CTET Paper 2 Maths & Science 22nd Dec 2021 (English-Hindi-Sanskrit) (Previous Year Paper)

The phenomena of cognitive domains and Psychomotor domain is proposed by Benjamin Bloom in his Taxonomy in 1956.

• Bloom explains taxonomy in three domains such as:
• Cognitive Domains
• Psychomotor Domains
• Affective Domains : Most of the school learning programmes we intend to develop cognitive skills related to the learning. content and also to bring in changes in the affective domain of the learner like interests, Affective and attitudes, values etc. It is clear that cognitive as well as affective learning take place Psychomotor Learning and their Organisation simultaneously and with the same content of learning, there are several learning situations in which psychomotor learning occurs along with cognitive learning and for affective learning.

Key Points

• According to Bloom's Taxonomy, changes are going on throughout life, So human skills and domains are also developed or changed, that's why they can learn and remember new things. And also they can modify their skills, their talent, and their interest also.

Important Points

• Outcomes can not be changed easily, they can change by practicing, gaining knowledge, etc.
• That's why option (3) is the correct answer to this question.

Additional Information

• There are six steps in the Cognitive domain, such as:
• Knowledge
• Comprehension
• Application
• Analysis
• Synthesis
• Evaluation​
• ​​These steps are revised in 2001 by Anderson and Krathwohl as-
• Remembering
• Understanding
• Applying
• Analyzing
• Evaluating
• Creating

Development is the process in which a child develops through all the aspects such as physical, social, environmental, emotional, language, cognitive, moral, etc. It happens throughout life.

Key Points

• The development follows the principle of  Spiral advancement, it can be back and forth throughout life.
• The pace of development is different from age to age.
• Example:
• A child can learn their primary language faster than the secondary language.
• The growth and development of the body organs of the child in the infancy stage are faster than the growth of organs after adolescence.
• That's why option (2) is correct.

Important Points

• The principle of uniformity means that the development of every child is the same in all aspects such as Physical development, Social development, emotional development, etc, at the same pace. but it is not possible. that's why option (1) is incorrect.
• The principle of uni-directional means that development in the child is only one direction/aspect, which is wrong in the context of child development, child development is multi-directional with different aspects.
• The principle of discontinuity in child development refers to the development is not continuous but as we know that development in a child is a continuous process throughout life. So option (4) is also irrelevant.

Additional Information

• Development is not linear in shape, it is Spiral in shape.
• Development is the product of both 'Heredity' and 'Environment'.
• Development is from General to Specific.
• Development is from whole to part.

Socialization is a way of learning in which humans are interacting with friends, family members, teachers, television, smartphone, newspaper etc. to built their knowledge, learning and skills.

Key Points  

• As we are well-known Television is a part of media.​
• ​So that option (1) is correct.
• ​The child learns through the process of intimation in the social environment.

Additional Information

• Socialization is the process that is continuous throughout the life
• Primary Socialization- In the Initial years of One's life                                             (Infancy).
• In primary socialization Identity of a child is formed.
• Secondary Socialization- It takes place after Birth.

Progressive education is an education in which values are given to experiences and practical knowledge than rote learning and formal learning.

Key Points

• The main focus of progressive education is on learning by doing.
• The student should enjoy their studies and gain concepts, not get involved in rote learning.
• It is a Teacher centered to child-centered approach.
• Integrated curriculum, Problem-solving methods, Critical thinking are the main part of Progressive education which helps to develop the concepts in a child's mind.

 Additional Information

• The Father of Progressive education is John Dewey.
• ​Dewey is a professor at Chicago University and he proposed "Learning by doing" in 1894 in Chicago.

Jean Piaget studied cognitive development among children of different age groups in different developmental stages. 

Key Points

• These stages are (sequentially):
• Sensorimotor stage: (birth to 2 years)
• Pre-operational stage: (2 to 6 years)
• Concrete operational stage: (6 to 11 years)
• Formal operational stage: (11+ to adolescence and adulthood)

Additional Information

• Jean Piaget is a Psychologist from Switzerland who proposed that development is based on Physical environment and Biological abilities.
• He ignores Social aspects in development.

Jean Piaget studied cognitive development among children of different age groups in different developmental stages, According to Piaget, development is based on Physical environment and Biological abilities, he ignores social Aspects.

Key Points

• According to Jean Piaget:
• Formal operational Stage (11+ years to adolescence)
• ​Development of creative thinking and Hypothetical-deductions takes place in the life of a child.
• And in option (2), If A is greater than B and B is greater than C. What is the relation between A and C?, that's why option (2) is correct.

Additional Information

• The rest three stages of Jean Piaget are**:**
• Sensorimotor stage: (birth to 2 years)
• Pre-operational stage: (2 to 6 years)
• Concrete operational stage: (6 to 11 years).

Vygotsky’s theory of Sociocultural development is proposed by Lev Vygotsky. He is a Russian scientist and he emphasizes the role of society and culture in the development of the child.

Key Points

• According to Vygotsky, the main needs in the development of a child is-
• Social interaction
• ​​Children try to interact with people.
• Example: Peer groups, family members, etc.
• Culture
• ​Children adopt the culture by interaction.
• Language
• ​​Children can easily intimate their primary language through interaction or communication.
• Negative reinforcement is a method that is used to teach some specific behavior, like an escape, avoidance, etc which is not proposed by Lev Vygotsky.
• ​So that's why option (3) is correct.​

Additional Information

• Vygotsky also proposed a model of speech during the development of the child:
• Social speech ( from 2 years)
• Private speech ( from 3 years)
• **Silent speech (from 7 years).**​

Lev Vygotsky proposed the needs of a child in learning as:​

• ZPD (zone of proximal development)
• Scaffolding
• **MKO (more knowledgeable others)**​

Key Points

• Scaffolding:​
• Temporary help is given to a child in learning by their peers, family members, teachers, etc.
• That's why option (4) is correct.
• reinforcement:
• ​The theory of Reinforcement is proposed by B.F. Skinner.
• ​Conditioning and Modelling are irrelevant to the question.

Additional Information

• ZPD (zone of proximal development)
• The difference between the learning of child by self and the learning of a child with the help of others(society, culture, etc.)
• MKO (more knowledgeable others)-
• In this process only Hint is giving to the child by others to learn.

The child's Moral development theory is proposed by Lawrence Kohlberg in 1958. he describes the theory on 3 different levels

• Pre conventional level ( 0 to 6 years)
• Conventional level (7 years to 11 years)
• Post conventional level (Above 11 years)

​These 3 levels are further classified into 6 stages.

Key Points

• Stage 3 of Kohlberg's moral development theory is:
• Good boy /Good girl morality.
• In this stage, the child avoids disapproval or dislike from others, so this stage refers to a golden rule.
• The child wants to capture the attention of everyone towards himself.
• The child wants to show that he is the best and he did not have any shortage.
• So option (1) is correct.

Additional Information

• The social system is dependent on the performance of one's duties is related to Kohlberg's 4th stage of moral development.
• Right actions according to the norms, needs, and rights that are unanimously accepted by society are related to Kohlberg's 5th stage of moral development.
• The child keeps the norms in mind as same as universal principles are applicable is related to Kohlberg's 6th stage of moral development.​

Howard Gardner proposed the 'theory of Multiple Intelligence'  Intelligence is practical goal-oriented activity.

Theory of Multiple Intelligence by Howard Gardner says- Howard Gardner's theory of multiple intelligences proposes that people are not born with all of the intelligence they will ever have.

This theory challenged the traditional notion that there is one single type of intelligence, sometimes known as “g” for general intelligence, that only focuses on cognitive abilities.

Key Points He divided his theory into 8 types

Stereotypes are anything that categorizes a large group of people into having one or many characteristics that may or may not actually be representative of who they are. It is a “quick and easy way of labeling or categorizing the world around us and making it understandable.

Key Points

• Stereotype thoughts can be eliminated from the life of the students as:
• If the teacher helps the student to think about each condition critically.
• If the students analyze the situations and then move forward toward the conclusion.
• If they live in unity, engaged in teamwork, group discussion.
• If the learning of the student is done in an inclusive education classroom.
• so that option (2) is the correct answer.

Hint

• The teacher should never encourage the student to accept someone's face value, without analyzing it.
• The teacher should not encourage the students to reach direct collusion without knowing about the situation.
• The teacher should never promote the student to imitate in a stereotype behaviors
• That's why all other options are irrelevant except option (2).

Additional Information  ​There are many negative impacts of stereotypes thoughts in the life of school children are-

• They become gender-biased.
• they start to judge people by their wealth, race, etc.
• Stereotype thoughts impact the performance of the children.
• This type of thought interferes with the learning of the children also.

Jean Piaget said that "Thought comes first than language"

Key Points Jean Paiget (1896-1980) - The swiss psychologist stated cognitive theory of the development of children in 1936.

Jean Piaget was a constructivist theorist, he said that the child learns by doing himself

Piaget said that language doesn’t have a direct influence on the cognitive development of the child, but he said the language will develop once the cognitive development will take place.

Piaget has given four factors that influence the child's cognitive development

• Maturation
• Social experience
• Activity
• Equilibrium

Maturation- according to Piaget heredity have an influence on maturation which helps in cognitive development. The child will develop as it gets mature. That is the reason he gave these theories in stages.

Social Experience- As the child will grow he has physical interaction with the other. Like his parents, relatives. It is likely that child will have social interaction with others as it is  having physical interaction

Activity-  said that the children are little scientists, they learn by doing. When they do the activity they learn by themselves.

Equilibrium- Piaget says that when an organism fails to handle a new substance with its previous knowledge it creates an imbalance. To reduce the imbalance he focuses on the stimuli that have created an imbalance. This process of restoring the balance is called equilibrium

Additional Information Lev Vygotsky- He proposed the theory of Socio-cultural development.

B.F Skinner- Theory of operant conditions

Jerome Bruner- Theory of conditioned learner

Hint Vygotsky mentioned the effect of the language on the cognitive development of the child which he said as private speech in his theory of socio-cultural development.

The New Education Policy lays particular emphasis on the development of the creative potential of each individual. It is based on the principle that education must develop not only cognitive capacities - both the ‘foundational capacities ’of literacy and numeracy and ‘higher-order’ cognitive capacities, such as critical thinking and problem solving – but also social, ethical, and emotional capacities and dispositions. 

Key Points Following are the proposals made by National Education Policy 2020 (NEP):-

• a variety of methods and strategies such as group work and role plays be used for assessment.
• apart from assessment by the teacher, other ways such as self-assessment and peer-assessment should be encouraged.
• report card of the student should include progress in the cognitive, affective, and psychomotor domains.
• focus on regular formative assessment for learning rather than the summative assessment that encourages today’s ‘coaching culture.

