Leaderboard
Colorado
Rank
Level
1
Ryan Zhang
Fort Collins
88
2
Ellen Khat
Aurora
85
3
User
Westminster
81
4
Cody Goldman
Boulder
71
5
User
Denver
69
6
Will St. Pierre
Denver
67
7
User
Boulder
66
8
User
Denver
65
9
User
Denver
58
10
User
Fort Collins
56
11
Bosssssssss
Englewood
54
12
User
Castle Rock
53
13
Jordan Storz
Denver
49
14
User
Breckenridge
49
15
David Sprague
Denver
49
16
User
Denver
49
17
Mage of Antura
Lakewood
46
18
User
Castle Rock
46
19
User
Boulder
46
20
Alex Ziuraitis
Denver
44
21
mad genius
Louisville
44
22
User
Colorado Springs
43
23
User
Denver
42
24
User
Denver
41
25
Damon Achey
Colorado Springs
39
26
User
Denver
39
27
User
Greenwood Village
38
28
Erin B
Littleton
38
29
Kyle Kirkby
Fort Collins
38
30
Dipak Chaudhari
Centennial
37
31
User
Castle Rock
37
32
Abdullah Al Izzi
Denver
36
33
User
Colorado Springs
36
34
User
Longmont
35
35
User
Denver
33
36
Fred Yarger
Denver
32
37
User
Denver
32
38
User
Denver
31
39
User
Denver
31
40
Student Micah Kilburn
Castle Rock
31
41
Student Cooper Roberts
Castle Rock
31
42
User
Boulder
31
43
Dylan Clem
Fort Collins
30
44
User
Greenwood Village
30
45
User
Aurora
30
46
Daniel Talero
Boulder
30
47
User
Denver
30
48
User
Denver
29
49
User
Denver
29
50
User
Denver
28
51
Julian Harig
Littleton
28
52
Kathryn Sprague
Denver
27
53
Gabriela Carcasson
Fort Collins
27
54
Brandon Watson
Gypsum
27
55
User
Highlands Ranch
27
56
User
Aurora
27
57
User
Aurora
26
58
Neil Carlson
Colorado Springs
26
59
User
Arvada
26
60
User
Aurora
26
61
User
Denver
25
62
User
Fort Collins
25
63
Student Konnor Ramirez
Castle Rock
25
64
User
Fort Collins
24
65
User
Denver
24
66
User
Denver
24
67
User
Fort Morgan
23
68
User
U.S. Air Force Academy
23
69
User
Parker
23
70
User
Castle Rock
23
71
User
Centennial
22
72
Cecil Macgregor
Boulder
22
73
User
Denver
22
74
User
Boulder
22
75
User
Denver
22
76
User
Castle Rock
22
77
User
Castle Rock
22
78
User
Castle Rock
22
79
User
Boulder
22
80
User
Parker
22
81
User
Colorado Springs
21
82
User
Denver
21
83
User
Denver
21
84
User
Denver
21
85
User
Fort Lupton
21
86
User
Castle Rock
21
87
User
Fort Collins
21
88
User
Castle Rock
21
89
User
Littleton
21
90
User
Boulder
21
91
User
Broomfield
21
92
Darryl Lim
Parker
20
93
User
Commerce City
20
94
Josh Leigh
Greeley
20
95
User
Denver
20
96
User
Castle Rock
20
97
Haze
Centennial
19
98
Nikhila Punuru
Denver
19
99
User
Lakewood
19
100
User
Castle Rock
19
101
User
Boulder
19
102
User
Gypsum
18
103
Amari Valentine
Pueblo
18
104
User
Pagosa Springs
18
105
User
Ken Caryl
18
106
User
Boulder
18
107
User
Denver
18
108
User
Denver
17
109
User
Denver
17
110
User
Fowler
17
111
User
Denver
17
112
User
Lafayette
17
113
User
