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Hamza, Mohammed.A

Q.1: In mathematics, patterns are more than a beautiful design (though they are often that too), patterns follow a predictable rule and that rule allows us to predict what will come next. Mathematicians say that mathematics is the study of pattern—of patterns and structure in numbers, and patterns and structure in geometry.

Q.2: to help them identify facual, conceptual and debatable inquiry questions

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how could this statement relate to Mathematics

aw: because if you use logic in math it'll eventually lead you to a complete and simple awnser

how could it be used in other contexts

aw: it can be used in physics because of the equations and formulas and algebra quetions

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Humans observed patterns and generalized to make logical rules thus inventing algebra.

We could observe patterns and generalize to make logical rules thus inventing new methods.

It can be used in physics, in formulas and equations.

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Global context: scientific and technical innovation

how is adaptation important to me?

to upgrade, to improve personality for the good, to succeed in life, and learn new things

How is ingenuity important to me?

Ingenuity is the quality of being clever, original, and inventive. It is an aquired skill which people develop as they progress in life.

Why is progress important to me?

Because progress is a reward for consistency on the journey to achievement.

Why is adaptation important to the community?

Get used to a new environment, and improvise.

Why is ingenuity important to the community?

To help.

Why is progress important to the community?

Progress guides us to make a meaningful difference and leave a lasting legacy.

Why is adaptation important to the world?

Adaptation is one of nature's most important transformation tools, and a key mechanism of natural selection.

Why is ingenuity important to the world?

Share creativity all around the world.

Why is progress important to the world?

To help improve the world.

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have you heard this concept before? if so when

We have heard it in colour's and numbers and shapes

What might this concept mean in maths?

A group of numbers in the same order

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have you heard the word patterns before:

yes, when I look at art.

what might this concept mean in math:

it might mean patterns in numbers.

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When have you heard “Paterns”? If so when? KG2-g3

What does Patterns mean in math? In Mathematics, a pattern is a repeated arrangement of numbers, shapes, colours and so on. The Pattern can be related to any type of event or object. If the set of numbers are related to each other in a specific rule, then the rule or manner is called a pattern.https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwja5YjW0vqCAxXmcPEDHVU0CBMQFnoECAkQAw&url=https%3A%2F%2Fbyjus.com%2Fmaths%2Fpatterns%2F%23%3A~%3Atext%3DIn%2520Mathematics%252C%2520a%2520pattern%2520is%2Cmanner%2520is%2520called%2520a%2520pattern.&usg=AOvVaw2ck3K3V2gJbFjzuHcDRCvk&opi=89978449

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Mathematics is all about numbers. It involves the study of different patterns. There are different types of patterns, such as number patterns, image patterns, logic patterns, word patterns etc. Number patterns are very common in Mathematics. These are quite familiar to the students who study Maths frequently. Especially, number patterns are everywhere in Mathematics. Number patterns are all predictions. In this article, we will discuss what is a pattern, and different types of patterns like, arithmetic pattern, geometric pattern and many solved examples.
Table of Contents:
Patterns in Maths

In Mathematics, a pattern is a repeated arrangement of numbers, shapes, colours and so on. The Pattern can be related to any type of event or object. If the set of numbers are related to each other in a specific rule, then the rule or manner is called a pattern. Sometimes, patterns are also known as a sequence. Patterns are finite or infinite in numbers.

For example, in a sequence 2,4,6,8,?. each number is increasing by sequence 2. So, the last number will be 8 + 2 = 10.

Few examples of numerical patterns are:

Even numbers pattern -: 2, 4, 6, 8, 10, 1, 14, 16, 18, ...

Odd numbers pattern -: 3, 5, 7, 9, 11, 13, 15, 17, 19, ...

Fibonacci numbers pattern -: 1, 1, 2, 3, 5, 8 ,13, 21, ... and so on.

Number Patterns

A list of numbers that follow a certain sequence is known as patterns or number patterns. The different types of number patterns are algebraic or arithmetic pattern, geometric pattern, Fibonacci pattern and so on. Now, let us take a look at the three different patterns here.

Arithmetic Pattern

The arithmetic pattern is also known as the algebraic pattern. In an arithmetic pattern, the sequences are based on the addition or subtraction of the terms. If two or more terms in the sequence are given, we can use addition or subtraction to find the arithmetic pattern.

For example, 2, 4, 6, 8, 10, __, 14, __. Now, we need to find the missing term in the sequence.

Here, we can use the addition process to figure out the missing terms in the patterns.

In the pattern, the rule used is "Add 2 to the previous term to get the next term".

In the example given above, take the second term (4). If we add "2" to the second term (4), we get the third term 6.

