Best books for mental math

Best books for mental math DEFAULT

mental math3 mental math myths from Laura Ingalls Wilder, and 4 ways to bring homeschool mental math into the 21st century. 

I was obsessed with Laura Ingalls Wilder and the Little House on the Prairie books when I was a little girl.

I had a green calico prairie-girl dress that I insisted on wearing to family events for years, even when the dress literally began to fall apart.

I dreamed about attending a one-room schoolhouse.

And one rainy Saturday afternoon, I even sloshed water all over the carpet as I “hauled water” from the bathroom to the kitchen for my ever-patient mother–because I just had to pretend to be Laura fetching water from the well.

One of my favorite scenes is the school exhibition at the end of Little Town on the Prairie. Laura and her classmates prepare for weeks to show off their skills.

Finally, the big evening arrives. After geography and grammar, Laura braces herself for the subject she dreads the most: math.

“Mental arithmetic was even harder. Laura disliked arithmetic. Her heart beat desperately when her turn came and she was sure she would fail.”

And then she’s given this problem to solve:

“Divide 347,264 by 16.”



Much as I love Laura, I don’t love the misconceptions about mental math that one-room schoolhouse scenes like this one have created. Mental math isn’t about wowing other people by solving long, complex problems in your head. (And it’s definitely not about the stress of having to keep all those numbers straight!)

A lot has changed since Laura went to school 150 years ago. But mental math is still relevant, even in the age of smart-phone calculator apps. Let’s bust these mental math myths so your kids can reap all the benefits that mental math has to offer—without all the anxiety, dread, and fear of failure that Laura went through.

Myth 1: “Mental math” just means doing math in your head.

On the prairie, paper was expensive, and it wasn’t readily available. Ma couldn’t just toss a pack of paper in her cart at Target—nor did she have a calculator app on her phone!—and so solving complex problems without writing anything down was a useful skill.

“Divide 347,264 by 16. Sixteen into 34 goes twice, put down 2 and carry 2; sixteen into 27 goes once, put down 1 and carry 11…”

But these days, our kids don’t need to be able to solve 6-digit division problems mentally. Scraps of paper litter our homes, and a calculator app is never far away.

Yes, mental math is done “in your head.” But, it doesn’t mean lining up the digits and solving the problem the same way you’d do it on paper. Because…we have paper for that!

(And if you’re not sure how else anyone could solve problems mentally, you’re not alone. Don’t miss the quiz at the end of the post to learn more about mental math techniques that you can teach your kids. )

So, if that’s the case, why teach mental math at all? Which brings us to our second myth…

Myth 2: The purpose of mental math lessons is to solve problems on the fly.

Yes, it’s helpful to be able to quickly figure out how many packs of juice boxes you should buy at Costco, or to calculate a tip at a restaurant. But solving problems in your head is actually a side benefit of mental math practice—not the main purpose.

The main purpose of mental math is to make kids better at all kinds of math–written or mental.

Here’s why: When kids solve problems mentally, they can’t rely on written procedures that they may or may not understand.

Instead, they have to think deeply about the operations (addition, subtraction, multiplication, and division) and how the numbers relate to each other.

They have to apply properties like the commutative or distributive property, and they have to think hard about place-value as they take numbers apart and put them back together again.

Plus, mental math also helps kids practice the sub-skills they need for their written work.

For example, when a second-grader adds 28 + 5 mentally, she’s not just finding an answer. When she adds the 8 and 5 together to make 13, and then realizes that she needs to add the 10 from the 13 to the 20, she’s developing a deep understanding of regrouping that she won’t get if she just “carries the 1” on paper because her mom told her to.

Mental math isn’t just something you do only when you don’t have paper around. It’s an important tool for understanding math better in the first place. That’s why you don’t even have to do it all mentally. Which brings us to our final myth…

Myth 3: Nothing should ever be written down during mental math practice.

Poor Laura wasn’t allowed to write anything down during her never-ending division problem:

“…sixteen into 112 goes seven times, put down 7 and carry naught; sixteen into 6 does not go, put down naught; sixteen into 6 does not go, put down naught; sixteen into 64 goes 4 times, put down 4.”

Can you imagine how worried she must have been at this point that she’d messed up? One small mistake, and the whole problem is wrong. It’s a very impressive memory feat.

But, the point of mental math these days is to raise a child who understands math well, not to create a memory champion.

