CTET Paper 2 Maths & Science September 2014 (English-Hindi-Sanskrit) (Previous Year Paper)

Diversity refers to the use of different languages, and cultures, by different groups of people in a society. 

• Diversity can be explained on the basis of the abilities, talents, interests, and values of all the students in the class.
• India has a lot of linguistic and cultural diversity.

Key Points

If the teacher is to explain 'diversity' in her class, she can explain it by adopting the following methods: -

• Assigning tasks that can develop the art of differentiating between children
• Accepting and valuing differences in the class among students
• Engaging children in co-educational activities other than education
• Using the social, cultural, and background education of children as a classical resource
• By adjusting the different learning styles
• Diversify learning using different learning styles and resources
• Explaining the different relationships between the children by clarifying the differences between social, educational, physical, cultural, and spiritual values
• To make aware of the conditions of housing, surroundings, food, goods, nature, values, knowledge, etc.

Hence, it becomes clear that giving standard instruction and setting benchmarks are not the criteria to address diversity.

The child with Special needs: The also known as a specially-abled child, a child with special needs is the one who needs special attention and requires necessities which other children do not.

• There are many types of such special needs on of which is for visually impaired children.
• A teacher asks her to keep the sharp edges of the furniture covered with cotton in her classroom and use the placards that 'touch and feel'. She is trying to meet the needs of the students belonging to the class of visually impaired students.

For Visually Impaired Students, Teacher should:-

• Give children enough time to touch and feel objects
• Provide adequate opportunities to children for activities
• Creating activities that arouse interest in learning of such children
• Opening the way for all-round development by emphasizing inclusive learning

For Socially Disadvantaged Students, Teacher should:-

• Connect students to social activities
• Explain every aspect of society in a practical way after education
• Pay attention to all the students irrespective of their caste, religion, sex, place of birth, etc. of the child

Hence, it becomes clear that in the given activity, teacher is attempting to cater to Visually - impaired learners.

Gifted children are those who have high intellectual ability, specific academic aptitude, leadership ability, creative thinking and they are capable of high performance. Children whose IQ score is 130 and above are referred to as highly abled or gifted.

Characteristics of a Gifted Child:

• Gifted children display a higher rate of concentration and memory capacity.
• Gifted children have creative, productive thinking and leadership ability.
• A gifted child engages in convergent thinking, while a creative child is associated with divergent thinking.
• The gifted child has an I.Q. around 120.

Important Points

The best educational programs for gifted children are those which stimulate children's thinking and give them opportunities to engage in different thoughts.

Key Points

Other Major Reasons for Organizing Educational Programs for Talented and Ordinary Children are:-

• Developing co-scholastic talents of students
• To develop the creative power of children
• To develop moral, social, cultural, spiritual, educational values
• Health, promotion, environmental improvement programs
• Strive for freedom from misdeeds and addictions
• To maintain unity, equality, and integrity of the country and awaken the feeling of nationality
• Increasing trends in outdoor school activities

Hence, gifted children are best catered to by educational programs that stimulate their thinking and give them opportunities to engage in divergent thinking.

Failure is the state or condition of not meeting a desirable goals and may be viewed as the opposite of success. There are many physical, intellectual, scholastical, emotional, and cultural causes for the failure of students. 

Reasons for the Failure of Students in Schools are:

• Lack of adequate practice
• Not being compatible with the school environment
• Students fail because teaching is not done in a way that is meaningful to them
• Teaching through incorrect teaching methods
• Because the school system does not take care of the needs and interests of every student
• Non-coordination between teaching and learning
• A continuous decrease in the intellectual development of the child

Hence, students' failure in schools because teaching is not done in a manner in which it is meaningful to them, and the school system does not cater to the individual system.

Learning is the acquisition of new behaviour or the strengthening or weakening of old behaviour as a result of experience. It represents progressive changes in behaviour. It also involves the acquisition of knowledge, habits, and attitude. 

Two students read the same passage yet construct entirely different interpretations of its meaning. It is possible because different factors affect the learning of individuals in varied ways.

 

There are Other Possible Reasons for This:

• Different intellectualism of children
• Differentiation of understanding and ability in children
• Varying interest in learning
• The different processes of thinking
• Focus strength of both students are different

Hence, it becomes clear that the given possibility is because of different factors affect learning of individuals in varied ways.

The National Council for Educational Research and Training (NCERT) published a document called the National Curriculum Framework (NCF). NCF 2005 has been translated into 22 languages and influenced the syllabi in 17 states.

• According to the National Curriculum Framework 2005, the learning is active and social in nature because a passive curriculum cannot contribute to the social, physical, intellectual development of the child.
• Because all-around development of the children is not necessary only in the social form of book knowledge Behavior is also necessary.

The Five Major Salient features of NCF 2005 are perspective reforms, learning and knowledge process reforms, curriculum and assessment reforms, school and class environment reforms, and systemic reforms.

• Its main objective was to constructivist learning with the child-centric learning process, learning without burden, promoting multilingual education, replacing rote learning.
• It ensures that students do not just learn mechanically without thinking.
• A lot of examination and assessment reforms were also introduced through NCF.
• Financial reforms are not the feature of NCF 2005.

Hence, it becomes clear that according to the NCF 2005 learning is active and social​ in its character.

Thinking is a kind of functional process in which the brain controls the dynamics of thoughts and gives rise to new ideas.

According to J.P Guilford, "Thinking is symbolic behavior related to all types of substitution". 

Following are the Requirements for Independent Thinking in Children and Making them Effective Learners:

• Finding and resolving new problems
• Promote learning by doing effort and error
• To teach students how to monitor their learning
• It should move from gross to subtle
• One should learn to be oriented towards the goal
• By giving prizes to the children on each of their successes, there will be positive reinforcement, rather the concept of independent thinking will develop
• Providing information in an organized manner can be helpful in recollection
• Providing information in small units or blocks makes learning easier and easier.

Hence, to enable students to think independently and become effective learners, teach students how to monitor their own learning.

Problem-Solving Method: In this approach, teachers create a problematic situation for students and then assist them in perceiving, defining, and stating the problems in a fear-free classroom environment. 

Key Points

• Under the problem-solving method, a problem is given to the children by the teacher, which the children have to solve with their intellectual development.
• To acquire problem-solving skills, students should be engaged in activities that involve inquiring, reasoning, and decision making.
• The problem-solving method is used to develop critical and analytical thinking in secondary and higher level classrooms.

Important Points

Characteristics of Problem-Solving Method:

• In this method, capacity building in children is done.
• It is a child-centered method, it emphasizes on learning.
• It emphasizes developing a scientific approach.
• The rote method has not only decreased the child to develop analytical abilities but also stops micro-intellectual development.

NOTE: The other given options are not appropriate to acquire problem-solving skills.

Hence, to acquire problem-solving skills, the students should be engaged in activities that involve inquiring, reasoning, and decision making.

Naive Conceptions (also referred to as commonsense theory or folk theory) is a coherent set of knowledge and beliefs about a specific content domain (such as physics or psychology), which entails ontological commitments, attention to domain‐specific causal principles, and appeal to unobservable entities.

• Teaching and learning are complements of each other.
• Changes in teaching methods and techniques are required to make learning more effective.
• As a teacher, it is very important to understand children's needs, curiosities, and problems.

By knowing the naive conceptions, the teacher can plan to make his teaching work more meaningful.

For example, if the child is comfortable reading and learning in the mother tongue if his concept is taught, then teaching can be made more meaningful for the teacher.

Hence, knowing the naive conceptions that students bring to the classroom, helps the teacher to plan to teach more meaningfully.

Learning is the acquisition of new behaviour or the strengthening or weakening of old behaviour as a result of experience. It represents progressive changes in behaviour. It also involves the acquisition of knowledge, habits, and attitude. 

Key Points

Factors Affect Learning:

The main factors affecting learning are Motivation of the learner, Maturation of the learner, Teaching strategies, and Physical and emotional health of the learner.

• The Interest of the Student - The factor of interest is very closely related in nature to that of symbolic drive and reward.  A favourable mental attitude facilitates learning.
• Teaching Strategies - The strategies or steps taken by the teacher to make the class environment interactive and that also engrave interest among students regarding the topic.
• Physical and Emotional Health of the Learner: Concentration needs emotional and mental poise and absence of mental conflict or complexity. Some children find it difficult to prepare for the examinations, simply because of fear of the examination and anxiety neurosis.
• Giving motivation to the learner can increase their interest in learning.
• Maturation of the learner affects learning because ​maturation is related to the structure and potential capacity. Maturation is the process by which we change, grow, and develop throughout life.