Similarly, we can find the unknown terms in the sequence.

First missing term: The previous term is 10. Therefore, 10+2 = 12.

Second missing term: The previous term is 14. So, 14+2 = 16

Geometric Pattern

The geometric pattern is defined as the sequence of numbers that are based on the multiplication and division operation. Similar to the arithmetic pattern, if two or more numbers in the sequence are provided, we can easily find the unknown terms in the pattern using multiplication and division operation.

For example, 8, 16, 32, __, 128, __.

It is a geometric pattern, as each term in the sequence can be obtained by multiplying 2 with the previous term.

For example, 32 is the third term in the sequence, which is obtained by multiplying 2 with the previous term 16.

Likewise, we can find the unknown terms in the geometric pattern.

First missing term: The previous term is 32. Multiply 32 by 2, we get 64.

Second missing term: The previous term is 128. Multiply 128 by 2, we get 256.

Fibonacci Pattern

The Fibonacci Pattern is defined as the sequence of numbers, in which each term in the sequence is obtained by adding the two terms before it, starting with the numbers 0 and 1. The Fibonacci pattern is given as 0, 1, 1, 2, 3, 5, 8, 13, ... and so on.
Explanation:
Third term = First term + Second term = 0+1 = 1

Fourth term = second term + Third term = 1+1 = 2

Fifth term = Third term + Fourth term = 1+2 = 3, and so on.

Rules for Patterns in Maths

To construct a pattern, we have to know about some rules. To know about the rule for any pattern, we have to understand the nature of the sequence and the difference between the two successive terms.

Finding Missing Term: Consider a pattern 1, 4, 9, 16, 25, ?. In this pattern, it is clear that every number is the square of their position number. The missing term takes place at n = 6. So, if the missing is x n, then x n = n ². Here, n = 6, then x n = (6) ² = 36.

Difference Rule: Sometimes, it is easy to find the difference between two successive terms. For example, consider 1, 5, 9, 13,....... In this type of pattern, first, we have to find the difference between two pairs of the sequence. After that, find the remaining elements of the pattern. In the given problem, the difference between the terms is 4, i.e.if we add 4 and 1, we get 5, and if we add 4 and 5, we get 9 and so on.

Types of Patterns

In Discrete Mathematics, we have three types of patterns as follows:

Repeating - A type of pattern, in which the rule keeps repeating over and over is called a repeating pattern.

Growing - If the numbers are present in the increasing form, then the pattern is known as a growing pattern. Example 34, 40, 46, 52, .....

Shirking - In the shirking pattern, the numbers are in decreasing form. Example: 42, 40, 38, 36 .....

Examples of Arithmetic and Geometric Pattern
Example 1:
Determine the value of P and Q in the following pattern.

85, 79, 73, 67, 61, 55, 49, 43, P, 31, 25, Q.
Solution:
Given sequence:85, 79, 73, 67, 61, 55, 49, 43, P, 31, 25, Q.

Here, the number is decreasing by 6

The previous number of P is 43. So, P will be 43 - 6, P = 37

The previous number of Q is 25. So, Q will be 25 - 6, Q = 19

Therefore, the value of P is 37 and Q is 19.
Example 2:
Determine the value of A and B in the following pattern.

15, 22, 29, 36, 43, A, 57, 64, 71, 78, 85, B.
Solution:
Given sequence: 15, 22, 29, 36, 43, A, 57, 64, 71, 78, 85, B.

Here, the number is increasing by +7

The previous number of A is 43. So, A will be 43 + 7, A = 50

The previous number of B is 85. So, B will be 85 + 7, B = 92

Therefore, the value of A is 50 and B is 92.
Example 3:
Find the missing value in the geometric pattern: 120, 60, __, 15, __.
Solution:
Given: Geometric pattern is 120, 60, __, 15, __.

In this geometric pattern, the rule used is "Divide the previous term by 2 to get the next term".

Then, the first missing term = 60/2 = 30

Second Missing term = 15/2 = 7.5

Frequently Asked Questions on Patterns

Stay tuned with BYJU'S - The Learning App and also download the app to learn with ease.

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Patterns in Maths (Definition, Types & Examples) | Arithmetic & Geometric Pattern

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In Maths, a list of numbers that follows a certain sequence using rules is known as patterns. Visit BYJU'S to learn different types of patterns like arithmetic, geometric pattern, and so on.

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We have heard this concept before?

we all heard it in school on monday.

what might this concept mean in maths?

The color or code of something that has colors in it.

