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