​Thus, it is concluded that NEP 2020 proposes shift from formative to summative assessment regarding proposals made by National Education Policy 2020 (NEP) is not correct.

Inclusive education means creating effective classrooms where the educational needs of all children are addressed irrespective of ability or disability.

• No matter whether the student is a boy or a girl, intelligent or weak in academics, rich or poor, perfect or physically disabled, the education and treatment by the teachers for all the students are the same in all aspects.

Key Points

• According to inclusive education, teachers should have to treat all the students in same aspects, so that the categorization among the students as "slow learners", "brilliant",  and "average" possesses a negative impact on the students.
• Inclusive education doesn't allow the teacher to categorize the students by their abilities or disabilities.
• So, that option (2) is the correct answer.

Important Points

• Aims of inclusive education-
• Provide equal opportunities to all the students.
• Promotes Unity in diversity.
• Embrace all students irrespective of race, gender, disability, medical or other needs.
• Not categorized the students on the bases of their talent, performance, etc.

Diversity means collective differences, that is, differences that mark one group of people from another. These differences may be of any sort: biological, religious, abilities, physical conditions, appearances, cultural, linguistic, etc.

• . On the basis of biological differences, for example, we have racial diversity.
• On the basis of religious differences, we have religious diversity.

Key Points

• Socio-cultural diversity concerns aspects of culture that can influence an individual's interactions with others of different backgrounds.
• A teacher should have to pay respect and also have to include the socio-cultural diversity of students which helps students as-
• Emphasis on the ability to live in unity.
• Students can learn about different cultures when different types of students are there.
• Opportunity for the student to gain knowledge about engaging with different types of people who are different by language, gender, culture, and tradition.
• So that's why option (2) is the correct answer.​

Hint 

• ​Students should never be judged by the teachers by their physical appearances, economic conditions, disabilities, etc.
• ​Because this type of judgment harms students learning as well as their cognition.​

Learning disabilities are those types of disorders that affect the ability to understand problems in spoken or written language, in doing mathematical calculations, coordinate movements, or direct attention. Although learning disabilities occur in very young children, the disorders are usually not recognized until the child reaches school age.​

Key Points

• Dyslexia:
• ​This is a disability in which student faces difficulty regarding the spelling of words, difficulty in reading letters, unable to make the best arrangement of the alphabets in words, faces difficulty matching sounds. These are the common difficulties in Dyslexia.
• So option (3) is the correct answer.​

Important Point

• Dyspraxia:
• In this disability, the student faces difficulties related to their body movement, and body balancing, students are unable to do activities like, playing sports, jumping, dancing, etc
• ​Dyscalculia:
• Dyscalculia is the disability in which difficulties related to mathematical calculations are found in a student.
• Example: student faces difficulties during addition, multiplication, subtractions, etc.​​​
• ​Dysgraphia:
• ​Dysgraphia is a disability in which student faces difficulties related to writing, they can not write properly.
• Example: A student writes a number "0' in place of the alphabet "O".

A teacher can identify creative children in her class by their innovative style of thinking.

Creativity - It helps us to view and solve the problem more openly with the innovations. creativity opens minds.

When the child develops an innovative style of thinking, he is approaching the same problem with different ideas. These lead the child to develop creativity.

Key Point

Convergent thinking- When the solution to the problem can only be deduced by the established rules and logical reasoning.

Examples- MCQ types of the test don't allow to think, It focuses more on the memorisation of the fact.

Divergent thinking- It helps to develop the ideas beyond prescribed way and rote memory. It helps to think about the same problem in multiple ways.

Examples- Give the pile of blocks and ask them to create a different structure each time with that block.

Additional Information  Their popularity among the peers- This doesn't have any direct link with creativity as there are many reasons to be popular among the peers. Eg such a child might be good at sports.

Their selection of simple and recall based tasks-  This shows that the child depends on the rote memory, he selects the simple task which is easy to recall, This doesn't develop creativity because he is not using ideas for the problems.

HintConvergent thinking helps in developing uniformity.

Divergent thinking help in developing creativity.

Attention deficit hyperactivity disorder(ADHD) is a brain disorder that affects how you pay attention, sit, still, and control your behaviour. It happens in children and teens and can continue into adulthood. Children with ADHD may have trouble paying attention and controlling impulsive behaviours. ADHD is the most commonly diagnosed mental disorder in children.

Key Points

• The three main symptoms of ADHD include the following:
• ​Inattention: Short attention span for age (difficulty sustaining attention) Difficulty listening to others.
• Impulsivity: Has difficulty waiting for his or her turn in school and/or social games, Takes frequent risks, and often without thinking before acting.
• Hyperactivity: Has difficulty remaining in his/her seat even when it is expected, Fidgets with hands or squirms when in his or her seat; fidgets excessively.
• So Impulsivity, low attention span, fidgeting, and inability to sit for long are primary characteristics of Attention Deficit Hyperactivity Disorder.
• ​That's why option (3) is the correct answer.​

​​

Additional Information

• ADHD can't be prevented or cured. But spotting it early, plus having a good treatment and education plan, can help a child or adult with ADHD manage their symptoms.
• Medication, education, skills training, and psychological counselling can also help a student to reduce ADHD.

Ability Grouping

Ability grouping is a method in which a teacher looks at the ability of each student individually and places him/her in a group with other students possessing the same ability.

Key Points

• It is a group-learning approach used to achieve an extremely wide range of educational objectives, especially higher-cognitive objectives of all types like problem-solving, decision-making, and other complex life skills.
• Effective for group activities in subjects like mathematics and language.
• It gives challenging tasks to the high-ability group whereas the low-ability group is given simple tasks which makes the teaching-learning process biased.
• Due to this low ability groups don't participate in the activities and start building fear of missing out in the classroom.
• It is also an approach for developing creative thinking and other divergent thought processes.

Hence, we can conclude that Ability grouping does not promote Inclusion.

Additional Information

Strategies for inclusive education-

Differentiated Instruction- The teacher should give different instructions to students according to their needs. because every child is unique so common instructions will not be useful for every child.

Reasonable curriculum accommodation- The curriculum should be based on the need of the students and learned and should be flexible.

The eagerness in repeating the same task multiple times is not the characteristic of the gifted child.

• Gifted children do not like to do the same thing multiple times as doing the same things multiple times make them feel unattracted towards the problem.

Key Points Gifted Children- A child who is naturally empowered with a high level of general mental abilities or extraordinary abilities in the specific spare of knowledge.

The gifted children on the intelligent quotient IQ Scale

• Average-100
• Mildly gifted-115 to 130
• Moderately gifted- 130-144
• Highly gifted-145-159
• Exceptionally gifted-160-179

Additional InformationCharacteristics of the gifted children-

• High level of intensity
• Enjoys learning
• Depth of perception
• Keen sense of observation
• extraordinary memory
• Enjoys their own company
• Ability to recognise the more option
• Dislike repeating the same things which they know

Hint Gifted children are highly active children.

Classroom management does not mean a strict order but shaping of a positive environment in the classroom. The teacher's behavior is the main contributing factor. A skillful and efficient teacher manages the class in such a manner that he never faces discipline problems.

Key Points

• A good teacher should :
• give ample opportunities to children for self-reflection.
• be flexible in classrooms do not have rigid behavior for students.
• create an emotionally pleasant and stimulating environment
• set meaningful goals.
• make the subject matter meaningful.
• make unity among the student in diversity.
• try to avoid punishments for the students.
• give all the students the same and equal opportunities.

So for all the above reasons, option (4) is the correct answer.

Additional Information 

• Rigid or fearful behavior of the teacher demotivates the students, also increasing the fear of learning in the soul of students. 
• So that the behavior of teachers should be flexible and learning in the classroom should be child-centered instead of teacher-centered.
• ​The rigid rules should not be made by the teachers for the students to follow**, without question,** this type of behavior impacts students learning as well as increases the chance to make them rigid.

Concept development is an innovative process in which schools should design structure and systems to unleash the creative potential of the students in the schools. It is necessary to understand that being creative and innovative means not just novelty but essentially innovation incorporating a high degree of usefulness.

Key Points

• Ways to encourage conceptual development in children-
• By giving them best suitable examples related to the concepts.
• By organizing Hand-on-activities, group discussions, and experiments to build their concept best.
• By connecting the concept to the daily life and environment of the students, by which they can get it easily.
• By using teaching-learning materials, models, and projects.
• By using different methods of teaching such as Inductive method, deductive method etc.
• So by all the above point we conclude that option (3) is the correct answer.​

Important Points 

• Punishment is not a way to develop concepts in students, it can affect students' minds negatively.
• It is also possible that the student should be pushed towards rote or memorized learning by giving them rewards, surprises, etc.

Effective teaching is a term used to describe the knowledge, strategies, and conduct of a successful Teacher. It's the ability to make a positive impact on a student's life and academic career, including the capacity to teach important skills, introduce new concepts and manage any classroom concerns.

Key Points

• Characteristics of effective learning:
• ​It makes the thought process of the students conceptually.
• In this type of teaching, the teacher should value the emotional needs of the students.
• The teacher is flexible also makes the environment of the classroom flexible and helps the students where they need it.
• Teachers understand the needs of the students and arrange the classroom activities according to the needs of students.
• No rigidity in the classroom.
• Teaching-learning leads toward the holistic development of the students.
• So by all the above mention points, we can conclude that the correct answer is Option (2).

Hint

• Effective teaching doesn't have rigidity for the students, It is always done in favor of the students.
• In effective learning, the learning should be child-centered instead of teacher-centered.

Discovery learning is the type of learning in which students can learn by finding the correct approach for the problem through their cognition.

• Example: Find the river Ganga on the map.

Key Points

• Discovery learning helps students to think critically.
• Discovery learning helps to make commands of the problem conceptually.
• Discovery learning improves the skills of the students and makes their thinking divergent.
• It de-emphasis rote learning or learning based on the memorisation.
• Discovery learning is mostly based on activities, experiments, and critical thinking based which also encourages the interest in learning in students.
• No direct instruction is given to the students by the teachers in discovery learning, students can learn by making guesses or concepts through their cognition.
• So option (2) is the correct answer.

Additional Information

• Rote memorization is defined as memorization by repetition, often without an understanding of the reasoning or relationships involved in the material that is learned.
• Direct instruction is where teachers use explicit teaching techniques to teach a specific skill to their students. This type of instruction is teacher-directed, where a teacher typically stands at the front of a room and presents information.
• ​​Example: Announcement by the teacher.
• Expository teaching is a lecture presentation or telling strategy used during instruction. The teacher is in control of presenting the subject matter and directs the students through the lesson.

