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number patterns:
In Mathematics, number patterns are the patterns in which a list number that follows a certain sequence. Generally, the patterns establish the relationship between two numbers. It is also known as the sequences of series in numbers.
How to teach kids number patterns
Number patterns are a sequence of numbers with a common relationship. For example, in the sequence 3,6,9,12, each number is increasing by three. Generally speaking, once a child is confident enough with numbers to count unassisted, they are ready to start exploring sequences.
Why are number patterns and sequences important?
At its core, mathematics is the study of numbers and their relationship to each other. That’s why it’s important to make sure kids have a solid understanding of number patterns and sequences before progressing onto more complex mathematical topics.
The ability to recognize patterns in groups of numbers will help a child develop critical thinking skills and prepare them for more complex mathematical operations in years to come.
And patterns are not just found in math, but also in nature, art, and music, as well. So being able to identify, recognize, and build upon sequences will help them in science, geography, social studies, and other classes, too.
Teach them rhymes and games
Songs and rhymes like “One, Two, Buckle My Shoe” and “The Ants Go Marching” are fun ways to teach kids numbers and ensure they can count without confusion. Use your fingers to count as you go along to give them a visual aid.
Incorporate numbers into daily tasks
Numbers are everywhere, so it’s easy to take your education away from the classroom. If you’re a math teacher, why not take the class for a walk around the playground and look for number sequences in trees and plants — notice how a tree tends to branch off from 1 trunk to 3 branches, to 5 smaller branches? That’s a number sequence in action! If you’re a homeschooler, ask your child to set the table with four forks, or to create patterns with the pieces of pasta on their plate.
Patterns don’t have to be numbers
If your child is struggling a little with numbers, take a step back and first introduce patterns with drawings. Rather than using numerals, you can make patterns out of clusters of dots. If you have a dominoes set, that’s also a great way to demonstrate patterns in a less overwhelming way.
Need and importance of mathematics in our life:
In Market: Most of the students might have gone to a market with their parents. They must
have observed and participated in the way of buying and selling of goods and also the approach the buyer and seller. One should take the advantage of real situations and utilize the experience of the
students in calculation of profit & loss, preparation of bills, process of weighting, counting of money,
amount and price etc.
In Garden: Students prepare plots in home, schools and also in playing with peers. During that
time they may not know counting, measurement construction of angles, different types of geometrical
figures, areas, different types of geometrical figures, areas, different lines, average etc., but they may
do it using their perception. How can one prepare a plot of two meters each side. You may share the
experience of the students in these activities.
In Real ife experience: A frog climbs 30 meters on a pole in a day and slides back 20 meter
in a night. If the pole is 70 meters high, then how many days the frog will take to climb to the top
of the pole? Most of our students of upper primary classes may calculate the answer as 7. One student
told the answer is 5 as the frog climbs 40 meters in 4 days and in the tith day it reached on the top
ie. 70 meters. Students get opportunities to work in a natural setting, they work according to their own
perceptions. So their real life experiencc must take into consideration.
In Making designs: Students cover their note books, paint pictures, decorate their houses,
plants trees in garden, design their play1ng KiuS etc. At nat time, are they using mathematics? How
many matchsticks arce required to design your name? Teacher must observe the process of making
design and utilize it in classroom.
In Festivals: We celebrate many festivals in our homes as well as in our schools. Students
heartily involved on the Independence day, Republic day, Teacher's day, Children's day, Saraswati
uja, Ganesh Puja, Id, Christmas etc. They involve themselves in ditferent activities to make these
special occasions memorable. They go to market to buy various materials, decorate the schools.
astribute swects, calculate expenditure etc., at the same time they also learn mathematics.
In Playground: Students are playing kabaddi, football, cricket, volleyball, basketball and al
ents
nany indoor games. They frame their rules of their own, prepare playground in a group. Student.
construct circles, rectangles, squares, triangles etc., in their playground without knowing the rules
construction. They count individual and group seores through their own strategies. Ramesh scored tw
fours, two twos and single in a cricket match. How can he ealculate his total score without knowing
f
multiplication.
