Leaderboard
Poland
Poland
Worldwide
Rank
Level
1
Maciej Jaworski
Dolnośląskie
98
2
Maciej Kopanski
Mazowieckie
91
3
Aleksandra Strzelecka
Wielkopolskie
76
4
Janek Terlikowski
Mazowieckie
72
5
Jaroslaw Kaczynski
Mazowieckie
68
6
User
Lubelskie
66
7
Krevvel
Lubelskie
59
8
Przegrywacz
Podlaskie
57
9
Marek Jopek
Mazowieckie
56
10
User
Mazowieckie
52
12
Iwona P
Mazowieckie
50
13
User
Mazowieckie
48
14
Albert
Śląskie
47
15
James Kopkiewicz
Mazowieckie
46
16
User
Mazowieckie
45
17
User
Lubelskie
45
18
Kuba Lolkowski
Mazowieckie
45
19
User
Mazowieckie
44
20
Amalgam
Mazowieckie
43
21
User
Mazowieckie
43
22
Kajetan Kowalski
Dolnośląskie
41
23
User
Małopolskie
41
24
User
Małopolskie
41
25
User
Podkarpackie
41
30
Fariel
Mazowieckie
40
31
Grabarczyk Jakub
Łódzkie
39
33
User
Podkarpackie
39
34
Jacu
Mazowieckie
38
35
Jakub Wilk
Małopolskie
36
37
User
Podlaskie
36
38
User
Małopolskie
35
39
M Pak
Opolskie
35
40
Bartlomiej
Podkarpackie
35
41
User
Mazowieckie
34
42
User
Mazowieckie
34
43
Kacper L123
Łódzkie
34
45
Jagoda
Mazowieckie
33
46
User
Mazowieckie
32
47
Ace Yong
Dolnośląskie
31
48
User
Pomorskie
31
50
User
Pomorskie
31
51
User
Śląskie
31
52
Joanna Bartkiewicz
Małopolskie
31
53
Albin Owczarski
Dolnośląskie
30
54
User
Mazowieckie
29
55
User
Mazowieckie
28
56
User
Łódzkie
26
57
Kaj fil
Dolnośląskie
26
58
Bruno Banaszczyk
Śląskie
26
60
User
Łódzkie
25
61
User
Mazowieckie
25
62
User
Śląskie
25
63
Janusz I Grażyna Kowalscy
Podlaskie
25
64
User
Mazowieckie
24
65
User
Lubelskie
24
66
User
Śląskie
24
67
User
Mazowieckie
24
69
User
Małopolskie
23
70
TheNewSaga
Mazowieckie
22
71
User
Małopolskie
21
72
User
Mazowieckie
21
73
User
Lubelskie
20
76
Eugene Karastoyanov
Mazowieckie
19
78
Jarek
Mazowieckie
19
79
Chris
Mazowieckie
19
81
User
Pomorskie
19
82
Mariusz Siemanko
Lubelskie
19
83
User
Mazowieckie
18
84
User
Małopolskie
18
85
User
Śląskie
18
86
User
Mazowieckie
17
87
Karol Wojtyła
Śląskie
17
88
User
Mazowieckie
17
89
User
Mazowieckie
16
90
User
Śląskie
16
91
User
Mazowieckie
16
92
User
Pomorskie
16
93
im at
Małopolskie
16
94
User
Mazowieckie
16
95
User
Mazowieckie
15
96
User
Mazowieckie
15
97
Seweryn Piotrowski
Świętokrzyskie
15
98
User
Mazowieckie
15
99
User
Mazowieckie
15
100
Aleksander Dróżdż
Śląskie
15
101
User
Mazowieckie
15
102
Jan Kociniak
Mazowieckie
14
103
User
Lubuskie
14
104
User
Mazowieckie
14
105
Kasia
Mazowieckie
13
106
User
Śląskie
13
107
User
Mazowieckie
13
110
Patryk
Małopolskie
13
111
medon
Podkarpackie
13
112
User
Mazowieckie
12
113
User
Mazowieckie
12
114
Jane Doe
Małopolskie
12
115
User
Mazowieckie
12
116
Jacek Winter
Łódzkie
12
117
User
Wielkopolskie
12
118
User
Małopolskie
12
119
User
Śląskie
12
120
User
Mazowieckie
12
121
User
Mazowieckie
12
122