Hence, from the above-mentioned points, it becomes clear that all the given factors affect learning.

Learning is the acquisition of new behaviour or the strengthening or weakening of old behaviour as a result of experience. It represents progressive changes in behaviour. It also involves the acquisition of knowledge, habits, and attitude.

• Meaningful learning results when a person consciously and explicitly ties new knowledge to relevant concepts they already possess.
• It is the active creation of knowledge structures from personal experience.
• When meaningful learning occurs, it produces a series of changes within our entire cognitive structure, modifying existing concepts and forming new linkages between concepts.
• Meaningful learning implies that what has been learned is intellectually linked and understood in the context of what was previously known.

Characteristics of Meaningful Learning:- 

• It stresses the ability of the learner to apply what is learned because of the involvement of the learners.
• Meaningful learning is the human mechanism par excellence for acquiring and storing the vast quantity of ideas.
• Meaningful learning is possible only when learners make deliberate effort to relate new knowledge to the relevant concept they already know.

Thus, from above-mentioned points, it is clear that Meaningful Learning is an active creation of knowledge structures from personal experience.

Effective learning involves not only the use of tools, techniques, and strategies to optimize student learning but an understanding of context, in particular how your students learn, how they process information, what motivates them to learn more, and what impedes the learning process. 

Teacher plays a vital role in the classroom. Here are some primary task of a teacher for effective student learning:-

• Build a warm environment, mentor and nurture student
• The teaching of knowledge in its various forms is still considered to be the primary goal for teachers.
• Teaching students how to monitor and improve their own learning by effort.
• Knowing the concepts that students bring to the classroom.
• Developing independent learning skills in students has never been more acute.
• Requiring students to respond to higher-order questioning.
• To convey large amounts of information as meaningfully and efficiently as possible.

Didactic Method:- It is one of the teacher-centered methods in which instruction is based on text, books, or lectures. It is a scientific approach to present information to the student. This method is used in higher education.

Therefore, transmitting information to the students in a didactic manner is not one of the primary tasks of a teacher for effective student learning.

Development, which is continuous change is a phenomenon which is observed both in terms of quality and quantity. Principles of Human Development defines in what way a person will develop.

• The development includes a series of qualitative and progressive change, and it can not be measured precisely.
• Development is a process of adaptation that depends on the interaction of natural forces and environmental influences. It considers as, a total process whereby individuals adapt to their environment.
• The development includes growth, maturation. and learning.

Principles of Development-

• The two basic sources of development namely: heredity and environment, also called ‘nature and nurture’, are in a continuous process of interaction with each other.
• Development is a continuous process that begins at conception and ends with life.
• Every child goes through stages of development, yet there are wide individual differences among children.
• Development is unique for all individuals.
• The changes brought about by the process of development follow a sequential order.

Hence, Development is not a quantitative process and it can not be measured precisely.

The development includes a series of qualitative and progressive change. Development can be defined as the changes in the structure, thought or behaviour, of a person that occurs as a function of both biological and environmental influences.

• It is a continuous process that happens throughout the lifetime, takes place even after attaining maturity of physical growth and not a predetermined factor.
• Development is a unique interaction of heredity and the environment.
• Heredity or genetic influences lead to similarities between parents, their children, and siblings. Conversely, they also lead to differences between two individuals. These genetic influences on development are internal, occur naturally, and are difficult to modify.
• ‘Environment’ on the other hand comprises all the external factors, excluding hereditary, which influences growth and development. These external influences help in gaining experience in the social and cultural world.
• The two basic sources of development namely: heredity and environment, also called ‘nature and nurture’, are in a continuous process of interaction with each other.
• Heredity determines the probable biological limits and lays the foundation for development, whereas the environment creates the opportunities, provides the necessary practice and experience, and sets the level up to which these limits can be utilized.

Therefore, we can say that development is a unique interaction of heredity and the environment.

Socialization is a process by which an individual becomes a member of society through a mechanism of interaction.

• Its purpose is to prepare individuals for future roles.
• Socialization is a process of acquiring values, beliefs, and expectations.
• Socialization is a process in which a person adapts all the social behaviour as-
• Adaptation of social values and principles.
• Adaptation of cultural rituals
• Adaptation of skills
• Socialization is a combination of personality development and cultural development.

Key Points Agents Responsible for Socialization:

• Primary Agents of Socialization- They are family members and relatives as they are the ones whom children interact with since birth.
• Secondary Agents of Socialization- These are a school, neighbourhood, media, peer group, laws of society etc.
• School is an important agent of socialization.
• During the secondary phase, more than the family, some other agents of socialisation like the school and friends’ group begin to play a role in socialising the child.

Hence, from the above-mentioned points, it becomes clear that School is an important agent of socialization.

​Jean Piaget’s Theory of Cognitive Development:

• Jean Piaget observed his children and their process of making sense of the world around them and developed a model of how the mind processes new information encountered.
• According to him, cognitive structures are the basic mental pattern people use to process any information.

Piaget explained that children progress through four stages. The Four Stages of Cognitive Development are as follows:-

• Cognitive development is not a continuous process, it occurs in the above 4 stages.
• The stages are invariant which means that no stage can be skipped.
• According to Piaget, assimilation, accommodation, and equilibrium are the ways through which children integrate new experiences into already existing cognition structures (schema).

Hence, it becomes clear that the stages are invariant which means that no stage can be skipped.

Jean Piaget’s Theory of Cognitive Development:

• Jean Piaget observed his children and their process of making sense of the world around them and developed a model of how the mind processes new information encountered.
• According to him, cognitive structures are the basic mental pattern people use to process any information.

The concrete operational stage is the third stage in Piaget's theory of Cognitive Development.

• In this stage, children gain the abilities of conservation of number, area, volume, and orientation.
• Conservation is the understanding that something stays the same in quantity even when its appearance changes.
• Conservation certain physical properties remain the same even when outward appearances change.
• It can also be defined as an operational process of the mind which produce the realization that certain aspects of changing conditions are invariant, despite those change.

Hence, it becomes clear that according to Piaget, the concept of ‘conservation’ means that certain physical properties remain the same even when outward appearances change.

ntelligence refers to the capacity to acquire and apply knowledge. It is the ability to solve problems, learn from experiences, and apply knowledge to deal with new situations.

• There are many theories related to intelligence. These theories are propounded by eminent psychologists to provide a framework to understand different aspects of human intelligence.
• The theory of Multiple Intelligence which consists of eight different kinds of intelligence is propounded by an American psychologist 'Howard Gradner'.

Key Points

This theory emphasizes that:

• intelligence is of several kinds rather than dominated by a general factor.
• intelligence can't be tied to a single domain as each individual has his/her own abilities.
• how cultures shape the potential of the human using Intelligence as a multi-dimensional set of complex abilities.

There are eight kinds of Intelligence as listed below:

 

Hence, from the above-mentioned table it becomes clear that option (a - iv, b - ii, c - i, d - v) is correct.

Vygotsky’s Sociocultural Theory of Learning:

• Vygotsky was a Russian psychologist who believed that social interactions play a key role in development.
• According to Lev Vygotsky, language development changes the nature of human thought.
• According to him, learning occurs when children interact with people and the environment.
• His greatest contribution was the emphasis on the role of sociocultural influences in our development.
• 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.

Thus, according to Lev Vygotsky language development changes the nature of human thought.

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

Important Points

Criticisms of Kohlberg's Theory of Moral Development:

• Carol Gilligan has suggested that Kohlberg's theory was gender-biased since all of the subjects in his sample were male.
• Kohlberg has based his study primarily on a male sample.
• Critics have pointed out that Kohlberg's theory of moral development overemphasizes the concept of justice when making moral choices.

Hence, the statement 'Kohlberg has based his study primarily on a male sample', is correct in the context of this criticism.

Assessment is integral to the teaching-learning process which helps in facilitating student learning and improving instruction.

Assessment for learning:

• Assessment of Learning is the assessment that becomes public and results in statements or symbols about how well students are learning.
• It often contributes to pivotal decisions that will affect students’ futures. It is important, then, that the underlying logic and measurement of assessment of learning be credible and defensible.