EDUCATIONAL VALUES OF TEACHING MATHEMATICS.
Mathematics provides an effective way of building mental discipline and encourages logical reasoning and mental rigor. In addition, mathematical knowledge plays a crucial role in understanding the contents of other school subjects such as science, social studies, and even music and art.
Mathematics has great practical value. Everyone uses some mathematics in every form of life.
A common man sometimes can do without reading or writing but he cannot do without counting and calculating. Any person who is ignorant of mathematics can be easily cheated. He will always be at the mercy of others. We have to make purchases daily. We buy cloth, food items, fruit, vegetables, grocery etc.
We have to calculate how much we have to pay for everything. A house-wife also needs mathematics for looking after her house, preparing family budgets and estimates, writing various expenses and noting down various household transactions.
Mathematics is needed by all of us whether rich or poor, high or low. Not to speak of engineers, bankers, accountants, businessmen, planners etc., even petty shopkeepers, humble coolies, carpenters and labourers need mathematics not only for earning their livelihood but also to spend wisely and save for future. Whoever earns and spends uses mathematics.
Mathematics trains or disciplines the mind also. It develops thinking and reasoning power. it develops the power of concentration.The study of mathematics develops inventive faculty of the students.Mathematics develops patience and perseverance in the students.
design an activity to teach concept of angle in mathematics:
Looking for Angles in Letters
Have students use a ruler to create the letter of their first name. Then, with the ruler, draw random lines within their letter and colour as they wish. Students then need to find as many angles as they can and measure each angle! Simple, fun and worthwhile!
Measure Angles in Pictures
We have some gorgeous angle worksheets with cute pictures that have different types of angles for your students to identify.
This could be done individually, alternatively, print onto an A3 piece of paper and provide small groups with a copy. Each student in the group could be allocated a particular angle to find, or the sheet could be passed around for each student to find one angle at a time!.
Make an Angles Display
Angles can be pretty tricky when you are trying to learn all the different types and terms. Having a classroom display to help your students remember the different terms and angles is a must! We have a range of posters that are perfect to display in your classroom.
Contribution of Ramanujan in the field of Mathematics
Ramanujan : The Man Who Knew Infinity
Srinivasa Ramanujan (1887-1920), the man who reshaped twentieth-century mathematics with his various contributions in several mathematical domains, including mathematical analysis, infinite series, continued fractions, number theory, and game theory is recognized as one of history's greatest mathematicians.he never received any formal mathematics training. Every year, Ramanujan’s birth anniversary on December 22 is observed as National Mathematics Day.
Ramanujan’s major contributions to mathematics:
Ramanujan's contribution extends to mathematical fields such as complex analysis, number theory, infinite series, and continued fractions.
Infinite series for pi: In 1914, Ramanujan found a formula for infinite series for pi, which forms the basis of many algorithms used today.
Game theory: Ramanujan discovered a long list of new ideas for solving many challenging mathematical problems that have given great impetus to the development of game theory. His contribution to game theory is purely based on intuition and natural talent and is unmatched to this day.
Mock theta function: He elaborated on the mock theta function, a concept in the field of modular forms of mathematics.
Ramanujan number: 1729 is known as the Ramanujan number which is the sum of the cubes of two numbers 10 and 9.
Circle Method: Ramanujan, along with GH Hardy, invented the circle method which gave the first approximations of the partition of numbers beyond 200. This method contributed significantly to solving the notorious complex problems of the 20th century, such as Waring's conjecture and other additional questions.
Theta Function: Theta function was studied by extensively Ramanujan who came up with the Ramanujan theta function, that generalizes the form of Jacobi theta functions and also captures general properties. Ramanujan theta function is used to determine the critical dimensions in Bosonic string theory, superstring theory, and M-theory.
Contribution of Brahmagupta in Mathematics
What are the 6 Contributions of Brahmagupta in the field of Mathematics
Brahmagupta was one of the famous Indian mathematicians and astronomers. He was the first mathematician who described Zero and Negative Numbers.