User
Mazowieckie
12
123
User
Śląskie
12
124
User
Mazowieckie
12
126
User
Wielkopolskie
11
127
User
Pomorskie
11
128
User
Małopolskie
11
129
User
Śląskie
11
130
User
Mazowieckie
11
131
User
Pomorskie
11
132
User
Mazowieckie
11
133
User
Mazowieckie
11
134
User
Podlaskie
11
135
User
Małopolskie
11
136
User
Śląskie
11
138
User
Małopolskie
11
139
User
Mazowieckie
11
140
User
Mazowieckie
11
141
User
Małopolskie
11
142
User
Mazowieckie
10
143
User
Małopolskie
10
144
User
Mazowieckie
10
145
User
Małopolskie
10
146
Niclas Lundquist
Małopolskie
10
147
WojciechN
Dolnośląskie
10
148
User
Mazowieckie
10
149
User
Małopolskie
10
150
User
Wielkopolskie
10
151
Darek
Mazowieckie
10
152
User
Małopolskie
10
153
User
Łódzkie
10
155
Konrad Nowacki
Małopolskie
9
156
Alberto
Pomorskie
9
157
User
Mazowieckie
9
158
Robert
Małopolskie
9
159
User
Mazowieckie
9
160
User
Mazowieckie
9
161
Mirtha Fuerza
Małopolskie
9
162
Jakub Kowalski
Mazowieckie
9
163
User
Mazowieckie
9
164
User
Śląskie
9
166
Marek
Śląskie
9
167
User
Mazowieckie
9
168
User
Mazowieckie
9
169
User
Podkarpackie
8
170
User
Małopolskie
8
172
User
Mazowieckie
8
173
User
Mazowieckie
8
174
User
Mazowieckie
8
175
- JMBeats -
Mazowieckie
8
176
User
Mazowieckie
8
177
User
Pomorskie
8
179
Minion Music
Mazowieckie
8
180
User
Mazowieckie
8
182
User
Mazowieckie
8
183
User
Mazowieckie
8
184
User
Mazowieckie
8
186
Stëfänië Vids
Mazowieckie
8
187
User
Mazowieckie
8
188
User
Mazowieckie
8
189
User
Mazowieckie
8
191
User
Śląskie
7
193
User
Małopolskie
7
195
User
Mazowieckie
7
196
User
Mazowieckie
7
197
User
Mazowieckie
7
198
User
Mazowieckie
7
199
User
Pomorskie
7
202
User
Śląskie
7
204
User
Mazowieckie
7
205
User
Pomorskie
7
207
User
Podlaskie
7
208
User
Mazowieckie
7
211
User
Śląskie
6
212
User
Mazowieckie
6
213
User
Śląskie
6
214
User
Mazowieckie
6
216
User
Mazowieckie
6
217
User
Mazowieckie
6
219
User
Mazowieckie
6
220
User
Małopolskie
6
221
User
Mazowieckie
6
222
User
Małopolskie
6
223
User
Pomorskie
6
226
User
Lubelskie
6
227
User
Małopolskie
6
228
User
Małopolskie
6
229
User
Region
5
230
User
Mazowieckie
5
231
User
Mazowieckie
5
232
User
Mazowieckie
5
233
User
Mazowieckie
5
234
User
Małopolskie
5
235
User
Mazowieckie
5
236
User
Mazowieckie
5
238
User
Śląskie
5
239
User
Lubelskie
5
243
User
Podkarpackie
5
244
User
Pomorskie
5
245
Pyjter Hazok
Śląskie
5
246
User
Lubelskie
5
248
User
Śląskie
5
249
User
Mazowieckie
5
250
User
Mazowieckie
5
251
User
Śląskie
5
252
User
Mazowieckie
4
254
User
Mazowieckie
4
255
User
Łódzkie
4
256
User
Lubelskie
4
257
User
Śląskie
4
258
User
Mazowieckie
4
260
User
Małopolskie
4
261
User
Mazowieckie
4
262
User
Małopolskie
4
264
User
Małopolskie
4
265
Marcin Ogorzałek
Mazowieckie
4
266
User
Mazowieckie
