art of problem solving math jams

• WellTrainedMind.com
• WTMAcademy.com
• High School and Self-Education Board
• Existing user? Sign In

I am an Art of Problem Solving Drop-out.

• art of problem solving

By Jenn in Mo , September 21, 2010 in High School and Self-Education Board

• Reply to this topic
• Start new topic

Recommended Posts

We're a mathy family here, so I'm feeling kind of like a failure here, but I closed the book today and said, "Enough." My math-loving son was diligently struggling through hours of math a day and getting nowhere. It took nearly two months to get through two chapters and I know he couldn't pass any review tests. He understands algebra, but this is....different. My husband and I are struggling to understand half of the problems ourselves...and this is our *thing*, ya know?

I haven't heard a negative word about AoPS yet, so it's kind of embarrassing to admit, but I just do not "get" some of these questions. Anyone that gets it feel like helping to clear the mud on this one?

2.38 What number must be in the blank in the expression 3(x+7)-_(2x+9) if the expression is the same for all values of x?

The solution manual says that "if the expression is the same for all values of x, then the x's in 3(x+7) must cancel out with those in _(2x+9).

My question is...WHY must they cancel out? It's a random, unfinished number sentence. What is in the original problem that tells me they must cancel? What am I missing here? Knowing they must cancel, we can work the problem, but I'm not grasping why I should know they cancel each other out. :svengo:

My other question is, what do I do with this book now? Do I take him through NEM and then come back to this or avoid it forever? I've never given up on a program before. I chose it because the other algebra books were too easy. We've ran into hard things in other books before, but stopped and worked through and moved on. Every day I see him patiently ramming his head into the AoPS wall and it's not something I can help him just "work through" this time. Even though I know that, I still hear Frankie Avalon in my head singing AoPS Drop-Out. :blush:

Link to comment

Share on other sites.

2.38 What number must be in the blank in the expression 3(x+7)-_(2x+9) if the expression is the same for all values of x?   The solution manual says that "if the expression is the same for all values of x, then the x's in 3(x+7) must cancel out with those in _(2x+9).   My question is...WHY must they cancel out? It's a random, unfinished number sentence. What is in the original problem that tells me they must cancel? What am I missing here? Knowing they must cancel, we can work the problem, but I'm not grasping why I should know they cancel each other out. :svengo:   My other question is, what do I do with this book now? Do I take him through NEM and then come back to this or avoid it forever? I've never given up on a program before. I chose it because the other algebra books were too easy. We've ran into hard things in other books before, but stopped and worked through and moved on. Every day I see him patiently ramming his head into the AoPS wall and it's not something I can help him just "work through" this time. Even though I know that, I still hear Frankie Avalon in my head singing AoPS Drop-Out. :blush:

(Okay LOL on the Frankie Avalon - I love that song!)

But if the value of the expression is the same for all values of x, that means there won't be any x's left when you simplify it. Otherwise the value of the expression would change for each different possible x.

Have you considered the classes? I know it's a lot of money for a maybe (although I think you have three weeks to bail and get a refund) but I find that there are things I should know but can't always blurt out right when DS needs them... and I like the idea of having someone else who is prepared to do it and other kids who can add to the discussion. Even one math jam left me going "wow - this guy rocks"... :) DS is starting two AoPS classes this year, so I'm not really speaking from experience yet, but I know I'd be stuck going "uhhhhhh...." even on things I really should be able to get. It is hard stuff, and not the "I can teach this in my sleep" of other algebra and geometry programs. I've tutored those for years, but AoPS really is quite a bit more.

8filltheheart

Well, I was in a serious minority (a group of 1, me ;) ) on the k8 board when a mom asked about AoPS for a slow, methodical avg student and I said I would not recommend it. Everyone else was saying that they were accessible to all students.