Key Points

Teachers' Role in Assessment for Learning-

• The teacher assesses the conceptual understanding of the students besides focussing on the processes of thinking.
• A range of alternative mechanisms for assessing the same outcomes.
• Creating differentiated teaching strategies and learning opportunities for helping individual students move forward in their learning
• Teachers use assessment as an investigable tool to find out as much as they can about what their students know and can do, and what confusions, preconceptions, or gaps they might have.
• Identifying the particular learning needs of students or groups.

Hence, it becomes clear that the teacher assesses the conceptual understanding of the students besides focusing on the processes of thinking highlights assessment for learning.

Pedagogy refers to the study of teaching methods, including the aims of education and the ways in which such goals may be achieved. The appropriate mix and match of technology and pedagogy make technology better than another.

Child-Centered Method:

• A child-centered method is one that gives primacy to children's experiences and needs and provides ample opportunities for the children to foster their strategy of learning to perform a task or classroom activities.
• The active participation and involvement of children play a very vital role in learning and shaping the personality of a child.
• In this method, teachers facilitate students as a facilitator by providing with proper environment and materials to learn at their own pace.
• Students take leadership in the classroom, present their work, and facilitate groups.
• Students work in flexible, cooperative groupings to solve problems and analyze texts to demonstrate an understanding of a task.
• Students are assessed for process, group work, and product.

Hence, it becomes clear that ‘Child-centred’ pedagogy means giving primacy to children’s experiences and their voices.

According to Piaget-

Thought emerges first and language becomes the intermediary providing the means by which later concepts and conceptual thinking are furthered. 

Key Points

According to Vygotsky-

• Vygotsky argues that language plays an important role in development.
• It develops indeed not only the intelligence of the individual but also the whole learning process as a result of his communication and his collaboration with others.
• According to Vygotsky, language has a profound effect on thought.
• Vygotsky focuses on language dialogues. It is primarily through their speech that adults are assumed to transmit to children the core of knowledge existing in their culture.
• In his learning process, the child develops his own way of communication as a primary tool for his intellectual development.

Hence, it becomes clear that according to Piaget, a thought emerges first and according to Vygotsky, language has a profound effect on thought.

Gender bias in teaching leads to differential learning experiences, even though the girls and boys of a class sit in the same classroom and attended by the same teacher.

• It refers to the belief when someone prioritizes one gender more than the other one.

The above statement reflects gender stereotypes about the attributes of girls and boys. 

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.

• Gender stereotyping has been identified as a psychological process illustrating an individual's structured sets of beliefs about the personal attributes of men and women.
• The communal role is characterized by attributes, such as nurturance and emotional expressiveness, commonly associated with domestic activities, and thus, with women.
• The agentic role is characterized by attributes such as assertiveness and independence, commonly associated with public activities, and thus, with men.

Hence, the above statement reflects Gender stereotypes about the attributes of girls and boys.

Assessment is integral to the teaching-learning process which help स्कूल  s in facilitating student learning and improving instruction.

• It 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.

Assessment Helps the Students in the Following Ways:

• Students are able to learn about themselves as learners and become aware of how they learn – become mega cognitive (knowledge of one’s own thought processes).
• Assessment help students to see their strengths and gaps and help the teacher fine-tune her teaching accordingly.
• Students reflect on their work on a regular basis, usually through self and peer assessment, and decide what their next learning will be.
• Assessment should assess not only memory but also understanding and application.
• Assessment as learning helps students to take more responsibility for their own learning and monitoring future directions.

Hence, it becomes clear that Assessment help students see their strengths and gaps, helps the teacher, and it assesses not only memory but also understanding and application.

Right to Education Act (RTE Act), 2009 ensures “Every child of age 6-14 years must be given free and compulsory education”.

Right to Education Act 2009: To provide free and compulsory education of all children in the age group of six to fourteen years as a Fundamental Right in such a manner as the State may, by law, determine.

• According to RTE 2009, the school should ensure the Inclusion of Students with disabilities/special needs as per the provision of the Act. (which means inclusive education).
• According to the RTE Act, children with special needs should study in inclusive education setups with provisions to cater to their individual needs.

Inclusive Education: It refers to an education system that accommodates all children regardless of their physical, intellectual, social, emotional, linguistic or other conditions.

• It provides a provision to include disabled children and children with special needs along with normal children in a regular classroom environment.
• It is restructuring the school policies and teaching practices so as to cater to the diversity of students.
• A centrally sponsored scheme of “Inclusive Education for Disabled at Secondary Stage” (IEDSS) has been implemented which objective is to enable the disabled children.

Hence, according to the RTE Act, children with special needs should study in inclusive education setups with provisions to cater to their individual needs.

A teacher often plays various roles in the life of a student. One of the key roles played by a teacher is that of a motivator.

The National Curriculum Framework for teacher education programs suggests that teacher has to be responsive and sensitive to the social context of education, the various disparities in the background of learners, national concerns for achieving the goals of equity, parity, social justice, and excellence.

Roles of an Effective Teacher in a Diverse Classroom: 

• The increasingly diverse student population requires teachers to be sensitive and have skills and knowledge to meet the needs of the student body.
• The challenge for the teachers is to interweave the students thinking with the course content and help students to analyze their own social, cultural, and historical context.
• when students come from diverse backgrounds, the teacher should focus on their cultural knowledge to address individual differences among the group.
• Teachers interact with students on a daily basis, so their perceptions, beliefs and attitude towards multiculturalism must be implicit.
• Teachers can attain equity pedagogy by modifying their teaching styles so that they use a wide range of strategies and teaching techniques such as cooperative groups, simulations, role-playing, and dramatization to enable children from diverse groups to achieve equality.

Hence, if students come from diverse backgrounds, the teacher should focus on their cultural knowledge to address individual differences among the group.

A child develops in an orderly sequence which is almost similar in all children. The rate and speed of development may vary in individual cases but the sequence of development patterns is almost the same in all children. Thus human development is based on certain principles.

Important Points

Principle of Development and Their Description:

 

Hence, from the above-mentioned points, it becomes clear that option (1) is correct.

Emotion is a mental state associated with fear, anger, love, etc. Cognition is the process of acquiring knowledge through experiences and senses. Cognition describes how mental processes i.e. learning, remembering, problem-solving, and thinking develop from birth until adulthood. Understanding cognitive development is useful in determining the kind of thinking children are capable of at different age levels.

• The relationship between cognition and emotion has fascinated important thinkers within the intellectual tradition. Physical, cognitive, emotional, and social development in a child is the development of an integrated and holistic fashion.
• Cognition is closely intertwined with emotions and language. Mind states are powerful determinants of one’s current judgments and decision making, that often effect once performance outcome in a task both in social and non-social context.
• Emotions or emotional approach is a psychological construct that involves the use of emotional processing and emotional expression in response to a different situation.
• The relationship between cognition and emotions is bi-directional - a dynamic interplay.
• Emotions are experienced as positive feelings, negative feelings, undesired reactions to any stressful situation, these often impact decision making i.e. cognition.
• The Emotional Approach involves the conscious use of emotional expression and processing to better deal with stressful situations.

 

Hence, we conclude that Cognition and emotions are intertwined and affect each other.

Inclusive Education:

• It refers to an education system that accommodates all children regardless of their physical, intellectual, social, emotional, linguistic, or other conditions.
• It provides a provision to include disabled children along with normal children in a regular classroom environment.

Inclusive classroom refers to an education system that includes children regardless of physical, intellectual, social, linguistic, or other differently-abled conditions.

• In an inclusive classroom with diverse learners, cooperative learning and peer-tutoring should be actively promoted to facilitate peer-acceptance.
• Cooperative learning: It refers to a heterogeneous group where students work collaboratively to achieve learning outcomes. It develops critical thinking, brainstorming, communication, and life long learning skills.
• Peer tutoring: It refers to the learning process where fellow students teach each other. In this strategy, a higher-performing student is paired with a lower performing student to teach specific skills.
• An inclusive classroom is not limited to children with a disability but also gifted children, economically disadvantaged children, children from remote populations, children belonging to ethnic, linguistic, or cultural minorities or children from other marginalized groups.

Therefore, in an inclusive classroom with diverse learners, cooperative learning, and peer-tutoring should be actively promoted to facilitate peer-acceptance.

CONCEPT:

Mode: Mode is the number that is repeated more often than any other.

Range: Range is a difference between the largest and the smallest number.

