Level 1

About Math Trainer

Math Trainer is a web app for learning mental arithmetic. It is designed to adapt to a user's current ability, offering highly-tailored practice questions, tips for improving, and accurate performance assessments.

How It Works

There are 100 levels which range in difficulty from beginner to expert. You advance levels by answering a series of problems, not more than ten, within a given time limit. The time limit for a round depends on the difficulty and number of the questions.

Every question has a target time associated with it. The target time can be thought of as an acceptable time period in which to solve the problem. Some factors that determine this duration are the number of mental computations necessary to solve the problem, whether carrying or borrowing is required, the number of digits in the answer, and so on.

The time limit for a round of questions is the sum of the target times. Therefore you can miss one question's target and still advance to the next level if you make up the time on other questions.

Every time a user answers a question on Math Trainer, their performance is added to a database that we use to determine how long each problem should take. If a particular question has enough responses from previous users, this data is directly used for the target time.

The target time for a question does not depend on the level the user is on. A question may appear on more than one level, but the likelihood it will appear will be different. The purpose is to solve increasingly difficult mental math problems in an acceptable amount of time, rather than to achieve ever-faster performance on easier problems.


Why is there no Enter button?

The user interface works by automatically advancing when the correct answer is input. Therefore there is no penalty for wrong answers, so guessing can be abused, but less so at higher levels. You're unlikely to guess the right answer for large numbers.

Why isn't it multiple choice?

Many mental math apps employ multiple choice to minimize the need for user input. However, there's no way to prevent a user from using process of elimination, which is really a different skill.

How are the target times determined?

For questions with enough user data, the target time is set to the 15th percentile time. This means 85% of responses are faster than the target time. On questions with insufficient data, performance percentiles are estimated using simulation algorithms and statistical methods.

Where can I get more help?

We recommend Arthur Benjamin's book Secrets of Mental Math. It can be found on Amazon:

Advanced techniques:

If you have questions or comments, contact us by email.

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