Leaderboard
Oregon
Rank
Level
1
ChessWhiz
Lebanon
63
2
Mark Hernandez
Beaverton
59
3
Chris Davis
Metzger
56
4
Logan McGuire
Beaverton
48
5
Hassan Abderahman
Portland
44
6
Ben Schumacher
Sandy
43
7
User
Portland
41
8
Austin Timchuk
Beaverton
39
9
Shirley Nelson
Beaverton
36
10
carlo vega
Portland
35
11
Shine Lee
Portland
35
12
User
Vernonia
34
13
User
Portland
32
14
User
Beaverton
29
15
User
Portland
29
16
Temujin
Portland
28
17
User
Eugene
28
18
User
Hillsboro
27
19
User
Hillsboro
27
20
User
Beaverton
27
21
User
Beaverton
26
22
User
Portland
25
23
User
Seaside
24
24
User
Eugene
24
25
User
Portland
23
26
User
Silverton
23
27
User
Beaverton
23
28
User
Klamath Falls
23
29
User
Beaverton
22
30
User
Beaverton
22
31
User
Beaverton
22
32
User
Boardman
22
33
User
Portland
22
34
User
Beaverton
21
35
User
Corvallis
21
36
User
Hillsboro
21
37
User
Beaverton
20
38
Top Music 999.99
Portland
20
39
User
Beaverton
20
40
User
Lebanon
20
41
User
Portland
20
42
Lindsey
Beaverton
19
43
User
Portland
18
44
User
Ashland
18
45
User
Bend
18
46
User
Beaverton
17
47
User
Portland
17
48
User
Beaverton
17
49
Taylor Allen
Portland
16
50
Sofie Miller
Albany
16
51
User
Portland
16
52
User
Portland
15
53
User
Beaverton
15
54
Alyssa Jantz
Sandy
15
55
User
Eugene
15
56
User
Portland
15
57
User
Portland
15
58
User
Wilsonville
14
59
Aidan Amal
Portland
13
60
Sofia Waters
Beaverton
13
61
User
Beaverton
13
62
User
Beaverton
13
63
User
Hillsboro
13
64
User
Beaverton
13
65
User
Portland
13
66
User
Salem
12
67
User
Beaverton
12
68
User
Beaverton
12
69
Cyrus Fisher
Sandy
12
70
Jani
Albany
12
71
User
Sandy
11
72
User
Wilsonville
11
73
Logan Campbell
Sandy
11
74
User
Beaverton
11
75
User
Sandy
11
76
User
Banks
11
77
User
Portland
11
78
User
Tualatin
11
79
User
Hillsboro
11
80
User
Portland
11
81
User
Beaverton
10
82
User
Beaverton
10
83
User
Albany
10
84
User
Portland
10
85
Trent
Portland
10
86
User
Portland
10
87
User
Beaverton
9
88
Irelyn Sare-Hagerman
Sandy
9
89
User
Albany
9
90
User
Beaverton
9
91
User
Beaverton
9
92
User
Klamath Falls
8
93
User
Beaverton
8
94
User
Beaverton
8
95
User
Milwaukie
8
96
User
Vernonia
7
97
User
Beaverton
7
98
User
Sandy
7
99
User
Sandy
7
100
User
Beaverton
7
101
User
Portland
7
102
User
Sandy
7
103
User
Bend
7
104
User
Albany
7
105
User
Oak Grove
7
106
User
Corvallis
7
107
User
Tualatin
7
108
Carlo Gambino
Portland
6
109
User
Beaverton
6
110
User
Corvallis
6
111
Lillian Feist-Fosnot
Sandy
6
112
User
Sandy
6
113
User
Sandy
6
114
User
Sandy
6
115
User
Sandy
6
116
Sawyer Pratt
Sandy
6
117
kenny Antonio
Portland
6
118
User
Sandy
6
119
User
Hillsboro
6
120
User
Redmond
6
121
User
Eugene
6
122
User
Oatfield
6
123
User
Newport
6
124
User
Springfield
6
125
User
Portland
5
126
User
Sandy
5
127
User
Sandy
5
128
User
Keizer
5
129
Steven Newberry
Sandy
5
