Best elementary arithmetic books according to redditors

Got Ds and Fs in math throughout middle/high school.

Took my first math class at the ripe age of 30 in college; could barely do simple multiplication/division so I started from the ground up by taking the most remedial course.

3 math classes later (all A+) I'm now in pre-calculus, tutoring other students, and planning to teach math at a high school or college level. Khan Academy and Pre-Algebra for Dummies by Mark Zegarelli were huge helps for getting me up to speed (which is good, because 2 out of 3 of my teachers weren't very good at teaching).

I grew up with the idea that I was "bad at math" and I internalized this idea as a "truth". I had internalized the idea to such an extent that it influenced my entire educational and professional career; I actively avoided any STEM degrees and went into law instead. I threw away my potential because of the lie/self-degradation that some people are simply "bad" at math. I wasn't bad at math; I just didn't have the tools I needed to succeed.

Today I have my choice of teachers, teacher review sites, video tutorials like Khan Academy, alternative text books, and text book reviews. I didn't have those tools as a high school student. High school math was an exercise in humiliation and debasement. I want to be a math teacher because I NEVER want another student to feel the way that I felt.



EDIT 1: Thanks for the gold stranger!

EDIT 2: Here's the book I used to prepare me for my first math class. It's a newer edition than the one I used:

https://www.amazon.com/Basic-Math-Pre-Algebra-Dummies-Zegarelli/dp/1119293634/ref=sr_1_4?ie=UTF8&qid=1481730619&sr=8-4&keywords=pre-algebra+for+dummies

Just change your reference number to something that can be used easily, such as 50, 20, 10, 100, 1000, etc. Then you just take the numbers, such as 45 and 55, for ease of use, set 50 as the reference. 45 is 5 below 50, so -5 for its # and +5 for 55. Then add their number to the opposite number, so +5 to 45 or -5 to 55; it always comes out the same. You get 50; multiply the result with your reference number, so that gets you 2500. Then to tie it all off, add the product of your 45 and 55's initial differences from the previous result, +5 (-5) = -25. 2500 + (-25) = 2475.

It's easier to see if you write it out like that guy has it

50) 55 45

50) 55 45
+5 -5

50) 55 45 (The product of [the sum of one of the differences and the
+5 -5 opposite multiplicand] and the reference number)


50) 55 45 2500
+5 -5

50) 55 45 | 2500
+5 -5 |+ (-25)
-------
2475

Like we've said in this thread, it's not magic. It just takes advantage of the distributive property, given you have a good grasp of decimal (i.e. base 10) mathematics.

Speed Mathematics by Bill Handley

Here you go

You may want it.

There would have been a time that I would have suggested getting a curriculum
text book and going through that, but if you're doing this for independent work
I wouldn't really suggest that as the odds are you're not going to be using a
very good source.

Going on the typical

Arithmetic > Algebra > Calculus

****

Arithmetic

Arithmetic refresher. Lots of stuff in here - not easy.


I think you'd be set after this really. It's a pretty terse text in general.

*****

Algebra

Algebra by Chrystal Part I

Algebra by Chrystal Part II

You can get both of these algebra texts online easily and freely from the search

chrystal algebra part I filetype:pdf

chrystal algebra part II filetype:pdf

I think that you could get the first (arithmetic) text as well, personally I
prefer having actual books for working. They're also valuable for future
reference. This filetype:pdf search should be remembered and used liberally
for finding things such as worksheets etc (eg trigonometry worksheet<br /> filetype:pdf for a search...).

Algebra by Gelfland

No where near as comprehensive as chrystals algebra, but interesting and well
written questions (search for 'correspondence series' by Gelfand).

Calculus

Calculus made easy - Thompson

This text is really good imo, there's little rigor in it but for getting a
handle on things and bashing through a few practical problems it's pretty
decent. It's all single variable. If you've done the algebra and stuff before
this then this book would be easy.

Pauls Online Notes (Calculus)

These are just a solid set of Calculus notes, there're lots of examples to work
through which is good. These go through calc I, II, III... So a bit further than
you've asked (I'm not sure why you state up to calc II but ok).