A graphic organizer is a visual and graphic display that depicts the relationships between facts, terms, and or ideas within a learning task.

Key Points

• Graphic organizers are of value in developing/arranging ideas graphically.
• It is a concept of presentation of a concept and its sub-concepts in an interconnected manner.
• Four types of graphic organizers have been found appropriate for content area subjects. These are:
• The thematic map shows the elements and details of these materials.
• The sequential episodic map shows time to order.​
• The classification map shows relationships among concepts.
• The comparative-contrastive map compares and contrasts two or more groups or events.

Hence we conclude that the Presentation of a concept and its sub-concepts in a hierarchical and interconnected manner is called a graphic organizer.

Additional Information

• A mnemonic is a word, short poem, or sentence that is intended to help you remember things such as scientific rules or spelling rules.
• ​Example: Roy G. Biv is a name used to remember the colors of the rainbow: red, orange, yellow, green, blue, indigo, and violet.
• Heuristics is totally based on previous memory and understanding and by using these phenomena a person can solve the correct facing problems.
• It is an interconnected way to the current problem with the previous knowledge.
• It is also hierarchical in a manner as problem facing, recalling by older understandings then coming to a conclusion.
• Algorithms are a set of instructions for solving a problem.
• ​Example: Recipe of the baking cape.

Learning level: Learning level is a minimum criterion that defines how much a student should learn according to age.

Example: A child of class 1st well known how to hold a pencil. If he faces any problem in holding a pencil then it may be considered that there is some learning problem with the child.

There are many factors that make a gap in the learning of the student such as-

• Their development.
• Their environment
• Their School system
• The way of teaching by which they are going through.
• Their Teachers, etc.

Key Points

• School system: School system plays an important role in the learning of the student, if a student is underperforming then the first unit to analyze is the school system. There are many major factors in the student that affect the learning of the student such as-
• The environment of the school.
• The behavior of the teachers.
• Teaching methods.
• Interaction with the students, etc.
• Because the failure of the students is the failure of the school system. So that we can say that "System" is the first unit that should be analyzed if the student is underperforming. Hence, Option (1) is the correct answer.

Additional Information

• There are many ways that make the learning of the student effective, these are-
• Inclusive classroom - Students of different abilities, and disabilities are learning under the same roof.
• Play-way method - Learning gaps can be reduced if the learning should be done in a play-way method, interesting activities, experimental based, etc.

Motivation: The term motivation has been derived from the Latin word ‘movere’, which means ‘to move. “the factors that direct and energize the behavior of humans and other organisms”.

Motivation is of two types, which are:

• Intrinsic Motivation.
• Extrinsic Motivation.

Key Points

• Intrinsic Motivation: Intrinsic motivation can be defined as “motivation that comes from within a person and includes the elements of challenge, enjoyment, mastery, and autonomy”.
• Example: There could be an activity that an individual enjoys doing.
• These four components of intrinsic motivation are-
• Challenge- It relates to the extent to which an individual enjoys the excitement that accompanies a new challenge.
• Enjoyment- It relates to the pleasure that an individual may obtain from carrying out the task.
• Mastery- It relates to the sense of pride and accomplishment that an individual may experience when he/ she carries out a difficult task.
• Autonomy and self determination- It relates to the autonomy that an individual enjoys while carrying out the task, that is, the freedom with which the individual can determine what is to be done and how is it to be done.
• So by all these explanations, we can say that intrinsic motivation comes from the soul of the students, and it will be enhanced if the learning environment of the student fosters their sense of belonging and and intensity in their action.
• Hence, option (3) is the correct answer.

​

Additional Information

• Extrinsic Motivation: Extrinsic motivation can be defined as “motivation that comes from outside the person and usually involves rewards and praises”.
• Example: reward, praise, money, feedback.

Meaningful learning: Meaningful learning results when a person consciously and explicitly ties new knowledge to relevant concepts they already possess. When meaningful learning occurs, it produces a series of changes within our entire cognitive structure, modifying existing concepts and forming new linkages between concepts.

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 a vast quantity of ideas.
• Meaningful learning is possible only when learners make a deliberate effort to relate new knowledge to the relevant concept they already know.
• It is the active creation of knowledge structures from personal experience.

Key Points

• There are many emotions that facilitate the process of meaningful learning, these are-
• ​Happiness
• Hope
• Pride
• Curiosity
• Enjoyment
• ​Curiosity: The impulse/emotion or desire to investigate, observe, or gather information, particularly when the material is novel or interesting. It refers students to get the roots of the problem conceptually.
• So option (1) is the correct answer.​

Important Points 

• Hopelessness, shame, and fear are the emotions that did not facilitate meaningful learning, these emotions make a negative impact on the student toward learning.

Intuitive- Intuitive means having the ability to understand or know something without any direct evidence or reasoning process.

Characteristics of the Naive or Intuitive abilities-

• These abilities make the students think divergent.
• These abilities help the students to cover all the aspects related to the situations.
• These preconceptions help the student to influence their understanding in school.

Key Points

• Teachers should have to encourage students to share their thoughts, and their intuitions about the problem, which helps the students-
• to put their thoughts freely in the classroom.
• make them fearless to say something or to ask something.
• helps them to get motivated.
• help them to connect their pre-conceptions with the problems to make their learning better.
• so that option  (1) is the correct answer.

Additional Information

• A teacher should make their classroom environment as per the student's needs.
• Teachers should have to encourage the students which helps the student to get motivated.
• The classroom should be child-centered, not teacher-centered.

Socio-constructivism focuses on the collaborative nature of learning. Knowledge develops from how people interact with each other, their culture, and society at large.

In Socio-constructivist classroom students rely on others to help create their building blocks, and learning from others helps them construct their own knowledge and reality.

Characteristics of Socio-constructivist classroom:

• It emphasizes collaboration with others for learning.
• It allows learners to foster their own strategy of learning to perform an activity.
• It views learners as makers of meaning and creators of knowledge through social interaction.

Key Points

• Social-constructivist classroom gives primacy to:
• peer tutoring.
• group activity.
• Challenging environment.
• Emphasis on students to think divergently and critically.
• cooperative learning among the students.
• So option (1) is the correct answer.

Important Points

• In a socio-constructivist classroom, the student performs different tasks which helps them to make their thoughts divergent. There is no repetition of the task in socio-constructivist classrooms, hence option (2) is incorrect.
• Rote memorization, learning based on recalling, and repetition are not allowed in a socio-constructivist classroom, so option (3) is also incorrect.
• The classroom should be child-centered, not teacher-centered so that students are allowed to ask questions freely that's why option (4) is also incorrect.

Given:

The three fractions are 7/18, 11/250, 21/28

Concept used:

Terminating decimal: A terminating decimal has an end digit that has a finite number of digits or terms.

Calculation:

7/18 = 0.38888... = $0.3\bar8$ (Non terminating decimal)

11/250 = 0.044 (Terminating decimal)

21/28 = 0.75 (Terminating decimal)

∴ The fractions 11/250 and 21/28 can be written as a terminating decimal.

Hence, option 3 is the correct answer.

Solution:

$547.527 \over 0.0082$ = x 

Now,

⇒ x = (547527/82) × (10000/1000)

⇒ x = (547527/82) × 10

⇒ (547527/82) = x/10

Given:

The distance between the Earth and Moon = 384000000 m

Formula used:

The standard form of a decimal number is also known as scientific notation. It involves expressing a given decimal number by its first digit followed by a decimal point and its remaining digits, multiplied by a power of 10 such that it is equivalent to the original value. For example, the number 4359.892 written in the standard form of a decimal would be:

4.359892 × 10³ 

Calculation:

The given distance = 384000000 m

= (3.84 × 100000000) m

= (3.84 × 10⁸) m 

Comparing (3.84 × 108) with (p × 10n),

⇒ p = 3.84

⇒ n = 8

∴​ The value of p and n are respectively 3.84 and 8.

Given:

The given five numbers are $-1\frac{3}{5}, -2\frac{1}{3}, \frac{1}{2}, \frac{2}{5}, {\left(\frac{2}{5}\right)^{100}}$

Concept used:

There are two negative numbers and three positive numbers. Negative numbers are always less than positive numbers.

Formula used:

Ascending order: Ascending order means arranging terms from smaller to greater.

Calculation:

Justifying $-1\frac{3}{5}$ and $-2\frac{1}{3}$ to find the smaller number,

$-1\frac{3}{5}$ = -(8/5) = $-{\frac{8 \times 3}{5 \times 3}}$ = -(24/15)

$-2\frac{1}{3}$ = -(7/3) = $-{\frac{7 \times 5}{3 \times 5}}$ = -(35/15)

$-2\frac{1}{3}$ is the smaller number in this case.

Now justify all three positive numbers.

1/2 = 0.5

2/5 = 0.4

(2/5)¹⁰⁰ = (0.4)¹⁰⁰

Here, 0.4 < 0.5 and 0.4 > (0.4)100

⇒ (0.4)100 < 0.4 < 0.5

After justifying all cases, we get

$-2\frac{1}{3}$ < $-1\frac{3}{5}$ < (2/5)100 < (2/5) < (1/2)

The ascending order will be $-2\frac{1}{3}$, $-1\frac{3}{5}$, (2/5)¹⁰⁰, 2/5, 1/2

Hence, option 3 is the correct answer.

Given

The given number = 78x3945

Formula used:

Divisibility rule of 11: A number will be divisible by 11 if the difference between the sum of digits at even places and the sum of digits at odd places is divisible by 11.

Calculation:

The given number = 78x3945

The sum of digits at odd places = 7 + x + 9 + 5 = 21 + x

The sum of digits at even places = 8 + 3 + 4 = 15

Now, 15 - (21 + x) = (-6 - x) is divisible by 0 or 11.

From the four option, if we put x = 5,

The (-6 - x) = (-6 -5) = -11 will be divisible by 11

The number will be 7853945

∴ The digit at the place of 'x' will be 5.

Given:

The term is (x - 3)2 + 5(x - 3) + 4

Calculation:

Suppose, (x - 3) = a

Therefore, (x - 3)2 + 5(x - 3) + 4

= a2 + 5a + 4

= a² + 4a + a + 4

= a (a + 4) + 1 (a + 4)

= (a + 1) (a + 4)

= {(x - 3) + 1} {(x - 3) + 4}  [∵ (x - 3) = a]

= (x - 2) (x +1)

The factors of (x - 3)2 + 5(x - 3) + 4 are (x - 2) and (x + 1)

∴​ One of the factors of (x - 3)2 + 5(x - 3) + 4 is (x - 2)

Given:

$\frac{{{x^{{a^2}}}}}{{{x^{{b^2}}}}} = x^{12}$

x > 1 and (a - b) = 3

Formula used:

x^m/xⁿ = x^{(m - n)}

(a2 - b2) = (a + b) (a - b)

Calculation:

$\frac{{{x^{{a^2}}}}}{{{x^{{b^2}}}}} = x^{12}$

⇒ $x^{{(a^2 - b^2)}} = x^{12}$

⇒ (a² - b²) = 12  [∵ x > 1]

⇒ (a + b) (a - b) = 12

⇒ (a + b) × 3 = 12  [∵ (a - b) = 3]

⇒ (a + b) = 12/3 = 4

∴ The value of (a + b) is 4.

