How to master the verbal score students and adults
Forming Educational Program / / December 19, 2019
In addition to excellent marks in mathematics, numeracy in mind gives many benefits throughout life. Practicing in the calculations without a calculator, you:
- Keep your mind sharp. For efficient operation of the intellect, like muscles, need regular training. Expense in the mind develops memory, logical thinking and concentration, increases the ability to learn, it helps to quickly navigate the situation and make the right decisions.
- Take care of their mental health. studies showCould mental math boost emotional health?That at oral account involving parts of the brain responsible for depression and anxiety. The more active the work area, the lower the risk of neurosis and melancholy black.
- Insured against punctures in everyday situations. The ability to quickly count change, tip size, number of calories or interest on the loan protects you from unexpected expenses, excess weight and scams.
Learn fast counting techniques can be at any age. It does not matter if at first you are a little "slow down." Daily practice basic arithmetic operations for 10-15 minutes, and after a couple of months will reach significant results.
How to learn to put in mind
We summarize the single digits
Begin training with the elementary level - adding single digits with transition through dozens. This technique learn in the first grade, but for some reason, often overlooked with age.
- Suppose you need to add 7 and 8.
- Count how many sevens is not enough to ten: 10 - 7 = 3.
- Spread eight amounting to three and the second part is 8 + 3 = 5.
- Add a second portion to ten 10 + 5 = 15.
The same technique of "relying on the top ten" are used in the summation of single digits to double-digit, three-digit, and so on. Hone simplest addition, until you learn to make one operation for a couple of seconds.
Sum up big numbers
The main principle - to break the terms of the ranks (thousands, hundreds, tens and units) and to add the same to each other, starting with the largest.
Let's say you add 1574 to 689.
- 1574 is decomposed into four classes: 1 000, 500, 70 and 4. 689 - to three: 600, 80 and 9.
- Now summarize: thousands of thousands (1 000 + 0 = 1 000), hundreds to hundreds (500 + 600 = 1 100), tens to tens (70 + 80 = 150), with units of a unit (4 + 9 = 13).
- Group the number as it is convenient, and we add the fact that we have: (1 000 + 1 100) + (150 + 13) = 2 100 + 163 = 2 263.
The main difficulty - to keep in mind all the intermediate results. Practicing in this account, you are at the same time train the memory.
How to learn to subtract in your mind
Subtract the single digits
Again we return to the first class and sharpen the skills subtract single digit with transition through dozens.
Suppose you want to subtract 8 from 35.
- Introduce 35 as the sum of 30 + 5.
- 8 can not be subtracted out of 5, 8 so decompose the sum of 5 + 3.
- Subtract 5 of 35 and 30 obtain. Then, subtract 30 from the remaining three 30 - 3 = 27.
We subtract big numbers
Unlike the constitution, by subtracting multi-digit numbers at the level you need to break only what you take away.
For example, you are asked to subtract 347 from 932.
- The number 347 is made up of three bit parts: 300 + 40 + 7.
- First subtract hundreds: 932 - 300 = 632.
- We turn to the tens: 632 - 40. For convenience, 40 can be represented as the sum of 30 + 10. First, subtract 30 and get 632 - 30 = 602. Now subtract 10 from 602 remaining and obtain 592.
- It remains to deal with the units, using all the same "support on the top ten." First subtract from 592 deuce: 592 - 2 = 590. Then, what is left of sevens: 7 - 2 = 5. We get: 590 - 5 = 585.
How to learn to multiply in the mind
Layfhaker already wrote about how to quickly master multiplication table.
We add that the greatest difficulties in children and adults is the multiplication of 7 to 8. There is a simple rule that will help you to never be wrong in this matter. Just remember: "five, six, seven, eight" - 56 = 7 × 8.
And now let's move on to more complex cases.
Multiply the single digits in the multi-valued
In fact, everything here is simple. Splitting a multi-valued number on bits, multiply each digit and to summarize the results.
Let us examine a specific example: 759 × 8.
- Splitting bit 759 at portion 700, 50 and 9.
- Multiply each bit individually: 700 × 8 = 5600, 50 = 400 × 8, 9 × 8 = 72.
- Fold results, breaking them into categories: 5 600 + 400 + 72 = 5 000 + (600 + 400) + 72 = 5 000 + 1 000 + 72 = 6 000 + 72 = 6 072.
Multiply two-digit numbers
There is already a hand itself stretches to the calculator or even a pen and paper to take advantage of the good old multiplication in a column. While there is nothing daunting in this operation there. Just need a little to train short-term memory.
Let's try to multiply 47 by 32 by breaking the process into several steps.
- 47 × 32 - is the same as the 47 × (30 + 2) or 47 × 30 + 47 × 2.
- First multiply 47 by 30. Simply nowhere: 47 × 3 = 40 × 3 + 7 × 3 = 120 + 21 = 141. Attributed to the right toe and get: 1410.
- Off on: 47 = 2 × 40 × 7 × 2 + 2 = 80 + 14 = 94.
- It remains to fold the results: 1 410 + 94 = 1 500 + 4 = 1 504.
This principle can be applied to the numbers with a large number of bits, but keep in mind many operations are not everyone's strength.
simplifying multiplication
In addition to the general rules, there are several life hacking, easy multiplication by certain single digits.
Multiplication on 4
You can multiply the number by 2-valued, and then again at 2.
