Leaderboard
Kansas
Rank
Level
1
User
Lawrence
84
2
User
Overland Park
80
3
Heath Vincent
Manhattan
68
4
Connor Stanton
Hays
54
5
rocksbox
Overland Park
52
6
Nathan Ward
Hays
51
7
Chau Le
Atchison
49
8
User
Wichita
46
9
Caden Gatschet
Hays
42
10
Aubree Thomas
Hays
42
11
User
Hays
42
12
Jalen Smith
Hays
42
13
User
Hays
40
14
Isaac Thornton
Hays
37
15
User
Bucklin
33
16
User
Overland Park
31
17
Erika Linn
Hays
31
18
Julia Zadina
Hays
31
19
User
Lenexa
31
20
User
Topeka
30
21
User
Hays
30
22
Xavier Catura
Hays
29
23
Caleb King
Hays
29
24
User
Hays
29
25
Kolynn Denning
Hays
29
26
User
Lawrence
28
27
Canon Meder
Hays
28
28
User
Hays
28
29
John Weisenborn
Hays
28
30
User
Shawnee
26
31
User
Hays
25
32
User
Hays
25
33
User
Hays
25
34
User
Wichita
25
35
User
Overland Park
24
36
User
Hays
24
37
Caleb Wilson
Hays
24
38
User
Fort Riley
23
39
User
Hays
23
40
User
Hays
23
41
Abbie Norris
Hays
23
42
Cooper johnson
Hays
23
43
User
Hays
23
44
Braden Quintero
Hays
23
45
Addison Otte
Hays
23
46
User
Bel Aire
22
47
User
Hays
22
48
User
Hays
22
49
Leo Hernandez
Hays
22
50
Gavin
Hays
22
51
User
Tonganoxie
22
52
User
Hays
21
53
Alexis Burton
Hays
21
54
User
Hays
21
55
Malik bah
Hays
21
56
User
Hays
21
57
User
Hays
21
58
Savanna kuhn
Hays
21
59
User
Hays
21
60
User
Overland Park
20
61
Paige Seib
Hays
20
62
Brock Summers
Hays
20
63
User
Hays
20
64
User
Hays
20
65
Joanna Mendoza
Hays
20
66
Brynn Kinderknecht
Hays
20
67
User
Kingman
20
68
Suganya Balakrishnan
Kingman
20
69
User
Dodge City
19
70
Charles Roe
Hays
19
71
Lily Garrison
Hays
19
72
User
Hays
19
73
Bailey Lowry
Hays
19
74
User
Hays
19
75
Clare Tholstrup
Hays
19
76
User
Hays
19
77
User
Hays
19
78
User
Dodge City
18
79
User
Overland Park
18
80
User
Altamont
18
81
User
Hays
18
82
Evan Cosgriff-Guthrie
Hays
18
83
User
Hays
18
84
User
Hays
18
85
User
Hays
18
86
Emily Stenzel
Hays
18
87
User
Dodge City
17
88
User
Hays
17
89
Hailey Bond
Hays
17
90
Isabelle Jones
Hays
17
91
Isaac Thornton
Hays
17
92
User
Hays
16
93
Brenlynn Albers
Hays
16
94
User
Hays
16
95
User
Hays
16
96
Nolan Dreher
Hays
16
97
Chantal Gonzalez
Hays
16
98
User
Manhattan
16
99
User
Olathe
16
100
User
Overland Park
15
101
User
Andover
15
102
Hannah Klein
Hays
15
103
User
Hays
15
104
User
Wichita
15
105
User
Topeka
14
106
User
Dodge City
14
107
User
Dodge City
14
108
User
Hays
14
109
User
Hays
14
110
User
Hays
14
111
User
Olathe
14
112
User
Olathe
13
113
User
Dodge City
13
114
User
Dodge City
13
115
Dezarae Schmidt
Hays
13
116
User
Hays
13
117
Avrianna Burk
Hays
13
118
User
Hays
13
119
User
Lawrence
12
120
User
Dodge City
12
121
User
Dodge City
12
122
User
Hays
12
123
User
Tonganoxie
12
124
User
Dearing
11
125
Math Nub
Colby
11
126
User
Hays
11
127
User
Hays
11
128
User
Leawood
11
129
User
Scott City
11
130
User
Hays
11
131
User
Lenexa
11
132
Benjamin Stover
Olathe
10
133
User
Dodge City
10
134
User
Hays
10
135
Ethan Marshall
Hays
10
136
User
Salina
10
137
Le azien
Dearing
9
138
User
Newton
9
139
User
Dodge City
9
140
kaiden
Hays
9
141
Mahala Gregg
Hays
9
142
User
Hays
9
143
User
Olathe
9
144
User
Overland Park
9
145
User
Dodge City
8
146
User
Dodge City
8
147
User
Dodge City
8
148
User
Hays
8
149
Morgan Geerdes
Hays
8
150
Katie Gutierrez
Hays
8
151
User
Overland Park
8
152
Allison Kitchen
Hays
8
153
User
Topeka
8
154
User
Pittsburg
8
155
User
Overland Park
7
156
User
Overland Park
7
157
User
Dodge City
7
158
User
Dodge City
7
159
User
Hays
7
160
User
Hays
7
161
Salvador Luna
Hays
7
162
User
Hays
7
163
User
Overland Park
7
164
User
Hays
7
165
User
Hays
7
166
Hms66372
Hays
7
167
Addyson Brown
Hays
7
168
User
Hays
7
169
User
Hays
7
170
Hazy Tolentino
Hays
7
171
User
Hays
7
172
Corbin Werth
Hays
7
173
User
Overland Park
7
174
User
Dodge City
6
175
User
Tonganoxie
6
176