Spivak - Calculus

If you've gone through Chrystals algebra then you'll be used to a formal
approach. This text is only single variable calculus (so that might be calc I
and II in most places I think, ? ) but it's extremely well written and often
touted as one of the best Calculus books written. It's very pure, where as
something like Stewart has a more applied emphasis.

**

Geometry

I've got given any geometry sources, I'm not too sure of the best source for
this or (to be honest) if you really need it for the above. If someone has
good geometry then they're certainly better off, many proofs are given
gemetrically as well and having an intuition for these things is only going to
be good. But I think you can get through without a formal course on it.... I'm
not confident suggesting things on it though, so I'll leave it to others. Just
thought I'd mention it.

****

There's a couple pages about him in the book Weird US. If I remember correctly, he traveled the route with such accuracy that he always showed up in the same places within several hours of when he was expected to arrive.

As others have mentioned, you can use various online resources such as Khan Academy. I'm assuming you know basic arithmetic (multiplication, exponents, working with fractions, percentages, etc...), if not you'll have to start with that. After that, you may need to learn what is usually called "Pre-Calculus". These are the topics you need to master before you can start learning Calculus. Usually they include study of functions (polynomials, logarithmic, etc...), trigonometry, analytic geometry.

Here's a list of stuff you should investigate:

• Arithmetic Refresher: Improve your working knowledge of arithmetic
  
  
• US Navy mathematics courses
  
  This is a collection of PDFs which are taken from some US Navy mathematics courses. The courses are:
  
  >US Navy course - Mathematics, Basic Math and Algebra NAVEDTRA 14139
  
  >US Navy course - Mathematics, Trigonometry NAVEDTRA 14140
  
  >US Navy course - Mathematics, Pre-Calculus and Introduction to Probability NAVEDTRA 14141
  
  >US Navy course - Mathematics, Introduction to Statistics, Number Systems and Boolean Algebra NAVEDTRA 14142
  
  The Basic Math and Algebra course covers arithmetic and could be used instead of the Arithmetic Refresher, if you'd like.
  
  You may also want to look into books on world problems, as that's where most people have difficulty with. World problems mirror our real-life problem solving process, where we have to translate some real problem into mathematical language in order to tackle it.
  
  
• http://www.artofproblemsolving.com
  
  > The Art of Problem Solving mathematics curriculum is specifically designed for outstanding math students in grades 6-12, and presents a much broader and deeper exploration of challenging mathematics than a typical math curriculum. The Art of Problem Solving texts have been used by tens of thousands of high-performing students, including many winners of major national contests such as MATHCOUNTS and the AMC.
  
  If you look at their bookstore, you will see that they have books for the various subjects your kid will encounter during school. They also have the Beast Academy which is an on-going project to release books for kids in grades 2-5.
  
  Note that they say that the books are for gifted math students since the exercises are taken from math competitions. What's nice about these books though is that they offer the full solutions (not just a final answer, but the full explanation). Also, for every book they have a Diagnostic Test (pre-test) to check and see if you are capable of starting the book.
  
  
• Pre-Calculus stuff...
  
  There are plenty of various Pre-Calculus books which contain all this material. I can't really recommend anything with certainty since I've never read any.
  
  But here's a book you could try by a well-known mathematician who also seems to write really well (it also appears to have solutions to the problems):
  http://www.amazon.com/Precalculus-Prelude-Calculus-Sheldon-Axler/dp/1118083768/
  
  
  ---------------------------
  Once you have some specific subject you're having difficulty with, you can always ask for help or look for a friendly book. The problem with math is that some authors/teachers teach subjects very dryly, so it makes it boring... the challenge for people who aren't naturally motivated for maths is to find teachers/books that excite the student -- and there are a few authors that can do it, so you just have to ask around.
  
  By the way, you should also look for various popular math books that could make studying the subject all the more interesting.

Get this book. It will seriously help you with little tricks to do these problems in half the time or less. It really helped me not be shy about my maths skills at work.

https://www.amazon.com/Short-Cut-Math-Gerard-W-Kelly/dp/0486246116/ref=nodl_

To anyone interested, this method is used in this book, as well as other mathematical shortcuts.

Enjoy.

http://www.amazon.com/gp/aw/d/0471467316

The error is that you are adding fractions incorrectly.

Remember that common denominator stuff you learned in primary school?