CALCULATION:

Rewrite the data in ascending order-

1, 2, 2, 3, 3, 4, 4, 4, 6, 8, 8, 9, 14

Total of 13 numbers.

Median is the middle value- 

Total numbers are 13 (odd),

so Median = (13 + 1) / 2 = 7th term = 4

A mode is the most repeated term = 4

Range: Difference between the largest and smallest number.

Range = 14 - 1 = 13

Mean of median, mode and range.

Mean = (4 + 4 + 13) / 3 = 21 / 3 = 7

Mathematics teaching often criticized for its emphasis on memorizing basic facts, rules, and formulae.

• If some students in your class are not able to do well in the mathematics tests consistently, then as a teacher you will first diagnose the reasons and take remedial steps.
• Giving more and more tests to practice without knowing and diagnosing the reasons is the act of putting mental pressure on the children.
• Children who do not perform well in the classroom, make them sit with high achievers, can develop an inferiority complex in children and a negative attitude can arise, so such children need to diagnose the causes and take steps for remediation.

Reasons for Children not Performing well in Mathematics Examinations and Tests:-

• Lack of proper academic direction
• Children's low interest in mathematics
• Difficulty in quickly acquiring mathematical knowledge
• The low socio-economic level of family
• The mental weakness of children

Diagnosis and Remedial Steps for Those Who were not Consistently Doing well in the Mathematics Class:-

• Understanding the problems of students
• Find out the causes of problems
• Adopting a collective remedial method for weakness in mathematics
• Directing study methods and making changes according to situation
• To arrange learning by dividing students into small groups on the basis of weakness
• Repeat the specific text and identify and remove the weakness

Hence, it becomes clear that for the above case a teacher diagnoses the causes and takes steps for remediation.

Inclusive classroom refers to an education system that includes children regardless of physical, intellectual, social, linguistic, or other differently-abled conditions.

​In the teaching-learning process, visually challenged learners suffer from an issue with sight or vision but when they are facilitated with the right training and tools, they develop a good literacy ability.

• An alternative teaching learning and assessment system should be developed to meet the needs of visually impaired students in the inclusive classroom of mathematics.

Strategies for Addressing the Needs of Visually Challenged Learners:

• Speaking clearly and loudly with appropriate pauses and reiterations.
• Using the braille system as it's raised dots help in studying words through the pattern.
• Teaching can be done by a skilled teacher in Braille script.
• • Braille System: It refers to a pattern of raised dots called "Braille"  to represent letters, numbers, and punctuation marks, that can be felt with a finger.
• Such children can be added to the mainstream by sitting with other children so that they do not feel inferior.
• Design alternate teaching-learning and assessment methods.
• Changing the objective/subject due to any inefficiency or problem is not a part of the teaching method to solve the problem or alternative formal steps will be taken.

Hence, in an inclusive mathematics classroom, for addressing the needs of visually challenged learners, design alternate teaching-learning and assessment methods.

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.

Important Points

The Assessment Strategies that can be used to encourage interdisciplinary in 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.
• The differences among these integrative strategies are rooted in the goals of the interdisciplinary curriculum and the purposes of the discipline driving the integration.

Key Points

The Following are the Major Methods of Evaluation:-

• Portfolio: Portfolio contains samples of the learner's work like project reports, assignments, etc. to evaluate academic achievement and learning progress over time.
• Checklist: Checklist consists of a list of items prepared by the teacher to study the relevant problems. The students just have to answer them in yes/no to show the absence or presence of that specific item.
• Project: It is a evaluation method that emphasizes the voluntary participation of students by working in a group to complete a specific project.
• Classroom Participation: It is really important in evaluation as It relates to the active involvement of students. Classroom Participation makes learning enliven and meaningful.

Hint

• Paper - pencil test is not suitable in the context as it related to the summative assessment which helps to measure, certify, and report the level of student learning at the end of the term.

Hence, Checklist, Portfolio, Project, Class participation can be used to assess learners' interest in and attitude to mathematics.

Mathematics teachers play an interactive role in fostering the potential of young seedlings to grow and bloom. Their patience and perseverance significantly impact a child's success in the classroom.

Neeta, a teacher of class VII mathematics, gives a lot of Survey based projects in the classroom of Mathematics.

This Activity has the Following Objectives:-

Students will get the opportunity to collect authentic data, understanding of learning in children develops and other qualities of the survey are also developed.

• Using this for alternative assessment, it will help to know the performance of students.
• To promote problem-solving skills.
• Surveys given by the teacher in the classroom will not disturb the monotony of the classroom but serve to bring unity and encourage children by giving them interesting work.

Some Benefits of Survey Based Projects​ & Assessment:-

• Authenticity
• motivation
• metacognition
• collaboration
• creativity
• Skill development of communication
• Skill development of co-operation

Hence, it becomes clear that breaking the monotony of the classroom is not the purpose of the given activity.

Mathematics is the study of numbers, shape, quantity, and patterns. Mathematics is the ‘queen of all sciences’ and its presence is there in all the subjects. It acts as the basis and structure of other subjects.

• In Geometry, we have several undefined terms, Line, Point, and Plane are undefined terms in geometric mathematics.
• From these three undefined terms, all other terms in Geometry can be defined.

Some Defined Terms in Geometry Mathematics:-

• Line segment,
• Beam
• Diagonal of quadrilateral
• Opposite ray
• Angle

Diagonal of Quadrilateral:- A line segment drawn from one vertex of a quadrilateral to the opposite vertex is called a diagonal of the quadrilateral.

Point:- A point just defines someone's position that all a point is where are you at that is the point. All latitude and longitudes are points. Point is a location and has no size

Line:- A line is it just a set of many points that extends to one direction. It's also can we work backward.

Plane:- A plane is the same as a line but except you have many points everywhere and the points don't go one specific direction it is a whole field of many points.

Line Segment:- A line segment is a portion of a line that has two endpoints.it is also a part of a line that connects two points it is the shortest distance between two points.

Hence, it becomes clear that the diagonal of the quadrilateral is defined in mathematics.

Mathematics is the study of numbers, shapes, quantities, and patterns. Mathematics is the ‘queen of all sciences and its presence is there in all subjects. It acts as the basis and structure of other subjects.

Key Points

Some Important Aspects in Algebra:

• Visualization: On observing a mathematical problem first thing is to visualize in mind what methods or approaches one should take to arrive at a solution quickly and smoothly.
• It is often used when solving word problems in mathematics.
• Transposition: While solving algebraic equations one often needs to transfer values from one side to another.
• It is mathematically termed as transporting values from RHS to LHS or vice versa as per requirement.
• Generalization: It is usually referred to as something like the generalization of a concept, i.e. a version of the concept is provided that is less restrictive than the original from which it is derived.
• It typically becomes more general by dropping or weakening some of the original requirements or some of the original axioms.

NOTE: Measurement is not an important aspect of algebra. Measurement is an important aspect of geometry.

Hence, it becomes clear that Measurement is not an important aspect of ‘algebra’.

In a mathematics class, students enjoy learning, solving problems, develop mathematical curiosity, and become confident in using mathematics to analyze and solve problems.

• Problem posing in mathematics means creating problems from the content.
• In mathematics, problem-posing refers to generating new problems and new questions aimed at exploring a given situation as well as the reformulation of a problem during the process of solving the problems.
• Problem posing is important in mathematics teaching and learning because in this process students will gain the knowledge and required confidence.

NOTE:

• The inability to solve math problems is called dyscalculia.
• Dyscalculia is a math learning disability that is also called number dyslexia or math dyslexia.
• Raising doubts in the classroom is enlightening for the students as it also imparts knowledge indirectly to students who are hesitant in the classroom and unable to ask questions.
• Solving problems of mathematic topics can increase confidence. The more questions you try to solve, the more knowledge will increase and confidence will increase.

Hence, it becomes clear that 'Problem posing' in mathematics means creating problems from the content.

Mathematics is the study of numbers, shape, quantity, and patterns. Mathematics is the ‘queen of all sciences’ and its presence is there in all the subjects. It acts as the basis and structure of other subjects.

Qualities of a Good Textbook of Mathematics:

• It should be child-centered subject matter should be arranged from "simple to complex" and "concrete to abstract" method the subject matter should create interest in the pupil.
• It should contain a sufficient number of examples and questions.
• The language used in the text would be simple and easily understandable.
• The books should be written in listed simple, precise, and practical language.
• At the end of the book, there should be given tables and appendices.
• The most important and general specialty is it should be free from mistakes.
• In the textbook, there should also solve examples so that the child can develop concept understanding and he can easily solve the practice questions based on it.
• Practice questions develop the child's ability to solve questions within the time limit and provide an opportunity to follow practice and error theory.

