Leaderboard
Arizona
Rank
Level
1
User
Scottsdale
76
2
Sunil Devaraj
Mesa
65
3
User
Chandler
63
4
User
Tempe
56
5
Gabe Korer
Phoenix
56
6
User
Tempe
53
7
Julie F
Phoenix
52
8
User
Scottsdale
47
9
User
Florence
47
10
chad
Phoenix
45
11
User
Phoenix
45
12
User
Phoenix
44
13
User
Phoenix
44
14
User
Scottsdale
44
15
User
Phoenix
41
16
User
Phoenix
41
17
User
Phoenix
40
18
User
Tucson
40
19
Clayton Garnier
Mesa
40
20
User
Phoenix
39
21
User
Phoenix
39
22
User
Tempe
39
23
Julian T.
Phoenix
37
24
Bianca Supomo
Tucson
37
25
Amy Andrews
Glendale
36
26
User
Phoenix
35
27
User
Mesa
35
28
User
Phoenix
34
29
User
Phoenix
34
30
User
Mesa
33
31
User
Mesa
33
32
SBmath
Phoenix
32
33
User
Phoenix
31
34
User
Mesa
31
35
User
Tempe
30
36
User
Tucson Estates
30
37
Courtney Dozier
Scottsdale
30
38
User
Scottsdale
29
39
User
Phoenix
29
40
User
Tortolita
28
41
User
Yuma
28
42
User
Phoenix
27
43
jakob miller
Glendale
27
44
Naiya Martinez
Glendale
27
45
User
Scottsdale
27
46
User
San Tan Valley
26
47
User
Glendale
26
48
Jaydan Solorio
Glendale
26
49
User
Mesa
26
50
User
Tempe
26
51
Matt
Phoenix
26
52
User
Phoenix
25
53
Briant Trejo
Avondale
25
54
User
Tempe
25
55
Tara Ruhland
Phoenix
25
56
User
Phoenix
25
57
User
Tempe
24
58
Sonia Devaraj
Mesa
24
59
User
Mesa
24
60
User
Phoenix
23
61
User
City
22
62
Emanuele Saladini
Phoenix
22
63
User
Maricopa
22
64
Brayden Duran
Tucson
22
65
User
Bullhead City
22
66
steven pace
Glendale
22
67
User
Phoenix
22
68
kiernan Waite
Mesa
22
69
User
Tucson
22
70
User
Gilbert
22
71
User
Phoenix
22
72
User
Phoenix
21
73
User
Tucson
21
74
User
Scottsdale
21
75
User
Scottsdale
21
76
User
Scottsdale
21
77
Danny Harvell
Phoenix
20
78
User
Phoenix
20
79
User
Glendale
20
80
User
Phoenix
20
81
User
Show Low
20
82
User
Flagstaff
20
83
yellp1
Phoenix
20
84
tlannister
Flagstaff
19
85
User
Phoenix
19
86
User
Tempe
19
87
Nellie Garcia
Tucson
19
88
User
Glendale
19
89
User
San Luis
19
90
User
San Tan Valley
18
91
User
City
18
92
User
Tucson
18
93
User
Tempe
18
94
User
Tucson
18
95
User
Mesa
17
96
User
Fountain Hills
17
97
User
Chandler
17
98
User
Phoenix
16
99
User
Phoenix
16
100
Gordon He
Mesa
16
101
User
Glendale
16
102
User
Chandler
15
103
User
Phoenix
15
104
User
Tempe
15
105
User
Gilbert
15
106
User
San Tan Valley
14
107
User
Glendale
14
108
User
Phoenix
14
109
User
Tucson
14
110
User
Chandler
14
111
User
Gilbert
13
112
User
Tempe
13
113
User
Phoenix
13
114
User
Surprise
13
115
User
Phoenix
13
116
User
Phoenix
13
117
User
Phoenix
12
118
User
Scottsdale
12
119
User
Phoenix
12
120
User
Casas Adobes
12
121
Allie Williams
Tempe
12
122
User
Tucson
12
123
User
Gilbert
12
124
User
Mesa
11
125
User
Phoenix
11
126
User
Glendale
11
127
User
Phoenix
11
128
User
Chandler
11
129
User
Mesa
11
130
User
Phoenix
11
131
User
Chandler
11
132
User
Queen Creek
11
133
User
Phoenix
11
134
User
Tucson
11
135
User
Glendale
10
136
User
Phoenix
10
137
User
Queen Creek
10
138
User
Avondale
10
139
User
Tempe
10
140
User
Tucson
10
141
User
Phoenix
10
142
User
Tolleson
10
143
User
Tucson
10
144
User
Phoenix
9
145
Brett Gustafson
Flowing Wells
9
146
User
Tucson
9
147
User
Glendale
9
148
User
Phoenix
9
149
User
Phoenix
8
150
User
Phoenix
8
151
User
Phoenix
8
152
User
Scottsdale
8
153
User
Phoenix
8
154
Efren Ponce
Glendale
8
155
User
Mesa
8
156
julian pippins
Glendale
8
157
User
Tucson
8
158
User
Gilbert
8
159
Tammy
Phoenix
8
160
User
Phoenix
8
161
User
Bullhead City
8
162
User
Phoenix
8
163
User
Paradise Valley
8
164
User
Goodyear
7
165
User
Phoenix
7
166
User
Oro Valley
7
167
User
Glendale
7
168
User
Phoenix
7
169
User
Tempe
7
170
User
Scottsdale
