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