Number Patterns

Types of Number Patterns in Math

Arithmetic Sequence

A sequence is group of numbers that follow a pattern based on a specific rule. An arithmetic sequence involves a sequence of numbers to which the same amount has been added or subtracted. The amount that is added or subtracted is known as the common difference. For example, in the sequence “1, 4, 7, 10, 13…” each number has been added to 3 in order to derive the succeeding number. The common difference for this sequence is 3.

Geometric Sequence

A geometric sequence is a list of numbers that are multiplied (or divided) by the same amount. The amount by which the numbers are multiplied is known as the common ratio. For example, in the sequence “2, 4, 8, 16, 32...” each number is multiplied by 2. The number 2 is the common ratio for this geometric sequence.

Square Numbers

In a square number sequence, the terms are the squares of their position in the sequence. A square sequence would begin with “1, 4, 9, 16, 25…”

Cube Numbers

In a cube number sequence, the terms are the cubes of their position in the sequence. Therefore, a cube sequence starts with “1, 8, 27, 64, 125…”

Triangular Numbers

The numbers in a sequence are referred to as terms. The terms of a triangular sequence are related to the number of dots needed to create a triangle. You would begin forming a triangle with three dots; one on top and two on bottom. The next row would have three dots, making a total of six dots. The next row in the triangle would have four dots, making a total of 10 dots. The following row would have five dots, for a total of 15 dots. Therefore, a triangular sequence begins: “1, 3, 6, 10, 15…”)

Techniques

How to Solve Math Problems Faster: 4 Techniques to Show Students

1. Squaring a Two-Digit Numbers that Ends with 5

Squaring numbers ending in 5 is easier, as there are only two parts of the process.

First, students will always make 25 the product’s last digits.

Second, to determine the product’s first digits, students must multiply the number’s first digit — 9, for example — by the integer that’s one higher — 10, in this case.

So, students would solve 952 by designating 25 as the last two digits. They would then multiply 9 x 10 to receive 90. Putting these numbers together, the result is 9,025.

Just like that, a hard problem becomes easy multiplication for many students

2. Calculating Percentages

Cross-multiplication is an important skill to develop, but there’s an easier way to calculate percentages.

For example, if students want to know what 65% of 175 is, they can multiply the numbers together and move the decimal place two digits to the left.

The result is 113.75, which is indeed the correct answer.

This shortcut is a useful timesaver on tests and quizzes.

3. Multiplying Odd Numbers by 5

This is another time-saving tactic that works well when teaching students the 5 times table.

This one has three steps, which 5 x 7 exemplifies.

First, subtract 1 from the number being multiplied by 5, making it an even number. Second, cut that number in half — from 6 to 3 in this instance. Third, add 5 to the right of the number.

The answer is 35.

Who needs a calculator?

4. Subtracting from 1,000

You can give students confidence to handle four-digit integers with this fast technique.

To subtract a number from 1,000, subtract that number’s first two digits from 9. Then, subtract the final digit from 10.

Let’s say students must solve 1,000 – 438. Here are the steps:

• 9 – 4 = 5
• 9 – 3 = 6
• 10 – 8 = 2
• 562

This also applies to 10,000, 100,000 and other integers that follow this pattern.

Media Violence

Famous Mathematicians

Pythagoras (c. 570 – c. 495 BC)
Nationality: Greek
Famous For: Pythagorean theorem
Pythagoras is best known in mathematics for the Pythagorean Theorem.

Archimedes (c. 287 – c. 212 BC)
Nationality: Greek
Famous For: Greatest mathematician of antiquity
Archimedes provided principles and methods used in mathematics today. He provided the exact numerical value of pi, developed a system for large numbers to be expressed, and the method of exhaustion.

John Forbes Nash, Jr. (1928)
Nationality: American
Famous For: Nash embedding theorem
The work of American mathematician John Nash includes studies in differential geometry, game theory, and partial differential equations. He is best known for the Nash embedding theorem. His work in algebraic geometry is also seen as milestone in mathematics.

Blaise Pascal (1623-1662)
Nationality: French
Famous For: Pascal’s Triangle
Pascal is recognized for two mathematical areas of study, projective geometry and probability theory. He describes in his paper, Treatise on the Arithmetical Triangle, an easy to understand table of “binomial coefficients” known as Pascal’s Triangle

Euclid (c. 365 – c. 275 BC)
Nationality: Greek
Famous For: Father of geometry
The earliest known “math books” is one written by Greek mathematician Euclid, Elements is its title. It serve as a textbook to teach geometry and mathematics. His mathematical system is known as “Euclidean geometry.”

Aryabhata (c. 476 – c. 550)
Nationality: Indian
Famous For: Writing Āryabhaṭīya and the Arya-siddhanta
Indian mathematician Aryabhatta’s contribution include his work on providing an approximate value to pi. He likewise touched on the concepts of sine, cosine, and the place-value system.

