestion⇒absorption⇒assimilation⇒egestion.
• Ingestion: It is the process of intake of food.
• Digestion: The complex food is now acted upon by various enzymes in the mouth & stomach region, and converted into smaller substances this is called digestion.
• Absorption: The digested food gets absorbed by the body via the numerous villi (finger-like projections) present in the small intestine.
• Assimilation: It is the next step after the absorption, here the food is assimilated by the body to form various substances needed for growth.
• Egestion:  The remaining undigested waste passes into the rectum and remains there as semi-solid faeces. The fecal matter is removed through the anus from time to time. This is called egestion.

Concept:

Absorption in Small Intestine

• The food stored in the stomach, after going through the required processes goes to the small intestine.
• The absorption of food takes place here first.
• This is the process of absorbing food by the blood vessels.
• For the process to happen, finger-like projection is present in the small intestine which is called villi.
• They have thin walls and mostly covered with a thin channel of blood capillaries.
• This increases the surface area and ensures maximum absorption.
• Each villus has a network of thin and small blood vessels close to its surface.

Conclusion:

• A. They are finger-like projections. This is true.
• B. They have very thin walls. This is also true as this helps in absorption.
• C. They have small pores through which food can pass easily. This is not true.
• D. They have a network of thin and small blood vessels close to the surface. This is also true.

So, the correct statements are D, A and B.

Key Points

• Plants prepare their food by the process called photosynthesis.
• During photosynthesis, plants trap solar energy or light energy with the help of chloroplast present in the green leaves and convert it into Chemical energy.
• A pigment called chlorophyll is present in the chloroplasts which are required in trapping sunlight.
• Plants utilize Carbon dioxide and water for the synthesis of carbohydrates during photosynthesis, oxygen is liberated as a side product.
• This gaseous exchange occurs through the stomata present on the leaf surface.

These events can be demonstrated by the following equation:

$\rm \underset{(Carbon\ dioxide)}{6CO_2} + \underset{(Water)}{6H_2 O} \xrightarrow[Chlorophyll]{Sunlight} \underset{(Carbohydrates)}{C_6H_{12}O_6} + \underset{(Oxygen)}{6O_2}$

Thereby, statements A & B are true about photosynthesis.

The following events occur in plant cells during photosynthesis. 

1. Absorption of light energy.
2. Conversion of light energy into chemical energy.
3. Storage of chemical energy in sugars.

Key Points

• The Pitch of the sound is related to its shrillness.
• Pitch depends upon the frequency of sound.
• Frequency is number of vibrations by a source per unit time.
• Sitarist adjust pitch by changing the tension.

Additional Information

The amplitude of sound determines loudness.

Concept:

Pressure:

• The force per unit area is called pressure. It is denoted by P.
• The SI unit of pressure is the pascal (Pa).
• It is a scalar quantity because the pressure acts in all directions at a point inside a gas.
• The basic formula for pressure is given by:

${\rm{Pressure (P)}} = \frac{{{\rm{Force (F)}}}}{{{\rm{Area (A)}}}}$

Explanation:

• More pressure signifies more stress.
• If the same force is applied in a lesser area of contact, then more stress will be felt.
• If the area of contact is increased, stress will be reduced.
• Potters who carry heavy luggage keep cloth on the head to reduce the pressure by increasing the area of contact.
• The correct option is to 'increase the area of contact of a load of luggage with their head.'

Concept:

• Forestry is defined as the theory and practice of all that constitutes the creation, conservation and scientific management of forests and the utilization of their resources.
• It is an applied science which is concerned with not only the raising or cultivation of forest crops but their protection, perpetuation, mensuration, management, valuation and finance as well utilization of the forest products for the service of the nation.
• In favourable localities, this science is applied to get maximum returns.

Explanation:

• For the conservation of forests, a successful strategy is essential. This strategy should involve
• Not just the Protection of herbivores or consumers just because, if one's population in the food chain increases it will disrupt the whole food cycle.

So, the correct option will be a comprehensive programme for the protection of all the physical and biological components of forests.

Key Points 

• Evolution: Evolution is a process of change happening over generations.
• During the course of evolution, a change that is useful for one property to start with can become useful later for quite different functions.
• For example - some dinosaurs had feathers, although they could not fly using the feathers. Birds seem to have later adapted the feathers to fly.
• This indicates that feathers become useful during the course of evolution.
• This also means that birds are very closely related to reptiles since dinosaurs were reptiles it can be said that birds have evolved from reptiles.

Important Points

• Charles Darwin is known as the father of ''Evolutionary Biology''.

Geothermal Energy:

The heat that comes from the earth's subsurface is known as geothermal energy.

• It can be present in the minerals and fluids underneath the earth's surface, as well as in the hot molten rock known as magma.
• Mile deep wells are drilled into underground lakes to access steam and hot water, which can then be used to power turbines attached to electricity generators.
• Dry steam, flash, and binary geothermal power plants are the three types of geothermal power plants.
• Hotspots over crust are idea for geothermal energy as more heat can be obtained.

Additional Information

Advantages

• It can be extracted without burning a fossil fuel such as coal, gas, or oil.
• Geothermal fields produce only about one-sixth of the carbon dioxide that a relatively clean natural-gas-fueled power plant produces. Hence statement 3 is not correct.
• Binary plants release essentially no emissions.
• Unlike solar and wind energy, geothermal energy is always available, 365 days a yea

Key Points

• Metals react with water and oxygen present in the air.
• Metal with higher reactivity has vigorous reactions.
• For example, sodium catches fire in the air, hence it is kept in kerosene oil.
• Due to such reactivity of metals, most of the metals are not available in nature in a free state.
• They are present in form of their compounds (oxides, carbonates, sulphides etc,)
• Few metals which are least reactive are available in a free state.
• Such metals are gold, silver, Platinum,
• These metals are available in the free state.

The correct option is Silver, gold, platinum.

Reactivity Series. 

Metals below in the series are least reactive and present in the free state.

Concept:

Displacement Reaction:

• A displacement reaction is a type of reaction in which part of one reactant is replaced by another reactant.
• An example of the reaction of Iron with copper sulphate solution:

 Fe + CuSO4 → FeSO4 + Cu

• ​Displacement reaction can occur if metal reacting is more reactive than the metal which it have to replace in solution.
• The above reaction is possible because Iron is more reactive than Copper.
• The reactivity is determined by the reactivity series.

Reactivity Series

• The metals are arranged in an activity order that is known as the metal activity series.
• The more active metals are present at the top of the series whereas the less active metals are put at the end of the series.
• The metal activity series is as follows-

Explanation:

• The metals present in the options are Aluminium (Al), Copper (Cu), Iron (Fe) and Zinc (Zn).
• The reactivity in increasing order is Al, Zn, Fe, Cu.
• Higher reactive metal can displace lower reactive metal from its salt.
• Any metals cannot displace Al
• So, reactions A and D are not possible.
• Zinc can displace iron. So, B is possible.
• Iron can displace copper. So, C is possible.

The correct option is B and C.

Key Points  

• Fertilisers are chemical substances that are rich in a particular nutrient.
• Fertilisers are very rich in plant nutrients like nitrogen, phosphorus & potassium.
• Some examples of fertilisers are— urea, ammonium sulphate, superphosphate, potash, NPK (Nitrogen, Phosphorus, Potassium).
• They are used to ensure good vegetative growth (leaves, branches and flowers), giving rise to healthy plants.
• The use of fertilisers leads to a better yield of crops such as wheat, paddy and maize. But excessive use of fertilisers also makes the soil less fertile.
• Fertilisers have also become a source of water pollution.

Additional Information

Differences between Fertiliser and Manure