(4/5) + (3/4) = (16/20) + (15/20) = (31/20)

Avg ( 4/5 and 3/4 ) = ( 31/20) / 2 = 31/40 --- not 7/9

The formula for averaging two fractions (a/c) + (b/d) would be

(ad+bc) / (2cd)

[incidentally, I think it would be a lot less confusing if you had written the fractions a/b and c/d, but I've stuck with your convention)

Everything that follows from your incorrect formula is wrong as a result.

P.S.
If you need to revise fractions - my Kindle book about them is free all of this week, until and including Friday:

http://www.amazon.com/You-Can-Do-Math-Fractions-ebook/dp/B00N3970NU/

http://www.amazon.co.uk/You-Can-Do-Math-Fractions-ebook/dp/B00N3970NU/

Here are all the local Amazon links I could find:


amazon.com

amazon.co.uk

amazon.ca

amazon.com.au

amazon.in

amazon.com.mx

amazon.de

amazon.it

amazon.es

amazon.com.br

amazon.nl

amazon.co.jp

amazon.fr

Beep bloop. I'm a bot to convert Amazon ebook links to local Amazon sites.
I currently look here: amazon.com, amazon.co.uk, amazon.ca, amazon.com.au, amazon.in, amazon.com.mx, amazon.de, amazon.it, amazon.es, amazon.com.br, amazon.nl, amazon.co.jp, amazon.fr, if you would like your local version of Amazon adding please contact my creator.

Columbus: 2,078,723 > Cleveland: 2,058,844

>had a difference in 3,000

The difference is 19,879, and while Cleveland has shrunk since 2010, Columbus has surged by over 9%.

I know that you want to be right, but unfortunately you are not. [I recommend this book to help you in the future!] (https://www.amazon.com/Basic-Math-Pre-Algebra-Dummies-Science/dp/1119293634/ref=sr_1_1?ie=UTF8&qid=1537499491&sr=8-1&keywords=basic+arithmetic). Best of luck!

Rapid Math Tricks & Tips: 30 Days to Number Power

by Edward H. Julius

I did LA to Chicago. It was more to get from Point A to Point B than for sightseeing and we had a U-Haul trailer, so we did it in 3-4 days. But here are some pointers that may apply to you.

• I can't advise on national parks since I've never been to many, but I hear Bryce Canyon and Arches are amazing, or Glacier and Yellowstone if you're taking a northern route. I have been to Joshua Tree and highly recommend it especially if you like rock climbing/free climbing and weird fuzzy alien trees. I also liked Boulder, CO - fun uni town with a gorgeous range of mountains in the background.
  
  
• Going over the Grapevine into Southern California, be prepared to roast in your car. Because of the high desert temperatures and the steep grade of the road, it's easy for your engine to overheat and there are signs to turn off your air conditioner. I've seen a few cars pulled over with the hood up and the engine smoking on that stretch.
  
  
• If you're taking an extremely southern route then you don't have to worry about this, but most likely you'll be going through the Rockies. Look up some info/tips on crossing mountains because temperatures can drop pretty quickly and you should have proper supplies with you. In any case it's a good idea to have extra water & food, spare tire and jack, first aid kit, road flare, blanket, snow scraper etc. I wouldn't rely entirely on a cell phone because reception can be spotty.
  
  
• If you see signs for "Next gas station [large number of] miles", take them seriously and don't be afraid to turn around for gas. Especially in the Kansas/Nebraska/Wyoming area.
  
  
• There's a book called "Weird U.S." that lists quirky out-of-the-way spots.
  
  
• In the large cities like LA & NY, pubs and bars sometimes won't accept an out-of-state driver's license if you look young so it helps to have your passport handy. On the other hand, those are the places where it's most likely to get lost/stolen so you'll have to weigh the risks. It's not like the UK where you only need ID to get a drink (if even that) - a lot of times they won't even let you in the door without one.
  
  I lived in LA for a long time so if you want specific recommendations for places to eat and things to do there, let me know :)

I teach middle school and use many of the mental math shortcuts in this book, Arithmetricks.

If that book doesn't keep you busy enough, then move on to Rapid Math and its sequel.

If you like videos, these are effective and fun:
Mental Math Secrets - Volume 1 - done by Jason Gibson of the MathTutorDVD series. Short, sweet, and to-the-point.