Contribution of Brahmagupta in Mathematics
1. Brahmagupta wrote many mathematical and astronomical textbooks while he was in Ujjain, including Durkeamynarda, Khandakhadyaka, Brahmasphutasiddhanta, and Cadamakela.
2. His significant contributions to astronomy are calculating the lunar and solar eclipses and predicting the position and motion of the planets. He calculated the length of the solar year down to the second as 365 days, 5 minutes, and 19 seconds.
3. Brahmagupta's most remarkable finding in geometry is his formula for cyclic quadrilaterals which is also known as Brahmagupta's formula. The cyclic quadrilateral refers to any four-sided figure whose corners touch the inside of a circle.
4. Brahmagupta introduced zero as a number in its own right. Brahmasphutasiddhanta is the earliest known text that established rules for mathematical manipulation that applies to zero.
5. Brahmagupta also introduced the concept of negative numbers. He established the basic mathematical rules for dealing with negative numbers in equations.
6. He also explained the ‘geometrical’ theories, similar to the ‘Pythagorean Theorem’. He also introduced the principles and rules of trigonometry and brought a guide to knowing the area of a triangle.
Different between Inductive and deductive method:
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How to make Mathematics Joyful?
ways in which teachers can make math interesting for students,
1. Create an effective environment that is open for discussion
Teachers should start by laying down the agenda
of the class and must keep an open platform
wherein each and every student must be
encouraged to raise questions.
Teachers should understand that students
will take time in understanding the concepts
of mathematics. Therefore, provide them
with due feedback, practice assignments,
doubt clearing sessions, and revision papers.
Explain to them the purpose behind learning
a particular topic.
2. Introduce the topics using multiple examples
Mathematics is a subject which could actually be
visualized and compared to practical life. Therefore,
teachers can come up with creative ways like images
or videos to teach maths in an interesting way to students.
They can illustrate the problem sets by making a child
visualize the practical side of
what is mentioned in the problem.
3. Encourage students for reasoning when solving
problems
In order to determine that every student has actually
learned the objective of a class,
it is necessary that every student communicate both
orally and in writing with the
proper reason.
Reasoning gives a proper idea about the understanding
of the student about the
concept. This will promote their engagement and learning.
4. Finish the class by giving a summary and homework
As stressed upon before, mathematics is the subject where
you require constant
practice. Therefore, we encourage every teacher to provide
students with some
practice assignments for their home.
Make sure that these assignments are not very tough and
help the student to
understand the concept in a better way. These assignments
are given in order to
boost the morale of the students and make them get a
relevant hold of the subject.
5. Raise the difficulty level slowly
Before starting to teach any particular topic in mathematics,
it is very important to
segregate the problem sets based on that level of difficulty.
Start with a few easier
problems.
Teachers must keep raising the bar for all the students
slowly and steadily.
6. Observe, modify, and re-evaluate
Many teachers become very rigid in the pace of completing
a particular topic.
They often forget to evaluate the homework given by them.
Well, we say this is not
a problem.
But a teacher must walk through the classroom and observe
the dynamics of the
students. The teacher must talk to every student individually
and ask them questions.
This will give them a fair idea about how much a student is
understanding.
7. Encourage maths talk and games
This will help the students to develop their mental abilities
and skills. This will also
give them a whole new learning and thinking process. They
will be able to describe
and solve a problem in their own certain way.
8. Using modern technology: modern technology can broaden
perspectives and give students new ways to engage with the world around them.
Tablets and smartphones give students new ways to engage with math on their own
terms.
Activity for make maths joyful
WHAT IS MATHEMATIZATION?
the mathematization of a problem or area of study consists of applying mathematical ideas
to that problem or field so as to think more precisely or clearly about things.
Inductive Method: Induction is the form of
reasoning in which a general law or principle
is denived from a study of particular objects
or specific processes. Induction is based on
the logic that if something is true for a
particular case and is further true tor a
reasonable adequate number of cases,
then it is true for all such cases. Students
observe the relatiotnship among such cases,
which lead them to guess a common pattern.