I have a lot of good math students (I had 1 take alg in 5th, 1 in 6th grade, and 3 others in 7th), but I only have 1 child that I would use AoPS with. He is not just good at math; he is passionate about math. He lives and breathes math. He has taken several AoPS classes and they are tough. He spent hours this summer on their alg 3 challenge sets. Thing is........he wants the challenge. That sort assignment literally makes him smile and jump right in.

My other kids do not desire that type of math depth. They used/are using programs like Foerster. I do not think they are being deprived at all. My ds that loves AoPS thinks mathematically and sees the world that way. The others are just good at math. :)

FWIW......I don't think you have anything to be ashamed of. The books are designed for the top 2-3% of all math students (not all students). They just aren't for everyone. (I couldn't teach them if I tried. He either takes their online classes or has a math coach for them. They are wayyyyyyyyyy beyond my abilities and my dh's as well (and he is an engineer! ;) )

ETA: Thought I should share that if I had known about AoPS umpteen yrs ago, I would have wanted my oldest to try them. I do think they stretch mathematical comprehension beyond the norm......basing that on the fact that my 14 yos now talks some strange language that I don't have a clue about what he is saying. All that said, I **know** that the rest of my older kids would say no way. (as a matter of fact my 11th and 6th graders did!! )

Guest Cheryl in SoCal

Well, I was in a serious minority (a group of 1, me ;) ) on the k8 board when a mom asked about AoPS for a slow, methodical avg student and I said I would not recommend it. Everyone else was saying that they were accessible to all students.   I have a lot of good math students (I had 1 take alg in 5th, 1 in 6th grade, and 3 others in 7th), but I only have 1 child that I would use AoPS with. He is not just good at math; he is passionate about math. He lives and breathes math. He has taken several AoPS classes and they are tough. He spent hours this summer on their alg 3 challenge sets. Thing is........he wants the challenge. That sort assignment literally makes him smile and jump right in.   My other kids do not desire that type of math depth. They used/are using programs like Foerster. I do not think they are being deprived at all. My ds that loves AoPS thinks mathematically and sees the world that way. The others are just good at math. :)   FWIW......I don't think you have anything to be ashamed of. The books are designed for the top 2-3% of all math students (not all students). They just aren't for everyone. (I couldn't teach them if I tried. He either takes their online classes or has a math coach for them. They are wayyyyyyyyyy beyond my abilities and my dh's as well (and he is an engineer! ;) )

:iagree:I haven't used it yet but have been looking through the Intro to Counting and Probability and a bit of the Intro to Algebra and from what I have seen I wholeheartedly agree. No math curricula is the answer for every student but IMHO AoPS is going to be a good fit for the minority of students. One of my ds's would DIE if I had him use AoPS and another I think will like it because he thinks that way, though we'll only know after we try it.

I had a look at the algebra and geometry and found the layout visually confusing, which is kind of weird since in some ways it is not as busy or distracting as textbooks in general. But it is packed solid, and hard to read as a text, if that makes any sense. And algebra is my own strength. My dd went for Discovering Algebra instead.

The geometry book struck me similarly as user-unfriendly, but that may be again just my visual reaction to such a dense text.

However, that similar packing did not bother dd with the data and probability books, which she greatly enjoys. So maybe it depends on the kid (and grown-up) as well as on the area of math involved.

(Okay LOL on the Frankie Avalon - I love that song!)   But if the value of the expression is the same for all values of x, that means there won't be any x's left when you simplify it. Otherwise the value of the expression would change for each different possible x.

Ha! Lightbulb! Thank you! Regardless of what x is, the expression will equal the same thing. You're speaking my language. The book is not. :tongue_smilie:

I am relieved to hear these responses. He loves math and enjoys a challenge, but I couldn't at all say that he is passionate about math. I had forgotten that Foerster was on my list of maybes before I heard that AoPS was the crème de la crème of algebra texts. So....NEM or Foerster....thoughts?