Given:

a - b = 7

a2 + b2 = 29

Formula used:

a2 + b2 = (a - b)² + 2ab

Calculation:

a2 + b2 = 29

⇒ (a - b)2 + 2ab = 29

⇒ (7)² + 2ab = 29  [∵ a - b = 7]

⇒ 49 + 2ab = 29

⇒ 2ab = 29 - 49 = -20

⇒ ab = -20/2 = -10

Now, 1/a - 1/b

= (b - a)/ab

= -(a - b)/ab

= $-\frac{7}{- 10}$  [∵ a - b = 7; ab = -10]

= 7/10

∴ The value of 1/a - 1/b is 7/10

Given:

p = 2x4 - x3y3 + 7y4

q = x4 + 3x3y3 - 5y4

r = 3x4 - 4x3y3 + 2y4  

Calculation:

Therefore, p + q - r

= (2x4 - x3y3 + 7y4) + (x4 + 3x3y3 - 5y4) - (3x4 - 4x3y3 + 2y4)

= 2x4 - x3y3 + 7y4 + x4 + 3x3y3 - 5y4 - 3x4 + 4x3y3 - 2y4

= 6x3y3

∴​ The value of p + q - r is equal to 6x3y3

Given:

(7 - x)/(5x + 1) = 3

Calculation:

(7 - x)/(5x + 1) = 3

⇒ 3 × (5x + 1) = (7 - x)

⇒ 15x + 3 = 7 - x

⇒ 15x + x = 7 - 3

⇒ 16x = 4

⇒ x = 4/16

⇒ x = 1/4

Therefore, (x + 1)/(x - 1)

= $\frac{{1\over4} + 1}{{1\over4} - 1}$  [∵ x = 1/4]

= $\frac{\frac{1 + 4}{4}}{\frac{1 - 4}{4}}$

= (5/4)/(-3/4)

= (5/4) × -(4/3)

= -(5/3)

∴ The value of (x + 1)/(x - 1) is -(5/3). Hence, option 1 is the corect answer.

Given:

The mean of the five observations = 15

Number of observations = 5

The observations = x, x + 3, x + 6, x + 9, x + 12

Formulae required:

Mean or Average = Sum of observations/Number of observations

Calculations:

Sum of observations = x + x + 3 + x + 6 + x + 9 + x + 12

⇒ 5x + 30 = 5(x + 6)

Mean = [5(x + 6)]/5

⇒ 15 = x + 6

⇒ x = 9

First three observations =  x + x + 3 + x + 6

Sum of three observations = 3x + 9

⇒ 3(x + 3)

The number of observations = 3

Mean of first three observations = [3(x + 3)]/3

⇒ x + 3 = 9 + 3

⇒ 12

∴ The mean of first three observations is 12

Given:

A card is selected at random from a standard deck of 52 playing cards.

Formula used:

Probability of an event = Total number of favorable outcomes/Total number of outcomes

Calculation:

Total number of cards = 52

∴ Total number of outcomes = 52

We know, total number of kings in the cards = 4

∴ Total number of favorable outcomes = (52 - 4) = 48

The probability of the selected card is not a king = 48/52 = 12/13

∴​ The probability of the selected card is not a king is 12/13.

Given:

Diameter of wheel = 105 cm

Total distance = 330 m

Formula used:

Radius of circle = Diameter/2

Circumference of circle = 2 × π × radius

Calculation:

According to the question, the diameter of the wheel = 105 cm

Radius of the wheel = 105/2

Total distance = 330 m = (330 × 100) cm = 33000 cm

Therefore, the circumference of the wheel = 2 × π × (105/2)

= 2 × 22/7 × 105/2

= 330 cm

The wheel will cover 330 cm by rotating one time.

Total time of rotation by the wheel to cover the distance = 33000/330 = 100

∴ The wheel will rotate 100 times to cover a distance of 330 m.

Given:

The radius of the first cylinder = 7 cm

The height of the first cylinder = 12 cm

Formula used:

V = πr²h

Where,

V = Volume of cylinder

r = Radius of cylinder

h = Height of cylinder

Calculation:

The radius of the first cylinder = 7 cm

The height of the first cylinder = 12 cm

The volume of the first cylinder = π × 7² × 12

= 22/7 × 49 × 12 = 1848 cm³

 Another cylinder is formed by interchanging its radius and height.

The radius of the second cylinder = 12 cm

The height of the second cylinder = 7 cm

The volume of the second cylinder = π × 122 × 7

= 22/7 × 144 × 7 = 3168 cm3

Volume of first cylinder : Volume of second cylinder

= 1848 : 3168

= 7 : 12

∴​ The ratio of the volumes of the two cylinders is 7 : 12

Given:

Area of square A = Area of circle B

Formula used:

Area of square = a²

The perimeter of the square = 4a

Where, a = Length of each side of the square

Area of circle = πr²

The perimeter of the circle = 2πr

Where, r = Radius of circle

Calculation:

Suppose, S = Each side of square A

R = Radius of circle B

Area of square A = Area of circle B

⇒ S² = πR2

⇒ S = √π R   .....(1)

Suppose, P1 = Perimeter of square A

P2 = Perimeter of circle B

Then, P1 : P2 = 4S : 2πR

⇒ 4 √π R ∶ 2 π R      ----(S = √π R)

⇒ 4 √π ∶ 2 π

⇒ $2 : \sqrt π$

∴​ The ratio of perimeters of A and B is $2 : \sqrt π$

Shortcut Trick

In SAS congruence, the angle must be the included angle between the two sides.

Side pair 1: AB and BC → Common vertex is B → Included angle is ∠B.

Side pair 2: PR and QR → Common vertex is R → Included angle is ∠R.

To satisfy SAS, the included angles of both triangles must be equal.

∴ The correct answer is ∠B = ∠R.

Alternate Method

Given: ΔABC ≅ ΔPRQ, AB = PR, BC = QR

Formula Used: SAS (Side-Angle-Side) Congruence Rule states that two triangles are congruent if two sides and the included angle of one triangle are equal to the corresponding sides and the included angle of the other triangle.

⇒ In ΔABC, the sides given are AB and BC.

⇒ The angle included between AB and BC is ∠ABC, or simply ∠B.

⇒ In ΔPRQ, the sides given are PR and QR.

⇒ The angle included between PR and QR is ∠PRQ, or simply ∠R.

⇒ According to the SAS rule, for ΔABC ≅ ΔPRQ, the included angles must be equal.

⇒ ∴ ∠B = ∠R.

∴ The correct answer is ∠B = ∠R.

Additional Information

SAS (Side-Angle-Side) Congruence

Two triangles are congruent if two sides and the included angle of one triangle are equal to the corresponding parts of the other triangle.

CPCT Rule

Corresponding Parts of Congruent Triangles are equal. Once congruence is proved, all remaining corresponding sides and angles are equal.

Other Congruence Rules

SSS (Three sides), ASA (Two angles and included side), AAS (Two angles and non-included side), and RHS (Right-angle, Hypotenuse, and Side).

Congruence vs Similarity

Congruent triangles have the same shape and size, while similar triangles have the same shape but may differ in size (ratios of sides are equal).

Given:

The given statements are,

S1: A triangle is completely determined by its three sides.

S2: A unique quadrilateral cannot be constructed if measures of its four sides are given.

Calculation:

S1 is the completely correct statement. A triangle can be complete by knowing its three sides only.

S2 is also a correct statement. A unique quadrilateral cannot be constructed if the only measure of its four sides is given because we don't know about angles.

There will be various types of quadrilaterals, not a unique one.

Hence, both S1 and S2 are true.

Given:

There is an assertion and reason about lines of symmetry.

Concept used:

Lines of symmetry are imaginary lines that pass through the center of the shape or object and divide it into identical halves.

Calculation:

Assertion (A): A rectangle has 2 lines of symmetry.

The assertion is completely right. A rectangle has 2 lines of symmetry.

Reason (R): Since every rectangle is also a parallelogram, therefore the number of lines of symmetry of a parallelogram is also 2.

But the reason is not right because every parallelogram doesn't have lines of symmetry whether it is square, rectangle, or rhombus.

An irregular parallelogram does not have any lines of symmetry.

Hence, (A) is true, but (R) is false.

Given:

n = F + V

Where, F = The number of faces of a polyhedron

V = The number of vertices of a polyhedron

The number of edges of the polyhedron = 30

Formula used:

Euler's formula for the polyhedron,

F + V = E + 2

Where,

F = The number of faces of a polyhedron

V = The number of vertices of a polyhedron

E = The number of edges of a polyhedron

Calculation:

The number of edges of the polyhedron = 30

Therefore, F + V = 30 + 2

⇒ F + V = 32   .....(1)

According to the question, n = F + V   .....(2)

Justifying equations (1) and (2),

n = 32

Now, (2n + 1) = (2 × 32) + 1 = 65

∴ The value of (2n + 1) is 65.

Given:

The two given statements for the congruency of two polygons having the same number of sides,

S1: Their corresponding sides are equal

S2: Their corresponding angles are equal

Concept used:

All the sides and angles of a polygon are equal to the corresponding sides and angles of its congruent polygon.

Calculation:

According to the given concept S1 and S2 both are correct.

Both S1 and S2 are true  The correct answer is option 3.

Manipulatives are concrete objects that allow students to engage in active, hands-on exploration of a concept. For example- tangrams, tiles, rods, Diene's blocks, etc. The use of manipulative helps children to learn concepts through hands-on experience.

Key Points

Importance of manipulatives in the mathematics classroom:

• It helps the children connect mathematical ideas and symbols to physical objects, thus promoting better understanding.
• It provides support in dealing with a subject that can be difficult and confusing and help students build confidence by giving them a way to test and confirm their reasoning.
• Manipulative is imperative for exploration and experimentation with math ideas as students develop meaning.
• It facilitates students understanding of mathematical concepts and links them to representation and abstract ideas.
• It makes learning math interesting and enjoyable and also motivates children to learn.