Castle Rock
17
114
Student Tanner Fitzsimons
Castle Rock
17
115
User
Loveland
16
116
User
Denver
16
117
User
Aurora
16
118
Grace Regnier
Cherry Hills Village
16
119
User
Denver
16
120
User
Arvada
16
121
User
Boulder
16
122
User
Denver
16
123
User
U.S. Air Force Academy
16
124
User
Boulder
16
125
User
Denver
15
126
User
Denver
15
127
User
Thornton
15
128
User
Castle Rock
15
129
User
Denver
15
130
Student Kaleid Headley
Castle Rock
15
131
Student Vitorio Dante
Castle Rock
15
132
User
Denver
15
133
User
Fort Collins
14
134
User
Denver
14
135
jay shah
Broomfield
14
136
User
Stonegate
14
137
User
Castle Rock
14
138
User
North Washington
13
139
User
Denver
13
140
User
Centennial
13
141
User
Denver
13
142
User
Boulder
13
143
User
Denver
13
144
User
Denver
13
145
User
Loveland
12
146
User
Fowler
12
147
User
Lakewood
12
148
User
Denver
12
149
User
Grand Junction
12
150
User
Vail
12
151
User
Aurora
12
152
Jacob Hough
Denver
12
153
User
Denver
12
154
User
Denver
12
155
User
Denver
12
156
User
Denver
11
157
User
Fowler
11
158
User
Boulder
11
159
User
Denver
11
160
User
Denver
11
161
User
Air Force Academy
11
162
User
Denver
11
163
User
Denver
10
164
User
Denver
10
165
Grace Wilson
Fort Collins
10
166
User
Ponderosa Park
10
167
User
Castle Rock
10
168
User
Castle Rock
10
169
User
Denver
10
170
User
Lakewood
9
171
User
Fort Collins
9
172
User
Denver
9
173
User
Fowler
9
174
User
Holly
9
175
User
Colorado Springs
9
176
User
Broomfield
9
177
User
Thornton
9
178
User
Denver
9
179
User
Denver
9
180
User
Denver
9
181
User
Aurora
9
182
User
Greeley
9
183
User
Castle Rock
9
184
User
Broomfield
9
185
User
Colorado Springs
9
186
Olivia Beck
Denver
8
187
User
Lakewood
8
188
User
Longmont
8
189
User
Holly
8
190
Noah Lievers
Fort Collins
8
191
User
Holly
8
192
User
Wheat Ridge
8
193
User
Denver
8
194
Nicholas Heil
Denver
8
195
User
Denver
8
196
User
Thornton
8
197
User
Gypsum
8
198
User
Limon
8
199
User
Denver
8
200
User
Denver
8
201
User
Denver
8
202
User
Denver
8
203
User
Denver
8
204
User
Denver
8
205
User
Durango
7
206
User
Holly
7
207
User
Holly
7
208
User
Aurora
7
209
User
Longmont
7
210
User
Fort Collins
7
211
User
Fort Collins
7
212
User
Denver
7
213
User
Lakewood
7
214
User
Denver
7
215
User
Lakewood
7
216
Curtis Turner
Colorado Springs
7
217
User
Castle Rock
7
218
User
Castle Rock
7
219
User
Castle Rock
7
220
User
Castle Rock
7
221
User
Castle Rock
7
222
User
Boulder
7
223
User
Loveland
6
224
User
Pueblo
6
225
User
Denver
6
226
User
Glenwood Springs
6
227
User
Denver
6
228
User
Lakewood
6
229
User
Holly
6
230
User
Colorado Springs
6
231
User
Boulder
6
232
User
Colorado Springs
6
233
User
Boulder
6
234
User
Fort Collins
6
235
Nick P.