I know absolutely nothing about NEM, so I can't offer any insight there. I have used Foerster with all of my older kids, including my ds that now uses AoPS. He used Foerster for both alg 1 and alg 2. His first AoPS courses were Intro to Counting and Prob and their alg 3 courses online and he owns several of their other "off normal track" math books that he works through on his own.

My oldest used Foerster and it more than prepared him for university level cal and an engineering major.

I'm not sure I can explain the differences very easily. Foerster is a solid math program and they absolutely learn the math skills they need to perform high level math problems, etc. No question.

AoPS helps them process math in a completely different fashion. Ds goes around "discovering" concepts and "proving" things like why x equals some bizarre thing or how an indefinite number of fractions add.......I don't know......I just nod my head!!! :lol: He thinks he wants to double major in astrophysics and math. For him it is a match. I have only ever met 2 other people that think that way.......one is now majoring in math and the other has a phD in math. For the rest of mere mortals, I think we are fine w/o it!

In The Great White North

Dc used/are using Foerster. They arde very solid math books. I have the AoPS Problem Solving, Counting & Probability and Number Theory books. Dc don't like them. They are not straight forward. Dc like to have an example, an explanation and get the problems done. Foerster does this for them. AoPS does not.

AoPS is for people who like to PLAY with their math. If your idea of a great time is to go round and round with a math problem til you figure it out, AoPS is for you. Yes, the top 2-3% of math students in the country are more likely to enjoy that, but even they don't always like that.

I've seen but not used Foerster, so I can't compare... but NEM is good challenging work. Most of it is more straightforward than AoPS (examples first, exercises second) but there are Challenge sections and Mathematical Investigations that could be frustrating in the same ways AoPS can be. They do (in those sections) throw you in and expect you to dig yourself out. And to some extent they leave some gaps in the regular explanations too -- nothing huge, but enough that sometimes the student (or the teacher) has to connect the dots.

C_l_e_0..Q_c

I'm in the opposite situation. We're a NEM drop-out. I'm so much happier as a mom with AoPS *and* the online class. Someone else is teaching math to my math kid!

(and I"m good at math too, I did math all the way to a Master's level, although it was not my major - I'm an engineer, we need math )

My son is truly having a blast with the online class. He did Algebra 1 over the summer. The kids at the summer pool who learned he was doing a math class assumed it was remedial, until they saw a problem! LOL. Sweet nerd revenge. :)

The math classes are totally worth the cost. Plus they force the kids to move forward, and not spend 2 months on 2 chapters. In 15 weeks, they did 14 chapters (possibly 13, I'm not sure) so the interest is kept high.

at the beach

I agree that AoPS is for people who enjoy playing around with math. I think I am one of those who said something along the lines that more people can be successful with it than the top few percent. But I think I also said that sometimes the solutions/explanations gloss over things or skip a step, assuming readers will see that step in the problem when they might not. I felt it could be used by more than just the top few percent because I think that kids often underestimate their abilities. I also agree with the pp that even kids in the top few percent who can do it may not want to do it because it does take a lot of time and puzzling.

I was terrified of math from 8th grade on. I never took math in college but took logic to avoid it. When I signed my daughter up for AoPS this summer, I decided to give the book a try. I did the first three chapters. I wanted to help my daughter if she needed it, but she was the one helping me :001_huh: and the class moved so fast that I couldn't keep up.

The problem that you mention, to me, looks like it is asking you to make the 2x the same as the 3x so the only thing that works is 3/2. How do you know it will cancel? I think you know that because it's a subtraction problem. Maybe I am oversimplifying this.

Maura in NY

NEM is an integrated program - Algebra/Geometry/Trig and rolled together. It's challenging, in a good way, but it doesn't fit the typical Algebra/Geometry/Algebra II/Trig-PreCalc/Calc track.

FWIW, my ds used NEM 1 in 7th, thinking he would stick with it for 4 years. Instead, we switched. He didn't use Foerster's Algebra I, but he did use Foerster for Algebra II and PreCalc. Great real world application problems.