Since people have already mentioned Arthur Benjamin's book, I'm going to suggest his more enjoyable video from The Great Courses, The Secrets of Mental Math. (It's expensive, but goes on sale, so watch for them.)

How about learning to meditate in a way to tune out the sermon?

It might take a lot of work and practise but will be a fantastically useful skill for the rest of your life.

Maybe better than the passive approach of wearing earphones or earplugs or the self-destructive approach of getting stoned. This is actually doing something positive for yourself, even if it's hard work.

Start learning to meditate at home and introduce it bit by bit at church.

You might even be able to start doing something really useful, like maths problems in your head after a while and able to ignore the priest drone on.

These aren't novels, but I really enjoyed these books around that age:

The I Hate Mathematics Book

Math for Smarty Pants

They taught me a lot of fun math puzzles and concepts for the first time (prime numbers, perfect numbers, basic combinatorics, math magic tricks), each with a bit of a story attached.

Firstly, I would highly recommend camping over staying in motels/hotels, so take a route that allows this. I took a long road trip a few summers ago and picked destinations based on awesome places to camp, and had a killer time. That being said, Yosemite was fucking gorgeous, so maybe head that way?

Also check out the book Weird U.S. for some strange stops.

The I Hate Mathematics by Marilyn Burns is a classic and fantastic for extending mathematical thinking. She has a whole line of fun books.

The I HATE MATHEMATICS! Book

Math for Smarty Pants

I remember picking up both of these books at -some- point during elementary school book fairs. I have always really liked math, but they do have some interesting topics and random facts. The topics are always pretty short - I remember quite a few on statistics in various forms. I'm not sure they would 100% work for what you are looking for but they might be able to form springboards for projects?

You should pick up for 3usd this great book called e short cut math.

I learned a lot of techniques for all sort of operations.

A word of warning: it works when practised. Maths both theory and practise is like a muscle: you need to keep it trained.

I've come accross these tricks before in Rapid Math Tricks & Tips. Useful stuff back in middle and high school on math team.

Yes . . . I'm in the middle of The Foundations of Arithmetic by Gottleb Frege right now. It's a book about what number is. I wouldn't recommend it unless you enjoy math, as it's rather dry.

When I'm done with that, I plan to finally plow through Heiddeger's Being and Time, mostly because ontology has been popping up a lot for me. It doesn't seem as daunting as it used to. Probably because I've grown sine I first picked it up, and poked around a few of his other writings.

After that, I might read Husserl's _Origin of Geometry__ which lays some groundwork for his ideas on the science of phenomenology. I'm using the translation present in the appendix of Derrida's introduction to the Origin of Geometry. It was actually a gift from someone who knew I liked math and philosophy. At the time, I was a bit "WTF!?" and buried it someone. I've since become interested in Derrida, phenomenology and Husserl so it was a welcomed surprise when I rediscovered it.

Then comes the "eminant reads" category, which come in some order after the above.

I also have to read Warped Passages by Lisa Randal, which is a very good layman's guide to String Theory. It was a recommendation from my philosophy professor. I've poked around in it and it does seem quite good.

I was also recommended the The Evolution of God by Robert Wright. Don't know much about it, beyond the fact that the title is accurate, but I do plan on picking it up.

Then Tillich's book would fall in this rather "eminent" category along with Guns, Germs and Steel.

After that are a bunch of other books I want to read. And standing in its own category are leisurely books. Right now, I'm reading Stephen King's Under the Dome!

If you want a fairly solid explanation on what arithmetic really is I recommend Frege's "The Foundations of Arithmetic". It's not the final story (Peano simplified the formal details afterwards) but I found it enlightening nevertheless.

If 2+2= 4 has to be taught - who taught the first person that?

Are you really asking me for a book that teaches 2+2=4 is true?

https://www.amazon.com/Addition-Practice-Worksheet-Arithmetic-Workbook/dp/1536932760/ref=sr_1_1?s=books&ie=UTF8&qid=1484546343&sr=1-1&keywords=addition+for+kids

Example of an email being sent out based on this conversation. I always say you can always learn something from someone new every day. The mindset just needs to be focused on the bigger picture.

Last week, someone messaged me and asked, “I read your book, what else should I do?”


