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Mathematics starts from ‘home learning’ established in the child before he/she comes to school.

• It's based on understanding and puts great emphasis on the child’s own methods of calculating and solving problems and rejects the previous practice of heavy emphasis on standard written algorithms.

 Key Points

• Mathematics is regarded as a powerful tool for interpreting the world and therefore should be rooted in real experience across the whole curriculum.
• The different mathematical concepts require different ways of learning.
• A slide rule is a calculating device based on the principle of logarithms. It consisted of two graduated scales devised in such a manner that suitable alignment of one scale against the other, made it possible to perform additions, multiplication, division, etc. just by inspection.
• The slide rule is a mathematical algorithm used in Multiplication and division.

Thus, it is concluded that Slide rule is used in Mathematics for Multiplication and division.

Hint

• Angle measurement is a practical concept that implies a specific method of measuring angles.
• Making the shape smaller and larger is a way of scaling the shapes to different sizes.
• Measurement of angle of elevation is a process used in trigonometry.​

Mathematics today is a diverse discipline that deals with data, measurements, and observations from science; with inference, deduction, and proof; and with mathematical models of natural phenomena, human behavior, and of social systems that makes it a universal subject.

Key Points Nature of Mathematics:

• Numbers, places, measurements, etc. are the basis of Mathematics.
• The special role of mathematics in education is a consequence of its universal applicability.
• The results of mathematics--theorems and theories--are both significant and useful; the best results are also elegant and deep.
• Through its theorems, mathematics offers science both a foundation of truth and a standard of certainty. Thus, it has a wide scope of generalization.
• In pure mathematics, we start from certain rules of inference, by which we call infer that if one proposition is true, then some other proposition is also true.
• These rules of inference constitute the major part of the principles of formal logic. These ideas point out the abstract nature of mathematics.

​Hence, from the above-explained points, we can say that area of generalization is limited in Mathematics is not related to the nature of mathematics.

Curriculum is a formal plan of educational experiences and activities offered to a learner under the guidance of an educational institution. It is more structured in schools and more flexible in higher education.

Key Points

The term "curriculum" is derived from the Latin word "currere", which means "run". Thus curriculum means a course to be run for reaching a certain goal or "destination" here education is imagined as a race, with its aim as the goal and curriculum as the course leading to that goal.

The success of a curriculum depends on certain principles, which need to be born in mind while developing a curriculum. These are:

• The purpose of the Educational Objectives of the Programme should be fulfilled.
• The educational objective should be stated in clear, unambiguous, and behavioral terms, which should be achievable and measurable.
• The students and teachers of the particular educational program should have a clear perception of the expected results i.e., objectives as well as the purpose of the educational program.
• The learning activities to provide learning experiences related to the theoretical, practical, and clinical components should be in conformity with the educational objectives of the program.
• The teaching-learning activities should relate to classroom activities, clinical fields, and community.

Hence, it could be concluded that the word "Curriculum" is taken from the Latin language.

Mathematics starts from ‘home learning’ established in the child before he/she comes to school and it is based on understanding. There are different ways of learning mathematics that can facilitate classroom situations. 

Key Points

• Making tables develop skills among children. They learn how to make it and start practicing it, so it enhances their creativity, thinking skills, etc.
• Learning mathematics has several specific objectives :
• develop the knowledge, skills, and attitudes necessary to pursue further studies in mathematics.
• develop abstract, logical, and critical thinking and the ability to reflect critically upon their work and the work of others
• develop a critical appreciation of the use of information and communication technology in mathematics
• Manipulation of objects: through the manipulation of concrete objects the children acquire mathematical skills at an early stage like comparison, categorization, counting, and fundamental four operations.
• Placing tasks in meaningful contexts: In real situations, where mathematics serves real purposes, young children quickly and easily develop their own informal concepts.

 Hence, it is concluded that Making tables in Mathematics comes under skill objective.

Calculation:

Number name: Ten lakh twenty thousand three hundred five

Concept:

Divisible by 4: If the last digits is 0, 2, 4, 6, 8 then it is divisible by 2.

Divisible by 6: The divisibility rule of 6 states that a number is said to be divisible by 6 if it is divisible by 2 and 3 both

Divisible by 5: A number is divisible by 5 if the last digit in the number is 0 or 5.

Divisible by 7:  A number to be divisible by 7, the last digit of the given number should be multiplied by 2 and then subtracted with the rest of the number leaving the last digit. If the difference is 0 or a multiple of 7, then it is divisible by 7.

Divisible by 9: The sum of digits of a number should be divisible by 9, then the number will be divisible by 9.

Divisible by 2: The last digit of the number should be 0, 2, 4, 6 and 8, then the number will be divisible by 2.

Divisible by 3: The sum of digits of a number should be divisible by 3, then the number will be divisible by 3.

Calculation:

The greatest number = 8,752

The smallest number = 2,578

Difference = 8752 - 2578 = 6174

⇒ 6174 is not divisible by 5 as 4 is at one's place.

⇒ 6174 is divisible by 2 as last digit is 4.

6 + 1+ 7 + 4 = 18

18 is divisible by 3. So, 6174 is divisible by 3.

⇒ 6174 is divisible by 3 and 2 both. So, it is divisible by 6.

⇒ 6174 is divisible by 7.

4 × 2 = 8

617 - 8 = 609 

609 ÷ 7

Quotient = 87

Remainder = 0

∴ 6174 is not divisible by 5.

Concept used:

Place value are the value the number is multiplied by it place where the digit placed in number.

For example:

The place value of 3 in 356 is 300.

Calculation:

Option 1:

The place value of 5 in number 2569 is 500.

Option 2:

The place value of 5 in number 6529 is 500.

Option 3:

The place value of 5 in number 9256 is 50.

Option 4:

The place value of 5 in number 9562 is 500.

∴In number 9256, the place value of 5 is not equal to 500.

Given:

The fractions are: \(\frac{1}{2},\frac{2}{5},\frac{3}{4},\frac{2}{3}\)

Calculation:

Here, 

⇒ 1/2 = 0.5

⇒ 2/5 = 0.4

⇒ 3/4 = 0.75

⇒ 2/3 = 0.66

∴ The descending order of fraction is \(\frac{3}{4},\frac{2}{3},\frac{1}{2},\frac{2}{5}\).

Given:

The prime numbers between 1 to 30.

Concept used:

Prime numbers are numbers which have two factors 1 and itself.

Calculation:

The prime numbers between 1 to 30 is:

⇒ 2, 3, 5, 7, 11, 13, 17, 19, 23 and 29.

∴ The prime numbers between 1 to 30 is 10.

Given:

The fractions are:-

⇒ 7/3 , 25/7, 35/9, 19/2

Calculation:

Here,

⇒ 7/3 = 2.333

⇒ 25/7 = 3.571

⇒ 35/9 = 3.888

⇒ 19/2 = 9.5

∴ 19/2 is the greatest fraction.