Leaderboard
Wisconsin
Rank
Level
1
chemita
Madison
53
2
User
Madison
53
3
Arnav Gupta
Waukesha
51
4
Allison Dickman
Madison
47
5
Chris Leatherberry
Sauk City
44
6
Sandy M.
Janesville
44
7
User
Janesville
40
8
Diya Rao
Madison
38
9
User
Waukesha
38
10
Bob T
Rice Lake
38
11
User
Madison
37
12
User
Madison
37
13
User
Middleton
35
14
Allen “Wait For It” Dowe
Oconomowoc
35
15
User
Madison
33
16
User
Neenah
31
17
Bodi Russo
Middleton
29
18
Quinn
Madison
28
19
User
Madison
28
20
User
Milwaukee
28
21
User
Janesville
27
22
User
Elm Grove
27
23
User
Weston
27
24
User
Menomonee Falls
26
25
Elise Schedler
Madison
26
26
User
Milwaukee
25
27
User
La Crosse
25
28
Annabelle
Madison
24
29
User
Mount Horeb
24
30
User
Waunakee
23
31
User
Madison
23
32
User
Madison
23
33
Jayden Xiong
Wausau
23
34
User
Waunakee
22
35
User
Madison
22
36
User
Janesville
21
37
User
Racine
21
38
User
Prairie Du Chien
21
39
User
Milwaukee
20
40
TheSchaitel
Melrose
20
41
User
Whitefish Bay
20
42
User
Albany
20
43
Lynette Weis
Wausau
20
44
User
Stoughton
20
45
User
Madison
19
46
User
Brown Deer
19
47
User
Madison
19
48
User
Cross Plains
19
49
User
Madison
18
50
User
Madison
17
51
User
Madison
17
52
Isaac Weaver
La Crosse
17
53
User
Madison
17
54
John Reeder
Madison
16
55
User
Madison
16
56
User
Menomonee Falls
16
57
User
Oshkosh
16
58
User
Mount Pleasant
15
59
User
Milwaukee
15
60
User
La Crosse
15
61
Isaac Repinski
Milwaukee
15
62
User
Milwaukee
14
63
William Rzentkowski
Madison
14
64
User
Eau Claire
14
65
Michael Proite
Milwaukee
14
66
User
Madison
14
67
User
Hayward
14
68
User
La Crosse
14
69
User
Verona
14
70
Duncan Isbister
Grafton
14
71
User
Middleton
13
72
User
Mishicot
13
73
User
Antigo
13
74
User
Milwaukee
13
75
User
Wausau
13
76
User
Appleton
13
77
User
Madison
13
78
User
Waukesha
13
79
User
Marshfield
13
80
User
Sun Prairie
12
81
Aksel Cichocki
Madison
12
82
User
Madison
12
83
Chris
Sauk City
12
84
User
Oshkosh
12
85
User
Green Bay
12
86
User
Madison
12
87
User
New Berlin
12
88
User
Madison
11
89
User
Milwaukee
11
90
User
De Pere
11
91
User
Oshkosh
11
92
User
Kenosha
11
93
User
Albany
11
94
Justin
Janesville
11
95
User
Madison
10
96
User
Whitewater
10
97
User
Brookfield
10
98
User
Brooklyn
10
99
User
Madison
10
100
User
Madison
10
101
zach
Milwaukee
9
102
User
Madison
9
103
User
Madison
9
104
User
Madison
9
105
User
Wausau
9
106
User
Wausau
9
107
Zachary Hackbarth
Wausau
9
108
User
Madison
9
109
User
Beaver Dam
9
110
User
Milwaukee
9
111
Naomi R Dubin
Madison
8
112
User
Camp Lake
8
113
User
Oshkosh
8
114
User
Beaver Dam
8
115
User
Wausau
8
116
User
Madison
8
117
Savannah Kenny
Madison
8
118
User
Madison
8
119
User
Madison
8
120
User
Oconomowoc
8
121
Trevor N Thwing
Madison
7
122
User
Oshkosh
7
123
User
Whitefish Bay
7
124
User
Madison
7
125
User