Hence, it becomes clear that a good mathematics textbook contains a lot of questions for exploration.

"Every odd natural number is a prime number" The proof can be verified by method of disproof.

Numbers that are used to count or measure objects or substances are called natural numbers.

Natural numbers are denoted by N such that N = {1,2,3,4,5,6,............. infinite}

Prime Numbers: Numbers that are not divisible by numbers other than 1 and themselves. For example: 2,3,5,7,11,13,17 etc.

• The proof of contradiction method is a common proof technique that is based on a very simple principle something that leads to a contradiction cannot be true and if so the opposite must be true.
• Proof by contradiction is also called indirect proof.
• The method of disproof is the technique in mathematics where is statement is soon to be wrong by finding a simple example where it is not satisfied with both sides.
• Proof by contradiction is its type of proof used in mathematics and is a rule of inference.
• In the logic of Contrapositive of a statement can be formed by reversing the direction of inference and neglecting both terms.

Hence, it becomes clear that “Every odd natural number is a prime number”, this statement can be proved by Method of disproof.

Mathematics anxiety is a feeling of discomfort, high arousal, and physiological reactivity interfering with number manipulation and mathematical problem-solving. 

• Mathematics Anxiety is a negative emotional reaction to mathematics that can be debilitating.
• It has been defined as a feeling of tension and energy that interferes with the manipulation of numbers and solving the mathematical problems.

Key Points

Factor Responsible for Mathematics Anxiety:

• Curriculum defined as the lessons, learnings and the academic content taught in school or in a specific course or program.
• If the curriculum is tailored to children and has a positive outlook, learning capacity will be increased in children.
• The nature of the subject is also an important factor affecting the learning capacity of the children and due to this, the children are stuck in anxiety.
• The examination system is also a major reason for children's anxiety.
• Sometimes sudden changes in the examination system cause trouble for the children.
• Environmental Factors, Cognitive Factors, Psychological Factors, and Physical Factors are also responsible for mathematics anxiety.

Hint

• Gender refers to the socially and culturally constructed system that attributes meaning to what it means to be a male or a female in a particular society. It is not a contributing factor responsible for mathematics in anxiety.

Hence, it becomes clear that Gender is not a contributing factor responsible for mathematics anxiety.

Given:

Range = $\frac {-5}{6}$ and $\frac{7}{8}$

Calculations:

Simplifying the given terms,

Range = (–0.833, 0.875)

Option 1 → –0.916

Option 2 → 0.833

Option 3 → –0.708

Option 4 → –0.750

∴ Amongst the given options, only (–11/12) does not lie between the given range

Simplifying the given terms in fractional form,

Range = [(–20/24), (21/24)]

Option 1 → –22/24

Option 2 → 20/24

Option 3 → –17/24

Option 4 → –18/24

∴ Amongst the given options, only (–11/12) does not lie between the given range

Given:

$\left[ {{{\left( {\frac{3}{8}} \right)}^{ - 2}} \times {{\left( {\frac{{ - 4}}{5}} \right)}^{ - 3}}} \right]$

Concept used:

The reciprocal of a number is 1 divided by the number.

Calculations:

Solving the given expression,

$\Rightarrow \left[ {{{\left( {\frac{8}{3}} \right)}^{2}} \times {{\left( {\frac{{- 5}}{4}} \right)}^{3}}} \right]$

$\Rightarrow {{{\left( {\frac{64}{9}} \right)}} \times {{\left( {\frac{{- 125}}{64}} \right)}}}$

$\Rightarrow \frac{-125}{9}$

Reciprocal of the term,

$\Rightarrow \frac{-9}{125}$

∴ The reciprocal of the given expression is $\frac{-9}{125}$

Given:

(132 - 52)3/2 = 63 × A

Calculations:

Solving the given expression,

⇒ (169 - 25)^3/2 = 63 × A

⇒ 144^3/2 = 63 × A

⇒ 12³ = 63 × A

⇒ A = (12/6)³

⇒ A = 2³

∴ The value of A is 2³

Given:

$x\sqrt {243} = y\sqrt {867}$

Calculations:

Solving the given expression,

$⇒ x\sqrt {243} = y\sqrt {867}$

$⇒ x\sqrt {3^{5}} = y\sqrt {3 \times 17^{2}}$

$⇒ x\times 9\sqrt {3} = y\times 17\sqrt {3 }$

$⇒ x\times 9 = y\times 17$

$⇒ \dfrac {x}{y} = \dfrac{17}{9}$

x = 17a and y = 9a

∵ x and y are co-prime numbers, thus a = 1

x = 17 and y = 9

Putting the value of x and y,

⇒ x - y = 17 - 9 

⇒ 8

∴ The value of x - y is 8

Given:

4-digit number 547a is divisible by 3

Concept used:

Divisibility by 3 → A number is divisible by 3, if the sum of its digits is divisible by 3

Calculations:

Sum of digits of the given number 

⇒ 5 + 4 + 7 + a

⇒ 16 + a

Sum is divisible by 3 for the values of sum 18, 21, 24

Possible values of a, 

Sum = 18, a = 2

Sum = 21, a = 5 

Sum = 24, a = 8

Sum of all the possible values of a = 2 + 5 + 8

⇒ 15

∴ The sum of all the possible values of a is 15

Given:

x4 – 256

x3 – 4x2 + 3x – 12 

x2 – 7x + 12

Calculations:

Simplifying the given expressions,

x4 – 256 = (x - 4)(x + 4)(x² + 16) 

x3 – 4x2 + 3x – 12 = (x - 4)(x² + 3)

x2 – 7x + 12 = (x - 4)(x - 3)

∴ The common factor of the given expressions is (x - 4)

Given:

Divisor = 8x3 - 6x2 + 10x + 3

Dividend = (4x + 1)

Quotient = 2x2 + k

Calculations:

Dividing the given polynomial,

Quotient = 2x2 - 2x + 3 = 2x2 + k

⇒ k = -2x + 3

∴ The value of k is 3 - 2x

Calculation:

$\left( {9{x^2} + 15 - x} \right) \times \left( { - 1 - x + {x^2}} \right)$

$⇒ \left( {9{x^2} + 15 - x} \right) \times \left( {{x^2} - x - 1} \right)$

$⇒ 9{x^2}\left( {{x^2} - x - 1} \right) + 15;\left( {{x^2} - x - 1} \right) - x\left( {{x^2} - x - 1} \right)$

$⇒ 9{x^4} - 9{x^3} - 9{x^2} + 15{x^2} - 15x - 15 - {x^3} + {x^2} + x$

$⇒ 9{x^4} - 10{x^3} + 7{x^2} - 14x - 15$

Here, the coefficients of x³, x² and x are A, B and C then

A = -10

B = 7

C = -14

A/Q

(A + B - C) = (-10 + 7 - (-14)) = 11

⇒ Correct Option is 1

Given:

$x = \frac{1}{9}$

$y = \frac{-3}{4}$

81x2 + 16y2 - 72xy

Calculations:

Putting the given values of x and y in the expression

⇒ 81 × (1/9)² + 16 × (-3/4)² - 72 × (1/9) × (-3/4)

⇒ 81 × (1/81) + 16 × (9/16) - 8 × (-3/4)

⇒ 1 + 9 + 6

⇒ 16

∴ The value of the expression is 16

Given:

Age of Abhi = 2 × Age of daughter

Five years ago, Age of Abhi = 4 × Age of daughter

Calculations:

Let the present age of Abhi and his daughter be A and x

⇒ A = 2 × x      ----(i)

Five years ago,

⇒ (A - 5) = 4 × (x - 5)      ----(ii)

Substituting the value of A from (i) to (ii),

⇒ (2x - 5) = 4(x - 5)

∴ The correct answer is 4(x - 5) = 2x- 5

Given:

Principal = Rs. 6250

Rate of interest = 8%

Time period = $2\frac{3}{4}$ years

Formula used:

When the sum is invested for $2\frac{3}{4}$(time is in fraction)

${\rm{A;}} = {\rm{;P}}{\left( {1 + \frac{{\rm{R}}}{{100}}} \right)^{\rm{2}}}{\left( {1 + \frac{{\rm\frac{3}{4}{R}}}{{100}}} \right)}$

Calculations:

Let the amount be A

$⇒ {\rm{A;}} = {\rm{;6250}}{\left( {1 + \frac{{\rm{8}}}{{100}}} \right)^{\rm{2}}}{\left( {1 + \frac{{\rm\frac{3}{4}\times {8}}}{{100}}} \right)}$

$⇒ {\rm{A;}} = {\rm{;6250}}{\left( {\frac{{\rm{108}}}{{100}}} \right)^{\rm{2}}}{\left( {\frac{{\rm{106}}}{{100}}} \right)}$

$⇒ {\rm{A;}} = {\rm{;6250}}{\left( {\frac{{\rm{27}}}{{25}}} \right)^{\rm{2}}}{\left( {\frac{{\rm{53}}}{{50}}} \right)}$

$⇒ {\rm{A;}} = {\rm{;10}}{\left(729 \right)}{\left( {\frac{{\rm{53}}}{{50}}} \right)}$

⇒ A = Rs. 7727.4

∴ The sum amounts to Rs. 7727.40

Calculation:

<br>

Let the cost price of the goods is Rs 100.