We used AoPS for several months and also found some of the problems strangely worded. But, our biggest problem with AoPS was not enough repetition.

We are using Foerester's Algebra now. It has more than enough problems for us, but it's much easier to eliminate problems than try to add more in.

Miss Marple

Not a drop-out yet, but we are doing AoPS very slowly and I've added NEM2 back as the primary math. Ds is still working through the geometry book (45 minutes per day), but we've put the algebra book away because he already did LOF Beginning Algebra and the NEM should cover the bases thoroughly.

I'm finding that hormones cause my son to be less inquisitive and less dedicated right now. He does great with math, so I chose the other program I love - Singapore NEM, and it is going very well.

If we never finish the AoPS books that will be OK because NEM is the primary curriculum (which we will finish). I know that any exposure ds has had with AoPS has helped fine tune his mathematical abilities.

Well, I was in a serious minority (a group of 1, me ) on the k8 board when a mom asked about AoPS for a slow, methodical avg student and I said I would not recommend it

:iagree: I cannot imagine how frustrated a student and a parent would be trying to work through this program and thinking that it is accessible for all students!

The problems in NEM can be plenty challenging at times. My son did NEM 1 before switching to AoPS.

Regarding AoPS Algebra 1, they introduce Algebra 2 concepts, too. That doesn't make it easier! Ds thought the middle of the text was difficult and often trudged through the problems, but then he flew through the last few chapters. He thought they were easier, even many of the challengers. I don't know if they really were, or if he just started to get the hang of the text and problems.

When it comes to math, it's so important to pick what works and then bite off and chew well at a pace that's suitable for the student. I wouldn't hesitate to step back and reconsider if something wasn't working.

  AoPS is for people who like to PLAY with their math. If your idea of a great time is to go round and round with a math problem til you figure it out, AoPS is for you. Yes, the top 2-3% of math students in the country are more likely to enjoy that, but even they don't always like that.

I agree entirely with the bolded.

If anybody is deciding whether to go with the AoPS classes, there's a Math Jam on the subject this afternoon/evening (7:30 Eastern, I believe). It will include sample questions from the class, so you can try them out.

Math Jams are free informational sessions, usually hosted by Richard Rusczyk, who is always responsive to questions. If he can't answer your question within the confines of the session, he'll likely invite you to e-mail him and he'll help you decide whether a class is right for your family.

We're mathy. . . and we're AoPS drop outs as well.

Dd & I tried Number Theory for a couple/few months. It actually went OK so long as *I* worked through *every section* and *every problem* on my own before dd tried it (or simultaneously sitting together).

The exploration and problem solving was interesting. I rather enjoyed it. But, I just *don't have time* to do it right now.

We dropped it after a few chapters -- which were successful but slow b/c I just couldn't make myself find the time to do it often enough to keep up w/ dd's needed pace.

So sad. . .

Now y'all are scaring me. My dd loved the AoPS Number Theory book so much this summer, I bought Alg I for her (but we don't start for another year...) I had been planning on Foerster's, so I've got both ready to go (well, I still need that pesky Foerster's Solutions manual...)

We're mathy. . . and we're AoPS drop outs as well.   Dd & I tried Number Theory for a couple/few months. It actually went OK so long as *I* worked through *every section* and *every problem* on my own before dd tried it (or simultaneously sitting together).

Dd and I worked through all the examples together, but then she did the problem sets pretty much on her own (except I let her skip the challenge problems at the end of the chapters). Was your dd just needing you to sit with her for the "lesson" part, or also the problem sets? I didn't mind working through the lesson with her... I actually learned a lot myself and had fun... :tongue_smilie: For some reason I really like the layout and presentation of these books... OTOH the Lial's layout really drove me crazy when I first saw it (I'm getting used to it now that my other dd's working through BCM).