4
267
User
Mazowieckie
4
268
User
Mazowieckie
4
269
User
Pomorskie
4
272
User
Małopolskie
4
274
User
Mazowieckie
4
276
User
Lubelskie
4
277
User
Mazowieckie
4
278
User
Mazowieckie
4
279
User
Mazowieckie
4
281
User
Lubelskie
3
282
User
Lubelskie
3
283
User
Małopolskie
3
284
User
Mazowieckie
3
285
User
Mazowieckie
3
286
User
Mazowieckie
3
288
User
Mazowieckie
3
289
User
Podlaskie
3
290
User
Małopolskie
3
291
User
Podkarpackie
3
292
User
Mazowieckie
3
293
User
Mazowieckie
3
294
User
Mazowieckie
3
295
User
Śląskie
3
296
User
Mazowieckie
3
297
User
Lubelskie
3
298
User
Pomorskie
3
299
Malgorzata
Mazowieckie
3
300
User
Podkarpackie
3
301
Kornel
Małopolskie
3
302
User
Mazowieckie
3
303
Szymon
Mazowieckie
3
304
User
Mazowieckie
3
307
User
Mazowieckie
2
308
User
Podlaskie
2
309
User
Małopolskie
2
310
User
Pomorskie
2
312
User
Małopolskie
2
313
User
Mazowieckie
2
314
User
Mazowieckie
2
315
User
Mazowieckie
2
316
User
Mazowieckie
2
317
User
Mazowieckie
2
319
User
Mazowieckie
2
320
User
Mazowieckie
2
321
User
Łódzkie
2
323
User
Śląskie
2
324
Никита Ермоленко
Wielkopolskie
2
325
User
Mazowieckie
2
326
User
Mazowieckie
2
327
User
Małopolskie
2
328
User
Mazowieckie
2
329
User
Małopolskie
2
332
User
Łódzkie
2
333
User
Mazowieckie
2
334
User
Łódzkie
2
336
User
Łódzkie
2
338
User
Mazowieckie
2
339
User
Podlaskie
2
340
User
Mazowieckie
2
341
Maya
Pomorskie
2
342
User
Mazowieckie
2
343
User
Mazowieckie
2
344
User
Mazowieckie
2
349
User
Małopolskie
2
350
User
Mazowieckie
2
351
User
Mazowieckie
2
353
User
Mazowieckie
1
354
User
Mazowieckie
1
355
User
Małopolskie
1
357
User
Podlaskie
1
358
User
Mazowieckie
1
359
User
Lubelskie
1
360
User
Małopolskie
1
361
User
Mazowieckie
1
362
User
Śląskie
1
363
User
Mazowieckie
1
364
User
Mazowieckie
1
367
User
Śląskie
1
368
User
Śląskie
1
369
User
Mazowieckie
1
370
John Liliputa
Małopolskie
1
371
User
Mazowieckie
1
373
User
Małopolskie
1
374
User
Małopolskie
1
375
User
Mazowieckie
1
378
User
Pomorskie
1
380
User
Mazowieckie
1
381
User
Podkarpackie
1
382
User
Mazowieckie
1
384
User
Małopolskie
1
385
User
Mazowieckie
1
386
User
Pomorskie
1
387
User
Małopolskie
1
388
User
Małopolskie
1
389
User
Mazowieckie
1
390
User
Podkarpackie
1
391
User
Mazowieckie
1
392
User
Lubuskie
1
393
User
Mazowieckie
1
394
User
Małopolskie
1
395
User
Mazowieckie
1
396
User
Łódzkie
1
397
User
Łódzkie
1
399
User
Małopolskie
1
400
User
Mazowieckie
1
401
User
Podkarpackie
1
403
User
Mazowieckie
1
404
User
Śląskie
1
405
User
Podlaskie
1
407
User
Mazowieckie
1
408
User
Mazowieckie
1
409
User
Mazowieckie
1
410
User
Mazowieckie
1
413
User
Lubelskie
1
414
User
Małopolskie
1
415
User
Mazowieckie
1
416
User
Pomorskie
1
417
Nel Bauer
Małopolskie
1
418
User
Małopolskie
1