Hence, we conclude that middle-grade children sometimes do not regard rectangles and squares as parallelograms. As a teacher, to help such students, we should Give a variety of manipulatives to children that have the same mathematical properties but different physical characteristics.** 

Additional Information

• Math Manipulatives help make abstract ideas concrete.
• Math Manipulatives lift math off textbook pages. While we want students to become comfortable and proficient with the language of math--everything from the plus sign to the notations of algebra--words and symbols only represent ideas.
• Ideas exist in learners' minds, and manipulatives help them construct an understanding of ideas that they can then connect to mathematical vocabulary and symbols.
• In the same way, manipulative materials serve as concrete models for students to use to solve problems.,Math Manipulatives make learning math interesting and enjoyable.

Activities-based learning is the process of doing my own hands practically.it encourages the students to participate in their own learning experiences.

• The students in primary classes should be taught through various activities and hands-on experiences.

Key Points

• The mathematics laboratory refers to the place where students can experiment and explore patterns and ideas.
• The materials are meant to be used both by the students on their own and with their teacher to explore the world of mathematics, discover, learn, and develop an interest in mathematics.
• They provide opportunities to learners for experimentation and exploration in mathematics.
• The activities create interest among students or in anybody who wants to explore and test some of their ideas, and beliefs about mathematics.
• A mathematics laboratory is a place to enjoy mathematics through informal exploration. It is a place where anyone can generate problems and struggle to get an answer.
• It is a space to explore and design new mathematical activities. So, the math lab should not be used to assess students’ knowledge of mathematics.

Thus, we can conclude that 'Mathematics Laboratories' are an important part of the process of mathematics teaching and learning because they provide opportunities to learners for experimentation and exploration in mathematics.

Van Heile's theory provides an insight to the teacher about how the students learn geometry at different levels. It helps in describing how the students learn at each level and pass to another level and shapes their learning of geometry at each level of learning.

Key Points

The Van Hiele levels are described below:

• Level 0: Visualization-The students can recognize shapes by their whole appearance that should just like the exact shape. They can also compare the figures with their prototypes (exemplar) or everyday things but can not identify the properties of geometric figures. For example, they can compare the shape of a circle with bangles, coins, wheels, etc. but are unable to identify and describe the properties of a circle.
• Level 1: Analysis -They will learn the functions and parts of a figure. They can describe the properties of a figure and recognize the figures with the same properties. For example, they can identify the shapes and describe their properties such as a circle is a closed rounded figure with no corners.
• Level 2: Abstraction or informal deduction -The students will be able to understand the relationships between the properties of a figure. They can take part in informal deductive discussions and can discuss the different characteristics of figures*. For example, the opposite sides of a parallelogram are parallel. The opposite sides of a square and rectangle are also parallel which means the square and rectangle are also a parallelogram.*
• Level 3: Deduction or formal deduction -At this level, the students become aware of the more complex geometrical concepts. They can prove an abstract statement on geometric properties to conclude*. For example, they can prove that the square is a rectangle but a rectangle can not be a square.*
• Level 4:Rigor -The last level of geometrical learning belongs to the senior secondary and university-level classes. The students can compare different geometrical results*. For example, the sum of all three angles of a triangle is 180 degrees and is compared to the other properties or other results (to find exterior or interior angles of a triangle) related to the triangle to solve geometrical problems.*

Therefore, the correct sequence is  Recognition of figures, Analysis of components of figures, Relationships among figures, Deductive Reasoning & formal proofs, and Axiomatic Reasoning.

Algebra introduces a technique known as ‘transposition’. This is the most common way to solve algebra equations.

Key Points

• The basic principles - all equations have two sides: a Left Side (LS) and a Right Side (RS). In the example below 2x + 14 is on the Left Side of the equation and 26 is on the Right Side of the equation: 2x + 14 = 26
• Making the same thing (mathematically) to both sides of the equation is the common transposition method, with the aim of bringing like terms together and isolating the variable (or the unknown quantity).
• hence for solving this equation, first subtract 14 from both sides of the equation. This will get rid of number 4 from the LS ,   2x + 14 - 14 = 26 -14
• That will give us: 2x = 12
• Now, focus on the LS we have 2x. So we need to divide it by 3 to isolate x, and we need to do the same to the RHS,  $2x \over 2$ = $12 \over 2$
• we get x=6.

Thus, the Transposition method is adopted by Ravi.

Additional Information

• 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.
• Estimation: Getting an estimated solution while solving a mathematical problem. It is also referred to as the prediction of future projection by observing the current pattern or statistics.
• Trial-Error: The individual has, in the beginning, no knowledge about the method which he should follow in order to reach the goal. But after making a number of trials, in which some fail, he comes to a successful attempt.

The mean is calculated by adding all the numbers in a given data set and then dividing it by the total number of items within that set.

• The arithmetic mean (AM) for continuously distributed numbers is equal to the middlemost number.

Key Points

• Mean doesn’t have an effect on the position of the value in the data set. It takes into consideration each value of the data set.
• Finding an arithmetic mean is quite simple; even a common man having very little finance and math skills can calculate it.
• It’s also a useful measure of central tendency, as it tends to provide useful results, even with large groupings of numbers.
• The main disadvantage of the mean is that it is sensitive to extreme values/outliers, especially when the sample size is small. Therefore, the mean is affected by the extreme values because it includes all the data in a series.
• Thus, Mean is used everywhere as a measure of central tendency regardless of the context of the data is the common misconception the students have about "mean - as a measure of central tendency".

Questioning: Questions are the medium used to explore the feelings, beliefs, knowledge, opinion, ideas, and attitude of the person being questioned. This process activates all senses of students and allows them to think divergent.

Key Points

Benefits of questioning in the classroom :

• Questioning keeps learners active in the class.
• It makes learners feel confident about their ideas.
• Asking analytical questions helps learners to think critically.
• Students should be encouraged to ask questions in class.
• It helps children to express their views and thoughts.
• Questions that promote analysis and application foster higher-order thinking skills.
• Improves speaking and listening skills.
• It helps the teacher to evaluate himself, up to which he has achieved his goal.
• To stimulates interest.
• For clearing the topic-related doubts.

Thus, the statement-"Use questions whenever required since it will help children to express their views and thoughts and will help to improve critical thinking" is most appropriate regarding the use of questioning as a pedagogical tool in the mathematics classroom.

Given:

The given fractions are a/b and c/d

Where, $\frac{a}{b}\ne 0$

Concept used:

The multiplicative inverse of any number is another number that produces 1 when multiplied by the original number.

Calculation:

Here, $\frac{a}{b}\ne 0$

Therefore, a/b × b/a = 1

∴ The b/a is called the multiplicative inverse. Hence, option 1 is the correct answer.

Activities-based learning is the process of doing my own hands practically.it encourages the students to participate in their own learning experiences.

• The students in primary classes should be taught through various activities and hands-on experiences.

Key PointsWhen a teacher gives 1-cm grid paper to the students in her class and student explore the activity. 

• He analyses the relationship between perimeter and area through hands-on experience.
• He first counts several rectangles having an area of 48 m² then followed by a rectangle with a perimeter of 24 cm.
• By analyses and comparison, he predicts a better understanding of concepts of area and perimeter.
• This activity makes understanding the relationship between perimeter and area more clear and deeper.

Thus***,*** developing a deeper understanding of the relationship between perimeter and area is most desirable for the given activity from a reflective teacher's perspective.

Additional Information

*Inductive method -*It is based on the process of induction. It is a method of constructing a formula with the help of a sufficient number of concrete examples. 

• In this method, learners do not have any knowledge about formulas, principles, or methods for solving the given [problems. It is defined as the method of constructing a formula with the help of an adequate number of concrete examples.

Mathematics is a science that deals with logical reasoning, quantitative calculation, practices of counting describing shapes, abstraction of subject matter, etc. Mathematics plays a vital role in daily life.

Key PointsDavid Wheeler gave the statement: "It is more useful to know how to mathematize than to know a lot of mathematics”.

• Learners learn to enjoy mathematics. The important goal is based on the premise that mathematics can be both used and enjoyed lifelong, Thus, school is the best place to create such a taste for mathematics.

Thus,' It is more useful to know how to Mathematise than to know a lot of Mathematics' is given by David Wheeler.

Additional Information

• According to George Polya - Two kinds of aims for school education can be considered-
• A good and narrow aim - It means turning out employable adults who contribute to the social and economic development of the country.
• A higher aim - It means developing the inner resources of the growing child.
• Concerning school mathematics, the former aim specifically relates to numeracy. Primary schools teach numbers and operations on them, measurement of quantities, fractions, percentages, and ratios.
• Jules Henri Poincaré was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The Last Universalist", since he excelled in all fields of the discipline as it existed during his lifetime
• Srinivasa Ramanujan was one of India's greatest mathematical geniuses. He made substantial contributions to the analytical theory of numbers and worked on elliptic functions, continued fractions, and infinite series.

The Mathematics curriculum at the upper primary level aims to develop several mathematical skills and processes in children such as handling abstraction, problem-solving, mathematical communication, conjecturing, and searching for proofs.

Key PointsRole of a Teacher at the middle school level-

• The Aims of teaching-learning mathematics should include creativity, problem-solving skills, and critical thinking.
• He must have Knowledge of mathematics and content-specific pedagogy.
• The prime focus should be on engaging every child with a sense of success, while at the same time offering . challenges to the emerging mathematicians.
• Assessment needs to be focused on examining children’s mathematization abilities and understanding rather than procedural knowledge.
• He should always focus on the teaching-learning process and student learning.
• Multiple resources should be used by teachers of mathematics so that appropriate experiences can be provided to children according to their learning requirements.

Thus, Knowledge of mathematics and content-specific pedagogy and  Reflecting on the teaching-learning process and student learning envision the growth of a mathematics teacher at the middle school level.

Concept:

Malleable material

• A malleable material can be quickly transformed into a thin sheet.
• Gold is the most malleable metal.

Ductile Material 

• A material that can be easily drawn into a thin wire.
• Gold is also a most ductile material.

Conductivity

• It is a quality of a material through which an electric charge or heat can pass through them.
• SI unit= siemens per meter or mho/m

Melting Point 

• The point at which materials change from a solid-state to a liquid state.
• Metals have a high melting point.

Thermal Expansion

• When the temperature rises, the volume of the material expands, which is known as thermal expansion.
• A thermometer's main functioning concept is thermal expansion.

Therefore, option 3 is correct.

Additional Information

Concept:

• Vitamins are biomolecules needed in small quantities that regulate many biochemical functions and prevent the development of many diseases.
• A lack of many or one of the vitamins leads to many deficiency diseases.
• Most vitamins come from food because the body either does not produce them or produces very little.
• Vitamins are of two types.
• Fat-soluble vitamins- Vitamins A, D, E, K
• Water-soluble vitamins- Vitamin C and all the B vitamins.

