Leaderboard
Missouri
Rank
Level
1
The Rarest Frog
Ballwin
94
2
User
Kirkwood
75
3
William Pan
Creve Coeur
73
4
Brandt Lawson
Clayton
73
5
Elana Greenberg
Kansas City
72
6
User
St. Louis
70
7
User
Farmington
68
8
User
Kirkwood
65
9
User
University City
60
10
EVAN SOMMER - STUDENT
Wildwood
59
11
User
Maryville
57
12
Victoria Phillips
Kansas City
54
13
Soham Bose
Kansas City
52
14
Steven
Affton
50
15
User
Oakville
49
16
User
Columbia
46
17
User
Clayton
46
18
Koby Chadick
Kansas City
45
19
User
St. Louis
43
20
User
Ballwin
43
21
User
Columbia
39
22
Abheek Dhawan
Kirkwood
37
23
User
Springfield
36
24
User
Chesterfield
36
25
User
Berkeley
35
26
User
Ozark
35
27
Rishi Suri
Creve Coeur
35
28
User
St. Louis
35
29
User
Chesterfield
34
30
User
Columbia
32
31
User
Columbia
32
32
Sally Cosgrove
Saint Joseph
32
33
User
Waynesville
32
34
User
Creve Coeur
30
35
User
Clayton
29
36
Aditya Jain
Glendale
29
37
User
Columbia
29
38
User
Eureka
29
39
User
LeeS Summit
27
40
User
St. Louis
27
41
User
Columbia
27
42
User
Manchester
26
43
User
Kansas City
26
44
User
Fenton
26
45
User
Chesterfield
26
46
Tristan Gibson
Affton
26
47
User
Webster Groves
26
48
User
St. Louis
26
49
Walrus Here
LeeS Summit
25
50
User
Columbia
25
51
Keith Robertson
Kansas City
25
52
User
Springfield
24
53
User
Columbia
24
54
User
Columbia
24
55
User
Kirkwood
24
56
User
St. Louis
23
57
Greg Rainwater
Springfield
23
58
User
St. Louis
23
59
User
Creve Coeur
23
60
Clare
Overland
23
61
Maria Medrano
University City
23
62
Elizabeth Moreland
University City
22
63
User
Webster Groves
22
64
Lena Demura
Kansas City
22
65
User
LeeS Summit
22
66
User
Creve Coeur
22
67
User
Rolla
22
68
User
St. Louis
22
69
User
St. Louis
21
70
User
Columbia
21
71
User
LeeS Summit
21
72
mikki
Columbia
21
73
User
Liberty
21
74
User
Clayton
21
75
User
Florissant
21
76
Gavin Hofmeister
Cape Girardeau
21
77
User
Joplin
20
78
User
Creve Coeur
19
79
User
Kansas City
19
80
User
Florissant
19
81
User
Springfield
19
82
Monse A
Gladstone
19
83
User
Maryland Heights
19
84
User
St. Louis
19
85
User
St. Louis
19
86
User
Columbia
19
87
User
Columbia
18
88
User
Maryland Heights
17
89
User
Creve Coeur
17
90
User
Clayton
17
91
User
St. Louis
17
92
Ryan Waller
OFallon
16
93
Koby
Kansas City
16
94
User
Columbia
16
95
User
Clayton
16
96
User
LeeS Summit
16
97
User
Webster Groves
15
98
User
Columbia
15
99
User
Branson
15
100
User
Clayton
15
101
User
Glendale
15
102
User
St. Charles
15
103
User
Saint Cloud
14
104
User
Washington
14
105
User
St. Louis
14
106
User
Kansas City
14
107
User
University City
14
108
User
Kansas City
14
109
Stephanie Achoa
Clayton
14
110
Christopher Rhoda
Saint Robert
14
111
User
Columbia
14
112
User
Platte City
13
113
User
Kansas City
13
114
User
Noel
13
115
Russell Hart
Kansas City
13
116
User
Kansas City
13
117
User
St. Louis
13
118
User
Columbia
13
119
Linmei Amaya
Kansas City
12
120
User
Kansas City
12
121
User
Chesterfield
12
122
User
St. Louis
12
123
User
Richmond
12
124
User
Columbia
12
125
User
Clayton
12
126
User
Joplin
12
127
User
Webster Groves
11
128
User
Kirksville
11
129
User
Wentzville
11
130
User
Columbia
11
131
User
Branson
11
132
User
Kansas City
11
133
User
Columbia
11
134
Robert Gastler
Columbia
11
135
User
Kansas City
10
136
User
Liberty
10
137
Larae Fifer
Carl Junction
10
138
User
Clayton
10
139
User
St. Louis
10
140
Joshua Harris
Troy
10
141
Ronik Bhaskar
Manchester
10
142
User
Columbia
10
143
User
Columbia
10
144
User
Columbia
10
145
User
Columbia
10
146
Louie Fazio
Clayton
10
147
User
St. Louis
10
148
User
St. Louis
10
149
User
St. Louis
9
150
User
Columbia
9
151
User
Clayton
9
152
User
Belton
9
153
User
Columbia
9
154
User
Columbia
9
155
User
Kansas City
9
156
User
Wentzville
9
157
User
St. Louis
9
158
Kristin Droege
Kansas City
8
159
User
St. Louis
8
160
User
Webster Groves
8
161
User
Columbia
8
162
User
Parkville
8
163
User
Wildwood
8
164
User
Columbia
8
165
User
Columbia
8
166
User
Columbia
8
167
User
Florissant
8
168
User
Wildwood
7
169
User
Kansas City
7
170
User
Wentzville
7
171
User
Ballwin
7
172
User
Columbia
