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How to Teach Division to Grade 1

Division:

The Division is one among the arithmetic operation which is being performed. Division is defined as repeated subtraction of a number. Division as an equal distribution of terms or  number.

Symbol for Division:

Division is making required number of equal parts out of the given object. The symbol of division is given as :
Division : Example:10÷2
Long division : used  when computing a long division problem.
Fraction bar : $\frac{36}{6}$ dividend 36 is named as numerator and the divisor 6 is denominator of the given fraction.

Example: 10÷2 ,8) 64

          Dividend
Divisor  4)20(5   Quotient
              20
             ▬▬
              00  Remainder
             ▬▬
Dividend: is the number which is to be divided
Divisor: the number by which we divide.
Quotient: The result which is obtained by dividing.
Remainder: what remains after the division

Stages of Division:

Example: 8÷2
     
Step 1: Recall the table of 2 till u reach the number 8.
            2x1 = 2
            2x2= 4
            2x3 = 6
            2x4 = 8

Step 2: Write the multiplicative in division form as shown below

Step 3: Write the product of 2 and 4 below 8.

Step 4: Subtract the product from given number 8.



Step 5:  8 ÷ 2 = 4

Division of two digit Number:

Division of two digit number can be carried out using single digit or two digit number.

Example
 18 ÷ 2

Step 1: Recall the table of 2 till u reach the number 18.
             2x1 = 2
             2x2= 4
             2x3 = 6
             2x4 = 8
             2x5 = 10
             2x6 = 12
             2x7 = 14
             2x8 = 16
             2x9 = 18

Step 2: Write the multiplicative in division form as shown below

Step 3: Multiply the quotient with divisor

Step 4: Subtract the product from given number 18.



Step 5: 18÷2 = 9

Verification:
Add the remainder to the product obtained  18 + 00 = 18, the result obtained is same with dividend which shows the process of division is correct.

Zero as Dividend and Divisor:

Zero divided by a number equals zero.
Example: 0÷6 = 0
zero divided by a number equals to zero can be represented by multiplication. The expression 0÷6 shows 0x6 which is equal to 0, it is true that 0÷6 = 0

Zero as Divisor is impossible ,dividing a number by zero is indefinable. Multiplication shows that a number divided by zero is impossible.
Example:  6÷0
The expression  6÷0 is related with multiplication  __x0 = 0 any number times 0 equals 0,the division 0÷0 has no unique solution and is also not possible.

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From Wikipedia

Long division

In arithmetic, long division is a standard procedure suitable for dividing simple or complex multidigit numbers. It breaks down a division problem into a series of easier steps. As in all division problems, one number, called the dividend, is divided by another, called the divisor, producing a result called the quotient. It enables computations involving arbitrarily large numbers to be performed by following a series of simple steps.

Education

Today, inexpensive calculators and computers have become the most common way to solve division problems, decreasing the traditional educational imperative to know how to do so by paper and pencil techniques. (Internally, those devices use one of a variety of division algorithms). In the United States, long division has been especially targeted for de-emphasis, or even elimination from the school curriculum, by reform mathematics, though traditionally introduced in the 4th or 5th grades. Some curricula such as Everyday Mathematics teach non-standard methods, or in the case of TERC argue that long division notation is itself no longer in mathematics. However many in the mathematics community have argued that standard arithmetic methods such as long division should continue to be taught .

An abbreviated form of long division is called short division.

Notation in the UK, Canada, the U.S. Japan and China

Long division does not use the slash (/) or obelus (÷) signs, instead displaying the dividend, divisor, and (once it is found) quotient in a tableau. An example is shown below, representing the division of 500 by 4 (with a result of 125). 125 (Explanations) 4)500 4 (4 × 1 = 4) 10 (5 - 4 = 1) 8 (4 × 2 = 8) 20 (10 - 8 = 2) 20 (4 × 5 = 20) 0 (20 - 20 = 0)

The process is begun by dividing the left-most digit of the dividend by the divisor. The quotient (rounded down to an integer) becomes the first digit of the result, and the remainder is calculated (this step is notated as a subtraction). This remainder carries forward when the process is repeated on the following digit of the dividend (notated as 'bringing down' the next digit to the remainder). When all digits have been processed and no remainder is left, the process is complete.

Here is an example of the process not producing an integer result:

31.75 4)127 12 (12-12=0 which is written on the following line) 07 (the seven is brought down from the dividend 127) 4 3.0 (3 is the remainder which is divided by 4 to give 0.75) 2.8 (7 × 4 = 28) 20 (an additional zero is brought down) 20 (5 × 4 = 20) 0

In this example, the decimal part of the result is calculated by continuing the process beyond the units digit, 'bringing down' zeros as being the decimal part of the dividend.