<br>

M.P = C.P + 40% of C.P = 100 + 40% of 100 = Rs. 140

<br>

Now, He allowed discount of 40% on M.P

<br>

S.P = M.P - 40% of M.P = 

<br>

S.P = 140 - 40% of 140

<br>

S.P=140−(40100×140)S.P=140−(40100×140)

<br>

S.P = 140 - 56 = 84

<br>

C.P = 100, S.P = 84

<br>

⇒ Loss = 16

<br>

$Loss\% = \frac{{16}}{{100}} \times 100 = 16\%$

<br>

⇒ Option 3 is correct

Concept:

• Sum of the internal angles of the Quadrilateral is 360°
• Supplement of the angle is 180° - θ°  (where θ is the given angle).
• Compliment of the angle is 90° - θ°  (where θ is the given angle).

 

Calculation:

The given ratio's of angles of a quadrilateral are - 

2 : 3 : 5 : 8

Let the angles be 2x , 3x , 5x , 8x.

We know that, Sum of the angles of quadrilaterals = 360° 

⇒ 2x + 3x + 5x + 8x = 360° 

⇒ 18x = 360

⇒ x = 360° / 18 = 20° 

Now, each angles be,

2x = 2 × 20 = 40° 

3x = 3 × 20 = 60° 

5x = 5 × 20 = 100° 

8x = 8 × 20 = 160° 

The Suppliment of the largest angle = 180° - 160° = 20° 

The Comliment of the smallest angle = 90° - 40° = 50° 

Sum of these = 20° + 50° = 70° ∴ Option 1 is correct

Concept:

• Pythagoras' Theorem: The square of the hypotenuse of the right angle triangle is equal to the sum of squares of the other two sides.
• (Hypotenuse)² = (Base)² + (Height)²
• The hypotenuse is always the biggest side in triangle opposite to 90°

 

Calculation:

Given the two sides of the triangle are 15 cm and 17 cm

Here, it is not given which side is hypotenuse or the other sides so,

Let the missing side be hypotenuse,

⇒ x² = 15² + 17² = 225 + 289 = 514

⇒ x = √ 514 = 22.67, i.e. between 22 to 23 cm

Hence, statement B is correct

Let the other side is missing

⇒ (17)² = (15)² + x²

⇒ x² = 17² - 15² = 289 - 225 = 64

⇒ x = √ 64 = 8 cm 

8 does not lies b/w 4 to 7, hence, A is incorrect.

8 is less than 10, hence C is correct.

∴ Option 2  (i.e. both B & C) is correct.

Concept:

• Sum of the internal angles of the triangle is 180°
• The angle bisector bisects the angle in two equal parts.

Calculation:

We can draw the figure according to the question as below,

We know that, in Δ ABC

∠A + ∠B + ∠C = 180° 

∠B + ∠C = 180° - ∠A = 180° - 110° = 70° 

Now,

$\frac{1}{2}∠ B + \frac{1}{2}∠ C = \frac{1}{2}\left( {∠ B + ∠ C} \right) = \frac{{70^\circ }}{2} = 35^\circ$

Now in Δ OCB,

∠OBC + ∠BCO + ∠COB = 180° 

$;\frac{1}{2}\left( {\angle B + \angle C} \right) +\angle COB = 180^\circ$

∠COB = 180° - 35° = 145° 

∴ Option 4 is correct.

Concept:

• Congruent triangles: If the two triangles are congruent if they have equal same sides and the angles either by rotating the angles or flipping it.
• These are the following properties which makes two triangles congruent.
• SSS (side side side) property: If all the sides of both the triangles are equal they are congruent.
• SAS (side angle side) property: If the two sides of the triangles are equal along with the angle between them, then they are congruent.
• ASA (angle side angle) property: If the two angles of the triangles are equal along the side between them then, they are congruent.
• RHS (Right angle hypotenuse and side): If both triangles are of 90° each and the their hypotenuse and one side are equal then they are congruent.

Calculation:

In Δ ABC & Δ PQR

AB = 4 cm = PR

AC = 5 cm = PQ

BC = 6 cm = RQ

⇒ Δ ABC is congruent to Δ PRQ

⇒ Option 4 is correct

Concept:

• Volume of the cuboid = Length × Breadth × Height

Calculation:

Given, 

The maximum volume of the tank is 540 m³

The tank is only 2/3 is filled so now the volume of water = 2/3 × 540 = 360 m³

Length = 8 m and Breadth = 15 m

we know,

Volume of the cuboid = Lenght × Breadth × Height

360 m³ = 8 m × 15 m × Height

$Height = \frac{{360;{m^3}}}{{8m × 15m}} = 3;m$

∴ Option 3 is correct

Concept:

• Area of Triangle = 1/2 × base × height
• Area of Equilateral triangle = √ 3 / 4 × (side)²
• Perimeter of Equilateral triangle = 3 × side.

Calculation:

Let a is the length of the side of a larger triangle and b is the length of the side of a smaller triangle.

Given, the ratio of the areas of two equilateral triangles is 16 : 9

$\Rightarrow \frac{{\left( {\frac{{\sqrt 3 }}{4};{a^2}} \right)}}{{\left( {\frac{{\sqrt 3 }}{4};{b^2}} \right)}} = \frac{{16}}{9}$

$\Rightarrow \frac{{{a^2}}}{{{b^2}}} = \frac{{16}}{9}$

$\Rightarrow \frac{a}{b} = \frac{4}{3}$               ------(1)

Given, the perimeter of the smaller triangle = 63 cm

⇒ 3b = 63

⇒ b = 63/3

⇒ b = 21 cm

From equation 1, we get

$\Rightarrow \frac{{\rm{a}}}{{21}} = \frac{4}{3} \Rightarrow a = 28;cm$

So, 28 cm is the length of the side of a larger triangle and 21 cm in length of the side of smaller triangle.

Now, 28 - 21 = 7 cm

So, the length of the larger triangle than a side of the smaller triangle is 7 cm

∴ Option 2 is correct

Given:

Area of triangle = Area of circle

Perimeter of circle = 6 π cm

Base of triangle = 8 cm

Formula used:

Area of triangle = (1/2) × Base × Height

Area of circle = π R²

Perimeter of circle = 2 π R

Calculations:

Let the height of the triangle be H

Perimeter = 6 π 

⇒ 6 π = 2 π R

⇒ R = 3 cm

Area of circle = π × 3 × 3

⇒ 9 π = (1/2) × 8 × H

⇒ 9 π = 4H

⇒ H = 2.25 π 

∴ The height of the triangle is 2.25 π

Concept:

• When Sulphur is burned in the presence of oxygen it produces Sulphur dioxide gas.
• S + O₂ → SO₂
• Also, when Sulphur dioxide (SO₂) is mixed with water (H₂O), It produces Sulphurous acid (H₂SO₃).
• SO₂ + H₂O → H2SO3
• Litmus paper can have properties to change their colour in presence of acids and bases.
• Red litmus can turn blue when it is dipped in a basic solution.
• Blue litmus can turn Red when dipped in acidic solution.

Explanation:

Properties of sulphur dioxide gas -

• SO₂ is a colourless gas or liquid with a strong, choking odour.
• SO₂ is non-metallic oxide and generally, the oxides of non-metal are acidic in nature. This means it can turn blue litmus red.