7
173
User
Webster Groves
7
174
User
Kansas City
7
175
User
Kirkwood
7
176
User
OFallon
7
177
User
Columbia
7
178
User
Columbia
7
179
User
Columbia
7
180
User
Columbia
7
181
User
St. Louis
7
182
User
Kansas City
7
183
User
Joplin
7
184
User
Independence
6
185
User
Kansas City
6
186
User
Columbia
6
187
User
Springfield
6
188
Alexis Jackson
St. Louis
6
189
User
Chesterfield
6
190
User
Kirkwood
6
191
tyler
Columbia
6
192
User
Manchester
6
193
User
Clayton
6
194
User
Creve Coeur
6
195
User
Columbia
6
196
User
Columbia
6
197
User
Columbia
6
198
User
Columbia
6
199
User
Columbia
6
200
User
Columbia
6
201
User
Columbia
6
202
User
Columbia
6
203
User
Columbia
6
204
User
Grain Valley
6
205
User
Joplin
6
206
User
St. Louis
6
207
User
St. Louis
6
208
User
Springfield
6
209
User
Florissant
5
210
Ashley,Atkinson
Knob Noster
5
211
User
Kansas City
5
212
User
St. Peters
5
213
User
Ballwin
5
214
User
Ozark
5
215
User
Warrenton
5
216
User
Smithville
5
217
User
Springfield
5
218
User
Saint Joseph
5
219
User
Columbia
5
220
User
Columbia
5
221
User
Columbia
5
222
User
Columbia
5
223
User
LeeS Summit
5
224
STUDENT Claudia Kramer
Overland
5
225
User
St. Louis
4
226
User
Barnhart
4
227
User
Parkville
4
228
User
Saint Charles
4
229
User
Washington
4
230
Emily
Saint Thomas
4
231
User
Affton
4
232
User
Grain Valley
4
233
User
St. Louis
4
234
User
Branson
4
235
User
Chillicothe
4
236
User
Jefferson City
4
237
User
St. Louis
4
238
User
Clayton
4
239
User
Columbia
4
240
User
OFallon
4
241
User
Columbia
4
242
User
Columbia
4
243
User
Columbia
4
244
User
Grain Valley
4
245
User
Overland
4
246
User
Ballwin
4
247
User
Kansas City
4
248
User
St. Louis
3
249
User
Ferguson
3
250
User
Farmington
3
251
User
Carl Junction
3
252
User
Kansas City
3
253
User
Springfield
3
254
User
Cape Girardeau
3
255
User
University City
3
256
User
St. Louis
3
257
User
St. Louis
3
258
User
St. Louis
3
259
User
Ferguson
3
260
User
Ballwin
3
261
User
University City
3
262
User
OFallon
3
263
User
University City
3
264
User
Clayton
3
265
User
Columbia
3
266
User
Columbia
3
267
User
Columbia
3
268
User
Columbia
3
269
User
Clayton
3
270
User
Grain Valley
3
271
User
Arrow Point
3
272
User
Springfield
2
273
User
Kansas City
2
274
User
New Bloomfield
2
275
User
St. Louis
2
276
User
University City
2
277
User
OFallon
2
278
User
OFallon
2
279
User
Ballwin
2
280
User
Saint Joseph
2
281
User
Creve Coeur
2
282
User
Poplar Bluff
2
283
User
Marshall
2
284
BOB H
Wentzville
2
285
Lakyesha Massey
St. Louis
2
286
User
St. Louis
2
287
Rose Young
Bellefontaine Neighbors
2
288
User
St. Louis
2
289
User
St. Louis
2
290
anthem.electric@gmail.com
Belton
2
291
Emma Glassner
Cedar Hill
2
292
User
Farmington
2
293
User
Jefferson City
2
294
User
Warrenton
2
295
User
St. Louis
2
296
User
Webb City
2
297
User
Festus
2
298
User
St. Peters
2
299
User
Kansas City
2
300
User
Clayton
2
301
User
Clayton
2
302
User
Camdenton
2
303
User
Black Jack
2
304
User
OFallon
2
305
User
St. Louis
2
306
User
St. Louis
2
307
User
Kansas City
2
308
User
Saint Joseph
2
309
User
Kansas City
2
310
User
Columbia
2
311
User
Columbia
2
312
User
Columbia
2
313
User
Columbia
2
314
User
Columbia
2
315
User
Columbia
2
316
User
Columbia
2
317
User
Columbia
2
318
User
Columbia
2
319
User
St. Louis
2
320
User
St. Louis
2
321
User
Kansas City
2
322
STUDENT Atticus Kramer
Overland
2
323
User
Grain Valley
2
324
User
St. Louis
2
325
User
St. Louis
2
326
User
Kansas City
2
327
User
Kansas City
2
328
User
Kansas City
1
329
User
OFallon
1
330
User
St. Louis
1
331
User
Maryland Heights
1
332
User
Creve Coeur
1
333
User
City
1
334
User
Liberty
1
335
User
Springfield
1
336
User
Kansas City
1
337
User
Clayton
1
338
User
Raymore
1
339
User
Kahoka
1
340
User
Knob Noster
1
341
Demonte Haley
Florissant
1
342
User
Sedalia
1
343
User
St. Louis
1
344
User
St. Louis
1
345
User
Spanish Lake
1
346
Kenneth Prockl
Concord
1
347
Kenyada Brackett
St. Louis
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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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