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where have you heard logic before :

when Ive heard something that make sense

what does it mean in general: Logic is a method of reasoning that involves a series of statements, each of which must be true if the statement before it is true

https://www.collinsdictionary.com

what does logic mean in mathematics: Anything that lets us infer a new fact about something mathematical from given information

https://content.nroc.org

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Why is important to me?

Its important Because it will help you get used to changing your environment

Why is important to your environment?

to evolve and create inventions and ideas that help the world

why is it important to the world?

it is important because it makes the world technological

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Statement on Inquiry: Humans observed patterns and generalized to make logical rules thus inventing algebra.

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Statement on Inquiry: Humans observed patterns and generalized to make logical rules thus inventing algebra.

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how did this relate to maths? Algebra is in math.

How could it be used in other context? school/work.

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Have you heard this concept before? If so, when?

is making things easy and making things different

What might this concept mean in math?

To collect things together

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When hav you heard Generalization? Never

a general statement or concept obtained by inference from specific cases.

In the mathematics literature, generalization can be seen as a statement that is true for a whole category of objects; it can be understood as the process through which we obtain a general statement; or it can be the way to transfer knowledge from one setting to a different one.

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwighp6B1PqCAxVEU6QEHZ-yCJUQFnoECA8QAw&url=https%3A%2F%2Fwww.ijlter.org%2Findex.php%2Fijlter%2Farticle%2Fdownload%2F1022%2Fpdf%23%3A~%3Atext%3DIn%2520the%2520mathematics%2520literature%252C%2520generalization%2Csetting%2520to%2520a%2520different%2520one.&usg=AOvVaw1v6iAAITgN1ExXmaDRZkiO&opi=89978449

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when have you heard the concept generalizations before? if so, when? yes, when I make something common

what mite this mean in math :

having common factors in math

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Where have you heard this concept before? if so, when?

Ive heard Patterns before in art class!

Bissan

Ive heard it in art class probably in the first grade.

Alameen

First time to hear it.

Sharaf

What might this concept mean in maths?

an order of numbers like skip counting.

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Have you heard this concept before? if so when?

Ive heard it before while checking my settings on my device

Bissan

First time to hear it.

Alameen

Never heard of it.

Sharaf

What might this concept be in math?

making things common,making it more general.

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When have you heard this word before?

We have heard this word before when our teachers or parents told us that we have to have logic in our words.

What does it mean in general?

logic, the study of correct reasoning, especially as it involves the drawing of inferences.

“Logic.” Encyclopædia Britannica, Encyclopædia Britannica, inc., 7 Nov. 2023, www.britannica.com/topic/logic.

What does it mean in our subject of mathematics specifically?

We think that logic means to have working out in your answers so it is true

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When have you heard logic before?

Ive heard it in a book before, and in science class.

Bissan

When Im making decisions people tell me to use logic.

Alameen

It's my first time to hear it.

Sharaf

What does it mean in general?

a method of reasoning that involves a series of statements, each of which must be true if the statement before its true.

Collins. “Collins Online Dictionary | Definitions, Thesaurus and Translations.” Collinsdictionary.com, 19 July 2019, www.collinsdictionary.com.

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What does it mean in our subject of mathematics specifically

To formulate a method

byjus. “BYJU’S the Learning App.” Byjus.com, 2019, byjus.com.

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Hamza, mohamed.A, Sofia

Q.1: where have you heard the word logic before?

Mohammed: 3 months ago in his house

Hamza: 2 months ago in school

Jessy: 1 month ago in school

Natalie: 1 month ago in school

Q.2: what does Logic mean in general? reason or idea or word

Q.3: What does Login mean in Math?

When you are showing something in Math

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Where have you heard "LOGIC"? School.

logic is something that obviously makes sense.

Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory.[wikipedia] and from our POV math is torture. learning it is suffering

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Hamza, Mohammed.A, Sofia

Q.1: The importance of Adapt that it gives a higher chance of success and until make you mare happier and satisfied and you will become a better leader and you'll always be relevant.

Q.2: if like people open their minds to things it will help the community develop a better life to the civilians.

Q.3: it opens up your mind to new ideas and give you the willingness to go against convention.

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Global context: Scientific & Technical innovation 

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Global context: Scientific & Technical innovation 

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Well, adaptation is actually critical to protecting the well being of millions of people and species and has numerous important benefits : Preventing future losses (e.g. damage to infrastructure, ill health) Providing economic opportunities. Creating wider social and environmental benefits.Oct 14, 2022

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why is it important to me :

its important because to upgrade yourself and improve your self to be successful in life

why is it important to the community :

its important because communities have to progress too

why is it important t the world ;

its important because if the world doesnt progress we won't be able to survive