Dividing gives us the idea of dividing or distributing equally. That is why when we want to start teaching a child to divide, we need to relate it to concrete things. For example, if mom makes a pizza and she wants to cut it into equal parts, she will first cut it in half and thus have two equal parts (this is dividing by two), then if each half is cut into two equal parts, there will be 4 portions, that is to say that the pizza was divided into 4 and if you repeat the operation the pizza will be divided into 8, this is dividing by 8. You can also say if the pizza is cut into 10 slices how many each child will get if there are 5.
The child understands mathematical concepts through concrete things. That is why he always starts by distributing sweets in equal amounts, placing the same number of objects in boxes, etc.
When they are of an appropriate age to do a mathematical calculation you no longer need to do it with concrete things. But no child learns to divide before knowing how to add, subtract and multiply, mathematical operations accompany the development of the child and his maturity.
When the time comes to learn the division algorithm, the child must understand that they must think about how many times the number 2 fits in 18, that can represent if I have 8 candies, how many does each one get if I have to distribute them between two children in equal parts. In other words, it relates the problem posed to the operation and to solve the mathematical operation you must know the algorithm, that is, the steps to follow in solving the division. At Doncomos.com we will indicate the steps you need to know how to teach division.
Integer division may be exact, if the remainder is zero, the remainder may not be zero. They are the divisions that are taught first because they are those that do not use decimal numbers, we leave this for later.
What do you need to teach division?
- Pencil and paper
- Multiplication tables
Instructions to teach division
- To teach a child to divide, he must first know that the number we are going to divide (dividend) must be equal to or greater than the number we are going to divide by (divisor). I cannot distribute 5 sweets among 7 children because there will be 2 who will not receive anything. So that no child runs out of sweets, I must have at least 7. That is why in the integer division the dividend must be equal to or greater than the divisor.
- A first type of exercise is to apply the opposite procedure to multiplication since they are inverse operations, it consists of working with the multiplication tables, logically they will be exact divisions. When we multiply two numbers (called factors) we obtain a result called product, if we divide that number called product by one of the factors we will obtain the other factor as a result.
- For example in the table of 2:
- 2 x 2 = 4 so 4:2 = 2
- 2 x 3 = 6 so 6 : 2 = 3 or 6 : 3 = 2
- 2 x 4 = 8 so 8 : 2 = 4 or 8 : 4 = 2
- This helps us to memorize and consolidate the tables and start dividing by memorizing as well. For example in the table of 3: 3 x 7 = 21 then 21: 3 =7 and 21: 7 = 3
- Another way to divide is with the division algorithm for which we must learn the names of each part of the division:
- Dividend: number that we want to divide and must be greater than or equal to the divisor.
- Divisor: number by which we are going to divide the dividend and must be equal to or less than the dividend.
- Quotient: is the result of integer division.
- Remainder: is what is left or left over without being able to divide because it is a number less than the divisor. If the remainder is zero the division is
- For example: 24 : 3= 8 remainder 0 (exact integer division) but 25 : 3 = 8 remainder 1 (non-exact division)
- Another way of writing these divisions is as follows:
- We will see the process to divide by a number, which are the least complex divisions for when you start this learning. We will divide 724 into 4 as we follow the images. First we ask if it is possible to divide the first digit of the dividend (7) by the divisor (4). As it is, we do it and we put the result in the place of the quotient (1), to obtain this result we ask how much is 7 divided by 4? or how many times does the 4 fit into the 7? The result is 1.
What would happen if it does not reach the first figure? We just take two figures and do the same thing. Then we multiply that number by the divisor (1 x 4 = 4), put it under the 7, and subtract (7- 4=3). We are checking that this remainder is less than the divisor. So is. Then we lower the next figure, 2, the number 32 is formed and we start again: 32 : 4 = 8, we place the 8 in the quotient that with the 1 that we already had forms 18. We multiply 4 x 8 = 32 and we put it under the other 32, when subtracting it gives zero. We lower the last figure that is a 4 and repeat the process: 4 : 4 = 1, when we multiply and subtract we see that the remainder is zero. This means that the division is exact. - If we divide 727 by 4 we will see that the quotient is the same but the remainder is different, this division is not exact because the remainder is 3.
- We can always verify if we have worked well: if we multiply the result obtained by the divisor and to this result we add the rest we will obtain the dividend, for example in the last division: 181 x 4 + 3 =724 + 3= 727
Tips for Teaching Dividing
- To divide well, you have to know how to multiply well, that is, the multiplication tables must be incorporated and secured, otherwise division will be difficult to learn.
- Practice many divisions, it is the best way to learn and affirm knowledge or a procedure.
- Find a lot of useful information on your math problems in our category dedicated to them.