bramagupta teaching

                                                        bramagupta teaching: 

Arithmetic

In Brahmasphutasiddhanta, Multiplication was named Gomutrika. He explained how to find the cube and cube-root of an integer and gave rules facilitating the computation of squares and square roots.

He also gave rules for dealing with five types of combinations of fractions –  a/c + b/c; a/c × b/d; a/1 + b/d; a/c + b/d × a/c = a(d + b)/cd; and a/c − b/d × a/c = a(d − b)/cd .

He gave the sum of the squares of the first n natural numbers as n(n + 1)(2n + 1)⁄ 6 and the sum of the cubes of the first n natural numbers as (n(n + 1)⁄2)².

Zero

The most notable innovations that Brahmagupta is remembered for is his look and pursuit of the number zero. Until this time, the zero had not been thought of as a number. He formulated equations that allowed zero to be used in positives and negatives. Although he did not use those specific words, Brahmagupta did follow with the importance in the need of the zero placement. Without the use of zero and its value defined, according to him, arithmetic really had nowhere to go.

Brahmagupta describes operations on negative numbers. He first describes addition and subtraction,

The sum of two positives is positives, and sum of two negatives negative; of a positive and a negative [the sum] is their difference; if they are equal it is zero. The sum of a negative and zero is negative, [that] of a positive and zero positive, [and that] of two zeros zero.

A negative minus zero is negative, a positive [minus zero] positive; zero [minus zero] is zero. When a positive is to be subtracted from a negative or a negative from a positive, then it is to be added.

Brahmagupta’s Look at Zero listed:

• Zero minus zero is a zero.
• The product of zero multiplied by zero is zero.
• A debt minus zero is a debt.
• A fortune minus zero is a fortune.
• A debt subtracted from zero is a fortune.
• fortune subtracted from zero is a debt.
• The product of zero multiplied by a debt or fortune is zero.

Brahmagupta states that 0/0 = 0 and as for the question of a/0 where a ≠ 0 he did not commit himself. His rules for arithmetic on negative numbers and zero are quite close to the modern understanding, except that in modern mathematics division by zero is left undefined.

2019 calculation

multiplication facts

Dice Games to Teach Multiplication Facts

dice image by Olga Shelego from Fotolia.com

Capturing and holding the attention of students can be challenging in any content area, and math is definitely one of those areas. By using games in math, the interest of the student will be held, and while the student is playing the game, he is learning. Using dice to teach multiplication facts provides an excellent opportunity for the students to learn multiplication through a game. Once the game is learned at school, the students can play the game at home with siblings or parents and the only items needed are inexpensive dice.

Single Digit Multiplication

Students roll one die to see who goes first. The student who rolls the highest number goes first. The student rolls two dice and multiplies the numbers. That student writes down the problem and the answer. The partner checks the problem. If the answer is correct, the student who rolled the dice receives a tally mark. The students then switch roles. The first student to the predetermined amount of tally marks is the winner.

Double Digit Multiplication

Students role two dice to see who goes first. The numbers on the dice are multiplied and the highest answer goes first. Counters are used to determine the winner. Counters can be pennies, beans or other small objects. To add more excitement, use small pieces of candy as counters. The first student roles three dice one at a time. The first two dice are the "to" number for the multiplication problem. For example, if a three and a two are rolled, the number will be 32. The third dice is rolled to provide the single digit number to multiply the double digit number by. The student solves the problem on paper and another student checks her work. If the student is correct, a counter is given to that student. If the student is not correct, a counter is given to the other student. The student with the most counters after a preset time or number of problems is the winner.

maths in nature

                                            maths in nature:
The concept of ‘Math in Nature’ is as innate as a person taking their first breath. Most would agree that our conception of math in its basic form has been derived as a means to describe aspects of our environment as an element of a much larger sociological agreement. So to say that “math exists in nature” is as redundant a statement as saying that humans themselves exist in nature. However in researching this topic one can not help but marvel at how well ‘mathematics’ corresponds with the grand scheme of things and ultimately makes one wonder what came first; an issue of the chicken or the egg as it were. 
Whatever the case, we can rationalize that math in nature is factual in its tangibility. It is this outstanding quality that makes the use of math in nature a tremendous resource for the classroom. Too often we force mathematical concepts on the basis of blind faith, while examples such as these are quite literally all around us. Demonstrating math in nature is an ideal approach for illustrating what many students will regard as arbitrary information and should be utilized by all teachers as a tool to increase learner interest

mathematical symbols