Leaderboard
Connecticut
Rank
Level
1
Tyler Shen
New Haven
87
2
Daregs
New Haven
82
3
User
New Haven
81
4
User
Norwalk
80
5
Lukas Baker
Suffield
79
6
Cameron Allen
Stamford
70
7
Collin Crader
Avon
66
8
User
Greenwich
65
9
Alla Shved
West Hartford
63
10
User
Westport
63
11
User
Manchester
61
12
DG
West Haven
61
13
User
West Haven
59
14
D G
West Haven
57
15
User
Westport
57
16
User
Westport
56
17
User
New Haven
56
18
John Ordway
Westport
53
19
Euclid1023
Bristol
53
20
User
Stonington
52
21
User
Greenwich
50
22
User
Norwalk
49
23
User
Westport
49
24
David
Greenwich
47
25
andocides
New Haven
46
26
Kyle Bleakley
Trumbull
42
27
User
Norwalk
41
28
Darnell Payne
Hartford
41
29
Ryan Miklautsch
Greenwich
40
30
User
Westport
38
31
Xindy waneski
New Fairfield
37
32
User
West Hartford
36
33
User
Westport
35
34
Alex
Danbury
34
35
User
Westport
34
36
User
Stamford
34
37
User
New Haven
33
38
User
New Haven
33
39
User
New Haven
33
40
Yingjie
New Haven
33
41
User
Manchester
32
42
User
Westport
32
43
User
New Haven
32
44
User
New Haven
31
45
User
New Britain
31
46
User
Stamford
31
47
User
Trumbull
30
48
User
Waterbury
29
49
User
West Haven
29
50
User
Woodbury
29
51
User
Trumbull
29
52
User
Wallingford
28
53
User
New Haven
28
54
User
South Windsor
27
55
User
Milford
27
56
Soni Singh
Newtown
27
57
Becky
New Haven
27
58
User
West Haven
26
59
User
New Haven
26
60
User
New Haven
25
61
User
New Haven
25
62
User
Greenwich
24
63
Jill Studdard
West Haven
24
64
User
Greenwich
23
65
User
Bristol
23
66
User
Danbury
23
67
User
West Hartford
23
68
User
Greenwich
23
69
User
New Haven
22
70
User
New Haven
22
71
User
Trumbull
22
72
Ellie Nelson
Stamford
22
73
User
Trumbull
22
74
Ethan Labagnara (Class of 2020)
Cheshire
21
75
User
Westport
21
76
User
New Britain
21
77
User
Suffield
21
78
User
New Haven
21
79
User
West Haven
20
80
User
Trumbull
20
81
Danielle Payne
Wallingford
20
82
User
Darien
20
83
User
West Haven
20
84
User
Greenwich
19
85
User
New Milford
19
86
User
New Haven
19
87
User
West Haven
18
88
User
Westport
18
89
User
Groton
18
90
User
Stamford
18
91
User
New Haven
18
92
User
Hamden
18
93
User
Greenwich
17
94
User
New Britain
16
95
User
Berlin
16
96
User
Westport
16
97
User
Trumbull
16
98
User
New Haven
16
99
User
Norwalk
16
100
User
New Haven
15
101
User
West Haven
15
102
User
West Haven
15
103
User
Bristol
15
104
User
Trumbull
15
105
User
Redding
15
106
User
Norwalk
15
107
User
Hartford
15
108
User
New Haven
15
109
User
New Haven
14
110
User
New Milford
14
111
User
Westport
14
112
User
West Haven
14
113
User
West Haven
14
114
User
Stamford
14
115
User
New Haven
14
116
User
New Haven
14
117
User
Newtown
14
118
User
Trumbull
14
119
User
Cheshire
14
120
User
West Hartford
13
121
User
Clinton
13
122
User
Trumbull
13
123
User
New Haven
13
124
User
South Windsor
12
125
User
Farmington
12
126
User
West Haven
12
127
User
Watertown
12
128
User
New Haven
12
129
User
Hartford
12
130
User
Plainfield
12
131
User
Hamden
12
132
User
Meriden
11
133
User
Fairfield
11
134
User
Milford
11
135
User
Westport
11
136
User
New Haven
11
137
User
Manchester
11
138
User
New Britain
11
139
User
New Haven
11
140
User
Colchester
11
141
User
West Hartford
11
142
User
Fairfield
11
143
User
West Hartford
11
144
User
Hartford
10
145
User
Groton
10
146
User
Washington
10
147
User
New London
10
148
User
Trumbull
10
149
User
West Haven
10
150
User
Westport
10
151
User
New Haven
10
152
User
New Haven
10
153
User
Orange
10
154
User
Fairfield
10
155
User
New London
10
156
User
Wethersfield
10
157
User
West Haven
9
158
Aidan Smith
New Milford
9
159
User
Hartford
9
160
User
New Milford
9
161
User
Wallingford
9
162
User
Trumbull
9
163
User
Storrs
9
164
User
Danbury
8
165
User
Hartford
8
166
User
West Haven
8
167
User
West Haven
8
168
User
Milford
8
169
User
Newington
8
170
User
New Haven
8
171
User
Hartford
8
172
Maria Stadler
Fairfield
8
173
User
New Haven
8
174
Josefina
New Haven
7
175
Sridhar Nadendla