This example also illustrates that, at the beginning of the process, a step that produces a zero can be omitted. Since the first digit 1 is less than the divisor 4, the first step is instead performed on the first two digits 12. Similarly, if the divisor were 13, one would perform the first step on 127 rather than 12 or 1.

Notation in non-English-speaking parts of the world

The same general principles are used in other parts of the world, but the numbers are often arranged differently.

Latin America

In Latin America (except Mexico and Brazil), the calculation is almost exactly the same, but is written down differently as shown below with the same two examples used above. Usually the quotient is written under a bar drawn under the divisor. A long vertical line is sometimes drawn to the right of the calculations.

500 ÷ 4 = 125 (Explanations) 4 (4 × 1 = 4) 10 (5 - 4 = 1) 8 (4 × 2 = 8) 20 (10 - 8 = 2) 20 (4 × 5 = 20) 0 (20 - 20 = 0)

and

127 ÷ 4 = 31.75 12 (12-12=0 which is written on the following line) 07 (the seven is brought down from the dividend 127) 4 3.0 (3 is the remainder which is divided by 4 to give 0.75) 2 8 (7 × 4 = 28) 20 (an additional zero is brought down) 20 (5 × 4 = 20) 0 In Mexico, the US notation is used, except that only the result of the subtraction is annotated and the calculation is done mentally, as shown below:

125 (Explanations) 4)500 10 (5 - 4 = 1) 20 (10 - 8 = 2) 0 (20 - 20 = 0)

In Brazil, the European notation (see below) is used, except that the quotient is not separated by a vertical line, as shown below:

127|4 -12 31,75 07 - 4 30 -28 20 -20 0

Same procedure applies in Spain. As in Mexico, only the result of the subtraction is annotated and the calculation is done mentally.

Europe

In Russia and in French-speaking countries (Europe and Africa), the divisor is to the right of the dividend, and separated by a vertical bar. The division also occurs in the column, but the quotient (result) is written below the divider, and separated by the horizontal line.

127|4−12 |31,75 07 − 4 30 −28 20 −20 0

Often, teachers require the vertical bar to be extended so that none of the work flows underneath the quotient, as in the example below of 6359 divided by 17, which is 374 with a remainder of 1.

Unlike the English notation, decimal numbers are not divided directly. Instead the dividend and divisor are multiplied by a power of ten so that the division involves two whole numbers. Therefore, if one were dividing 12,7 by 0,4 (commas being used instead of decimal points), the dividend and divisor would first be changed to 127 and 4, and th


From Yahoo Answers

Question:Hey! I need a little help. See my school has an activity where high school students and higher grade levels would take-over the teachers of the 1st - 3rd graders. Im assigned to math with the 1st and 2nd graders? Any activities on how to introduce 1st graders with multiplication and 2nd graders with division (long)? My initial plan was to introduced them with a story (related with their lesson) , then discuss, then a group activity. In the activity, the students form groups, them I give each group a puzzle, once a group is done, I give them an activity sheet to answer, the first group who gets all the correct answers wins. Yeah, thats probably it. Any suggestions? and for the Intro-story thing, any goo ideas or examples? no I"M SERIOUS!! these were my lessons too when I was in their level.. I"M SEIOUS!!!!!!!!!!!!!!! and yeah i was told them to teach them these things...

Answers:Wow. What state are you in? I'm in California and that definitely does not align with the state standards at all. I taught second grade last year we introduced multiplication with them (but not until the last quarter of the school year). I'm teaching first grade right now and we are working on addition. What ever you do, make sure you keep things very concrete. Most students the age you are working with are not ready for much abstract thought. See if you can use manipulatives to help students understand what you are trying to accomplish.

Question:I am currently enrolled in introduction to education. I really am enjoying the class. I want to teach 1st grade. What would i expect when i go for the observation in the class room?

Answers:well im from texas and honestly the teaching system down here is getting outright rediculous! If you came into a Texas first grade room you would see calm organized rooms with a calander on a wall and posters with expectations of the kids like 'active listening' and other stuff. There would be lots of sit down and do your work sheet or instruction to something new. maybe even a few timed quizes and stuff. lots of reading and do it yourself work. Dont get me wrong this is all great b/c the kids are excelling in many areas..but you'll always have those "problem kids" who have things like ADD and cant sit still for that long and we as a school system seem to be going back to punishing them for not being able to concentrate. There probably wont be any centers or homeliving. a few puzzles if your lucky. a spelling bee would be to the extent of "fun" they get in the class room. No glue or scissors or fun art projects; that is limited to 20 min a week in a class with 50 other children and one teacher. And yet Im in the same position you are...going to 2 hrs a week of observations in local public schools so i can get a degree and be told by politicians and psychologists how to do the thing that I love to do the most in this whole world. Pay Raise anyone?? lol

