The ability to count in the mind is one of the basic skills to be developed in a child’s primary school mathematics learning process. The child must learn to name the result of any mathematical action quickly and correctly.
Math 1st grade. Main methods.
Methods of teaching the account
In children, visual thinking prevails. The problem is that most mathematical concepts are abstract and poorly understood or memorized by younger schoolchildren. Therefore, any mathematical operations should be based on practical actions with subjects.
Teachers use three main ways to teach a child to count in their mind:
based on knowing the composition of numbers;
by memorising the tables of mathematical actions by heart;
using special techniques to perform mathematical actions.
Let’s look at each of them.
Preparing to learn oral counting
Preparing for oral counting should begin with the first steps in math. Familiarizing the child with the numbers, be sure to teach him that each number indicates a group with a certain number of subjects. It is not enough to calculate, for example, up to three and show your child the number 3. Be sure to offer him to show three fingers, put three candies in front of you or draw three circles. If possible, connect the number to the child known fairytale characters or other concepts:
3 – three pigs;
4 – turtles – ninja;
5 – fingers on your hand;
6 – heroes of the fairy tale Repka;
7 – dwarves, etc.
The child should have clear images attached to each number. At this stage, it is very useful to play math dominoes with children. Gradually, they will have pictures with dots in their memory, which relate to the corresponding numbers.
You can also practice the study of numbers with a box of dice. Such a box should be divided into 10 cells, which are arranged in two rows. After learning each number, the child will fill in the required number of cells and memorize the corresponding combinations. The benefit of these games with dice is that the child will subconsciously notice and remember how many more dice to add to the number to 10. This is a very important skill for oral counting! Additional math 1st grade games.
As an option, you can use the details of the Lego constructor for such an exercise or apply the principle of pyramids from the Zaitsev method. The main result of all the described ways to get acquainted with numbers should be their recognizability. It is necessary to achieve, that the child at a glance at a combination of subjects at once (without recalculation) could name their quantity and corresponding number.
Oral account based on the composition of the number
Based on knowledge of the composition of the number, the child can perform addition and subtraction. For example, to say how many “five plus two” would be, he must remember that five and two are seven. And “nine minus three” is six, because nine is three and six.
However, it’s not as easy as it seems to us adults. A child needs to remember more than forty combinations! At school, every two to three lessons, a new number is studied and children learn about its composition. Under such conditions, the strength of knowledge is not sufficient for free operation. To help the child to learn this material better, it is recommended to offer them such tasks:
arrange the specified number of subjects on two plates, creating different combinations (variations of such a task can be different: hang toys on two Christmas trees, arrange flowers in two vases, settle dwarves in two houses, etc.);
add the number to the right one;
paint over the cells on which the composition of the specified number is written;
finish drawing the dominoes.
The more often the child will perform such exercises, the faster and stronger it will remember the composition of numbers. Ideally, this knowledge should be brought to automaticity. They are simply necessary to master the principles of addition and subtraction with a transition through the ten.
In the future, to solve examples of type 9 + 6, you need to teach the child to consistently perform several logical operations:
to supplement the first summation to 10 (based on knowledge of the composition of the number 10 is 9 and 1);
to calculate, how many more it is necessary to add (on the basis of knowledge of structure of number 6 – 1 have already added, there is 5);
calculate the result.
The same method (bringing it to 10) will be used by the child to subtract. The course of his thoughts is approximately the following:
to subtract 8 out of 14, you must first take 4 to get 10;
to remember the composition of number 8 is 4 and 4;
to subtract 4 from 10, based on the composition of 10 is 4 and 6.
Having mastered these methods, the child will later use them in solving examples with numbers within 100 and 1000. This addition and subtraction is based on the ability to determine the digit composition of a number and to perform actions in turn with each digit.
Learning to count orally by memorizing tables
At school, the main way to learn to count quickly in the mind is to memorize tables. And it is implied that the child should do it independently under the control of parents. Usually at the lesson, the teacher only introduces children to the principle of constructing a table and does only a few training exercises with children on its application.
There are many ways to memorize the tables. Almost half of the examples in the tables for addition and multiplication are automatically memorized by the children after they get acquainted with the shifting law.
You can also use poems and sings. The most famous example for such a case – the lines of the song “Twice two four, it’s known to everyone in the whole world. Good material can be found by reading the methodology of Nikolai Zaitsev or the program “Songknowledge”.
Another interesting method of familiarizing with the tables is the application of eidetics techniques. On their basis you can invent fairy tales or pictures using images – numbers. More on math 1st grade.
In order to consolidate the knowledge of the tables, children can be offered:
computer mathematical games – simulators;
Without knowledge of the relevant tables, the child is unlikely to learn to divide the numbers in his or her mind. Constant exercises in the use of tables significantly improve the speed of obtaining results in performing calculations in the mind.
Using computational techniques in oral counting
The highest level of oral counting skills is the ability to find the fastest and most convenient way to calculate the result. Such techniques should begin to explain to children as soon as they are familiar with the addition and subtraction actions.
For example, one of the first ways to teach a child to count in the mind in the 1st grade is the method of counting and “jumping”. Children quickly realize that adding 1 results in a subsequent number, and subtracting 1 results in a previous number. Then you should offer to meet the best girlfriend of number 2 – a frog that can jump over a number and immediately call the result of adding or subtracting 2.
Similarly, there is an explanation of how to perform these mathematical actions with number 3. This will help the example of a bunny that can jump far away – just two numbers.
Also, children need to demonstrate techniques:
permutations of combinations (for example, to count 3 + 68, it is easier to change numbers and add);
counting in parts (28 + 16 = 28 + 2 + 14);
reduction to a round number (74 – 15 = 74 – 4 – 10 – 1).
The counting process facilitates the ability to apply combination and distribution laws. For example, 11 + 53 + 39 = (11 + 39) + 53. Children should be able to see the easiest way to count.
How to learn to count quickly in an adult’s mind.
An adult person can use more sophisticated algorithms for oral counting. The most convenient way to quickly count numbers in your mind is to round up the numbers and then add them. For example, the example 456 + 297 can be counted as follows:
456 + 300 = 756
756 – 3 = 753
Subtracting is done in the same way.
To perform multiplication and division, special rules of action with separate numbers have been developed. For example, such rules:
to multiply a number by 5, it is easier to multiply it by 10, and then divide it in half;
multiplying by 6 includes doing the previous steps and then adding to the result of the first multiplier;
to multiply a two-digit number by 11, the first number must be written in place of hundreds, and the second number must be written in place of units. In place of dozens, the sum of these two digits is written down;
divided by 5 can be multiplied by 2 and then divided by 10.
There are rules for calculating actions with decimal fractions, calculating interest, erecting a degree.
You can learn these tricks at school or you can find the material on the Internet, but to learn from them to count quickly in your mind, you have to practice and practice again! During the training, many results will be remembered by heart and the child will call them automatically. He or she will also learn how to operate with large numbers, putting them into more simple and convenient combinations.