Stamford
7
176
Jeffrey Walker
West Haven
7
177
User
Wilton
7
178
User
New Milford
7
179
User
West Haven
7
180
User
New Haven
7
181
User
Westport
7
182
Average Ape
New Milford
7
183
William Feinberg
Guilford
7
184
User
Clinton
6
185
User
New Haven
6
186
User
Darien
6
187
User
West Hartford
6
188
User
Greenwich
6
189
User
Bridgeport
6
190
User
West Haven
6
191
Spencer
Stamford
6
192
User
Farmington
6
193
User
Stafford
6
194
User
Madison
6
195
User
Woodstock
6
196
User
New Haven
6
197
User
Groton
6
198
User
Danbury
6
199
User
West Haven
5
200
User
New Haven
5
201
User
Manchester
5
202
User
Watertown
5
203
User
West Haven
5
204
User
Hartford
5
205
User
South Windsor
5
206
User
Stamford
5
207
User
Danbury
5
208
User
Enfield
5
209
User
Enfield
5
210
User
Norwalk
5
211
User
Rocky Hill
5
212
User
Groton
5
213
User
Naugatuck
5
214
User
Wilton
5
215
User
Ledyard
4
216
User
Norwalk
4
217
User
Stamford
4
218
User
Stamford
4
219
Vandana Sood
Branford
4
220
User
New Haven
4
221
User
Stratford
4
222
User
West Haven
4
223
User
West Haven
4
224
User
New Milford
4
225
User
Stafford
4
226
User
East Haven
4
227
User
Wallingford
4
228
User
Bridgeport
4
229
User
Trumbull
4
230
User
Avon
4
231
User
New Milford
4
232
User
New Milford
4
233
User
New Milford
4
234
User
Stamford
4
235
User
Wallingford
4
236
User
West Hartford
4
237
User
East Lyme
4
238
Tom
New Haven
4
239
User
New Haven
4
240
User
Trumbull
4
241
User
Stamford
4
242
User
Middletown
4
243
User
New Haven
4
244
User
Middletown
4
245
User
Storrs
4
246
User
Stamford
4
247
User
Stamford
3
248
User
Norwich
3
249
User
New Haven
3
250
User
New London
3
251
User
Mansfield
3
252
User
Ansonia
3
253
User
West Haven
3
254
User
West Haven
3
255
User
New Haven
3
256
User
Suffield
3
257
User
Stamford
3
258
User
Stamford
3
259
User
New Haven
3
260
User
Darien
3
261
User
Trumbull
3
262
User
Trumbull
3
263
User
Avon
3
264
User
Mansfield
3
265
User
New Haven
3
266
User
Danbury
3
267
User
New Milford
3
268
User
Middletown
3
269
User
New Haven
3
270
User
Meriden
3
271
User
Stamford
3
272
User
Greenwich
3
273
User
New Britain
3
274
User
New Haven
3
275
User
Middletown
3
276
User
Middletown
3
277
User
Monroe
3
278
User
Norwich
3
279
User
New Haven
3
280
User
Windsor Locks
3
281
User
Windsor Locks
3
282
User
Danbury
3
283
User
Durham
2
284
User
Windham
2
285
User
Plainville
2
286
User
Marlborough
2
287
User
New Haven
2
288
User
Greenwich
2
289
User
Mansfield
2
290
User
New Haven
2
291
User
Farmington
2
292
User
Hamden
2
293
User
West Haven
2
294
User
West Haven
2
295
User
New Milford
2
296
User
Windsor
2
297
User
Hartford
2
298
User
Westport
2
299
User
Trumbull
2
300
User
Westport
2
301
User
New Milford
2
302
User
East Hartford
2
303
User
New Milford
2
304
User
New Britain
2
305
User
New Haven
2
306
User
Greenwich
2
307
User
Stonington
2
308
User
New Haven
2
309
User
Middletown
2
310
User
Sherman
2
311
User
Middletown
2
312
User
Middletown
2
313
User
Brookfield
2
314
User
Darien
2
315
User
New Canaan
2
316
User
Stratford
2
317
User
New Haven
2
318
User
Cheshire
2
319
User
Torrington
2
320
User
New Haven
2
321
User
Torrington
2
322
User
Greenwich
2
323
User
Weston
2
324
Chelsie
Watertown
1
325
User
Milford
1
326
User
Stratford
1
327
Hugh Seaton
Stamford
1
328
User
Farmington
1
329
User
Milford
1
330
User
Trumbull
1
331
User
West Hartford
1
332
User
Stonington
1
333
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Derby
1
334
User
Stonington
1
335
User
New Haven
1
336
User
Fairfield
1
337
User
New Haven
1
338
User
New Milford
1
339
User
Stamford
1
340
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Wethersfield
1
341
User
Stamford
1
342
User
Hartford
1
343
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New Canaan
1
344
User
Stamford
1
345
Alvin Chung
New Haven
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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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