∴ Option 3 is correct.

Concept:

• When Sulphur is burned in the presence of oxygen it produces Sulphur dioxide gas.
• S + O2 → SO2
• Also, when Sulphur dioxide (SO2) is mixed with water (H2O), It produces Sulphurous acid (H2SO3).
• SO2 + H2O → H2SO3
• Litmus paper can have properties to change their colour in presence of acids and bases.
• Red litmus can turn blue when it is dipped in a basic solution.
• Blue litmus can turn Red when dipped in acidic solution.

Explanation:

Properties of sulphur dioxide gas -

• SO2 is a colourless gas or liquid with a strong, choking odour.
• SO2 is non-metallic oxide and generally, the oxides of non-metal are acidic in nature. This means it can turn blue litmus red.
• When Sulphur mixed with water it produces sulphurous acid
• SO2 + H2O → H2SO3

∴ Option 1 is correct.

Concept:

• When Sulphur is burned in the presence of oxygen it produces Sulphur dioxide gas.
• S + O2 → SO2
• Also, when Sulphur dioxide (SO2) is mixed with water (H2O), It produces Sulphurous acid (H2SO3).
• SO2 + H2O → H2SO3
• Litmus paper can have properties to change their colour in the presence of acids and bases.
• Red litmus can turn blue when it is dipped in a basic solution.
• Blue litmus can turn Red when dipped in acidic solution.

Explanation:

Properties of sulphur dioxide gas -

• SO2 is a colourless gas or liquid with a strong, choking odour.
• SO2 is non-metallic oxide and generally, the oxides of non-metal are acidic in nature. This means it can turn blue litmus red.
• When Sulphur mixed with water it produces sulphurous acid
• SO2 + H2O → H2SO3

1. Observation is the gathering of information through the five senses. Scientists use sight, smell, hearing, taste, or touch to learn about our world.
2. Inferences are an explanation for an observation you have made. They are based on your past experiences and prior knowledge.
3. Measurement by knowing the amount required to make this chemical composition

All the three process skills can be measured while doing this activity.

∴ Option 3 is correct.

Most of the fluids are not ideal ones and offer some resistance to motion. This resistance to fluid motion is like internal friction analogous to friction when a solid moves on a surface. It is called viscosity. This force exists when there is relative motion between layers of the liquid. It is one of the characteristic properties of liquids.

Viscosity is a measure of resistance to flow which arises due to the internal friction between layers of fluid as they slip past one another while liquid flows. Strong intermolecular forces between molecules hold them together and resist the movement of layers past one another.

Key Points

A science teacher asks her students to put two drops each of oil and sugar solution on a flat surface. She then asks them to tilt the surface and observe the order in which the drops reach the bottom.

• The students observe that there is a measure of resistance to flow which arises due to the internal friction between layers of fluid as they slip past one another while liquid flows. Strong intermolecular forces between molecules of the sugar solutions hold them together and resist the movement of layers past one another. While because the fewer intermolecular forces between molecules of the oil did not hole them together and reach the bottom.

Thus from the above-mentioned points, it is clear that the property of the liquids is the teacher trying to bring to the students’ attention through this activity is viscosity.

Classroom Discussions plays a vital role in shaping or constructing the overall personality of a child. The discussions help the child to not only presents his or her point of view but to get an idea of other's perception as well and this helps in shaping the all-round thinking of a child.

Key Points

• If the teacher finds that many of his class 7 students believe that the raw material for plant growth is obtained only from the soil.
• To refute such an idea, the teacher should give the students a money plant planted in water and test its growth and ask them to draw conclusions.
• Providing amusing reading material to the students about the process of food production in plants will only arouse reading interest in children.
• Analysis, investigation, and testing will not develop their capabilities.
• By showing students a presentation about photosynthesis, students' technical knowledge and interest in the classroom can be increased. This cannot contradict any particular notion made in children.
• Explaining the process of photosynthesis and related chemical processes in detail will increase the written and intellectual knowledge of the children.
• If a particular perception develops in children that is not really true, then in such a situation, children must present correct information by 'learning by doing' and refuting their belief by 'experimental testing method'.
• If the students will see the money plant in the water and test its growth then they can understand that not only the soil is used as raw material for the growth of the plants but also water, air, sunlight are important.

Hence, providing the students with a money plant in water and ask them to observe its growth and make an inference would be the most appropriate strategy to counter the given idea.

Science education cultivates students' curiosity about the world and enhances scientific thinking.

This will prepare students to participate in public discourse in science-related issues and enable them to become life-long learners in science and technology.

• The creation of process validity of the science curriculum requires that learners should be engaged in the process that leads to the generation of scientific knowledge.
• Process Validity requires that the curriculum should engage the learner in acquiring the methods and processes that lead to the generation and validation of scientific knowledge and nurture the natural curiosity and creativity of the child in science.
• The main purpose of the science curriculum is to help children develop basic scientific ideas and understanding scientific theories.
• Students should be kept engaged in processes that can create new scientific thinking by eliminating their orthodox concoctions.
• Science should be taught as a subject that can arouse interest in scientific concepts such as analysis, exploration, testing, and conclusion by awakening scientific perspectives among children.
• Science should not be separated from social values at all and education should be done which will provide the children with scientific outlook as well as knowledge of social values and moral values.
• Learners should be familiarized with various natural processes so that students can develop their own understanding and thinking.

Hence, the criterion of process validity of the science curriculum requires that learners should be engaged in processes that lead to generation of scientific knowledge.

According to NPE-1986, Science Education should be strengthened so as to develop well-defined abilities and values such as the spirit of inquiry creativity, objectivity, the courage to question, and aesthetic sensibilities. 

Key Points

Co-curricular activities like practicals and experiments in science education are those activities that are usually organized to provide opportunities for students. They help:-

• To develop their special talents and to creatively express themselves through various forms.
• The objective of an experiment is to observe phenomena more minutely by the use of very sensitive instruments. It helps in a better understanding of the subject.
• Practicals/experimental activities in science do not aim to help in scoring high grades or marks.
• They help in developing manipulative skills.
• Experiments and activities in science follow the principle of ‘learning by doing’ and it is a common saying that the best way ‘to learn science is to do science’.
• Experiments enhance understanding of science ideas.

Hence, it becomes clear that helping in high grades or marks is not the purpose of conducting practicals/experimental activities in science.

A few small wax pieces are fixed at nearly equal distances on a flat strip of aluminum. One end of the strip is claimed to a stand and the other and is heated.

Statement A: Wax pieces begin to fall one by one in the order of their increasing distance from the flame.

Statement ​B: The aluminum strip transfers heat from the end nearest to the flame to the other end.

• Statement A is observation and B is inference.
• According to the observation made in the question, if one of the metal rods is heated to one end of the rod, then the other end of the metal also starts to heat slowly, this process is called conduction of heat.
• When an experiment is done to define a law of science by man-made objects or natural objects, this is observation.
• The transfer of heat by the collision of particles present in a metal such as (molecules, atoms, electrons, photons) is called heat conduction. The same experiment has been proved in the question.

Hence, it becomes clear that statement A is observation and B is inference.

"Two identical cubes of ice are taken out of refrigerator one is crushed and the other is left as it is it is noticed that the crushed ice melts faster". This process is called hypothesizing.

Key Points

The hypothesis process refers to resize a testable statement of what the researcher predicts will be the outcome of the study.

• This process usually involves proposing a possible relationship between two variables.
• The word hypothesis consists of two words, where ‘hypo’ means tentative or subject to verification and ‘thesis’ implies a statement about the solution of a problem.
• A hypothesis is a principal instrument in conducting research. It is a proposed answer to a research question.

Hint

• Controlling variables is an important part of the experimental view in which controlled variables refer to variables that are calculated factors that are fixed or eliminated in order to clearly identify the relationship between an independent variable and an independent variable.
• An experiment is a set of actions and observations performed in the context of solving a particular problem or question to support a hypothesis or views.
• An observation is a process that consists of receiving knowledge through our senses or objects recording information using scientific tools and instruments.

Hence, it becomes clear that in the given question Hypothesizing skill is being promoted.

Co-curricular activities in Science class are usually organized outside the classroom to provide opportunities for students to develop their special talents and to creatively express themselves through various forms.

If a teacher of class VII demonstrates the following activity in the class.