130
Elijiah Gutierrez
Sandy
5
131
Iana Train
Beaverton
5
132
User
Sandy
5
133
User
Sandy
5
134
Jack Jansen
Sandy
5
135
User
Medford
5
136
User
Sandy
5
137
User
Hillsboro
5
138
User
Portland
5
139
User
Portland
5
140
User
Portland
5
141
User
Beaverton
5
142
User
Bend
5
143
User
Portland
5
144
User
Hood River
5
145
User
Albany
5
146
User
Bend
4
147
taylor
Sandy
4
148
User
Portland
4
149
Seamus Ferguson
Beaverton
4
150
User
Beaverton
4
151
User
Tualatin
4
152
User
Sandy
4
153
User
Sandy
4
154
User
Albany
4
155
User
Sandy
4
156
User
Portland
4
157
Henry Bennett
Sandy
4
158
User
Sandy
4
159
User
Brownsville
4
160
User
Portland
4
161
User
Corvallis
4
162
User
Salem
3
163
User
Aloha
3
164
User
Portland
3
165
User
Sandy
3
166
Benjamin Gottschalk
Corvallis
3
167
User
Corvallis
3
168
User
Beaverton
3
169
User
Sandy
3
170
User
Sandy
3
171
Jersey Hogan
Sandy
3
172
User
Sandy
3
173
User
Beaverton
3
174
User
Sandy
3
175
User
Sandy
3
176
Kaiya Hollenbeck
Sandy
3
177
Selene Garcia
Sandy
3
178
User
Sandy
3
179
User
Grants Pass
3
180
User
Gresham
3
181
User
Creswell
3
182
User
Portland
3
183
XXRyeun.sanXX
Eugene
3
184
User
Beaverton
3
185
User
Corvallis
3
186
User
Milwaukie
3
187
User
Portland
3
188
Jordan Frink
Beaverton
3
189
User
Portland
3
190
User
Portland
2
191
User
Portland
2
192
User
Sandy
2
193
User
Sandy
2
194
User
Sandy
2
195
User
Sandy
2
196
User
Banks
2
197
User
Sandy
2
198
User
Sandy
2
199
jacob
Sandy
2
200
User
Sandy
2
201
User
Sandy
2
202
User
Sandy
2
203
User
Sandy
2
204
User
Sandy
2
205
User
Sandy
2
206
User
Sandy
2
207
User
Sandy
2
208
User
Sandy
2
209
User
Portland
2
210
User
Sandy
2
211
User
Sandy
2
212
User
Sandy
2
213
User
Sandy
2
214
User
Sandy
2
215
Jonah Cornell
Sandy
2
216
Drake Bixel
Sandy
2
217
User
Sandy
2
218
Savannah Boswell
Sandy
2
219
User
Sandy
2
220
User
Sandy
2
221
User
Sandy
2
222
User
Hillsboro
2
223
User
Odell
2
224
User
Portland
2
225
User
Portland
2
226
User
Beaverton
2
227
User
Cloverdale
2
228
User
Grants Pass
2
229
User
Lake Oswego
2
230
User
Portland
2
231
User
Salem
2
232
User
Tigard
2
233
User
Beaverton
2
234
User
Independence
2
235
User
Corvallis
2
236
User
Salem
2
237
User
Bend
2
238
User
Portland
2
239
User
Hillsboro
2
240
User
Portland
2
241
User
Bend
2
242
User
Beaverton
2
243
User
Lebanon
1
244
User
Corvallis
1
245
User
Tualatin
1
246
User
Portland
1
247
User
La Grande
1
248
User
Portland
1
249
User
Beaverton
1
250
Cody Divish
Sandy
1
251
Aspen French
Sandy
1
252
Hannah
Sandy
1
253
Rosillo
Sandy
1
254
Sophia Rojas Alcocer
Sandy
1
255
Colin Spitler
Sandy
1
256
Elliott Leibham
Sandy
1
257
Mickelle Santos
Sandy
1
258
Isabella Ringeisen
Sandy
1
259
Uyen Tran
Portland
1
260
Carter Wilson
Portland
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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