Leaderboard
Kansas
Rank
Level
1
User
Lawrence
84
2
User
Manhattan
83
3
Heath Vincent
Manhattan
79
4
User
Lawrence
58
5
Connor Stanton
Hays
54
6
rocksbox
Overland Park
52
7
Nathan Ward
Hays
51
8
Chau Le
Atchison
49
9
User
Wichita
46
10
Caden Gatschet
Hays
42
11
Aubree Thomas
Hays
42
12
User
Hays
42
13
Jalen Smith
Hays
42
14
User
Hays
40
15
User
Manhattan
38
16
Isaac Thornton
Hays
37
17
User
Wamego
34
18
User
Bucklin
33
19
User
Dearing
31
20
User
Overland Park
31
21
Erika Linn
Hays
31
22
Julia Zadina
Hays
31
23
User
Lenexa
31
24
User
Topeka
30
25
User
Hays
30
26
Xavier Catura
Hays
29
27
Caleb King
Hays
29
28
User
Hays
29
29
Kolynn Denning
Hays
29
30
User
Lawrence
28
31
Canon Meder
Hays
28
32
User
Hays
28
33
John Weisenborn
Hays
28
34
User
Shawnee
26
35
User
Overland Park
25
36
User
Hays
25
37
User
Hays
25
38
User
Hays
25
39
User
Wichita
25
40
User
Overland Park
24
41
User
Hays
24
42
Caleb Wilson
Hays
24
43
User
Fort Riley
23
44
User
Hays
23
45
User
Hays
23
46
Abbie Norris
Hays
23
47
Cooper johnson
Hays
23
48
User
Hays
23
49
Braden Quintero
Hays
23
50
Addison Otte
Hays
23
51
User
Wichita
22
52
User
Bel Aire
22
53
User
Hays
22
54
User
Hays
22
55
Leo Hernandez
Hays
22
56
Gavin
Hays
22
57
User
Tonganoxie
22
58
User
Hays
21
59
Alexis Burton
Hays
21
60
User
Hays
21
61
Malik bah
Hays
21
62
User
Hays
21
63
User
Hays
21
64
Savanna kuhn
Hays
21
65
User
Hays
21
66
User
Overland Park
20
67
Paige Seib
Hays
20
68
Brock Summers
Hays
20
69
User
Hays
20
70
User
Hays
20
71
Joanna Mendoza
Hays
20
72
Brynn Kinderknecht
Hays
20
73
User
Kingman
20
74
Suganya Balakrishnan
Kingman
20
75
User
Dodge City
19
76
Charles Roe
Hays
19
77
Lily Garrison
Hays
19
78
User
Hays
19
79
Bailey Lowry
Hays
19
80
User
Hays
19
81
Clare Tholstrup
Hays
19
82
User
Hays
19
83
User
Hays
19
84
User
Dodge City
18
85
User
Overland Park
18
86
User
Altamont
18
87
User
Hays
18
88
Evan Cosgriff-Guthrie
Hays
18
89
User
Hays
18
90
User
Hays
18
91
User
Hays
18
92
Emily Stenzel
Hays
18
93
User
Dodge City
17
94
User
Hays
17
95
Hailey Bond
Hays
17
96
Isabelle Jones
Hays
17
97
Isaac Thornton
Hays
17
98
User
Hays
16
99
Brenlynn Albers
Hays
16
100
User
Hays
16
101
User
Hays
16
102
Nolan Dreher
Hays
16
103
Chantal Gonzalez
Hays
16
104
User
Manhattan
16
105
User
Olathe
16
106
User
Overland Park
15
107
User
Andover
15
108
Hannah Klein
Hays
15
109
User
Hays
15
110
User
Wichita
15
111
User
Topeka
14
112
User
Dodge City
14
113
User
Dodge City
14
114
User
Hays
14
115
User
Hays
14
116
User
Hays
14
117
User
Olathe
14
118
User
Olathe
13
119
User
Dodge City
13
120
User
Dodge City
13
121
Dezarae Schmidt
Hays
13
122
User
Hays
13
123
Avrianna Burk
Hays
13
124
User
Hays
13
125
User
Olathe
12
126
User
Lawrence
12
127
User
Dodge City
12
128
User
Dodge City
12
129
User
Hays
12
130