User
Dodge City
6
177
User
Dodge City
6
178
User
Hays
6
179
User
Hays
6
180
User
Hays
6
181
Emily hernandez
Hays
6
182
User
Hays
6
183
Dezarae
Hays
6
184
User
Hays
6
185
Tamia Smith
Hays
6
186
User
Olathe
5
187
User
Dodge City
5
188
Sierra Puryear
Overland Park
5
189
User
Dodge City
5
190
User
Dodge City
5
191
User
Dodge City
5
192
User
Topeka
5
193
User
Hays
5
194
Kinkee may
Hays
5
195
User
Hays
5
196
User
Hays
5
197
Nick Mermis
Hays
5
198
Braxton Banker
Hays
5
199
User
Hays
5
200
User
Hays
5
201
Christian Burkholder
Hays
5
202
User
Hays
5
203
User
Dearing
5
204
User
Salina
5
205
User
Wamego
4
206
User
Lawrence
4
207
User
Dodge City
4
208
User
Dodge City
4
209
User
Hays
4
210
Kerra Nix
Hays
4
211
Sukesh Kamesh
Pratt
4
212
Evan Tschanz
Hays
4
213
User
Leavenworth
4
214
Jacob Wente
Hays
4
215
Emma Bollig
Hays
4
216
User
Hays
4
217
User
Salina
4
218
User
Dearing
4
219
User
Emporia
3
220
User
Wichita
3
221
User
Dodge City
3
222
User
Dodge City
3
223
User
Dodge City
3
224
User
Tonganoxie
3
225
User
Rose Hill
3
226
User
Dodge City
3
227
User
Dodge City
3
228
User
Dodge City
3
229
User
Dodge City
3
230
User
Dodge City
3
231
User
Wichita
3
232
Stephanie
Hays
3
233
User
Leawood
3
234
User
Hays
3
235
Cameron Kohlrus
Hays
3
236
User
Hays
3
237
User
Hays
3
238
Kerra nix
Hays
3
239
Xavier ellis
Hays
3
240
User
Hays
3
241
User
Hays
3
242
User
Hays
3
243
User
Hays
3
244
User
Olathe
3
245
User
Olathe
3
246
User
Wichita
3
247
User
Manhattan
3
248
User
Hays
2
249
User
Onaga
2
250
User
Dodge City
2
251
User
Dodge City
2
252
User
Dodge City
2
253
User
Dodge City
2
254
User
Dodge City
2
255
User
Dodge City
2
256
User
Dodge City
2
257
User
Dodge City
2
258
User
Lawrence
2
259
Everettshort
Dearing
2
260
User
Dearing
2
261
User
Lawrence
2
262
User
Hays
2
263
Daunte Younker
Hays
2
264
User
Hays
2
265
User
Hays
2
266
User
Hays
2
267
User
Hays
2
268
User
Hays
2
269
User
Hays
2
270
User
Hays
2
271
User
Hays
2
272
User
Kingman
2
273
Haley Rees
Hays
2
274
User
Hays
2
275
Corbin Luck
Hays
2
276
User
Hays
2
277
Cooper sanders
Hays
2
278
Melanie Custer
Hays
2
279
Lex Lummus
Hays
2
280
User
Hays
2
281
User
Hays
2
282
User
Hays
2
283
User
Hays
2
284
Jada
Hays
2
285
User
Hays
2
286
Trace hale
Hays
2
287
Kole Brown
Hays
2
288
McKenzie Miller
Hays
2
289
User
Hays
2
290
User
Hays
2
291
Daijah robinson
Hays
2
292
User
Hays
2
293
User
Hays
2
294
User
Lyndon
2
295
User
Olathe
2
296
User
Lenexa
2
297
User
Osage City
2
298
User
Minneola
1
299
User
Wichita
1
300
Furaha Kangethe
Overland Park
1
301
Ethan klaus
Hays
1
302
Lexie macumber
Hays
1
303
Gavin lamb
Hays
1
304
Kaden Tryon
Hays
1
305
Caven Krom
Hays
1
306
Cooper jones
Hays
1
307
Kade Wenta
Hays
1
308
Addyson Brown
Hays
1
309
Jacob Wente
Hays
1
310
Ty Dempsey
Hays
1
311
Madison Meis
Hays
1
312
Abigail Boyer
Hays
1
313
Kyler Riggs
Hays
1
314
Aiden Burton
Hays
1
315
Brygette Ross
Hays
1
316
Kim Del Real
Hays
1
317
Dakota Normandin
Hays
1
318
Hailey Klein
Hays
1
319
Konnor Dreiling
Hays
1
320
Dylan Stahl
Hays
1
321
Ben Zimmerman
Hays
1
322
Nohemi Lopez Vallejo
Hays
1
323
Kelby Hammerschmidt
Hays
1
324
Jaxon Zimmerman
Hays
1
325
Lilian McGrath
Hays
1
326
Bryan Camera
Hays
1
327
Gavin Flaska
Hays
1
328
Apryl Eschliman
Hays
1
329
Christapher Poage
Hays
1
330
Daniel Giebler
Hays
1
331
Harley Zimmerman
Hays
1
332
Lillyanna Alvarez
Hays
1
333
Orion Williams
Hays
1
334
Kaleb yaseen
Hays
1
335
Rhett Shelton
Hays
1
336
Carsen Riat
Hays
1
337
Chasey Wasinger
Hays
1
338
Kaylee Hammerschmidt
Hays
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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 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, 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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