Leaderboard
Alabama
Rank
Level
1
Frank Qiang
Birmingham
71
2
Ben Brown
Birmingham
69
3
Arnav Gupta
Tuscaloosa
52
4
Aditya Gupta
Tuscaloosa
52
5
AruG
Tuscaloosa
50
6
User
Huntsville
45
7
JarredHodges
Sumiton
37
8
Super Frivolous
Madison
28
9
User
Vestavia Hills
28
10
User
Madison
28
11
User
Cullman
26
12
Changeabledead
Tuscaloosa
25
13
Amy Zhang
Hoover
25
14
Changeabledead
Tuscaloosa
25
15
Shane
Birmingham
24
16
Anna Claire Kinsey
Foley
23
17
User
Foley
19
18
User
Birmingham
19
19
Tim Robin
Vestavia Hills
17
20
User
Huntsville
16
21
Adam Haverkamp
Redstone Arsenal
16
22
User
Daphne
16
23
User
Daphne
16
24
User
Tuscaloosa
15
25
User
Birmingham
15
26
User
Mobile
15
27
User
Tuscaloosa
14
28
User
Huntsville
14
29
User
Hanceville
14
30
User
Huntsville
13
31
User
Tuscaloosa
12
32
User
Huntsville
11
33
User
Huntsville
11
34
User
Northport
11
35
Akari Horikita
Huntsville
11
36
User
Orange Beach
10
37
User
Daleville
10
38
User
Birmingham
10
39
User
Mobile
10
40
User
Foley
10
41
User
Huntsville
10
42
User
Tuscaloosa
9
43
User
Huntsville
9
44
User
Huntsville
9
45
User
Foley
9
46
User
Foley
9
47
User
Luverne
9
48
User
Foley
8
49
User
Tuscaloosa
8
50
User
Foley
7
51
User
Huntsville
7
52
Samuel Wegrzynowski
Tuscaloosa
7
53
User
Foley
7
54
User
Leeds
7
55
User
Huntsville
7
56
User
Montgomery
7
57
User
Foley
7
58
User
Foley
7
59
User
Huntsville
6
60
User
Foley
6
61
User
Auburn
6
62
User
Birmingham
6
63
User
Northport
6
64
User
Foley
6
65
User
Alabaster
5
66
User
Hoover
5
67
User
Foley
5
68
Christopher Smith
Greenville
5
69
User
Foley
5
70
User
Foley
5
71
User
Tuscaloosa
5
72
User
Huntsville
5
73
User
Foley
5
74
User
Foley
5
75
User
Foley
5
76
User
Foley
5
77
User
Huntsville
5
78
User
Opelika
5
79
User
Birmingham
5
80
User
Madison
5
81
User
Foley
5
82
User
Foley
5
83
User
Foley
5
84
User
Foley
5
85
User
Tuscaloosa
4
86
User
Enterprise
4
87
User
Madison
4
88
User
Northport
4
89
User
Foley
4
90
User
Foley
4
91
User
Foley
4
92
User
Florence
4
93
User
Homewood
4
94
User
Foley
4
95
User
Foley
4
96
User
Foley
4
97
User
Foley
4
98
User
Foley
4
99
User
Foley
4
100
User
Mobile
4
101
User
Foley
4
102
User
Dothan
3
103
User
Huntsville
3
104
User
Foley
3
105
User
Irondale
3
106
User
Daphne
3
107
User
Huntsville
3
108
User
Huntsville
3
109
User
Birmingham
3
110
User
Northport
3
111
Dolly Haze
Huntsville
3
112
User
Foley
3
113
User
Foley
3
114
User
Foley
3
115
User
Foley
3
116
User
Foley
3
117
User
Huntsville
3
118
User
Birmingham
2
119
User
City
2
120
User
Birmingham
2
121
User
Dothan
2
122
User
Birmingham
2
123
User
Foley
2
124
User
Foley
2
125
User
Foley
2
126
Molly Cameron
Marbury
2
127
User
Pelham
2
128
User
Birmingham
2
129
User
Birmingham
2
130
User
Birmingham
2
131
User
Mobile
2
132
User
Fairhope
2
133
User
Florence
2
134
User
Prattville
2
135
User
Birmingham
2
136
User
Tuscaloosa
2
137
User
Birmingham
2
138
User
Foley
1
139
User
Foley
1
140
User
Foley
1
141
User
Birmingham
1
142
User
Huntsville
1
143
User
Dothan
1
144
User
Montgomery
1
145
User
Huntsville
1
146
User
Walnut Grove
1
147
User
Hartselle
1
148
User
Opelika
1
149
User
Tuscaloosa
1
150
User
Madison
1
151
User
Montgomery
1
152
User
Clanton
1
153
User
Huntsville
1
154
User
Fort Benning
1
155
User
Foley
1
156
wack
Foley
1
157
User
Foley
1
158
User
Huntsville
1
159
User
Smiths Station
1
160
User
Florence
1
161
User
Tuscaloosa
1
162
User
Tuscaloosa
1
163
User
Tuscaloosa
1
164
User
Birmingham
1
165
User
Trussville
1
166
User
Hoover
1
167
User
Blue Ridge
1
168
User
Tuscaloosa
1
169
User
Birmingham
1
170
User
Foley
1
171
Monica Shubert
Huntsville
1
172
User
Auburn
1
173
User
Tuscaloosa
1
174
User
Huntsville
1
175
User
Selma
1
176
User
Redstone Arsenal
1
177
User
Foley
1
178
User
Birmingham
1
179
User
Madison
1
180
User
Montgomery
1
181
User
Huntsville
1
182
User
Huntsville
1
183
Peter Powell
Tuscaloosa
1
184
User
Birmingham
1
185
User
Madison
1
186
User
Huntsville
1
187
User
Atmore
1
188
User
Montgomery
1
189
User
Montgomery
1
190
User
Montgomery
1
191
User
Montgomery
1
192
User
Foley
1
193
Emmanuel Asiedu
Evergreen
1
194
User
Rogersville
1
195
User
Gardendale
1
196
User
Foley
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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