User
Tonganoxie
12
131
User
Dearing
11
132
Math Nub
Colby
11
133
User
Hays
11
134
User
Hays
11
135
User
Leawood
11
136
User
Scott City
11
137
User
Hays
11
138
User
Lenexa
11
139
Benjamin Stover
Olathe
10
140
User
Dodge City
10
141
User
Hays
10
142
Ethan Marshall
Hays
10
143
User
Salina
10
144
User
Olathe
9
145
Le azien
Dearing
9
146
User
Newton
9
147
User
Dodge City
9
148
kaiden
Hays
9
149
Mahala Gregg
Hays
9
150
User
Hays
9
151
User
Olathe
9
152
User
Overland Park
9
153
User
Manhattan
8
154
User
Manhattan
8
155
User
Dodge City
8
156
User
Manhattan
8
157
Jason Vanhelleputte
Dearing
8
158
User
Dodge City
8
159
User
Dodge City
8
160
User
Dodge City
8
161
User
Hays
8
162
Morgan Geerdes
Hays
8
163
Katie Gutierrez
Hays
8
164
User
Overland Park
8
165
Allison Kitchen
Hays
8
166
User
Topeka
8
167
User
Pittsburg
8
168
User
Overland Park
7
169
User
Overland Park
7
170
User
Dodge City
7
171
User
Dodge City
7
172
User
Hays
7
173
User
Hays
7
174
Salvador Luna
Hays
7
175
User
Hays
7
176
User
Overland Park
7
177
User
Hays
7
178
User
Hays
7
179
Hms66372
Hays
7
180
Addyson Brown
Hays
7
181
User
Hays
7
182
User
Hays
7
183
Hazy Tolentino
Hays
7
184
User
Hays
7
185
Corbin Werth
Hays
7
186
User
Overland Park
7
187
User
Wichita
6
188
User
Overland Park
6
189
User
Dodge City
6
190
User
Manhattan
6
191
User
Dearing
6
192
User
Salina
6
193
User
Overland Park
6
194
User
Olathe
6
195
User
Lawrence
6
196
User
Dodge City
6
197
User
Tonganoxie
6
198
User
Dodge City
6
199
User
Dodge City
6
200
User
Hays
6
201
User
Hays
6
202
User
Hays
6
203
Emily hernandez
Hays
6
204
User
Hays
6
205
Dezarae
Hays
6
206
User
Hays
6
207
Tamia Smith
Hays
6
208
User
Mission
5
209
User
Dearing
5
210
User
Olathe
5
211
User
Dodge City
5
212
Sierra Puryear
Overland Park
5
213
User
Dodge City
5
214
User
Dodge City
5
215
User
Dodge City
5
216
User
Topeka
5
217
User
Hays
5
218
Kinkee may
Hays
5
219
User
Hays
5
220
User
Hays
5
221
Nick Mermis
Hays
5
222
Braxton Banker
Hays
5
223
User
Hays
5
224
User
Hays
5
225
Christian Burkholder
Hays
5
226
User
Hays
5
227
User
Dearing
5
228
User
Manhattan
4
229
User
Topeka
4
230
User
Lawrence
4
231
User
Dodge City
4
232
User
Dodge City
4
233
User
Hays
4
234
Kerra Nix
Hays
4
235
Sukesh Kamesh
Pratt
4
236
Evan Tschanz
Hays
4
237
User
Leavenworth
4
238
Jacob Wente
Hays
4
239
Emma Bollig
Hays
4
240
User
Hays
4
241
User
Salina
4
242
User
Dearing
4
243
User
Wichita
3
244
User
Dearing
3
245
User
Topeka
3
246
User
Emporia
3
247
User
Wichita
3
248
User
Dodge City
3
249
User
Dodge City
3
250
User
Dodge City
3
251
User
Tonganoxie
3
252
User
Rose Hill
3
253
User
Dodge City
3
254
User
Dodge City
3
255
User
Dodge City
3
256
User
Dodge City
3
257
User
Dodge City
3
258
User
Wichita
3
259
Stephanie
Hays
3
260
User
Leawood
3
261
User
Hays