But now you guys are intimidating me a bit... :001_huh: I do think the Algebra text looks more challenging than the Number Theory, but I'm hoping after she's gotten through Singapore DM1, she'll be preparerd (or I guess we'll do Foerster's after all...)

I found the solutions manual for Foerster this afternoon! I finally called the publisher and it turns out that they renamed the book and it is now called Classic Edition instead of Foerster's. The ISBN # is 0201861003. I can't find it used anywhere, but it is available new at pearsonschool.com.

I'm still torn though. I loved Singapore so well and would like to try going on with NEM. But I don't want to commit to it being his math for all of high school. I hear that Foerster does an excellent job with proofs, which I think are important. I may end of tossing a coin before this is over.

This is exactly what I was trying to express in the other thread! It's just as much about the approach as the difficulty, imo. Yes, you need to be a good math student, but I dont' think you need to be a TOP math student. Not in the sense of the top 2% to 3%, at any rate. I can't imagine my dd would score anywhere near that high, but she loves AoPS.

And you can be a top math student, but if you hate this approach, it will be very hard to persevere and succeed.

Join the conversation

You can post now and register later. If you have an account, sign in now to post with your account.

×   Pasted as rich text.    Paste as plain text instead

  Only 75 emoji are allowed.

×   Your link has been automatically embedded.    Display as a link instead

×   Your previous content has been restored.    Clear editor

×   You cannot paste images directly. Upload or insert images from URL.

• Insert image from URL
• Submit Reply
• Leaderboard
• Board Rules
• All Activity
• Classifieds
• Create New...

Summer Resources: Mathematics

• Computer Science
• History of the Human Community
• U.S. History
• AP European History
• Mathematics
• Modern Language
• Visual Arts

Books, puzzles, games, and websites?!?! Who knew math was in so many interesting places! Come explore a topic not presented in a typical math class through the Art of Problem Solving’s Math Jams, hone your deductive reasoning skills through a game of Mastermind, see a math idea explained with visuals, or read a book that brings math to life! 

Math Jams Through AoPS

Math Jams are free online discussions hosted by Art of Problem Solving for a variety of purposes, including:

• Informational sessions about Art of Problem Solving classes.
• Review of the AMC and AIME competitions.
• Introductions to new topics in math and other areas of study.
• Special events, such as our annual discussions with admissions officers and professors from outstanding universities such as MIT, Carnegie Mellon, Stanford, and Duke.

To attend a Math Jam, simply sign in to Art of Problem Solving just before the Math Jam begins, and click on the Classroom bar that will appear on the screen. The Math Jam classroom will open 10 minutes before the Math Jam begins.  Level guide:

Fun Math and Strategy Games!

KenKen  - arithmetic logic puzzles - the rules are  here

Mastermind  - code-breaking game - the rules are  here

X+Y , released in the US as A Brilliant Young Mind , is a 2014 British drama film directed by Morgan Matthews and starring Asa Butterfield, Rafe Spall and Sally Hawkins. The film, inspired by the documentary, Beautiful Young Minds , focuses on a teenage English mathematics prodigy named Nathan (Asa Butterfield) with autism who has difficulty understanding people, but finds comfort in numbers. When he is chosen to represent the United Kingdom at the International Mathematical Olympiad (IMO), Nathan embarks on a journey in which he faces unexpected challenges, such as understanding the nature of love. The character of Nathan was based on Daniel Lightwing who won a silver medal at the 2006 IMO. Source: Wikipedia.com

More Challenging Puzzles

Click the image for math puzzles!

"Every week, The Riddler offers up problems related to math, logic and probability. Two puzzles are presented each week: the Riddler Express for those of you who want something bite-size and the Riddler Classic for those of you in the slow-puzzle movement. Submit a correct answer for either,1 and you may get a shoutout in next week’s column."