A leaf is put in a test tube and spirit is poured over it then the test tube is put in a beaker half-filled with water and heated till the leaf is discolored. The leaf is then taken out and a few drops of iodine are put on it.

The leaf turns blue-black in colour.

Can this test be done without removing chlorophyll?

This statement would access "analysis".

• To answer this question, analysis has to be done, that is, the results obtained by removing chlorophyll and experimenting depends on the analysis itself.
• The method in which to solve a problem is to divide that problem into pieces and to analyze the expressions of the assembled object separately and test them.
• The analysis method is a research method that moves from "complex to simple", "unknown to known" and "inference to inference".
• In the analysis method, students develop a habit of deciding the reasoning power correctly.

Hence, from the given activity the assess ‘analysis’ is, Can this test be done without removing chlorophyll?

Co-curricular activities in Science Teaching are those activities that are usually organized outside the classroom to provide opportunities for students to develop their special talents and to creatively express themselves through various forms.

• If a teacher wants his class VI students to figure out that the property of solubility of salt in water can be used to separate a mixture of sand and salt.
• As a supporter of inquiry-oriented pedagogy teachers would provide a mixture of sand and salt to students and ask them to think of the different ways of separation and help them in trying out-there ideas.
• Inquiry-oriented teaching is a stance, a way of learning about teaching, and from teaching and general inquiry is conceptualized as a transformative force for teaching development student learning, and the changing of school.
• Specialties and Benefits of Inquiry-Based Teaching and Learning:- 
• Enhance the learning experience for children.
• Deepen student's understanding of topics
• Allow students to take ownership of their learning.
• Create a love of learning.
• Increase engagement with the material.

1. Separation of the sand and salt by the teacher itself and showing it to be isolated does not develop the student's sense of 'learning'.
2. It would not be easy for students to make different hypotheses of separation without providing a basic understanding of science (mixing chapters) to students.
3. The teacher should make himself available to the students with a mixture of sand and salt and ask them to think of ways to separate them and help them if the student makes a mistake.

Hence, as a supporter of inquiry-oriented pedagogy, you would provide a mixture of sand and salt to students, ask them to think up different ways of separation and help them in trying out their ideas.

Science aims at enabling students to develop their communication skills to be able to understand scientific information, such as data, ideas, arguments, and investigations, and communicate it using appropriate scientific language in a variety of communication modes.

Key Points

Science and Technology: 

• Science and technology have different purposes, ways of viewing, and knowing the world, and thus their relationship is often tense and complex.
• Science is a  system of acquiring knowledge based on proper methods in order to organize the body of knowledge gained through research. It is a broader endeavour.
• Technology is the usage and knowledge of tools, techniques, crafts, systems, or methods of organization in order to solve a problem or create an artistic perspective.
• Technology is goal-oriented and often locale-specific.
• Technologies significantly affect humans as well as other animal species’ ability to control and adapt to their natural environments.

Hence, it becomes clear that Science is a broader endeavour while technology is goal-oriented and often locale-specific.

Explanation:

The flower is mainly the reproductive part of the plant. Due to the different colours of flowers, we are able to recognize the plant.

• Sunflower is NOT considered as a single flower rather a bunch of flowers.

• This feature of sunflower is considered as inflorescence.

• Each flower of the sunflower is present at the head of it.

• Whereas each flower can produce seeds on their own.

 

Hence, Sunflower is not a single flower but a group of flowers.

Concept:

Types of Motion - 

• Circular Motion: When a body moves around a fixed point or on the circumference of the circle in the circular path then this type of motion is termed circular motion. Ex - A car on the curve, a stone tied with tread etc.
• Translational Motion: When every point of a body is moving with the same velocity in the same line or direction.
• Periodic Motion: When the motion repeats itself after a fixed interval of time then that kind of motion is termed periodic motion. Ex- pendulum, rotation of earth etc.

Explanation:

When a bicycle moves with a constant speed then -

It has a circular motion around its axis.

Translatory motion as every point of the wheels exhibits the same motion.

After each cycle, the motion repeats and forms periodic nature.

⇒ Wheels of bicycle exhibit all circular, translator, and periodic motion.

Hence, the wheels of the cycle exhibit circular, translational, and periodic motion.

Concept:

Types of Soils Based on Size:

• Clayey Soil: It consists of very fine particles of clay. The water holding capacity of this soil is very high and due to this, it is very sticky. This soil is used to grow crops which require more water to grow like paddy. It is also used in making toys.
• Loamy Soil: It consists of sand, clay and slit. It has enough humus and good water holding capacity. This soil is good for cultivation, crops like wheat, sugarcane, cotton, pulses can grow easily.
• Sandy Soil: It consists mostly of sand and clay. the water-holding capacity of this soil is very low. This soil is not good for cultivation but if the water is available we can grow maize, millets, barley and some fruits like melon and coconut.

Soils on the Basis of Their Colour:

• Black Soil: This is also known as black lava soil. This soil is black in colour and rich in clay and lava rocks. Crops suitable to grow in this are cotton, sugarcane, tobacco, millets, wheat and oilseeds.
• Red Soil: The colour of this soil is red due to the presence of iron oxide. This soil is not much fertile seems yellow when less iron and more water is present. Crops suitable to this are groundnuts, millets, pulses, cotton and tobacco.

Explanation:

• A farmer having black soil and want to grow fibre-Yeilding plants then the Cotton is the best option.
• Cotton is a soft and fluffy staple fibre.

∴ Cotton is the correct option

Concept:

All these terms are related to Female Reproduction System:

• Gamete: The gamete are also termed as reproductive/sex cells. The female gamete is called ova/egg cells whereas the male gamete is sperm.
• Embryo: It is the early-stage development of the unborn baby of the multicellular organism.
• Egg: It is a female reproductive cells or ovaries, this is the part of gamete.
• Ovum: Female reproductive cells ovum (singular) or ovaries (plural). When this fuse to sperms form zygote.

Explanation:

• In the female reproductive system, female produces eggs whereas the male having sperms. When they fuse forms zygote.

• Which after fertilization converts into embryo.

• Out of these four gametes (Ovum/egg + sperm), Egg and Ovum are the same in meaning whereas the Embryo is the later developed process.

Therefore Option 2 is correct.

EXPLANATION:

• Saliva contains a starch digestive enzyme, salivary amylase that digests the starch and converts it into maltose (disaccharide).

• Inhale: The process of breath is called inhale. Inhaled air has the same composition as normal air, it contains 78% nitrogen 21% oxygen 1% inert gas such as argon 0.04% carbon dioxide little water vapour.
• Exhale: The process of breath out is called exhale. Exhaled air contains  78% of nitrogen, 16.4% of oxygen, and 4.4% of carbon dioxide and other gases.

​Both inhaled air and exhaled air contain oxygen.

Additional Information

Human Respiraroty System

Concept:

• The distance of the image ‘behind’ the mirror is the same as the distance of the object in front of the mirror.

CALCULATION:

Firstly Ritu standing 5 m from the mirror.

Distance between ritu to mirror = distance between mirror to image

if she moves 2 m closer by mirror then its image will also get closer by 2 m.

New distance between Ritu and her image will be-

[(5-2) + (5-2)] = 3 + 3 = 6 m

Additional Information

In a plane mirror

• size of image = size of the object
• The image is laterally inverted.

CONCEPT:

• Phenolphthalein remains colourless in a neutral or acidic solution but turns out magenta or pink in basic solutions.

EXPLANATION:

• When phenolphthalein is added to NaOH, the solution has the colour of pink since sodium hydroxide is a strong base.
• If HCl is added the solution loses its colour and turns out colourless since HCl neutralizes sodium hydroxide being an acid.
• Salt is (NaCl) is a neutral solution so it shows colourless.

So X is colourless; Y is pink and Z is colourless.

EXPLANATION:

• In an adult human 32 teeth are found.
• The arrangement of different types of teeth in humans from front to back is incisor- canine-premolar-molar.

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• The first set of teeth grows during infancy and they fall off at the age between six to eight years. These are termed milk teeth.
• The second set that replaces them is the permanent teeth. The permanent teeth may last throughout life or fall off during old age or due to some dental disease.

EXPLANATION:

• Transpiration is the evaporation of excess water from the surface of a leaf, through the stomata.
• Transpiration produces a cooling effect and thus saves the plant from the hot sun.
• The evaporation of water from leaves generates a transpirational pull or suction force that can pull water from the roots to the top of the tree.