In the past century, teaching methods for such professions as an economist, salesman, merchandiser, and teacher of primary school arithmetic are erased from the memory of society, like remnants of the Soviet past. But they had a lot of useful things. In particular, such exercises, which intensified brain activity, developed logical thinking, using both hemispheres of the brain in order to find optimal solutions to mathematical problems and be able to count in mind quickly.
Oral counting techniques and exercises for adults
The range of tasks and problems of an adult person is much broader than that of a child. In a number of professions and in everyday life, people daily have to deal with mathematical tasks a hundred times a day:
- How much profit it will bring me.
- Do not cheat me in the store.
- Did not the dealers overestimate the margin on the purchased goods.
- It is cheaper to take a loan with a monthly interest payment or once every three months.
- What is better - hourly payment of 150 rubles or a monthly salary of 18,000 rubles.
The list can be continued, but the fact of the need for oral account skills is undeniable.
Preparatory stage - awareness of the need for oral accounts
Mental mathematics and any other technique designed to teach how to count at home in the mind more quickly and efficiently, teaches adults and children.
Their only difference is the sphere of application of knowledge. The developers of MM courses are trying to pick up puzzles for adults in such a way that they are in demand in their work.
You have in your hands a futures contract with a date of execution on January 1, 2019 and you set out to figure out on which day of the week this event will occur (all of a sudden Friday). All operations are carried out with the last two digits of the year, in our case, it is 19. First you need to add to the 19th quarter, this can be done by simple division: 19: 2 = 8.5, then 8.5: 2 = 4.25. Decimal numbers discarded. We add: 19 + 4 = 23. The day of the week is determined simply: it is necessary to take away the product closest to it from figure 7. In our case, it is 7 * 3 = 21. Therefore, 23 - 21 = 2. Futures expiration date is second day or tuesday.
It is easy to check, looking at the calendar, but if it is not at hand, this technique may be useful, and lift you in the eyes of others.
Methods of fast addition, subtraction, multiplication and division of different numbers
Examples with varying degrees of complexity require different amounts of time, although with constant practice the number of efforts is reduced.
Addition and subtraction in mental mathematics tend to be simplified. Complex and global tasks are divided into smaller and simpler ones. Large numbers are rounded.
☞ Example of addition:
17 996 + 2676 + 3592 = 18 000 + 3600 + 2680 - 4 - 8 - 4 = 21600 + 2000 + 600 + 80 - 10 - 6 = 23600 + 600 + 70 - 6 = 24200 + 70 - 6 = 24270 - 6 = 24264.
At first, it will be difficult to keep such a long chain in your head and you have to mentally pronounce all the numbers in order not to get lost, but as the short-term memory improves, the process will become easier and more understandable.
☞ Example of subtraction:
For subtraction, the process is identical. First we subtract the rounded number, and then add the excess. A simple example: 7635 - 5493 = 7635 - 5500 + 7 = 2135 + 7 = 2142
For multiplication and division there are their own little tricks, including those previously mentioned in the example with dates. In practice, the most common examples with percentages or proportions. The essence of their solution also comes down to fragmentation and simplification of the task. Some can be solved with just one click.
☞ Example of multiplication and division:
You put on deposit 36 000 at. e. at 11% and you need to calculate how much profit it will bring. The secret of calculation is simple - the first and last digit will remain the same, and the middle will be the sum of two extreme numbers. So 36 * 11 = 3 (3 + 6) 6 = 396 or in our case 396/100% = 3 960 y. e.
In most mental methods of multiplication and division, a mandatory and uncontested condition is knowledge of the multiplication table up to ten. For primary school children, the oral account training program will be different.
Children's oral exercise tips
Children have tasks of a different order. In addition to tedious memorization, they are also forced to multiply and divide apples and tomatoes, and if you ask why this is done - the teacher will say “right” at best, and the child will lose interest in the whole process.
It is impossible to change the educational system in a month, but to help a child develop oral account skills is quite real.
Explain to the child in an accessible language, why counting in the mind is not only useful, but also interesting. If you decide to work with him on your own, pick up illustrated materials from various sources and make a schedule of joint activities. Not necessarily engage daily and many hours. This will not benefit. It is enough to devote twenty minutes to this three times a week, but at the same time that the child is used to it.
Examples of exercises for children
Start with interesting tasks to "get involved in the game." Show how you can quickly get an answer to a difficult example and outrun all classmates. Develop leadership qualities.
We use the multiplication rule of two-digit numbers with the same first digits and the last, giving a total of "10", to solve the example of "44 * 46". The first digit is multiplied by the one that follows it in order. We also multiply the last digits: 44 * 46 = (4 * 5 = 20; 4 * 6 = 24) = 2024.
In school, such examples are solved in the old manner, in a column. It takes a lot of time just to rewrite everything. Knowing the multiplication table for 4, this example can be solved in the mind in a couple of seconds.
What is taught in school and can you believe everything
The classical school as a whole is skeptical of accelerated counting techniques, citing as an example children who, trained in methods of mental mathematics, then do not seek to think logically in other subjects, they want to do everything quickly, as they are used to, and not qualitatively.
But this is due more to the inertia of the educational program than to the real state of affairs.
Mental mathematics helps to activate thinking processes, but does not call for throwing out notebooks, not to count them in a column, and books, not to read. The methods of oral counting are well absorbed by the child in parallel with the methods of writing, which are more often used in primary school arithmetic. He sees several solutions to problems and feels more confident than his classmates.
Unfortunately, when checking a test for a teacher, it is more important to see the correct “as in a textbook” course of the decision, and not the child’s real knowledge, but here mental mathematics is already powerless.