Explanation:

From the above discussion, it is clear that A, D, and E are fat-soluble.

Concept:

Transpiration:

• The term "transpiration" refers to the process of removing surplus water from the plant's body.
• Water molecules in the plant tissues are removed from the aerial regions of the plants during transpiration.
• Plants only use a small portion of the water they absorb for growth and development.
• The remainder is expelled through transpiration.
• 90% of excess water is transpired by stomata present in the leaves of the plants.
• A very little amount of water is transpired from the stems or barks of the plants with the help of lenticels.

Explanation:

• Transpiration helps in cooling the structures of the plant when exposed to hot sunlight.
• Excess water is removed from the cells of the plant to prevent plant decay.
• The osmotic balance of the cell is maintained by the process of transpiration.
• Transpiration is the unavoidable consequence of gas exchange in the leaf. This is because the plant has to open pores on the leaves called the stomata.
• When they open gas exchange occurs and the plant releases Oxygen as waste while simultaneously absorbing CO₂ for use during photosynthesis.
• It also helps in the absorption and distribution of water along with minerals from the soil through roots.

Hence, all options A, B, C are the correct one.

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:

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

mm Hg unit of Pressure

• mm Hg unit of pressure is the pressure equivalent to
• It is the extra pressure exerted by the mercury column of one-millimeter high mercury.
• 1mm Hg =  133.322387415 pascals

Torr

• The torr is another unit of pressure.
• It is equivalent to 1/760 of an atmosphere.
• The unit of pressure was named after Evangelista Torricelli, an Italian Scientist.

Explanation:

• From the pressure formula, it is clear that pressure is inversely proportional to the area.
• Pressure is directly proportional to force, so both must be in the same direction.
• The unit of pressure is N/m² but a unit of force is Newton, so this is an incorrect statemtent.

So, from above  "Pressure is inversely proportional to the area" is the correct statement only.

Concept:

Acids and bases 

Explanation:

• The sting of any insect or plant contains acid. So, to neutralize the effect of the chemical of a sting, that portion of the area is nibbed with moist basic nature plants or substances to relieve the pain of that area.

Thus, from the above explanation, the correct answer is acidic - basic.

Concept:

• Respiration is a metabolic process common to all living things. It refers to one's breathing and the movement of air into and out of the lungs. The respiratory system provides oxygen to body tissues for cellular respiration, removes the waste product carbon dioxide, and helps maintain acid-base balance.
• Different animals use different organs for their respiration. Some examples are:-

Explanation:

Respiratory System of Fish:

Whales and dolphins:

• Both are mammals, and they, breathe air into their lungs. They don't have gills, so they can't breathe underwater like fish. They breathe through a set of nostrils on top of their heads known as a blowhole.

• Most fishes absorbed dissolved oxygen in water by means of the gills.
• Water taken in continuously through the mouth is passed between the gill and over the gill filaments, where the exchange of gases takes place.

Sharks:

• Like other fish, sharks breathe through their gills.
• Tiny blood vessels extract oxygen from the water as it passes over the gill membranes.

So, the option "Whales and dolphins breathe through lungs" is correct.

Concept: 

Human Excretory system:

• The system of the organ which is used to remove the waste product out from the body is called the human excretory system.
• The major waste product generated in the human body is urea, along with which some other toxins are also generated.
• Urea is eliminated by kidneys by the process of urination and solid wastes are removed from the body by the intestines.

Explanation:

• The human excretory system includes certain organs that eliminate the wastes such as salts, carbon dioxide, urea, uric acid and water produced by the body.
• The path of the urine in the human excretory system is -

 

• After filtering from the kidney → Urine through Ureter → Stored in the Urinary bladder → Exit through the urethra.

So, the correct option  is**,** Kidney → Ureter → Urinary bladder → Urethra

The correct answer is A - (i), B - (v), C - (iii), D - (iv).

Concept:

• Reproduction is the biological process that produces new individual organisms known as "offspring" from their "parents."
• In animals and plants, there are two modes of reproduction: sexual reproduction and asexual reproduction.
• The Different Modes of Reproduction in Plants are: Fission, Fragmentation, Regeneration, Budding, Vegetative Propagation.

Explanation:

Cutting:

• Cuttings are a type of asexual reproduction in plants, also known as vegetative reproduction.
• It is the mode of reproduction in which new plants are formed from vegetative parts (vegetative propagules) of the plant-like root, stem, etc.
• Example: Rose, Onion, Garlic, etc.
• Stem cuttings can be used for asexual reproduction in rose plants.

Spores formation: 

• It is a mode of asexual reproduction.
• Many Spores are stored  in sacs known as Sporangia. Sporangia bursts, producing minute single-celled, thin or thick walled structures known as spores. Under suitable conditions, these spores develop into a new Plant.
• Example: Ferns

 

Fragmentation:

• It is a mode of asexual reproduction in which the parental body breaks into two or more fragments and each of which grows into a new individual.
• Example: Spirogyra

Budding:

• It is a mode of asexual reproduction in which one or more outgrowths (buds) are produced that remain attached to the parent cell at first but eventually separate from it to grow into a new individual.
• Example: Yeast

Additional InformationPotato:

• The mode of asexual reproduction in potatoes is vegetative propagation from the nodes.
• Vegetative propagation is an asexual reproduction method in which new plants are produced from vegetative parts such as stems, roots, and leaves.
• Potato tubers have nodes or eyes where new plants are produced.

The correct answer is C and D.

Explanation:

• Before and after the chemical reaction, the number of atoms is the same.
• Atoms are rearranged to form different substances during a chemical reaction, but the total number of atoms and the types of atoms are the same before and after the reaction.
• Chemical reactions are balanced by adding coefficients to ensure that the number of atoms of each element on both sides is the same.
• A physical change, such as changing states or dissolving, does not result in the formation of a new substance, whereas a chemical change does.
• According to the law of conservation of mass, matter cannot be created or destroyed, so the total quantity of matter, i.e., the total mass, remains constant before and after a change. As a result, the mass of the substances before and after a chemical change will be the same.

Explanation: 

Metal Reaction with Acid

• The metal reacts with Acid to form metal salt and release hydrogen gas.
• The hydrogen gas obtained can be observed by a pop sound when a burning matchstick is brought near it.

Example:

• Zinc reacts with dilute hydrochloric acid to give zinc chloride and release hydrogen gas.

Zn (s) + HCl (aq) → ZnCl2 (aq) + H2 (g)

• Other metals which are more reactive than hydrogen, for example, Almunium will also release hydrogen gas by reacting with Hydrochloric acid.

So, when metal reacts with the acid, at that time Hydrogen gas is formed and can be seen by a popping sound.

Additional Information

• Acids react with base and form salt and water. Such reactions are called neutralization reactions.
• Carbon dioxide gas turns limewater milky.
• Nitrogen dioxide gives brown fumes.
• Hydrogen sulfide (H₂S) has the smell of rotten eggs.

The correct answer is A, B.

Key Points

• A good or valuable fuel has a low ignition temperature and a high calorific value.
• Good fuels have a high calorific value, which means that the energy released when a specific amount of fuel is heated is greater.
• The calorific value of a fuel is expressed in a unit called kilojoule per kg (kJ/kg).
• Good fuels have a low ignition temperature (the lowest temperature at which a substance catches fire).
• A good fuel is one which is readily available. It is cheap.
• It burns easily in air at a moderate rate. It produces a large amount of heat. It does not leave behind any undersirable substances.

Mistake Points According to the answer key answer is option D, but we have taken the reference of the NCERT book, so according to that option A is  correct one.

The correct answer is remove the organic impurities.

Key Points

• Potassium permanganate (KMnO₄) is a strong oxidising agent that oxidizes dissolved impurities from water such as iron, manganese, and hydrogen sulphide (H₂S) by converting them into solid particles.
• These impurities are then filtered out of the water.
• In addition, KMnO₄ is used as a regeneration chemical in well water treatment to remove hydrogen sulphide and iron.
• The purpose of adding potassium permanganate (KMnO₄) in water in a distillation plant is to remove the organic impurities.
• Potassium permanganate is also used as a disinfectant to treat skin conditions such as foot fungal infections and dermatitis.
• Another important use for potassium permanganate is the treatment of bacterial infections.

Concept:

• Electric conductor and insulator:
• Conductor: Materials that allow the electric current to pass through them are conductors of electricity. Ex - Metal wire, Iron nail, Metal Spoon, graphite, etc.
• Insulator: Insulators do not allow the electric current to pass through them. Ex - Cotton thread, Eraser, Plastic rope, Wood, glass, etc.
• Electric Circuit: It is a closed-loop network of electric wires, power sources, switches, and resistors.
• Electric wire: They are conducting material used in a circuit.
• Power Source: The batteries used in the electric circuit can be considered the power source.
• Switches: A device used for on or off the circuit.
• Resistors or bulbs: The Power consumption devices in the circuit.

Explanation:

• A switch is an electrical device used to make or break an electric circuit. It controls the flow of current in a circuit by the ON/OFF mechanism.
• Hence it is not a source of electric current in a circuit. An electric cell or battery acts as a source in a circuit.
• When the electric switch is in the open position, there will be an air gap between two terminals so that it breaks the circuit.

So, here A is false but R is true.

Concept:

Kinetic Energy 

• The ability of an object to do work due to its motion is called kinetic energy.
• K.E. = 1/2mv² (where m = mass of an object and v = velocity)

Explanation:

Let mass and velocity of the heavier body be m₁ and v₁

And mass and velocity of a lighter body are m₂ and v₂

Since K.E. of the heavier and lighter bodies are equal. 

So that, = ½m₁v₁² = ½m₂v₂²

= m₁/m₂= (v₂/v₁)²

So, m₁ > m₂

m₁/m₂ >1 

So, that v₂²/v₁²>1

v22>v12

v₂>v₁

So the result shows that the velocity of lighter body v₂ is greater than heavier body v₁.

Therefore, option 3 is correct.

Additional InformationPotential Energy

• The ability of an object to do work due to the position of an object is called potential energy.
• PE = mgh (where m = mass of an object, g = gravitational acceleration and h = heigh)
• Water collected by building a dam has potential energy.

Relation between Kinetic Energy and Momentum

• K.E = P²/2m

Where, P = Momentum (P = mv)

Important Points Momentum

• The product of the velocity and mass of an object is called momentum.
• The SI unit of momentum is kg-m/s.
• Dimension = MLT^-1

Concept:

Earthquake

• An earthquake is a natural occurrence that causes the earth's surface to shake.

Reason for an earthquake

• The imbalance is created on the earth's surface due to the construction of dams on the rivers.
• From mining.
• From the volcano.
• from missile tests
• From hydrogen and atom bomb tests.