And so, it’s okay to write down mental math problems so that your child doesn’t have to keep the numbers in his head.

It’s also okay for your child to write down numbers from the in-between steps of his or her calculations.

Keep the focus on the deep understanding that comes from taking numbers apart and putting them back together again—not the pure memory challenge of keeping all the numbers straight in his head.

4 Easy Ways to Teach Mental Math

1. Find the mental math in your homeschool math curriculum.

You don’t have to reinvent the wheel. Your math curriculum probably already has mental math exercises—you just have to make sure you do them! Look through your teacher’s guide and see.

  • If you use RightStart or Saxon, mental math practice is in the warm-ups.
  • If you’re a Singapore Math user, look at the back of your Home Instructor’s Guide.
  • If you use Math Mammoth, any problem written horizontally is intended to be solved mentally.
  • And if you use a different curriculum, take a look. I bet it’s in there!

2. Keep practice sessions short and sweet.

Whether you use mental math problems from your curriculum or you make up your own, keep practice sessions short. For most kids, 5-10 problems daily provide plenty of practice.

3. Focus on accuracy and overall understanding, not specific techniques.

Your curriculum may teach specific strategies for solving mental math problems. As you come across the strategies in the text, teach them to your child. Use manipulatives to help your child learn the strategy and make sure she understands why it works.

But once you’re satisfied that your child knows the strategy, allow her to use whatever strategy she wants as she solve problems.

As long as she can explain what she’s doing (and as long as her way will reliably get the right answer), it’s fine for her to use whatever mental math strategies she’s comfortable with. Some strategies click with certain kids more than others. What’s most important is that your child is thinking deeply about the numbers, not using one particular mental math strategy.

4. Play games that require mental math.

No one wants to interrupt a game to write out math problems, so games give kids a good reason to find answers mentally.

Cribbage, Monopoly, Life, and Yahtzee all provide lots of great opportunities for mental math practice, and you probably already have some of them stuck in a closet somewhere.

Now, let’s get back to Laura:

“Three hundred and forty-seven thousand, two hundred and sixty-four equals—twenty-one thousand, seven hundred and four.” She need not multiply back to make sure the answer was right. She knew it was right because Mr. Owen set another problem.


You don’t have to spend hours drilling (and stressing out) your kids to reap the benefits of mental math.

Ask your kids a few mental math problems each day, focus on deep understanding rather than specific techniques, and play games that require mental math.

You’ll be well on your way to raising mental math superstars…even if they never solve 6-digit division problems in their heads like Laura Ingalls Wilder.

Happy Math!





Answering your first question:

  1. They are all good in the part of market-sizing questions
  2. They are all pretty good in terms of quant problems as part of the case
  3. They are all very bad in terms of the solutions and structures. Thus the casebooks solutions cannot be used as the best practices

Answering your second question, there are no mental math books. However, there are several math skills that you can develop:

1) Learn how to work with zeros. Best way - always use 10^power instead of zeros


300x9000 = 3*10ˆ2 x 9*10ˆ3=3x9*10ˆ(2+3)=27*10ˆ5

Handwritten it looks not that complicated. If you get used to writing all the numbers that way, you will never lose zeros and all multiplications/divisions will be replaced with + or -.

In your case, it will look like 63 * 10ˆ5 / 72 * 10ˆ2

2) Learn how to multiply double digit numbers

Pls check this video - It takes an hour to learn this method

3) Learn how to divide the numbers fast

If you need the precise calculation - you can use the basic division technique, calculating 630 / 72 * 10ˆ2 = 875

If you don't need it precise -Learn the division table up to 1/11 (i.e. 5/6 = 83.3%). It will help you calculate any percentage problems

In your case, it will be roughly 6/7 * 10ˆ3 = 85.7 * 10ˆ3 or 857. Since I know that it was the rough calculation and the real number should be bigger, I would round the final result to 870


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Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks

These simple math secrets and tricks will forever change how you look at the world of numbers.

Secrets of Mental Math will have you thinking like a math genius in no time. Get ready to amaze your friends—and yourself—with incredible calculations you never thought you could master, as renowned “mathemagician” Arthur Benjamin shares his techniques for lightning-quick calculatThese simple math secrets and tricks will forever change how you look at the world of numbers.