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A Web App for Mathematics Training

Do you want to be fast at mental math? Many people do, but the options for doing the necessary exercises are simply too cumbersome for all but the most dedicated of trainees. In physical fitness, many people are interested in training their bodies but allocating the time, energy, and money for it is a significant obstacle. Likewise, lugging around books and whatnot for math practice is a threshold that just doesn't meet the standards of modern life.

Training yourself to be skilled at mental math needs to be quick and convenient. mathtrainer.org is a web app that works in your browser rather than a program you have to download and install on your computer or phone. This allows users to try and use the app without having to install new software. As a web app, updates are also much simpler. There is no need to download endless updates—the website will always be the most current version.

You can access a web app from any device connected to the internet and equipped with a web browser, including smartphones, tablets, and desktop computers. Moreover, you are free to use whichever browser you prefer, including Google Chrome, Safari, Firefox, and others. Google Chrome is the recommended browser for the best maths training since it tends to lead the pack in supporting the latest web technologies.

Math Trainer is designed to offer a similar experience regardless of what you’re using to access it, whether it be Android, iOS, Windows, or another operating system. Though an on-screen touch keyboard will appear on mobile devices, you may prefer to use the app on a desktop with a keyboard. Hopefully the advantages of a web app for convenient mathematics training are apparent.

Another part of making the app easy to use is eliminating the need for signing up and logging in. Users can get started with their math training as soon as they click the start button on this page. After progressing to higher levels in the app, your progress is automatically saved so long as your return to the site through the same browser.


What's a Mental Math Tip?

A mental math tip is a sequence of steps that can be taken to solve a math problem in your head. Click the arrow below to see an example for the following problem:

÷
984
3
328

A tip like this one is available for every problem in Math Trainer, so there's always help if you get stuck. With enough math practice, you'll be able to predict what the tips will say—you'll have learned mental math!


Get Better at Mental Math

The ability to quickly perform mental calculations offers advantages in certain circumstances. But even without applications, getting better at mental math is a great way to stimulate one’s mind. It develops better number sense and intuition for quantifying the world around us. Practicing mental calculation will strengthen your foundation for learning more advanced maths topics.

Nonetheless, the tangible benefits of improving at mental math are many. It is certainly expected that educated people are able to do simple arithmetic without having to pull out a calculator. An inability to do so may reflect poorly on you, while being well-practiced in mental calculation will leave your contemporaries impressed. In many scientific and technical circles, mental math ability is even more highly regarded.

For students, mental calculation speed will often have a direct impact on math and science test scores. At all grade levels, it is not sufficient to know how to solve math problems when tests have a time limit on them. The highest-scoring test takers are able to answer questions both correctly and efficiently. Improving mental math skills will only benefit a student’s academic career.

Calculating the solution to an arithmetic problem in your head is often faster than pulling out a device to tell you the answer. For example, figuring out how much to tip a server at a restaurant is a straightforward arithmetic problem that many people are unable to perform without a calculator. By training your brain to solve basic math problems, you can save time in situations like these.

Mental math can also be relied upon when calculation devices are not available. Even with the conveniences of modern life, we occasionally find ourselves without access to our cell phones or other capable devices. A mind skilled in mental math is always available to you.

Finally, getting better at mental math enables a quick estimate and sanity check on results obtained from calculators. While computers are extremely reliable at solving math problems, there is always the risk of incorrectly inputting the problem to the computer. By getting better at mental mathematics, you will develop an intuition for whether the results of calculators make sense.

In fact, the ability to estimate is often sufficient to avoid using calculators altogether. While the use of computers is widespread, estimation is an increasingly valued skill in many industries. There are many situations where complex math will eventually be required, but a preliminary estimate is needed quickly. A major boost to productivity!


Use a Math Trainer

Mental math ability is a lot like physical fitness training. You may be out of shape in the beginning, but with diligent training you can and will improve. Initially you might not enjoy the exercise, but you will reap significant rewards for your effort. As you become more fit, you’ll begin to enjoy the activity much more. If you are serious about it, your mental calculation fitness could become a source of energy, galvanizing you to face the challenges of life with enthusiasm.

In physical training, you break down the fibers in your muscles during a workout session. Your muscles actually sustain tiny tears during resistance training exercises. While you rest afterwards, your body repairs the damage, rebuilding the fibers thicker and stronger.

A similar process is believed to occur for cognitive tasks. A 2016 study found "extensive evidence that brain-training interventions improve performance on the trained tasks".1 Therefore you can expect training your brain to answer mental math questions will lead to improved performance over time.

In the context of physical fitness, a "trainer" often refers to a trained professional who guides the workout and recovery process. Personal trainers are tasked with assessing a trainee's level of ability, prescribing an exercise regimen, and offering feedback as the training goes along. The word "trainer" could also refer to a system that automates the role of a personal trainer. Many aerobic exercise machines today offer interactive training programs with feedback and analysis of a user's performance.

A math trainer is needed for optimal math fitness. Like in physical fitness, the trainer should be compatible with users at a variety of skill levels and should guide them to the next level. It should give an accurate assessment of a user's strengths and weakness, as well as offer helpful feedback on where to focus one's efforts. Learning the ropes of mental maths with a math trainer should be a seamless, rewarding journey to ever-greater abilities.


Mental Calculation

Mental calculation, or mental math, is performing arithmetical calculations without the aid of tools or supplies. As opposed to using a calculator or pencil and paper, mental math is performed entirely in one’s head.