 

Explanation:

The focus of the earthquake(hypocenter) is the point beneath the earth's surface where the earthquake begins, while the epicenter is the location directly above it on the earth's surface.

Fault zone of the earth

• A fault is a fracture between two blocks of rocks.
• Blocks can move relative to each other.
• This movement might be sudden like an earthquake or it can be gradual like a creep.

Seismic zone of the earth

• A seismic zone is a term used to define a region where earthquakes are more likely to occur.
• India is divided into four seismic zones.

Therefore, The place inside the earth's crust where the earthquake originates is called the focus of the earthquake. 

Important PointsRichter Scale

• The Richter Scale is used to measure the magnitude of an earthquake.
• This scale is expressed with a logarithmic scale.

Seismograph

• A seismograph is used to detect earthquakes.
• The study of earthquakes is known as seismology.

Mistake Points As, per the official answer key the answer is option 2, but as per the question statement option, 1 is the correct one.

Concept:

Magnet

• Any material capable of attracting iron and producing a magnetic field outside of itself is referred to as a magnet.
• The natural magnet is iron oxide(Fe₃O₄). It does not have a fixed size.
• When a magnet is suspended freely, aligns approximately along the geographical N-S line.

Magnetic Field 

• The area around a magnet in which the effect of the magnet can be felt is called the magnetic field.

Demagnetization

• To lose or remove magnetic property.

Explanation:

The following methods can be used to demagnetize a magnet:

• Repeatedly hammering the magnet.
• Rotating the magnet with an alternating current
• Repeatedly dropping the magnet on the floor
• Bringing the magnet's temperature to a very high level.

Hence, option 3 is correct.

Additional Information

Magnetic Lines Of Force

• Lines of force in a magnetic field are imaginary lines that continuously show the direction of the magnetic field in that place.
• Properties of Magnetic lines of force
• ​Two lines of force never intersect.
• Magnetic force lines always originate from the north pole of a magnet and enter the south pole.
• Where the magnetic field is strong, the line of force is closer.

Important Points

Types of magnets

Permanent Magnet

• They're called permanent magnets because once magnetized, they don't lose their magnetic properties.
• Permanent magnets are commonly used.

Temporary Magnet

• In the presence of a magnetic field, temporary magnets can be magnetized.
• These materials lose their magnetic properties when the magnetic field is removed.
• Examples the temporary magnets, iron nails, and paper clips.

Electromagnets

• An electromagnet is composed of a coil of wire wound around an iron core.
• When this material is exposed to an electric current, it generates a magnetic field, which causes it to behave like a magnet.

Concept:

Friction

• It is a force exerted by two surfaces sliding (or attempting to slide) across one another.
• Friction always acts in the opposing direction of the object's movement or tries to move.

  

Explanation:

Types of friction

Rolling friction

• An object that rolls along a surface experiences rolling friction.
• Rolling friction is weaker than sliding friction or static friction.

Sliding Friction

• An object that slides along a surface experiences sliding friction.
• Sliding friction is weaker than static friction.
• For the same weight, the rolling friction is less than the sliding friction.

A rolling body can perform both translation and rotational motion, but a sliding body can only perform the translational motion.

Static Friction

• A force that holds an object at rest is known as Static friction.

  

 

Therefore, the incorrect statement is Rolling friction is greater than sliding friction

Concept:

Convex lens

• A lens that is thinner at the edges and thicker in the middle is called a convex lens.
• The focal length of a convex lens is positive.
• It is a converging lens.

Concave Lens

• A lens that is thicker at the edges and thinner at the middle is called a concave lens.
• The focal length of a concave lens is negative.
• It is a diverging lens.

Explanation:

Let the refractive index of a convex lens is n₁ and the refractive index of the liquid be n₂.

n₂>n₁  (given)

From Lens Maker's Formula, 

1/f = (n-1)(1/R₁-1/R₂)

Where, f = the focal length of the lens

R₁ and R₂ = radius of curvature of both surfaces.

n= refractive index

n= n₁/n₂  

so, n₂>n₁

then n< 1

By the lens maker's formula, the focal length of the lens will be negative.

So, If you immerse a convex lens in a liquid with a refractive index greater than the refractive index of the lens's material, it will change its nature and become a concave lens, diverging rays rather than focusing them on a single point.

Therefore, A convex lens submerged in a liquid medium with a higher refractive index will act as a divergent lens.

Additional Information  Lens Maker's Formula

• Lens manufacturers create lenses with the required focal length using the lens maker's formula.
• Varying optical instruments require lenses with different focal lengths.
• The focal length of a lens is determined by its refractive index and curvature radii.
• 1/f = (n-1)(1/R1-1/R2)

Important Points Power of lens

P= 1/f diopter

• The inverse of the focal length of the lens is called the power of the lens.
• It is always in meters.
• It is donated by 'P'
• The power of a convex lens is positive.
• The **power of the concave lens is negative.**1f=(μ−1)×(1R1–1R2)1f=(μ−1)×(1R1

Concept:

Sound

• Sound is a vibration that propagates through a medium as a mechanical wave.
• The medium in which it spreads can be solid, liquid, or gas.
• Sound travels fastest in solids, relatively slow in liquids, and slowest in gases.
• The intensity of sound is expressed in decibels.

Timbre

• Timbre is the characteristic of a sound, due to which it is possible to distinguish between sounds of the same loudness and the same pitch.

Explanation:

Intensity

• It is a physical quantity that expresses the rate of transfer of energy by waves.
• Intensity is measured in Watt per meter square.

Amplitude

• The maximum displacement of a wave from the mean position is called amplitude.
• The size of sound waves is measured by amplitude.

Pitch or shrillness

• Pitch is a characteristic of a sound that depends on the frequency.
• A sound of high pitch is said to be shrill and its frequency is high.
• A sound of low pitch is said to be grave and its frequency is low.

Therefore, The characteristic of sound that distinguishes between two different sounds of the same pitch and loudness is timbre.

Additional Information

Explanation:

Refrigerator

• It is a device used to maintain a lower temperature as compared to surroundings by absorbing heat from the system.
• Refrigerator pipes are painted a black color to allow them to reflect heat into the environment and cool themselves.
• Black is a good heat-absorbing color that may also be used to radiate heat.
• Black color is also the best emitter
• Heat is well-radiated by black bodies. As a result, radiating pipes get blackened, allowing heat to escape quickly.
• Component of refrigerator system
• Evaporator
• Compressor
• Condenser
• Expansion valve

Therefore, Both A and R are true and R is the correct explanation. 

Additional Information

Laws of Thermodynamics

Zeroth law of thermodynamics

• Two thermodynamic systems are in thermal equilibrium with each other if they are each in thermal equilibrium with a third.

The first law of thermodynamics

• There is no way to generate or destroy energy. It can only change its appearance.
• The entire energy of the universe remains the same.
• The net heat provided to the system equals the net work done by the system in a thermodynamic cycle.
• δQ = ΔU + δW

The second law of thermodynamics

• An isolated system that is not in equilibrium will have its entropy rise over time, eventually reaching a maximum value at equilibrium.
• ΔS = ΔQ/T
• ΔSTotal = ΔSSystem + ΔSsurrounding
• The concept of entropy is introduced by the second law of thermodynamics.

Third law of thermodynamics

• The entropy of a system approaches a constant minimum as the temperature approaches absolute zero.
• ΔST = 0K = 0

The word Heuristic is derived from the Greek word ‘Heurisca’ which means ‘to find out. It is also known as the ‘Inquiry Approach’.

• According to Prof. Henry Edward Armstrong who introduced this method for teaching science, “Heuristic method is a method of teaching which involves our placing of children as far as possible in the attitude of a discoverer”.
• It is a method in which children discover and find things by themselves. They are placed in the position of discoverers or inventors.
• You need to involve your students in finding out the solutions to a problem by themselves instead of telling or lecturing them.
• Problems are provided to the students. The students are expected to take observations and conduct experiments as per the instructions. Conclusions are drawn by the students and hence they are introduced to reasoning skills from their observation and experiments.

Key PointsIn the given question, The sequence of planning for the science classroom using an inquiry approach in the teaching of the topic 'Heat and Temperature' should be as-

• First, ask students to explore what happens when they place a container with hot water inside a container with cold water so that they had experience by observing the real situation.
• Then, ask students to describe the relationship between heat and temperature so they can be made a conclusion based on experimental activity.
• At last, ask students to infer the direction of heat flow in different objects, this will be the application of knowledge gained by experimental activity.

Therefore, the correct sequence will be

• to ask students to explore what happens when they place a container with hot water inside a container with cold water.
• ask students to describe the relationship between heat and temperature.
• ask students to infer the direction of heat flow in different objects.

Hence, the correct answer will be option 3.

Science is defined as the process that involves experimentation, testing hypothesis, building evidence, and theoretical discussions as it undergoes an engagement with a constant process of reviewing and renewal. This depicts the importance of nurturing scientific creativity amongst students.

• Science needs a great deal of knowledge, imagination, and creative insight on the part of the learners.

Key PointsNurturing Scientific Creativity by followings-

Certain thinking abilities/cognitive processes concerning scientific creativity as identified by various researchers are:

• Divergent thinking abilities
• Encourage students to frame answers in multiple ways
• Provide a rich variety of learning experiences to students
• Application of science process skills
• Scientific inquisitiveness
• Assist students in developing models of inquiry.
• Openness
• Hypotheses formulation
• Guide students in the use of a multidisciplinary approach

Therefore, for nurturing creativity in the science classroom among students, a teacher can do all of the above, except encourage students to frame answers in a prescribed manner*.*

Activities-based learning is the process of doing my own hands practically.it encourages the students to participate in their own learning experiences.

• The students in classes should be taught through various activities and hands-on experiences.

Key PointsLearning experiences can be of different types. One significant method is ‘hands-on experience’. It is also known as learning by doing.

• Avoid situations where the students are passive listeners for a long period.
• Provide students with hands-on activities such as experiments, observation projects, etc.
• Encourage participation of students in classroom discussions and other collaborative activities.
• In hands-on experience, the learner gets an opportunity to handle, say, equipment, instruments, and other such materials by him or themselves.
• However, in the science teaching-learning process, many concepts can be taught using hands-on experiences. It is for the teacher to think and devise possible and relevant activities/experiments for students’ hands-on learning.
• It is also advisable to take care of a multi-sensory approach that is the activities included for hands-on experience may include seeing, listening, assembling, fixing, moving, etc.
• Students to perform experiments themselves.

Important PointsTherefore , for image-formation in plane mirrors, is being introduced in class VII,a teacher should 

• Encourage participation of students in classroom hands-on and other collaborative activities.

