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