Calculating Ada: The Countess of Computing (BBC)

Ada Lovelace was a most unlikely computer pioneer. In this film, Dr. Hannah Fry tells the story of Ada's remarkable life. Born in the early 19th century, Ada was a countess of the realm, a scandalous socialite and an 'enchantress of numbers.' The film is an enthralling tale of how a life infused with brilliance, but blighted by illness and gambling addiction, helped give rise to the modern era of computing. Source: YouTube.com

Math Channel

Click for math videos!

3blue1brown is a channel animating math.  Check out their playlists for expositions of various neat topics and some clever proofs, and see the "Essence of ______" series for some more student-focused material.

Recommended Reading

• << Previous: AP European History
• Next: Modern Language >>
• Last Updated: Jan 25, 2021 12:56 PM
• URL: https://nobles.libguides.com/SummerResources

Math Olympiads for Elementary and Middle Schools

Math Olympiads for Elementary and Middle Schools ( MOEMS ) is a large and popular mathematics competition for students in grades 4 through 8. The goal of MOEMS is to expose students to elementary methods of mathematical problem solving .

MOEMS Executive Director Richard Kalman and many talented MOEMS PICO's run online Math Jams at Art of Problem Solving . These Math Jams are designed to help PICOs learn new ways to teach mathematical problem solving to MOEMS students.

MOEMS Resources

• The MOEMS Homepage
• MOEMS Books at AoPS
• The MOEMS Forum at AoPS as well as a private MOEMS Teachers Forum .
• Subscribe here: https://www.youtube.com/channel/UC-Nt9Uo03VSo2QTNIzsE_cA and fill out this google form. https://forms.gle/1YNouth3P6oryjuF6 . This class shall prepare you.*
• List of mathematics competitions
• List of United States elementary school mathematics competitions
• List of United States middle school mathematics competitions
• Mathematics competition resources
• Academic competitions
• Math competition books
• Mathematics competitions
• Introductory mathematics competitions

Something appears to not have loaded correctly.

Click to refresh .

The USA Mathematical Talent Search (USAMTS) is a free proof‑based math contest for US middle and high school students. Students receive written feedback on their work, and can earn prizes based on their performance.

Solve the Problems

Each round consists of 1 puzzle and 4 proof-based problems. The problems vary in difficulty, so there is something challenging yet approachable for everyone.

Write Your Solutions

Unlike most other contests, you’ll have over a month to solve the problems and write up your solutions. You’re also allowed to consult certain reference material.

Get Feedback

Our graders not only give you a score, but also personalized written feedback to help you develop your mathematical and writing skills.

At the end of the year, the top 45% of students will receive prizes, including math books and T-shirts. Prizes may include Wolfram software subscriptions as well. The USAMTS is also one way to qualify for the American Invitational Mathematics Examination (AIME).

Interested? Join our mailing list to receive updates about the USAMTS, such as announcements that problems are available or that scores have been released. To compete, register today!

Qualifying Quiz Solutions

Curious about the solutions to the Qualifying Quiz problems, or looking for feedback on your own Quiz solutions? Each year, we hold an online, interactive class, facilitated by a Mathcamp instructor, to discuss the Qualifying Quiz problems. In addition to the solutions themselves, we talk about how you would come up with a solution and how to write up your solution so that all of the necessary pieces are in place. The event is a real-time conversation where participants help guide us through the solutions and are able to ask questions throughout.

Upcoming Event:

Join us for two upcoming conversations about the Mathcamp 2024 QQ, where Mathcamp instructors will discuss the solutions in a live, interactive classroom.

• The first session will be on Wednesday, May 15th , beginning at 7pm ET / 4pm PT (note the early start time), and will discuss problems #1, #2, and #3.
• The second session will be on Thursday, May 16th , beginning at 7pm ET / 4pm PT (note the early start time), and will discuss problems #4, #5, and #6.

Click here to participate.

The events are free and open to the public. To attend, you must have an account at the Art of Problem Solving website. Follow their instructions for "Math Jams" here .