People use mental calculation when computation aides are not available, when it is faster to do so, or when they wish to practice math, show off, or participate in mental math competitions. Most people perform basic mental calculation using elementary arithmetic on a daily basis. An inability to calculate mentally is a serious obstacle to many common tasks.

In U.S. schools, mental calculation is taught only for the most elementary arithmetic, such as single-digit addition and multiplication of two numbers between 0 and 12. To solve addition problems involving multiple digits, you are taught to add columns of digits from right to left, carrying the tens digit if the column sum exceeds 9. For example, how would you approach this addition problem?

Example of two-digit
addition problem

If you were trained like many of us were, you’d add the right column to obtain 12. Since that’s two digits, you’d write the 2 under the right column and carry the 10 by writing a 1 above the left column. Finally, you’d add the two tens digits and the carried 1 to obtain the answer, 52.

To solve an addition problem mentally, it’s best to add the columns from left to right. In our example, you could add the tens digit of the second number, 30, to the first number, 14, to obtain 44. This is easier than the full problem because you’re just doing one mental calculation and tacking on the 4 from the 14 as the singles digit. Then you’d add the remaining ones digit of the second number, 8, to 44 to arrive at the answer, 52.

Which approach seems simpler to you? Can you do the first approach without pulling out a pencil and paper? It turns out the same advantages of left-to-right addition apply to much larger numbers as well. It’s unlikely that difficult addition problems can be solved right to left without needing to write it all out, which of course is more time consuming.

Mental math should be distinguished from the memorization of math facts such as multiplication tables. A foundation of memorized answers to simple math problems will make mental math easier, but performing maths in your head requires both memorized facts and the manipulation of numbers and operations to solve problems. This combination of skill and memory allows us to solve far more complex math questions than can be answered with readily-memorized math facts.

Many mental math tricks are specific to particular numbers or types of problems, usually dependent on the base of the number system used. In the decimal numeral system, for example, it is trivially easy to multiply by 10—just add a 0 to the end of the number. This mental math trick wouldn’t work in the hexadecimal numeral system, though, because the base is 16 instead of 10.

Therefore mental calculation is the ability to manipulate complex arithmetic problems in such a way that they can be resolved using simple memorized math facts.


Arithmetic

Arithmetic is the branch of mathematics concerning basic number operations: addition, subtraction, multiplication, and division. As kids, we are taught to do arithmetic because real-world math problems depend on a mastery of elementary arithmetic. Higher-level study of arithmetic and the integers, or whole numbers, is known as number theory.

Though the math kids initially study is arithmetic, the word is rarely used in this context anymore. Originally it comes from the Greek arithmos, meaning “number”. It has however been included in the “three Rs” of elementary Western education: reading, writing, and arithmetic.

There is evidence prehistoric humans were using arithmetic as hunter-gatherers. Archaeologists have uncovered a tally stick, believed to be over 20,000 years old, which may exhibit the earliest known sequences of prime numbers. An understanding of prime numbers, which are only divisible by themselves and the number 1, requires knowledge of the operation in arithmetic known as division.

From tally marks came base-10 numerals such as those used in Egypt over 5,000 years ago. Number systems based on 10 probably arose because humans have ten “digits” as fingers on their hands (or toes on their feet). A later advance in arithmetic was positional notation, which allowed the same symbols to represent different magnitudes depending on their position in the written number. These numeral systems allowed complex arithmetic to be communicated, recorded, and applied to the challenges faced by our ancestors.

The basic operation of arithmetic is addition. It combines two or more numbers into one, the sum of the terms. The terms can be added in any order, which is known as the commutative property of arithmetic. On a number line, the sum of two numbers is the total distance from zero covered by both numbers.

The inverse arithmetical operation of addition is subtraction. It finds the difference between two numbers. Subtraction is not commutative because the order of the numbers determines whether the answer is positive or negative. On a number line, the difference between two numbers is the distance between their positions.

A second basic operation of arithmetic is multiplication, which scales a number by another number. This second number is called a factor. Like addition, multiplication is commutative—you can change the order of the factors and still get the same answer. Multiplication on a number line can be viewed as adding the first number a total number of times equal to the second factor.

Finally, division is an arithmetical operation that is essentially the inverse of multiplication. Rather than scaling a number, it is divided into a number of pieces equal to the second number. Dividing by the number 0 is not defined in arithmetic because dividing something into zero pieces is impossible.

Basic arithmetic allows us to evaluate the answers to an unlimited number of mathematical expressions. Arithmetical expressions can be purely mathematical, as in 2 + 2, or they can represent quantities in the physical world, such as two items plus two more. Understanding the laws of arithmetic is tremendously powerful.


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