Leaderboard
Wisconsin
Rank
Level
1
Sandy M.
Janesville
56
2
Anurag Gupta
Waukesha
51
3
Arnav Gupta
Waukesha
49
4
Colin
Oak Creek
48
5
James Milgram
Pewaukee
46
6
chemita
Madison
37
7
User
Waukesha
36
8
User
River Falls
33
9
User
Kenosha
33
10
User
Hudson
33
11
User
Green Bay
32
12
Caiyun Resler
Waterloo
32
13
User
Manitowoc
32
14
User
Burlington
31
15
User
Woodruff
30
16
Anna Lutz
Marshall
29
17
User
Franklin
29
18
Chris Leatherberry
Sauk City
28
19
User
Oconomowoc
28
20
User
Madison
28
21
User
Milwaukee
26
22
Indu Konduru
Brookfield
25
23
User
Sussex
25
24
Allison Dickman
Madison
25
25
User
Janesville
23
26
User
Madison
23
27
User
West Baraboo
22
28
Isabella Rodriguez-Toro
Cottage Grove
21
29
Diya Rao
Madison
20
30
User
Sturgeon Bay
19
31
User
Madison
17
32
User
Mayville
17
33
User
Middleton
17
34
User
Waterloo
17
35
User
Oconomowoc
17
36
Allen “Wait For It” Dowe
Oconomowoc
16
37
Bodi Russo
Middleton
16
38
Quinn
Madison
15
39
User
Waukesha
15
40
User
Janesville
15
41
Bob T
Rice Lake
15
42
Mari McPheron
Middleton
14
43
User
Elm Grove
14
44
User
Weston
14
45
User
Sheboygan
14
46
User
Menomonee Falls
13
47
Annabelle
Madison
13
48
User
Madison
13
49
User
Lake Mills
13
50
User
Waunakee
13
51
User
Milwaukee
13
52
User
Madison
12
53
User
Janesville
12
54
User
Fox Point
12
55
User
Milwaukee
12
56
User
Madison
12
57
User
Madison
12
58
User
Milwaukee
11
59
User
Kaukauna
11
60
User
Janesville
11
61
TheSchaitel
Melrose
11
62
User
Hartland
11
63
User
Mount Horeb
11
64
User
Racine
11
65
User
Sturgeon Bay
11
66
User
Madison
11
67
User
Madison
11
68
User
Neenah
10
69
DREAM
Oak Creek
10
70
User
Waunakee
10
71
Rory Pond
Mequon
10
72
User
Madison
10
73
Jayden Xiong
Wausau
10
74
User
Madison
10
75
User
Madison
10
76
User
Madison
10
77
User
Madison
10
78
Matthew Paunicka
West Bend
10
79
User
Milwaukee
9
80
User
Middleton
9
81
Isaac Weaver
La Crosse
9
82
Elise Schedler
Madison
9
83
Luke krause
Pewaukee
9
84
Dehvan
New Glarus
9
85
User
Milwaukee
9
86
John Reeder
Madison
8
87
User
Waukesha
8
88
User
Madison
8
89
User
Whitefish Bay
8
90
User
Madison
8
91
Emily F
New Berlin
8
92
User
Franklin
8
93
User
Mount Pleasant
8
94
User
Mishicot
8
95
William Rzentkowski
Madison
7
96
Aksel Cichocki
Madison
7
97
User
Prairie Du Chien
7
98
Michael Proite
Milwaukee
7
99
User
Madison
7
100
User
Madison
7
101
User
Beaver Dam
7
102
User
Milwaukee
7
103
User
Antigo
7
104
User
Manitowoc
7
105
User
Middleton
7
106
User
Madison
7
107
User
Albany
7
108
Lynette Weis
Wausau
7
109
User
Madison
6
110
User
La Crosse
6
111
User
Brown Deer
6
112
User
Stoughton
6
113
zach
Milwaukee
6
114
User
Madison
6
115
User
Milwaukee
6
116
User
Milwaukee
6
117
User
Madison
6
118
User
Madison
6
119
User
Oshkosh
6
120
Anaythebeast
Pewaukee
6
121
User
Pewaukee
6
122
User
Wausau
6
123
User
Green Bay
5
124
User
De Pere
5
125
User
Oregon
5
126
User
Menomonee Falls
5
127
User
Madison
5
128
User
Waukesha
5
129
User
Menomonee Falls
5
130
User
Brookfield
5
131
User
Oshkosh
5
132
User
Madison
5
133
Trevor N Thwing
Madison
5
134
User
Whitewater
5
135
User
Oregon
5
136
User
Brookfield
5
137
User
Oshkosh
5
138
User
Milwaukee
5
139
User
Whitefish Bay
5
140
User
New Berlin
5
141
User
Appleton
5
142
User
Madison
5
143
User
Cadott
5
144
User
Kenosha
5
145
User
Madison
5
146
User
West Bend
5
147
User
Oak Creek
5
148
Naomi R Dubin
Madison
5
149
User
Madison
5
150
User
Albany
5
151
User
Fitchburg
5
152
User
Fond Du Lac
5
153
User
Camp Lake
5
154
User
Wausau
5
155
User
Wausau
5
156
Zachary Hackbarth
Wausau
5
157
Duncan Isbister
Grafton
5
158
User
Madison
5
159
User
Mayville
4
160
User
Madison
4
161
Isaac Repinski
Milwaukee
4
162
User
Brooklyn
4
163
User
Milwaukee
4
164
User
Madison
4
165
User
Oshkosh
4
166
Justin
Janesville
4
167
User
Beaver Dam
4
168
User
Wausau
4
169
User
Whitefish Bay
4
170
User
Abrams
4
171
User
Hudson
4
172
User
Madison
4
173
User
Beaver Dam
4
174
User
Milwaukee
4
175
User
Pleasant Prairie
4
176
User
Waukesha
4
177
User
Madison
4
178
Savannah Kenny
Madison
4
179
User
Sheboygan
4
180
User
Wausau
4
181
User
Wausau
4
182
User
Madison
4
183
User
Milwaukee
3
184
User
Madison
3
185
User
Madison
3
186
User
Okauchee Lake
3
187
User
Menomonee Falls
3
188
User
Oshkosh
3
189
User
Fredonia
3
190
User
Germantown
3
191
User
Madison
3
192
User
Madison
3
193
User
Oshkosh
3
194
User
Manitowoc
3
195
User
Milwaukee
3
196
User
Madison
3
197
User
Madison
3
198
User
Sheboygan
3
199
User
Madison
3
200
User
Madison
3
201
User
Janesville
3
202
User
Sheboygan
3
203
User
Madison
3
204
User
Milwaukee
3
205
User
Elkhorn
3
206
Angie Resendiz
Madison
3
207
User
Madison
3
208
User
Madison
3
209
User
Wauwatosa
2
210
User