Secrets of Mental Math will have you thinking like a math genius in no time. Get ready to amaze your friends—and yourself—with incredible calculations you never thought you could master, as renowned “mathemagician” Arthur Benjamin shares his techniques for lightning-quick calculations and amazing number tricks. This book will teach you to do math in your head faster than you ever thought possible, dramatically improve your memory for numbers, and—maybe for the first time—make mathematics fun.

Yes, even you can learn to do seemingly complex equations in your head; all you need to learn are a few tricks. You’ll be able to quickly multiply and divide triple digits, compute with fractions, and determine squares, cubes, and roots without blinking an eye. No matter what your age or current math ability, Secrets of Mental Math will allow you to perform fantastic feats of the mind effortlessly. This is the math they never taught you in school.

Also available as an eBook...more

Paperback, 279 pages

Published August 8th 2006 by Three Rivers Press (first published 1993)

The Best Mental Math Tricks - New Book Available Soon

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Math is a subject that stays with people throughout their life. You are calculating, making comparisons, finding orientation, and doing spatial reasoning assessments – and all of these actions involve math. Sometimes, for the enlightenment of the self or to restart the course left in between to get a better edge over competitors, every adult needs some math learning resource. As a parent, when you found it difficult to answer the math queries posed by your kid, you must have thought of brushing up your knowledge. Even otherwise, you must have found yourself at a tight spot because of some math concepts that you failed to understand in your school days. So, why not know about some math books for adults that can help save you from a variety of embarrassing situations, apart from giving you a chance to keep your brain agile for long?

If the idea has really set you thinking, we enlist for you here the best selling math books for adults that cover various interesting aspects like puzzle solving, pattern decoding or simply revisiting basic math concepts. Take a look.

Best Selling Math Books for Adults

1. Brain Games #1: Lower Your Brain Age in Minutes a Day

Brain Games #1: Lower Your Brain Age in Minutes a Day

This math book is not a coursebook, but a collection of math-based reasoning and creative thinking centered puzzles, games, and questions. It is designed to keep those people in mind who have special needs as regards to developing math reasoning skills.

You will find a conspicuous change in memory power and reasoning ability after doing activities from this book in your free time. Many of the sections of this book can help you crack the math logical reasoning questions you come across in entrance exams also. Thus, it prepares you on various levels and helps prevent the early aging of the brain by providing it sufficient food to stay active and agile.

2. Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks

Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks

In school days exams, the examiners lay a lot of emphasis on checking the students’ methodical approach. However, the scene in real life is a little different and people have to depend on mental math more to achieve various objectives.

The authors of this book Arthur Benjamins and Michael Shermer have come up with an amazing collection of math tricks and ways to help you do lightning-fast calculations. The tricks like those useful for doing triple-digit multiplications and divisions, determining square and cube roots, and other complex equation solving can help you continue to grow into an avid mathematician. This book is certainly a useful resource for learning those things that are almost never taught in the school due to the curriculum’s limitations.

3. Math refresher course for adults

Math refresher course for adults

Scared of math problems and are not able to crack exams due to poor scores in maths? Are you planning to take a career where you will require a lot of math? Or you want to home mentor your child on math subject? If these are some of the objectives you want to accomplish, the book Math Refresher for Adults is the best choice.

This book can make you a fast problem solver, apart from helping you revisit all the principles and concepts of general math, geometry, and other school topics. All these topics continue to appear at some point in life. So, you can brush up your skills at any time by practicing with this math book for adults.

4. USA TODAY Jumbo Puzzle Book 2: 400 Brain Games for Every Day

USA TODAY Jumbo Puzzle Book 2: 400 Brain Games for Every Day

With lots of crossword puzzles including numbers and words and different kinds of numbers-based challenges to meet, this Jumbo Puzzle Book is a perfect resource for stimulating your mind and maintain its agility.

This puzzle book is a happening go-to when you want to utilize your free time in brushing your math reasoning and logical reasoning skills. It is a book for all ages and can be used for challenging the advanced learners to do different kinds of math problems in addition to what they do in their course work.

5. All the Math You’ll Ever Need

All the Math You'll Ever Need

All the Math You’ll Ever Need from Steve Slavin is the self-teaching guide that allows you to be proficient in math skills that you require for personal and professional purposes. In school days, just to catch up with peers, many important math concepts remain unlearned. This math guide for adults takes care of practical math, mental math, and math reasoning, that prepare you well for all day-to-day activities based on calculations.

You can find in it the concepts like fractions, decimals, discount calculation, mortgage value determination, and several important finance-focused math topics that help you make better decisions related to price and property matters. So, when you want to be math smart, use this book to self-learn and excel.