If you can't make it to the live class, you can always read the transcript, linked below after each event.

• The 2023 Quiz Jam: Mathcamp Quiz committee members Dan Gulotta and Tim! Black discussed solutions to the 2023 Quiz problems. Click here for the transcript (from May 23, 2023).
• The 2022 Quiz Jam: Mathcamp Quiz committee members Kevin Carde, Misha Lavrov and Tim! Black discussed solutions to the 2022 Quiz problems. Click here for the transcript (from May 17, 2022).
• The 2021 Quiz Jam: Mathcamp Quiz committee members Assaf Bar-Natan, Kevin Carde, Sara Fish, Laura Pierson, Mira Bernstein, and Misha Lavrov discussed solutions to the 2021 Quiz problems. Click here for the transcript (from May 19, 2021).
• The 2020 Quiz Jam: Mathcamp Quiz committee members Linus Hamilton, Kevin Carde, Marisa Debowsky, and Mira Bernstein discussed solutions to the 2020 Quiz problems. Click here for the transcript (from May 12, 2020).
• The 2019 Quiz Jam: Mathcamp Quiz committee members Adam Hesterberg, Kevin Carde, and Marisa Debowsky discussed solutions to the 2019 Quiz problems. Click here for the transcript (from May 14, 2019).
• The 2018 Quiz Jam: Mathcamp Quiz committee members Misha Lavrov, Yasha Berchenko-Kogan, and Yulia Gorlina discussed solutions to the 2018 Quiz problems. Click here for the transcript (from May 14, 2018).
• The 2017 Quiz Jam: Mathcamp instructors Marisa Debowsky, Kevin Carde, and Adam Hesterberg discussed solutions to the 2017 Quiz problems. Click here for the transcript (from May 17, 2017).
• The 2016 Quiz Jam: Mathcamp instructors Marisa Debowsky and Kevin Carde discussed solutions to the 2016 Quiz problems. Click here for the transcript (from May 18, 2016).
• Click here for the Problems #3, #5 and #6 transcript (from June 23, 2015).
• Click here for the Problems #1, #2 and #4 transcript (from June 29, 2015).
• The 2014 Quiz Jam: Mathcamp instructor Mira Bernstein discussed solutions to the 2014 Quiz problems. Click here for the transcript (from June 16, 2014).
• The 2012 Quiz Jam: Mathcamp instructor Yasha Berchenko-Kogan discussed solutions to the 2012 Quiz problems. Click here for the transcript (from June 26, 2012).
• The 2010 Quiz Jam: Mathcamp instructor Dan Zaharopol discussed solutions to the 2010 Quiz problems. Click here for the transcript (from June 15th, 2010).

We hope you have enjoyed working on the Qualifying Quiz problems!

Middle School Competition Math

If you are interested in math contests like  Math Olympiad (MOEMS), AMC 8, MATHCOUNTS, AMC 10, here is a  comprehensive list of the best books and resources to help you prepare.

Also, here is a list of Math Contests that you can participate in.

Online Reso urces

Mastering AMC 8 Book and Video Series

This free book covers the most important concepts on the AMC 8 and includes video lectures for every chapter, formulas for every topic, and hundreds of examples and practice problems with detailed video solutions.   

AMC 8 Fundamentals Course

These classes covered the fundamental concepts required for AMC 8. ​

AMC 8 Advanced Course

These classes covered more advances concepts required for AMC 8 and MATHCOUNTS competition. ​

AoPS Videos

Art of Problem Solving offers hundreds of free videos featuring AoPS founder Richard Rusczyk. They have videos aligned to the PreAlgebra text, the first half of their Introduction to Algebra text, and their Introduction to Counting & Probability text. They also regularly produce MathCounts Minis featuring problems from State-level MathCounts competitions, as well as videos for select AMC 10, AMC 12, and AIME problems. Activity sheets for the videos can be found on the MATHCOUNTS  website. All of these videos are hosted on YouTube, most on the Art of Problem Solving channel and the MathCounts videos on the MathCounts channel.