3
262
Cameron Kohlrus
Hays
3
263
User
Hays
3
264
User
Hays
3
265
Kerra nix
Hays
3
266
Xavier ellis
Hays
3
267
User
Hays
3
268
User
Hays
3
269
User
Hays
3
270
User
Hays
3
271
User
Olathe
3
272
User
Olathe
3
273
User
Wichita
3
274
User
Manhattan
2
275
User
Dodge City
2
276
User
Manhattan
2
277
User
Manhattan
2
278
User
Manhattan
2
279
User
Manhattan
2
280
User
Manhattan
2
281
User
Manhattan
2
282
User
Hays
2
283
User
Onaga
2
284
User
Dodge City
2
285
User
Dodge City
2
286
User
Dodge City
2
287
User
Dodge City
2
288
User
Dodge City
2
289
User
Dodge City
2
290
User
Dodge City
2
291
User
Dodge City
2
292
User
Lawrence
2
293
Everettshort
Dearing
2
294
User
Dearing
2
295
User
Lawrence
2
296
User
Hays
2
297
Daunte Younker
Hays
2
298
User
Hays
2
299
User
Hays
2
300
User
Hays
2
301
User
Hays
2
302
User
Hays
2
303
User
Hays
2
304
User
Hays
2
305
User
Hays
2
306
User
Kingman
2
307
Haley Rees
Hays
2
308
User
Hays
2
309
Corbin Luck
Hays
2
310
User
Hays
2
311
Cooper sanders
Hays
2
312
Melanie Custer
Hays
2
313
Lex Lummus
Hays
2
314
User
Hays
2
315
User
Hays
2
316
User
Hays
2
317
User
Hays
2
318
Jada
Hays
2
319
User
Hays
2
320
Trace hale
Hays
2
321
Kole Brown
Hays
2
322
McKenzie Miller
Hays
2
323
User
Hays
2
324
User
Hays
2
325
Daijah robinson
Hays
2
326
User
Hays
2
327
User
Hays
2
328
User
Lyndon
2
329
User
Olathe
2
330
User
Lenexa
2
331
User
Osage City
2
332
User
Olathe
1
333
User
Olathe
1
334
User
Dodge City
1
335
User
Olathe
1
336
User
Shawnee
1
337
User
Wichita
1
338
Matthew Jansen
Overland Park
1
339
User
Manhattan
1
340
User
Lenexa
1
341
User
Minneola
1
342
User
Wichita
1
343
Furaha Kangethe
Overland Park
1
344
Ethan klaus
Hays
1
345
Lexie macumber
Hays
1
346
Gavin lamb
Hays
1
347
Kaden Tryon
Hays
1
348
Caven Krom
Hays
1
349
Cooper jones
Hays
1
350
Kade Wenta
Hays
1
351
Addyson Brown
Hays
1
352
Jacob Wente
Hays
1
353
Ty Dempsey
Hays
1
354
Madison Meis
Hays
1
355
Abigail Boyer
Hays
1
356
Kyler Riggs
Hays
1
357
Aiden Burton
Hays
1
358
Brygette Ross
Hays
1
359
Kim Del Real
Hays
1
360
Dakota Normandin
Hays
1
361
Hailey Klein
Hays
1
362
Konnor Dreiling
Hays
1
363
Dylan Stahl
Hays
1
364
Ben Zimmerman
Hays
1
365
Nohemi Lopez Vallejo
Hays
1
366
Kelby Hammerschmidt
Hays
1
367
Jaxon Zimmerman
Hays
1
368
Lilian McGrath
Hays
1
369
Bryan Camera
Hays
1
370
Gavin Flaska
Hays
1
371
Apryl Eschliman
Hays
1
372
Christapher Poage
Hays
1
373
Daniel Giebler
Hays
1
374
Harley Zimmerman
Hays
1
375
Lillyanna Alvarez
Hays
1
376
Orion Williams
Hays
1
377
Kaleb yaseen
Hays
1
378
Rhett Shelton
Hays
1
379
Carsen Riat
Hays
1
380
Chasey Wasinger
Hays
1
381
Kaylee Hammerschmidt
Hays
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 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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