6. Mastering Essential Math Skills Problem Solving

Mastering Essential Math Skills Problem Solving

Be a master problem-solver of math concepts with this Math Skills exercise book by the author Richard W. Fisher. This math book for adults comes with a number of everyday math problems which any adult need to master to get decisions right.

The graphs, statistics, fractions, decimals, pie-charts are common to any office work that revolves around numbers. Thus, to make that impressive presence among peers, practice the problems in this book regularly and see how you become confident in math. Just 20 minutes of practice using this book, and you can pave your way to a successful career.

7. The 125 Best Brain Teasers of All Time

The 125 Best Brain Teasers of All Time

Want to be the master of math and logic, and like things like doing wordplay? Then, this brain-teasing book is your best bet. Having about 125 games, puzzles, and logic-improving problems, this math book fights away the fear of math in a fun-filled way even if you’re an adult.

You can give your brain that much needed creative break that it needs from doing monotonous kind of jobs. By making use of math word problems, wordplay puzzles, and various logical reasoning based problems, this book serves you the best when you want to befriend math. The best part is, you need not be a math nerd to solve the puzzles in this book; it is designed that creatively!

8. The Math Book: Big Ideas Simply Explained

The Math Book: Big Ideas Simply Explained

A lot of mugging up happens in the school days when the course size exceeds the reasoning power of the brain. So, what could be a better way of using adult life for revisiting those math portions that you could not understand as a young learner?

The book takes away the confusion around the terms and concepts that entered our lives at an early age. With the passage of time, almost all concepts mingle up and the real meaning is left far away from the mind. This book solves this issue like a pro and allows you to understand the real underlying meaning of terms like whole numbers, spheres, algebra, and other operations of math.

9. 300+ Mathematical Pattern Puzzles: Number Pattern Recognition & Reasoning

300+ Mathematical Pattern Puzzles: Number Pattern Recognition & Reasoning

The author Chris McMullen has created this amazing book to help math aspirants improve their pattern intelligence. Patterns are everywhere; all you need is a brain and a thought process to crack those. This puzzle book for solving pattern recognition, pattern identification, and reasoning problems open up your brain beautifully and helps it become more receiving and inquisitive in its abilities.

Important topics covered in this puzzle book are Fibonacci square, visual puzzles, roman numerals in the number pattern problems section. And, you also get ample practice in visual discrimination, analogy establishment, logic, and reasoning in the math reasoning section. If preparing for exams, it can help you crack logical reasoning and creative thinking based problems with better ease.

10. The Original Area Mazes: 100 Addictive Puzzles to Solve with Simple Math

The Original Area Mazes: 100 Addictive Puzzles to Solve with Simple Math

Simple math but clever logic are used in combination to find answers to the addictive puzzles given in this math book. This math problem-based puzzle book gives you all support that you need to develop your brain’s mental ability that due to some issues recede with age.

By practicing the problems in this puzzle book, you challenge your brain, give it a proper workout needed to keep it agile. Rules are pretty simple and do not involve more than the simple math formula like area = l x w. Whole numbers, geometry, and your love for Sudoku form the working tools for solving the puzzles given in this brain stimulating book that every adult should practice.

Why adults need these math books?

Growing cases of dementia, loss of reasoning skills, and poor spatial intelligence have started gripping people at an early adult age. The math books for adults give the grown-ups fuel for the brain so that it does not lose its thinking and logical reasoning capability with age.

Whether it is the revision of concepts that were missed in school days, or knowing the application part of the theories that you just memorized to score marks, these books offer the best support for handling all types of shortcomings.

With regular practice, the users of these math books for adults can gain confidence in the areas where they have been lacking proficiency. So, the overall result is a more confident side of yours, which you were forced to hide behind excuses.

More visible outcomes are likely to be better chances of winning promotions at the office, and better performance in exams in which math problems weight a lot.

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Categories articles, Books, Dyscalculia, Tools & ResourcesTags books, listicles, math resourcesSours:

Mental best math for books

Secrets of Mental Math


If you have strong association for digit pairs (eg. PAO, major) do you think it affects your “normal”, logical mental calculations?

I don’t know, but I think it could probably only help with mental math, because images are easier to remember than numbers.