Fitchburg
2
211
CAMBER BRUNSWICK
Elkhorn
2
212
JULIO HERNANDEZ VILLANUEVA
Elkhorn
2
213
User
Kimberly
2
214
User
Milwaukee
2
215
User
Elkhorn
2
216
User
Madison
2
217
User
La Crosse
2
218
Mira Russo
Madison
2
219
User
Madison
2
220
User
Sussex
2
221
User
Oregon
2
222
User
New London
2
223
User
Milwaukee
2
224
User
Belleville
2
225
User
Eau Claire
2
226
User
Antigo
2
227
User
Milwaukee
2
228
User
Cottage Grove
2
229
Alberto Rodriguez
Cottage Grove
2
230
User
River Hills
2
231
User
Milwaukee
2
232
User
Watertown
2
233
User
Elkhorn
2
234
User
Green Bay
2
235
NATASHA EDMUNDSON
Elkhorn
2
236
User
City
2
237
User
Hudson
2
238
User
Greenfield
2
239
User
Mequon
2
240
User
Stevens Point
2
241
User
Chaseburg
2
242
User
Milwaukee
2
243
Victor Cherchian
Madison
2
244
User
Middleton
2
245
User
Fitchburg
2
246
User
Neenah
2
247
User
De Pere
2
248
User
Monroe
2
249
Dominick D Lee
Madison
1
250
User
Elkhorn
1
251
User
Glendale
1
252
User
Lake Mills
1
253
User
Madison
1
254
User
Waupun
1
255
User
Mayville
1
256
User
Muskego
1
257
User
Madison
1
258
User
Madison
1
259
User
Madison
1
260
User
Hartland
1
261
User
Deforest
1
262
User
Madison
1
263
User
Madison
1
264
User
Madison
1
265
User
Superior
1
266
User
Milwaukee
1
267
User
Wausau
1
268
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Wausau
1
269
User
Cleveland
1
270
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Milwaukee
1
271
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Baraboo
1
272
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Superior
1
273
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Middleton
1
274
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Madison
1
275
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Milwaukee
1
276
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Milwaukee
1
277
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Lancaster
1
278
User
Wauwatosa
1
279
User
Appleton
1
280
User
Menomonee Falls
1
281
User
Marshfield
1
282
User
Rio
1
283
User
La Crosse
1
284
User
Sun Prairie
1
285
User
Madison
1
286
User
Madison
1
287
User
City
1
288
User
Milwaukee
1
289
User
Milwaukee
1
290
User
Elkhorn
1
291
User
Cottage Grove
1
292
User
Wausau
1
293
User
Elkhorn
1
294
User
Wausau
1
295
Noelle Greenwood
Kenosha
1
296
User
Madison
1
297
User
Laona
1
298
User
West Bend
1
299
User
Oak Creek
1
300
User
Janesville
1
301
User
La Crosse
1
302
User
Brookfield
1
303
User
Milwaukee
1
304
User
Kenosha
1
305
enzo
Oak Creek
1
306
User
Milwaukee
1
307
User
Madison
1
308
User
Madison
1
309
User
Waukesha
1
310
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Rice Lake
1
311
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La Crosse
1
312
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Hayward
1
313
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Reedsburg
1
314
Nevaeh A Phillips
Madison
1
315
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Waukesha
1
316
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Fitchburg
1
317
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Madison
1
318
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Madison
1
319
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Madison
1
320
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Madison
1
321
User
Madison
1
322
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Madison
1
323
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Middleton
1
324
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Milwaukee
1
325
User
Madison
1
326
User
Madison
1
327
User
Madison
1
328
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Middleton
1
329
Arnav Gupta
Pewaukee
1
330
User
Oak Creek
1
331
User
Milwaukee
1
332
User
Milwaukee
1
333
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Spooner
1
334
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Milwaukee
1
335
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Milwaukee
1
336
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Milwaukee
1
337
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Rhinelander
1
338
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Madison
1
339
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Union Grove
1
340
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West Allis
1
341
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Milwaukee
1
342
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Mount Pleasant
1
343
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Elkhorn
1
344
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Madison
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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