Thus a formula or the generaliSation is arrived
at through a process of nductive reasoning.
Let us study some examples: Example1:
* .... where I, 3, 5, and.... are odd numbers
and so also (a) =1,3=9,5 = 25,7 = 49, their
respective squared numbers 1, 9, 25, 49,
(b) 24,4= 16,6= 36, 8 = 64.. where 2, 4, 6, 8, .
are even number and so also their respective
squared numbers 4, 16, 36, 64, .. From
(a) we vet, 'square of an odd number is Odd.
And trom (b) we get, number 'square of
an even number is even
Deductive method: Here the learner proceeds
from general to particular, abstract to concrete and
formula to examples. A preconstructed formula or
principles be told to students and they are asked
to solve the different relevant problems with the
help of the earlier formula. So in this method first
vou give the relevant formula, principles and ideas
to students and explain further its application o the
formula to problems. The students in your class
come to understand how the formula can be use or applied.
Deductive approach of teaching follows
the steps given below
for effective teaching
clear recognition of the problem.
(i)for effective teaching clear recognition of the problem.
(ii) Search for a tentative hypothesis.
(iii) Formulating of a tentative hypothesis/
Choosing the relevant formula for solution.
(iv) Solving the problem.
(v) Verification of the result
Project Method:
There are number of students in your
classroom who are good in solving
mathematics the problems from the
textbook. You will find most of them
are unable to solve the real life the
problems where solution remains similar.
Take an example, students are familiar
to solve the problems on and loss from
the profit text book, but they fail to apply
the same is the knowledge during
marketing. The reason way of teaching
mathematics in the classroom. Students
are made to spend many hours of the
day in learning and repeating subjects
from textbooks without understanding
their value in daily In life reality, learning
mathematics prepares a child for life by
making him live in reality and provide
him opportunities where he/she can
exercise his/her ability of thinking and
skills of doing. Therefor, learning through
project is an important aspect for getting
real experiences.
Advantages of the Inductive Method
- The learners are more engaged in the teaching-learning process. With our facilitating skills, the learners formulate the generalization or rule.
- Learning becomes more interesting at the outset because we begin with the experiences of our students. We begin with what they know.
- It helps the development of our learners’ higher-order thinking skills (TS). To see patterns and analyze the same in order to arrive at realizations requires analytical thinking.
Disadvantages of the Inductive Method
- It requires more time and so less subject matter will be covered. We need much time to lead our students to the formulation of generalizations.
- It demands expert facilitating skills on the part of the teacher. We’ve got to ask the right questions, organized answers and comments to pave the way to the derivation of generalizations or principles.
Mathematics as the Science
of Logical Reasoning
Reasoning is based on previous
established facts. To establish
a new fact or truth one has to
put it on test of reasoning.
From our observation of physical
and social environment we form
certain intuitive ideas or notions
called postulates and axioms.
These postulates and axioms
are self-evident truths and need
no further proof or explanation.
Thus, postulates and axioms are
assumed to be true without
reasoning. But this does not
mean that here we ignore the
process of reasoning. Actually
self-evident truths are beyond
reasoning. That is why we can not
assume any evidence to be true.
Only those evidences can be assumed
as true that could not be proved untrue
or irrational by existing logical
knowledge. Thus, postulates
and axioms are bases of
mathematics as-well-as of our
process of logical reasoning.
In mathematics we make several
propositions and while proving a
proposition we base our arguments
on previously proved proposition.
Thus, each proposition is supported
by another proposition that has
already been proved or established.
Consequently if we go back
one-by-one, we reach to a
propositions that is based
on postulates and axioms.
Thus, in mathematics we
always use the process of
logical reasoning. Therefore,
mathematics may be called as
the science of logical reasoning.
father of heuristic method?
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”. In this method, the
student has to find out the answer to his/her
own problem by unaided efforts.
Thus, the child becomes a discoverer of
knowledge by developing a spirit of inquiry.
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