Hence we can say, Students place several objects at different positions in front of a mirror, and observing their images is the best way to introduce the image formation in a plane mirror.

Problem-solving is an important cognitive activity. It is so central to the process of thinking that many people use it interchangeably with thinking.

• Problem-solving refers to thinking directed towards solving a specific task/situation.
• A moment’s reflection will make it clear that all our day’s activities involve problem-solving.
• The problem may be simple or complex.

Key PointsThis type of thinking has three stages starting from the stage of occurrence of a problem followed by a set of mental operations, leading to the solution of the problem. A problem signifies a situation that requires a solution.

It has three stages or steps as stated below:

• Initial State: identify a problem
• Operation: Actions or steps to be taken
• Goal State: Solution

Thus, when a teacher wishes to apply the problem-solving strategy to help students understand various ways to conserve energy in a school, the first step in the problem-solving strategy will be Identifying wasteful practices.

In a Science classroom, the teacher is expected to provide opportunities for the learners to participate in some investigative activities which will help them to understand the nature of the scientific inquiry.

• Such practices will encourage the learners to think about the relationships between facts, options, processes, and incidents.
• It is expected that you will encourage your learners to identify relationships and analyze rationally the associated facts.

Key Points

• Controlling variables is defined as keeping all conditions the same except for the independent variable. Observe the growth of a plant after doubling up the water amount. In this, we can have variations in providing the amount of water.  the temperature can be classified as a control variable if it is controlled during an experiment. Other examples of control variables could be light, water, and time. - How much do they grow if we double the amount of water? Therefore, the Controlling variable skills are developing.
• Observation means using our various senses to obtain information (or data) about objects or events attended”. Observations are not to be limited to seeing things only. We use more than one sense organ to collect data (or information) about the objects in our daily acts. - How much are they growing every week? , Therefore Observation skill is developing.

Thus, when a teacher asks questions while involving students in an investigatory activity on the germination of seeds he tries to develop Controlling variables and Observation skills through these questions

Understanding Science is dealing with issues related to Perspectives and the Nature of Science, science is a process of inquiry and value development through science.

• Every moment in their life children are experiencing many things, and as a result of that, they are learning.

Key PointsChildren come to the classroom with a lot of exposure to the environment. They learn by imitation, observing, and questioning. knowingly or unknowingly they use Science and Mathematics at each moment of life. Whether it is at home or playground they use different types of science.

A teacher should-

• Use the previous knowledge of whatever science students know from their environment by connecting it with the topic of teaching.
• Make linkages between children’s experiential informal knowledge of science and school science.
• Connecting science concepts with the objects around the students is considered a successful teacher.
• Provide Numerous examples in which we use science in our daily life can be used with the various experiences of students in constructing science concepts.
• Science is an abstract subject with evidence having clear interconnectedness between scientific concepts.

Therefore, Science is an abstract subject with clear interconnectedness between scientific concepts and a teacher should teach each science concept assuming students knowingly or unknowingly use Science to make linkages between children’s experiential informal knowledge of science and school science.**

In science teaching-learning, investigatory projects are a method, which provides an opportunity to learners to examine and explore their ideas in their surroundings. This method helps learners to explore science in their immediate environment on their own.

Key PointsHow to do an Investigatory Project in Science?

• Investigatory projects use the scientific method. It starts with asking questions about something learners observe. When learners frame questions about their observation, they should be encouraged to arrive at a testable and precise question or the question on which they do their project.
• After this, they are advised to carry out some research i.e. searching and searching books in the school library. Learners identify the resources required, the process to be followed, support required from peers/teacher/parents or other members of the society, etc. •
• After researching, they frame hypotheses, i.e. the possible answers to their questions. Generally, learners use the terms like ‘if’/ ‘then’ to convert the question into a hypothesis. • When they frame hypotheses, they started thinking about the experimentation. How will they experiment? They plan and do the experimentation. •
• While doing experimentation, learners record the observations and analyze them to find out the answer to their questions. Sometimes, the hypotheses may be right and sometimes they may be wrong. If the hypothesis is wrong, they again reframe a new hypothesis and test it.
• Learners report their findings in clear terms in either case i.e. hypothesis is accepted or rejected.

Important Points

• Critical reflection is referred to an activity during which learners challenge the validity and appropriateness of their assumptions and beliefs within our present context.
• Hence, After completion of an investigatory project asking questions such as "Can you think of a different and better way of trying out your ideas?" after an investigatory project helps students to reflect critically.

Additional Information

• To hypothesize refers to making an assumption or having a theory that is considered to be true.
• Communicating is defined as the process of sharing and exchanging information, and ideas with somebody.
• Observing refers to the situation when someone watches (someone or something) carefully and attentively.

Contextual Teaching refers to a method of teaching and learning, based on a constructive theory, where the teacher presents information in a way that students are able to construct meaning based on their own experiences.

• Several community resources can be utilized to make the activity more meaningful and contextual.
• Locally available materials, folklore, folk songs, games, riddles, and puzzles can be used in different classroom activities in which the student can effortlessly get involved.

Key Points

• By contextualizing learning to the neighborhood and other real-world contexts, students will be able to better understand, transfer and apply their knowledge outside of the classroom.
• Contextualization adds another element to the learning experience and can spark interest, curiosity, motivation, and engagement with content.
• Providing authentic (real-world and contextual) tasks.
• Providing experiences from the immediate environment as possible.
• Providing real-world, context-based learning environments rather than predetermined instructional sequences for making learning more realistic, relevant, and contextual.
• Connecting the activities in the school with those outside the school.

Therefore,  A teacher introduced the topic of cyclones in a class by asking Have you heard about heavy rains in West Bengal and Odissa in 2021? Has anyone of you heard the term "Yaas"? , the objective of the teacher behind asking these questions to students is to contextualize the topic.

Additional InformationCyclone Yaas _23 May 2021 – 28 May 2021

Very Severe Cyclonic Storm Yaas was a relatively strong and very damaging tropical cyclone that made landfall in Odisha and brought significant impacts to West Bengal in late May 2021.

Scientific temper or (scientific thinking) is a way of looking at the processes of assumptions, scientific explanation, use, and merits of science.

• Science is a very practical subject and is applicable everywhere in our daily lives.
• Naturally, the teacher needs to give practical and concrete experiences to the students.
• It cannot be taught with explanation only. The teacher needs also to demonstrate the experiments

We consider such a person, who imbibes the essence of the scientific method in his outlook, and uses it in his everyday life, as possessing a “Scientific Temper”. She may not necessarily be a scientist, not even a science student, and yet have a scientific temper.

Key Points

This scientific temper or scientific attitude is characterized by the following traits :

• Healthy scepticism: The attitude of healthy scepticism implies that you do not accept others’ assertions unless these are logical, rational, and supported by proper evidence.
• Universalism: Universalism is thus an important characteristic of scientific temper.
• Freedom from prejudice or bias: There is no place for prejudice or bias, for otherwise, the conclusions can not be universal.
• Objectivity: The observations have to be objective. You observe things as they are, without trying to manipulate these to fit in some pre-conceived worldview.
• Open-mindedness and humility: The observations also demand an open-mindedness, willingness to change conclusions in the light of reliable evidence, and humility, freedom from pride and arrogance, which comes from the realization of the limitations of our intellect and ever-broadening horizons of knowledge.
• Rationality: The hallmark of all decision-making by a person with a “scientific temper” is logic and rationality.
• Perseverance - positive approach to failure: Perseverance, is another important characteristic of scientific attitude, for even the “flash of insight”, which characterizes many great scientific achievements, usually follows hard toil and reflection on the problem for long periods of time.

Hence, we can conclude that a Scientific temper or scientific attitude is characterized by open-mindedness and scepticism.

The word ‘Science’ has been derived from the Latin word ‘Scientia’ which means ‘knowing’. Science is the study of the nature and behavior of natural things.

Key Points

The Nature of science -

• Science demands evidence
• Science is a blend of logic and imagination
• Scientific knowledge is durable
• Scientific knowledge is subject to change
• Scientists attempt to identify and avoid bias
• Science is a complex social activity
• Science is both -a process and a product

Therefore, we can say that Science is a blend of logic and imagination.

The correct answer is 'better job opportunities there'.

Key Points

• As we can see in the first paragraph of the passage, it is clearly mentioned that "Cases of flight abroad caused by political persecution apart, people emigrate mostly for economic betterment".
• Refer to these lines too: And where they have spread, they have whetted the appetite for a better life so much that salaries from jobs in the Bengaluru back offices or call centres of international companies may not be able to meet. Most illegal Indian immigrants seem to be from Punjab, one of the most prosperous states in the country.
• It can be inferred that people migrate to other countries because of better job opportunities there.
• Hence, the correct answer is option 4.

The correct answer is 'poor people will stop going to the rich countries'.

Key Points

• As we can see in the first paragraph of the passage, it is clearly mentioned that "Cases of flight abroad caused by political persecution apart, people emigrate mostly for economic betterment.
• Pundits predict that with the advance towards a globalised economy, this sort of migration will become unnecessary".
• It can be inferred that when economy becomes globalised poor people will stop going to the rich countries or some other countries for economic betterment.
• Hence, the correct answer is option 4.

The correct answer is 'people are demanding higher salaries'.

Key Points

• As we can see in the first paragraph of the passage, it is clearly mentioned that "The rewards of globalisation have spread unevenly.
• And where they have spread, they have whetted the appetite for a better life so much that salaries from jobs in the Bengaluru back offices or call centres of international companies may not be able to meet".
• It can be inferred that globalisation has resulted in whetting the appetite of people for a better life and inspite of getting good amount of salaries they are not able to meet their demands.
• Hence, the correct answer is option 4.

The correct answer is 'by 'loosening up' the foreigners.'

Key Points 

• As we can see in the second paragraph of the passage, it is clearly mentioned that "Illegal immigration cannot be stopped. It can only be checked. For this, without doubt, border control regimes in the developed world that seek to keep out foreigners have to first loosen up".
• It can be inferred that illegal immigration can be stopped loosening up the foreigners and for that there needs to be a strict border control.
• Hence, the correct answer is option 3.

The correct answer is 'Both A and B are right'.

Key Points

• As we can see in the first paragraph of the passage, it is clearly mentioned that "And where they have spread, they have whetted the appetite for a better life so much that salaries from jobs in the Bengaluru back offices or call centres of international companies may not be able to meet".
• It can be inferred that statement (A) is true.
• As we can see in the second paragraph of the passage, it is clearly mentioned that "More than this, the realisation that they could be stranded without an adequate work force in the years to come has already spurred an awareness in many host countries that their immigration laws need to be relaxed". 
• It can be inferred that statement (B) is true.

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Hence, the correct answer is option 3.