At that point, I smiled and made myself some coffee. That night, after I'd gone to see a great movie, I responded: “First tell me what you're doing now with the book you already have.”


Like this message from one of our readers:


Hi Jack, I recently finished the Fractions Mini Workbook.  I wanted to understand more about decimals and was wondering if you could recommend any good books on that!


                                               -------Thanks a bunch.

​

This is a magical moment. A fork in the road and the conversation can go one of two ways:


Path 1: “I've worked through a lot of problem sets.  I'm comfortable with working through fractions problems.  When I try to do simple fractions problems, I usually get the right answer.”


Path 2:  "The main thing I have done so far is ordered some workbooks but I really haven't finished the exercises in them.  I did a few of the problems but gave up.  I still feel like a lost puppy when it comes to fractions.  It seems like I understand while I'm reading the explanations, but when I start to solve the problems on my own, I get stuck."

​

Translation of Path 2: "I haven't spent enough time on the basics.  And I need to focus more on these concepts before moving to a more advanced topic."

​

Guys, beware of looking to the next best thing instead of doing the work. This can apply to other areas of life:

• Buying more tools instead of learning how to use the ones you have
  
• Buying cookbooks before you master basic dishes
  
• Researching super-advanced diets without mastering portion control or counting calories
  
• Practicing alley-oops before getting basic footwork down
  
  I’m not against advanced material for anyone who is ready.  But for some of us, what’s in my book should be just fine, and it’s exactly the best place to start.

I only have one, it's not Algebra or even a site, but it's a good book.

• Rapid Math: tips and tricks
  
  It focuses on arithmatic, but allows you to do some of the same things that 'math geniuses' can do. Very handy, but read the other reviews so you can see what the strengths and weaknesses are. There is a sequel "More Rapid Math: tips and tricks". Starts out slow, so don't blow it off as too easy based on the first chapter or two. The best thing about it is that it will give you a good feel for numbers beyond the tricks that are taught in the book.

You know, I've had it for so long that I don't even remember where I got it from. Here is the book on Amazon, and here are a ton of cheap, used ones from Barnes and Noble, if you don't care about it being used.

https://www.amazon.com/Beginning-Algebra-Textbooks-Available-Cengage/dp/1111578702

Third Panel: Peasant Multiplication

Fourth Panel:Karatsuba Multiplication

Last Panel: It infuriates me how people can make money with this "magic" or "vedic" multipliction :|

I would highly recommend the "Weird" Series. They are separated into different states, but there are also two volumes for the USA as a whole and one that is all about the weirdness in England. The books cover all aspects of the bizarre in local areas from cryptids and ghosts to unusual buildings and people who lived in these places. I know that I loved these books myself as a kid, and they were largely responsible for my own infatuation with the supernatural. Here's a link to one of the first (and most popular) book in the series: http://www.amazon.com/Weird-U-S-Americas-Legends-Secrets/dp/1402766882 Hope you and your family have a happy holidays :)

I suggest you get this book: http://www.amazon.com/Rapid-Math-Tricks-Tips-Number/dp/0471575631

It has a lot of them.

It looks like it might be this?

https://www.amazon.com/Basic-Math-Pre-Algebra-Dummies-Zegarelli/dp/1118791983

https://www.amazon.com/Basic-Math-Pre-Algebra-Dummies-Lifestyle/dp/1119293634/ref=sr_1_1?ie=UTF8&qid=1505151378&sr=8-1&keywords=mathematics+for+dummies

Start with this

I'm a math tutor to junior- and senior-high school kids. Universally, everyone I work with always says the same thing before we even sit down: "I'm terrible at math!"

My response is always the following: "You're not bad at math; math is just a lot more challenging than you need it to be right now."

If you can manage to stop thinking of it as something you're "terrible at" and start thinking of it as something you "haven't learned how to do very well yet", that would be a very good start.

I understand that you didn't get a good foundation due to home-schooling, but where exactly does that leave you, in terms of your skill level? What is the highest level of math you feel comfortable working with or could do in your head? This info would help me to offer you some solutions or ideas on where to begin. In any event, you should definitely pick up a copy of this book, because it will show you exactly what you need to know to get a decent score in that section of the SAT.

Here's a recommendation for you.