Leaderboard
Minnesota
Rank
Level
1
Pinchen Fan
Northfield
58
2
User
Maplewood
57
3
User
Minneapolis
57
4
User
Saint Paul
54
5
Ca P
Minneapolis
51
6
User
Minneapolis
50
7
User
Mendota Heights
48
8
Flej100
Oakdale
46
9
User
Thief River Falls
44
10
User
Shakopee
43
11
User
Minneapolis
43
12
User
Minneapolis
42
13
User
East Grand Forks
40
14
Adam Lemay
Minneapolis
40
15
kyle
Winnebago
39
16
User
Thief River Falls
38
17
User
Winona
38
18
User
Edina
37
19
User
Mankato
36
20
User
Minneapolis
35
21
User
Saint Paul
34
22
User
Lakeville
33
23
Alexandra
Brooklyn Park
32
24
User
Rochester
32
25
Zachary Pfiz
Rochester
32
26
User
Edina
31
27
User
Eden Prairie
31
28
User
Shorewood
30
29
User
Saint Paul
30
30
User
Minneapolis
29
31
User
Saint Paul
28
32
User
Minneapolis
28
33
User
Minneapolis
26
34
Joe
Minneapolis
26
35
User
Northfield
25
36
User
Saint Paul
25
37
User
Saint Paul
25
38
April Prchal
Eden Prairie
24
39
mitch spack
Minneapolis
23
40
User
Winnebago
23
41
User
Eden Prairie
23
42
User
Chaska
23
43
User
Elko New Market
23
44
User
Minneapolis
22
45
User
Duluth
21
46
User
Saint Paul
21
47
User
Shakopee
21
48
User
Rochester
21
49
User
East Grand Forks
20
50
User
Saint Paul
20
51
rick kick
Brooklyn Park
20
52
Nil Borrell
Minneapolis
20
53
User
Minneapolis
19
54
User
Chaska
18
55
Ian
Mankato
18
56
User
Saint Paul
18
57
Trisha
Eagan
18
58
User
Saint Paul
18
59
User
Golden Valley
17
60
Liv Steen
Saint Louis Park
17
61
User
Minneapolis
17
62
User
Bloomington
17
63
User
Minneapolis
17
64
User
Pierz
16
65
MB
Duluth
16
66
User
Minneapolis
16
67
User
Shakopee
15
68
User
Hennepin County
15
69
Sophie Gorham
Minneapolis
14
70
User
Saint Paul
14
71
Jon Hasan
Winona
14
72
User
Minneapolis
14
73
User
Minneapolis
14
74
User
Minneapolis
14
75
User
Northfield
13
76
User
Bloomington
13
77
User
Golden Valley
13
78
User
Plymouth
13
79
User
Minneapolis
13
80
User
Saint Paul
13
81
User
Eagan
12
82
KATRIANA TRINH
Minnetonka
12
83
User
Eden Prairie
12
84
User
Minneapolis
12
85
User
Minneapolis
12
86
User
Bloomington
12
87
User
Plymouth
12
88
Elsa
Minneapolis
12
89
Luis Tinoco
Minneapolis
12
90
User
Hennepin County
12
91
User
Chaska
11
92
User
Edina
11
93
User
Cottage Grove
11
94
User
Fridley
11
95
User
Minneapolis
11
96
User
Minneapolis
11
97
User
Minneapolis
11
98
User
Minneapolis
11
99
User
Minneapolis
10
100
User
Blaine
10
101
User
Edina
10
102
User
Eagan
10
103
Connor Sanvik
Winona
10
104
User
Rochester
10
105
User
New Ulm
10
106
User
Saint Paul
10
107
User
Minneapolis
9
108
User
Rochester
8
109
User
Shoreview
8
110
User
Golden Valley
8
111
User
Grand Marais
8
112
User
Eagan
7
113
User
Stewart
7
114
User
Winona
7
115
User
Minneapolis
7
116
User
Saint Paul
7
117
Gian Hernandez
Minneapolis
7
118
User
Plymouth
6
119
User
Apple Valley
6
120
User
Minneapolis
6
121
User
Minneapolis
6
122
User
Hutchinson
6
123
User
Eagan
6
124
User
New Ulm
6
125
User
Saint Louis Park
6
126
User
Saint Paul
6
127
User
Burnsville
6
128
User
Minneapolis
5
129
User
Chaska
5
130
User
Minneapolis
5
131
User
Saint Charles
5
132
User
Minneapolis
5
133
User
Burnsville
5
134
User
Spicer
5
135
User
Inver Grove Heights
5
136
User
Northfield
4
137
Alex Richardson
Saint Paul
4
138
User
Alexandria
4
139
User
Eagan
4
140
User
Shoreview
4
141
User
Edina
4
142
User
Plymouth
4
143
User
Richfield
4
144
User
Eveleth
4
145
User
Minneapolis
4
146
User
Minneapolis
4
147
User
Hennepin County
4
148
User
Northfield
3
149
User
Minneapolis
3
150
User
Minneapolis
3
151
User
Blaine
3
152
User
Minneapolis
3
153
User
Minneapolis
3
154
User
Winnebago
3
155
User
Edina
3
156
User
Lino Lakes
3
157
User
Marshall
3
158
User
Fridley
3
159
User
Minneapolis
3
160
User
Brooklyn Park
3
161
User
Cambridge
3
162
User
Minneapolis
3
163
User
Minneapolis
3
164
User
Minneapolis
3
165
User
Minneapolis
3
166
User
Duluth
3
167
User
Saint Paul
3
168
User
Hennepin County
3
169
User
Saint Paul
3
170
User
Golden Valley
2
171
User
Richfield
2
172
User
Milan
2
173
User
South Saint Paul
2
174
User
Duluth
2
175
Karter
Winnebago
2
176
User
Winnebago
2
177
User
Champlin
2
178
User
Brooklyn Park
2
179
User
Hawley
2
180
User
Saint Paul
2
181
User
Eagan
2
182
User
Shoreview
2
183
User
Eden Prairie
2
184
User
Richfield
2
185
User
Minneapolis
2
186
User
Eagan
2
187
User
Minnetonka
2
188
User
Golden Valley
2
189
Robert Kaiser
Maple Grove
2
190
User
Chaska
2
191
User
Minneapolis
2
192
User
Forest Lake
2
193
User
Saint Paul
2
194
User
Minneapolis
2
195
User
Minneapolis
2
196
User
Minneapolis
2
197
User
Ramsey
1
198
User
Saint Paul
1
199
User
Minneapolis
1
200
User
Forest Lake
1
201
David
Woodbury
1
202
User
Golden Valley
1
203
User
Sartell
1
204
Tyler LePage
Chaska
1
205
HERVE IDJIDINA
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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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