For a while, I was experimenting with keeping track of my shopping cart price at the supermarket using only my mnemonic images. Each of my images has a one syllable pronunciation, so I would calculate like this:

$2.40 + $1.99 = $4.39

would be done with this pronounciation:
U-RO plus I-PUH equals A-MUH

Then I would hold “A-MUH” ($4.39 – flag and Marshal stack) in my mind until I added the next item. Then I would see how close my final mnemonic image was to the check out price. I really should start doing that again… :slight_smile:

I don’t think it helps with the calculation, but it might be good practice for combining mnemonic images with mental calculation.

Best Book To Learn Vedic Maths

Secrets Of Mental Math  (English, Paperback, Benjamin Arthur)

Here is a book on Mathematics that will have you thinking like a genius in no time. These secrets and tricks will make you better at Math and change the way you perceive numbers.

Summary of the Book

Be ready to amuse your friends and be in awe of yourself. It is a book on Mathematics that has some amazing calculations that you never would have imagined you were capable of mastering. This book by Arthur Benjamin, popularly known as a ‘mathemagician’, is a platform where he shares his techniques for quick calculations and mind-blowing number tricks. Use his methods to teach yourself to do math in your head faster than usual and improve your memory. For many, Mathematics will also become fun. This book will teach you how you can solve complex equations in your head. All that is required of you is to learn the few tricks that are given in the book. As you keep practicing, you will learn how to multiply and divide triple digits in a jiffy, compute with fraction, and determine squares, cubes and roots without much effort. Whatever your age and present aptitude for mathematics might be, Secrets of Mental Math is a book that will help you perform and score effortlessly. Get ready to learn mathematics is a new and remarkable way.

About Arthur Benjamin

Arthur Benjamin is a mathematician who specializes in combinatorics. He has been a Professor of Mathematics at Harvey Mudd College since the year 1989. He is known for his mental math capabilities and ‘Mathemagics’ performances in front of live audiences.


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From the sound of it, a lot of the answers you're getting are tailored more towards proper jail/prison as opposed to an FPC. So I'll throw in a bunch of extra info...

The level of Fed you go to will be determined by a score. I'm going to assume you're otherwise a straight up kind of person. So you'll likely get points mostly for your age and the severity of your crime. I'm going to guess you'll be around 7-9 points which should put you in Minimum. Getting over 11 (assuming you're male), will put you in Low. Your crimes also used telecommunications, so it's also possible you will be put in Low, by default. Just to give a quick overview, expect cubicle housing and double fences. There are also work programs to keep you busy. Key tip, surrender directly to the prison camp. Otherwise, your transport is through the prison system so you'll be shackled and spend way more time with hostile people than you'd ever want to. Your lawyer should have that all worked out for you. Do not surrender to the Marshals.

You will then be classified as either: Community, In, Out, or Maximum. You will be reviewed and put into any of those groups. Also of note, try to get any nagging medical conditions you may have out in the open as soon as possible. They may upgrade your medical level and you can get it worked on.

And if you also have a case by your State, you'll probably just serve in the state institution. Anyway, you'll probably have a facility support job and that will take up time.

Your typical day will involve waking up early, then doing your job. You'll be on your own from about 2:30, then there will be a census count probably by 4. Then around 5, you'll be released for meals, purchases, etc. If you wanted, you could fill your evenings with a class, or even teaching a class. And depending on your work schedule, you may even find yourself sleeping by 9.

If anything, I'd generally stay away from working with actual cards and sleights. For the most part, they're too precious of a resource. And odds are no one will be able to send you any. The biggest source of boredom in a prison setting is the lack of mental stimulation. I would suggest pursuing any of the normal mental aspects of magic.

Any books you receive will probably have to be paperback. And there may be a limit on how many you can receive each month. Hardback books, if allowed, usually need to come directly from the company (amazon,, etc). In fact, to have as few problems as possible, just have amazon send any books directly to you via US Post Office. And make sure it is AMAZON sending, not a third-party seller.

It would be a perfect time to learn a memorized deck, or even two. If you have your one deck to practice with on your own time, you'll be set by the time you're out. Get a copy of this book and you can be a human calculator by the time you get out. Get Harry Lorayne's Memory Book. Work out your killer presentation of Sam the Bellhop. Work out a cups and balls routine using foam cups and paper. Practice the Epitome Location (From Harry Lorayne's Personal Collection vol 1).

Best part of the memorized deck is many of the effects using one cause little wear and tear on your cards. So you'll get more mileage out of cards, if you have access to them at all.


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