Example: 146 × 4 = (146 × 2) × 2 = (200 + 80 + 12) × 2 = 292 × 2 = 400 + 180 + 4 = 584.
Multiplication on 5
Multiply the original number by 10 and then divide by 2.
Example: 489 × 5 = 4 890/2 = 2 445.
Multiplication 9
Multiply by 10 and then subtract the result from the original number.
Example: 573 × 9 = 5730 - 573 = 5730 - (500 + 70 + 3) = 5 230 - (30 + 40) - 3 = 5 200 - 40 - 3 = 5160 - 3 = 5157.
multiplication by 11
Admission is as follows: front and rear substitute the first and last digits of the original number. A series add up all the numbers between them.
When multiplied by a two-digit number, everything looks very simple.
EXAMPLE: 36 × 11 = 3 (3 + 6) 6 = 396.
If the amount goes through ten, it remains at the center of the discharge units, and add to the first digit one.
EXAMPLE: 37 × 11 = 3 (3 + 7) 7 = 3 (10) 7 = 407.
A little more complicated with the multiplication by a larger number.
Example: 543 × 11 = 5 (5 + 4) (4 + 3) 3 = 5 973.
How to learn to share in the mind
This is the inverse operation of multiplication, so success depends on the knowledge of all of the same school of the table. The rest - a matter of practice.
Divided by single digit
To do this, we divide the original multi-valued number into manageable chunks that are exactly divisible by our unequivocal.
Let's try to divide 2436 by 7.
- 2436 isolate from the greatest part, which evenly divided into 7. In our case it is 2100. We obtain (2 100 + 336) / 7.
- We continue in the same spirit, only now with the number 336. Obviously, 280 divided by 7. A at residue 56 will be.
- Now we divide each part 7: (2 100 + 280 + 56) / 7 = 300 + 40 + 8 = 348.
Divide by two-digit number
This is the aerobatics, but we still try.
Suppose you need to divide 1128 by 24.
- We figure out how many times 24 can fit in 1128. Obviously, 1128 is approximately two times less than 24 × 100 (2400). Therefore, for "zeroing" take multiplier 50: 24 × 50 = 1200.
- Until 1200 our dividend 1128 lacks 72. How many times have 24 fit into 72? That's right, 3. This means that 1128 = 24 × 50 - 24 × 3 = 24 × (50 - 3) = 24 × 47. Consequently, 1128/24 = 47.
We have not the most difficult example, but using the method of 'zeroing' and fragmentation into manageable chunks, you will learn how to perform more complex operations.
What will help to learn an oral account
Exercise every day will have to come up with more and more examples, but if you do want it. Otherwise, use other available methods.
Table games
Playing in those where the need to constantly calculate the mind, you do not just learn to count quickly. And you combine the useful with the pleasant pastime with family or friends.
Cards fun like "Uno" and all sorts of options of mathematical domino allow students playfully learn simple addition, subtraction, multiplication and division. More complex economic strategy a la "Monopoly" to develop financial flair and sophisticated hone skills account.
What to buy
- "Uno";
- "7 9";
- "7 to 9 multi»;
- "Traffic Jam";
- "Hekmek";
- "Mathematical Domino";
- "Umnozharium";
- "Pharaoh Code";
- "Superfermer";
- "Monopoly".
Mobile applications
With them you will be able to bring the score to a verbal automatism. Most of them offer examples to solve addition, subtraction, multiplication and division on the program of elementary grades. But you will be surprised how easy it is. Especially if the task you have to click at a time, without pen and paper.
Math: Mental calculation, the multiplication table
Covers job interpreting the score, which correspond to grades 1-6 the curriculum, including the tasks of the interest. It allows you to train the speed and quality of the account, as well as adjust the difficulty. For example, from a simple multiplication table can move to multiplication and division double and three-digit numbers.
Price: Free
Mathematics in mind
Another simple and intuitive Simulator oral account with detailed statistics and customizable difficulty.
Price: Free
1001 challenge for the account in the mind
The application uses the examples of the benefits of mathematics "1001 problem for mental account", which in the XIX century was a scientist and teacher Sergei Raczynski.
Price: Free
Price: Free
math Tricks
The app allows you to easily and unobtrusively learn basic mathematical techniques that facilitate and accelerate the oral account. Each technique can work in training mode. And then to play on the computing speed or an opponent.
Price: Free
Price: Free
Quick Brain
The goal - to correctly solve as many mathematical examples for a certain period of time. Trains knowledge of multiplication tables, addition and subtraction. And also contains a popular math puzzle "2048".
Price: Free
Web services
Regularly intellectual exercise with numbers and can be on the mathematical online simulators. Choose the desired type of action and the level of difficulty - and forward, to new intellectual heights. Here are just a few options.
- Maths. Club - fitness machine oral account.
- School Aristova - fitness machine oral account (covering two-digit and three-digit numbers).
- "Razvivayka" - training of oral account within a hundred.
- 7gy.ru - math fitness machine (calculation within a hundred).
- Chisloboy - online game account on development of speed.
- kid-mama - trainers of mathematics for grades 0-6.
see also🧠🎓😤
- 10 effective ways to become smarter
- How to learn English, with this 1 hour per day
- Why learn new languages so difficult and how to overcome it
- 5 books that will help to master speed reading
- How to remember more, using the method 50/50