Question:Either I'm having a really off day or the teacher is. Here are a couple math problems my daughter brought home. All the problems in the section were similar to these and all were marked wrong. The exact instructions were "Complete". And no, they don't have math books, all they get are work sheets from the teachers work book. Great system, huh? Anyway, I want to see if you adults come up with the same answers my daughter did or the teacher's. 12 divided by 4 = _ x 3 27 divided by 3 = _ x 3 That's what my daughter had! The way the problem is written up, it looks (at least to me) that the division problem and the multiplication problem should both equal out to the same number. Right? The teacher marked them wrong and putting that the answer to the first problem was '1' and the second problem was '3'. cathri69: hahaha, you're right! I really am off today. I think my biggest problem was the way the question is written up. It's pretty confusing to a child who has never done that sort of thing. Don't get me started on how they're teaching math. They started multiplication, two weeks later started algebra and now they are just beginning division. They didn't even do the memorization through the different sets of numbers. From day one they were multiplying 7s,, 9, 4, etc. on one sheet. It's been a struggle, even though we're using flash cards at home and working on the multiplication. Ugh!

Answers:Wow I wish all questions were this easy. Ok I see two different ways this could be worked however I'd say the latter is a grade 8/9 way of looking at it and not grade 3. First way 12 divided by 4 = 4 x 3 27 divided by 3 = 9 x 3 The other is: 12 divided by 4 = (3) So then it would be 1 x 3 27 divided by 3 = (9) So then it would be 3 x 3 **This is Algebra which isn't covered until grade 8/9 In this case you are solving for __ (or in algebra "x") Again the latter is not a grade 3 level question and if that is what the teacher believes the answer to be then perhaps you should suggest there should be more instruction or more age appropriate questions.

Question:We homeschool our 8 yr old - and he is in 3rd grade. He is learning multiplication and division. He knows his tables, but we are having a hard time with teaching him long division and complex mult. Any ideas, websites, etc would be helpful!

Answers:Make sure that he knows his tables (mutliplication and division) very, very well. He should know them instantaneously, without having to think about it; otherwise, he'll spend too much mental energy on figuring out the tables and is likely to not really get the more complicated ideas. Work on making sure that he really understands that multiplication and division are opposites of each other. Have him give you the other problems in a "fact family" when you give him a simple mutiplication or division problem. For example, if told that 4 x 6 = 24, he should be able to tell you that 6 x 4 = 24; 24 divided by 6 = 4; 24 divided by 4 = 6. Practicing this regularly for a while, will help him with some more complicated concepts. You can use objects to practice the basic concepts of division and mutiplication, such as taking 24 M & Ms and dividing them evenly amongst 4 imaginary people to act out 24 divided by 4. Make sure that he has really mastered the basic ideas. Eventually branch out to acting out problems with a remainder. Try to have him divide 13 blocks evenly amongst 4 stuffed animals, to get the idea that 13 divided by 4 = 3 with one extra block left over. Practice this sort of thing a lot with objects; then try doing it with objects and also writing out the division--so that he can see how the reality of dividing translates into writing out the math. Keep doing it with objects and writing out the math until he tells you that he doesn't need to bother with the objects any more. Some kids will master the notion sooner than others; go at his pace. (And meanwhile, continue working on reviewing the basic facts.) Don't be afraid to back off for a while and do some other topics in math for a while. Sometimes, a child isn't quite ready for the topic, or needs a break if he's felt frustrated or confused by it. Work on some fun math topics for a while (graphing, Roman numerals, etc.) to give him a break and then come back to it later. Try practicing basic facts in different ways. In addition to flash cards or copying them or reciting them, try watching the "Multiplication Rock" video. Or play "Multiplication War"--divide a deck of cards between 2 people (remove the face cards); each player places their pile of cards face down; turn over 2 cards each, at the same time; each player multiplies the 2 cards together; the person with the highest product takes all the cards that were turned over; if a player gives the wrong product, the other automatically wins the cards; the person who ends the game with the most cards wins. Or get a computer math game. Or use flashcards and give a small treat for every 5 (or 10) that he can get right instantaneously. Or use a board game and revise the rules to have moves determined by mutliplying the numbers on the dice together. (Or to practice larger facts, by specialty dice that have more than 6 sides and have numbers past 6 on them.) Hope this helps...

From Youtube

Third Grade Division :Step by step instructions on how to do a two digit division problem with remainder.

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