Omar Khayyám (1048-1131)
Nationality: Persian
Famous For: Treatise on Demonstration of Problems of Algebra
Omar Khayyam wrote one of the most important books in mathematics, Treatise on Demonstration of Problems of Algebra from which most algebraic principles have been drawn from. In the area of geometry, Khayyam worked on the “theory of proportions.”

Mathematics in other subjects

How Is Mathematics Used in Other Subjects?

Science and Technology

Science and math are intimately connected, particularly in fields such as chemistry, astronomy and physics. Students who can't master basic arithmetic skills will struggle to read scientific charts and graphs. More complex math, such as geometry, algebra and calculus, can help students solve chemistry problems, understand the movements of the planets and analyze scientific studies. Math is also important in practical sciences, such as engineering and computer science. Students may have to solve equations when writing computer programs and figuring out algorithms. Nursing majors may have great bedside manner. but they also need to know how to precisely calculate dosages to pass their courses

Social Studies

Social studies classes, such as history, often require students to review charts and graphs that provide historical data or information on ethnic groups. In geography classes, students might need to understand how the elevation of an area affects its population or chart the extent to which different populations have different average life spans. Knowledge of basic mathematical terms and formulas makes statistical information accessible.

The Arts

Students interested in pursuing careers in theater, music, dance or art can benefit from basic mathematical knowledge. Musical rhythm often follows complex mathematical series, and math can help students learn the basic rhythms of dances used in ballet and theater performances.Art thrives on geometry, and students who understand basic geometric formulas can craft impressive art pieces. Photographers use math to calculate shutter speed, focal length, lighting angles and exposure time.

Vedic Maths

Vedic Maths is a system of reasoning and mathematical working based on ancient Indian teachings called Veda. It is fast, efficient and easy to learn and use. Vedic mathematics, which simplifies arithmetic and algebraic operations, has increasingly found acceptance the world over.

The “Vedic Mathematics” is called so because of its origin from Vedas. To be more specific, it has originated from “Atharva Vedas” the fourth Veda. “Atharva Veda” deals with the branches like Engineering, Mathematics, sculpture, Medicine, and all other sciences with which we are today aware of. The Sanskrit word Veda is derived from the root Vid, meaning to know without limit. The word Veda covers all Veda-Sakhas known to humanity. The Veda is a repository of all knowledge, fathomless, ever revealing as it is delved deeper.

Vedic Mathematics introduces the wonderful applications to Arithmetical computations, theory of numbers, compound multiplications, algebraic operations, factorisations, simple quadratic and higher order equations, simultaneous quadratic equations, partial fractions, calculus, squaring, cubing, square root, cube root and coordinate geometry etc.

USES OF VEDIC MATHEMATICS:

• It helps a person to solve mathematical problems 10-15 times faster
• It helps m Intelligent Guessing
• It reduces burden (need to learn tables up to 9 only)
• It is a magical tool to reduce scratch work and finger counting
• It increases concentration.
• It helps in reducing silly mistakes

Benefits of Vedic Maths

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It creates interest towards mathematics.

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It will be beneficial throughout lifetime

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It helps in Intelligent Guessing (Knowing the answer without actually solving the problem)

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It is a magical tool to reduce scratch work and finger counting and improve Mental Calculation.

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It increases concentration.

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It improves confidence.

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It reduces burden (Need to learn tables up to nine only).

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The development of creativity at a young age is helpful towards understanding advanced concepts

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It can be applied even for numbers beyond 10 digits

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Saves time during Examination

Math Quotes and Quotation

Mathematics Quotes and Quotation

• "A mathematician is a blind man in a dark room looking for a black cat which isn't there." --Charles Darwin
• "A topologist is one who doesn't know the difference between a doughnut and a coffee cup." --John Kelley
• "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." --Albert Einstein
• "As long as algebra is taught in school, there will be prayer in school." --Cokie Roberts
• "Do not worry about your problems with mathematics, I assure you mine are far greater." --Albert Einstein
• "From the intrinsic evidence of his creation, the Great Architect of the Universe now begins to appear as a pure mathematician." --Sir James Jeans
• "God does arithmetic." --Karl Friedrich Gauss
• "God does not care about our mathematical difficulties. He integrates empirically." --Albert Einstein
• "He uses statistics as a drunken man uses lamp posts." -- for support rather than illumination." --Andrew Lang
• "He who can properly define and divide is to be considered a god." --Plato

• "I have no faith in political arithmetic." --Adam Smith
• "If your experiment needs statistics, you ought to have done a better experiment." --Ernest Rutherford
• "Life is good for only two things, discovering mathematics and teaching mathematics." --Simeon Poisson
• "Mathematical proofs, like diamonds, are hard and clear, and will be touched with nothing but strict reasoning." --John Locke
• "Mathematics consists of proving the most obvious thing in the least obvious way." --George Polye
• "Mathematics is a game played according to certain simple rules with meaningless marks on paper." --David Hilbert
• "[Mathematics] is an independent world created out of pure intelligence." --William Wordsworth