Parker
6
236
User
Denver
6
237
User
Loveland
6
238
User
Denver
6
239
User
Colorado Springs
6
240
User
Boulder
6
241
User
Denver
6
242
User
Denver
6
243
User
Berthoud
6
244
User
Denver
6
245
User
Castle Rock
6
246
User
Littleton
6
247
User
Denver
6
248
User
Denver
6
249
User
Parker
6
250
User
Gunnison
6
251
User
Colorado Springs
5
252
User
Lakewood
5
253
User
Wheat Ridge
5
254
User
Aurora
5
255
User
Fowler
5
256
User
Holly
5
257
User
Fowler
5
258
User
Colorado Springs
5
259
User
Laporte
5
260
User
Fort Collins
5
261
User
Centennial
5
262
User
Denver
5
263
User
Denver
5
264
User
Denver
5
265
User
Parker
5
266
User
Denver
5
267
User
Denver
5
268
User
Greenwood Village
4
269
User
Pueblo
4
270
User
Colorado Springs
4
271
User
Loveland
4
272
User
Aurora
4
273
User
Littleton
4
274
User
Broomfield
4
275
User
Conifer
4
276
User
Fowler
4
277
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La Junta
4
278
User
Fowler
4
279
User
Fowler
4
280
User
Denver
4
281
User
Ken Caryl
4
282
User
Lakewood
4
283
User
Denver
4
284
User
Lakewood
4
285
User
Lakewood
4
286
User
Commerce City
4
287
User
Denver
4
288
User
Fort Collins
4
289
User
Denver
4
290
User
Denver
4
291
User
Loveland
4
292
User
Castle Rock
4
293
User
Castle Rock
4
294
User
Castle Rock
4
295
User
Castle Rock
4
296
User
Castle Rock
4
297
User
Woodland Park
4
298
User
Denver
4
299
User
Centennial
3
300
Mr. Frog
Thornton
3
301
User
Loveland
3
302
User
Longmont
3
303
User
Fowler
3
304
User
Durango
3
305
User
Colorado Springs
3
306
User
Colorado Springs
3
307
User
Limon
3
308
User
Denver
3
309
User
Gypsum
3
310
User
Colorado Springs
3
311
User
Grand Junction
3
312
User
Colorado Springs
3
313
User
Parker
3
314
User
Colorado Springs
3
315
User
Denver
3
316
User
Denver
3
317
User
Thornton
3
318
User
Colorado Springs
3
319
User
Denver
3
320
User
Rocky Ford
3
321
User
Denver
3
322
Student Tyler Garcia
Castle Rock
3
323
User
Castle Rock
3
324
User
Castle Rock
3
325
Student Juliana Woodward
Castle Rock
3
326
User
Castle Rock
3
327
User
Castle Rock
3
328
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Castle Rock
3
329
User
Castle Rock
3
330
Rebecca Herman
Colorado Springs
3
331
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Denver
3
332
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Loveland
2
333
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Loveland
2
334
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Denver
2
335
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Johnstown
2
336
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Greeley
2
337
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Castle Rock
2
338
Melanie Burke
Centennial
2
339
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Holly
2
340
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Denver
2
341
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Boulder
2
342
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Colorado Springs
2
343
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Thornton
2
344
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Denver
2
345
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Denver
2
346
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Denver
2
347
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City
2
348
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2
349
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2
350
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Lakewood
2
351
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Aurora
2
352
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Aurora
2
353
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Battlement Mesa
2
354
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Parker
2
355
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Boulder
2
356
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Denver
2
357
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Denver
2
358
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Boulder
2
359
User
Greeley
2
360
User
Fort Collins
2
361
User
Denver
2
362
Student Avery Hancock
Castle Rock
2
363
User
Denver
2
364
User
Lafayette
2
365
User
Denver
2
366
User
Denver
2
367
User
Denver
2
368
User
Arvada
2
369
User
Castle Rock
2
370
User
Castle Rock
2
371
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Castle Rock
2
372
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Castle Rock
2
373
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Castle Rock
2
374
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Castle Rock
2
375
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Castle Rock
2
376
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Castle Rock
2
377
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Castle Rock
2
378
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Castle Rock
2
379
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Castle Rock
2
380
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Castle Rock
2
381
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Castle Rock
2
382
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Castle Rock
2
383
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Colorado Springs
2
384
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Air Force Academy
2
385
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Loveland
2
386
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Denver
2
387
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Loveland
1
388
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Denver
1
389
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Lakewood
1
390
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Aurora
1
391
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Loveland
1
392
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Loveland
1
393
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Denver
1
394
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Loveland
1
395
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Greeley
1
396
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Windsor
1
397
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Denver
1
398
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Denver
1
399
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Windsor
1
400
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Denver
1
401
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Evergreen
1
402
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Highlands Ranch
1
403
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Grand Junction
1
404
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Denver
1
405
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Aurora
1
406
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Aurora
1
407
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Broomfield
1
408
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Brighton
1
409
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1
410
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1
411
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1
412
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1
413
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1
414
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1
415
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Fowler
1
416
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1
417
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1
418
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Aurora
1
419
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Louisville
1
420
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Rocky Ford
1
421
Emmerie Cantrell
Battlement Mesa
1
422
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Battlement Mesa
1
423
Student Tessa Doherty
Castle Rock
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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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