7
171
User
Tucson
7
172
User
Prescott
7
173
User
Oro Valley
6
174
User
Phoenix
6
175
User
Kingman
6
176
User
Phoenix
6
177
User
Maricopa
6
178
User
Bisbee
6
179
User
Nogales
6
180
User
Phoenix
6
181
User
Catalina Foothills
6
182
User
Phoenix
6
183
User
Glendale
6
184
User
Glendale
6
185
Andy Guerra
Glendale
6
186
User
Phoenix
6
187
User
Litchfield Park
6
188
User
Tucson
6
189
User
Phoenix
6
190
User
Tucson
6
191
User
Gilbert
6
192
User
Fountain Hills
6
193
User
Phoenix
5
194
User
Chandler
5
195
User
Mesa
5
196
User
Phoenix
5
197
User
Phoenix
5
198
User
Prescott Valley
5
199
User
Glendale
5
200
User
Glendale
5
201
User
Glendale
5
202
User
Scottsdale
5
203
User
Glendale
5
204
User
Phoenix
5
205
Nyla Blattner
Glendale
5
206
User
Mesa
5
207
User
Scottsdale
5
208
User
Phoenix
4
209
User
Phoenix
4
210
User
Casas Adobes
4
211
User
Phoenix
4
212
User
Phoenix
4
213
User
Chandler
4
214
User
Oro Valley
4
215
User
Maricopa
4
216
User
Mesa
4
217
User
Globe
4
218
User
Glendale
4
219
User
Glendale
4
220
User
Gilbert
4
221
User
Phoenix
4
222
User
Marana
4
223
User
Gilbert
4
224
User
Phoenix
4
225
User
Phoenix
4
226
User
Phoenix
4
227
User
Phoenix
4
228
User
Phoenix
4
229
User
Mesa
4
230
User
Scottsdale
4
231
User
Chandler
4
232
User
Phoenix
3
233
User
Phoenix
3
234
User
Phoenix
3
235
User
Phoenix
3
236
User
Tucson
3
237
User
Phoenix
3
238
User
Phoenix
3
239
justin bainey
Phoenix
3
240
Danny Lisker
Phoenix
3
241
User
Glendale
3
242
User
Tucson
3
243
User
Apache Junction
3
244
User
Glendale
3
245
User
Tucson
3
246
User
Tucson
3
247
User
Mesa
3
248
User
Glendale
3
249
User
Tempe
3
250
User
Glendale
3
251
User
Phoenix
3
252
User
Glendale
3
253
User
Surprise
3
254
Colette Blattner
Glendale
3
255
User
Phoenix
3
256
User
Phoenix
3
257
User
Tucson
3
258
User
Phoenix
3
259
Peter Giaccone
Tucson
3
260
User
Phoenix
3
261
User
Phoenix
3
262
User
Chandler
3
263
User
Phoenix
2
264
User
Phoenix
2
265
User
Phoenix
2
266
User
Casas Adobes
2
267
User
Chandler
2
268
User
San Luis
2
269
User
Tempe
2
270
User
Tucson
2
271
User
Phoenix
2
272
User
Maricopa
2
273
User
Casas Adobes
2
274
User
Phoenix
2
275
User
Phoenix
2
276
User
Glendale
2
277
User
Phoenix
2
278
User
Mesa
2
279
User
Oro Valley
2
280
User
Glendale
2
281
User
Glendale
2
282
Pedro Hernandez Sanchez
Glendale
2
283
User
Glendale
2
284
User
Glendale
2
285
User
Glendale
2
286
User
Glendale
2
287
User
Glendale
2
288
User
Mesa
2
289
User
Phoenix
2
290
User
Tempe
2
291
User
Mesa
2
292
Maitri Bhakta
Mesa
2
293
Nic Guererro
Mesa
2
294
User
Phoenix
2
295
User
Phoenix
2
296
User
Kingman
2
297
User
Phoenix
2
298
User
Gilbert
2
299
User
Gilbert
2
300
User
Glendale
2
301
User
Surprise
2
302
User
Tucson
2
303
User
Mesa
2
304
User
Arizona City
2
305
User
Arizona City
2
306
User
Bullhead City
2
307
User
Gilbert
2
308
User
Tucson
2
309
User
Phoenix
2
310
User
Phoenix
2
311
User
Tempe
2
312
User
Sahuarita
2
313
User
Phoenix
2
314
User
Tucson
2
315
User
Yuma
2
316
User
Chandler
1
317
User
Peoria
1
318
User
Peoria
1
319
User
Phoenix
1
320
User
Gilbert
1
321
User
Phoenix
1
322
User
Phoenix
1
323
User
Phoenix
1
324
User
Tempe
1
325
User
Phoenix
1
326
User
Buckeye
1
327
User
Mesa
1
328
User
Tucson
1
329
User
Flagstaff
1
330
User
Gilbert
1
331
User
Phoenix
1
332
User
Goodyear
1
333
User
Tucson
1
334
User
Tucson Estates
1
335
User
Tucson
1
336
Justin Rainey
Phoenix
1
337
Dual Shotero
Phoenix
1
338
Freddy Hernandez
Glendale
1
339
Daniel Lopez
Glendale
1
340
Sally
Tucson
1
341
Marcus Singleton
Marana
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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