Mayville
7
126
User
Milwaukee
7
127
User
Pleasant Prairie
7
128
User
Wausau
7
129
User
Wausau
7
130
User
Madison
7
131
User
Madison
7
132
User
Baraboo
7
133
User
Whitefish Bay
6
134
User
Abrams
6
135
User
Okauchee Lake
6
136
User
Oshkosh
6
137
User
Oshkosh
6
138
User
Janesville
6
139
User
Madison
6
140
Angie Resendiz
Madison
6
141
User
Madison
6
142
User
Madison
6
143
User
Wauwatosa
6
144
User
Menomonee Falls
6
145
User
Madison
5
146
User
Menomonee Falls
5
147
User
Madison
5
148
User
Milwaukee
5
149
User
Elkhorn
5
150
User
Milwaukee
5
151
User
Madison
5
152
User
La Crosse
5
153
User
New London
5
154
User
Stoughton
5
155
CAMBER BRUNSWICK
Elkhorn
4
156
JULIO HERNANDEZ VILLANUEVA
Elkhorn
4
157
User
Elkhorn
4
158
Mira Russo
Madison
4
159
User
Oregon
4
160
User
Milwaukee
4
161
User
Watertown
4
162
User
Elkhorn
4
163
User
Green Bay
4
164
User
Hudson
4
165
User
Chaseburg
4
166
User
Madison
4
167
User
Madison
4
168
User
Madison
4
169
User
Madison
4
170
User
Milwaukee
4
171
User
Baraboo
4
172
User
Eau Claire
4
173
Alberto Rodriguez
Cottage Grove
3
174
User
Cottage Grove
3
175
User
River Hills
3
176
User
Milwaukee
3
177
NATASHA EDMUNDSON
Elkhorn
3
178
User
City
3
179
User
Greenfield
3
180
User
Stevens Point
3
181
Victor Cherchian
Madison
3
182
User
Middleton
3
183
User
De Pere
3
184
User
Monroe
3
185
User
Elkhorn
3
186
User
Glendale
3
187
User
Waupun
3
188
User
Mayville
3
189
User
Wausau
3
190
User
Wausau
3
191
User
Milwaukee
3
192
User
Milwaukee
3
193
User
Marshfield
3
194
User
Madison
3
195
User
Madison
3
196
User
Cottage Grove
3
197
User
Kenosha
3
198
User
Milwaukee
3
199
Dominick D Lee
Madison
2
200
User
Superior
2
201
User
Cleveland
2
202
User
Superior
2
203
User
Middleton
2
204
User
Madison
2
205
User
Wauwatosa
2
206
User
Menomonee Falls
2
207
User
La Crosse
2
208
User
Sun Prairie
2
209
User
City
2
210
User
Milwaukee
2
211
User
Elkhorn
2
212
User
Wausau
2
213
User
Elkhorn
2
214
User
Wausau
2
215
User
Oak Creek
2
216
User
La Crosse
2
217
User
Milwaukee
2
218
User
Waukesha
2
219
User
Rice Lake
2
220
User
La Crosse
2
221
User
Reedsburg
2
222
User
Fitchburg
2
223
User
Madison
2
224
User
Madison
2
225
User
Madison
2
226
User
Madison
2
227
User
Madison
2
228
User
Madison
2
229
User
Middleton
2
230
User
Madison
2
231
User
Union Grove
2
232
User
West Allis
2
233
User
Madison
2
234
User
Appleton
2
235
User
Oak Creek
2
236
User
Madison
2
237
User
Columbus
2
238
User
Oak Creek
1
239
User
Milwaukee
1
240
User
Madison
1
241
User
Milwaukee
1
242
NEVAEH A PHILLIPS
Madison
1
243
User
Spooner
1
244
User
Milwaukee
1
245
User
Milwaukee
1
246
User
Milwaukee
1
247
User
Rhinelander
1
248
User
Milwaukee
1
249
User
Mount Pleasant
1
250
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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