MATHCOUNTS Minis

Art of Problem Solving 's Richard Rusczyk has been making MATHCOUNTS Minis since September 2009. Each MATHCOUNTS Mini video provides detailed explanations for at least one MATHCOUNTS problem and its associated concepts. Each Mini also features an activity sheet to complement the discussed concepts. Here is a YouTube playlist with all the videos.

AoPS Alcumus  

Alcumus offers students a customized learning experience, adjusting to student performance to deliver appropriate problems and lessons. Alcumus is specifically designed to provide high-performing students with a challenging curriculum appropriate to their abilities.

AoPS MathCounts Trainer

MathCounts trainer helps students practice for MathCounts. There are multiple levels in MathCounts trainer just as there are multiple rounds for MathCounts.

AoPS For The Win

FTW has it all: an unparalleled array of MATHCOUNTS-style problems, elite competition, customizable games, and player rankings. If you’re looking to sharpen your competition skills, or just want to engage in good old-fashioned mathematical battle with friends or strangers, then this is the arena for you.

AoPS Keep Learning

The AoPS team has assembled fun activities to help kids keep learning, collaborating, and having fun even while safe at home.

AoPS Math Jams

Math Jams are free online discussions hosted by Art of Problem Solving for a variety of purposes, including:

Informational sessions about Art of Problem Solving classes

Review of the AMC and AIME competitions

Introductions to new topics in math and other areas of study

AMC 8/AJHSME Tests

The AMC 8 was previously known as the AJHSME (American Junior High School Mathematics Exam). This link has all of the past AJHSMEs  and AMC 8's. Check out Math Contests  for information about the AMC 8.

AHSME Tests

AHSME (American High School Mathematics Exam) is basically an old version AMC 10/12 from 1950 to 1999.

AMC 10 Tests

Art of Problem Solving has all of the past AMC 10's. Check out   Math Contests  for information about the AMC 10.

AMC 12 Tests

This page has all of the past AMC 12 tests. Check out Math Contests for information about the AMC 12.

This page has all of the past AIME tests. Check out Math Contests for information about the AIME.

Parallelogram

Dr Simon Singh , author of the No. 1 bestseller  Fermat’s Last Theorem  and  The Simpsons and Their Mathematical Secrets  has created a set of weekly maths challenges – just 15 minutes of interesting, fun and challenging material that goes beyond school maths: mystery and history, activities and oddities, puzzles and problems.

MATHCOUNTS Previous Year's Competition

Last year's school, chapter and state competitions are available for free on MATHCOUNTS website.

MATHCOUNTS Categorized Resources

MATHCOUNTS provides many free problem sets, videos, lesson plans and activities that can complement in-person and online learning. The've categorized some of the best resources for several middle school math topics.

MATHCOUNTS Problem of the week

MATHCOUNTS releases a problem every week. The full archive can be be found at this link.

ThePuzzlr's  Introduction to Number Theory Course

This FREE course serves as a fundamental basis of Number Theory for premiere competitions like the AMC 8 and MATHCOUNTS. It covers all the essential topics needed to tackle Number Theory questions. Each topic in this course has a video, explanations, and practice questions/quizzes.

AMC 8 Mock Contest from Po-Shen Loh

Try the AMC 8 Mock Test written by Po-Shen Loh. All problems are original and were created by analyzing the American Mathematics Competitions middle school math contests.

Beauty of Math Channel

This is a channel initially focusing on all Competition Math such as American Mathematics Competitions, AIME, Math Counts, Math Kangaroo, content from Art of Problem Solving and various other Mathematical Topics.

Aops Wiki Problem Generator

This problem generator generates random problems from the aops wiki 1 at a time or in groups. 

Brilliant (use this link to get a 20% discount)

Brilliant helps to build quantitative skills in math, science, and computer science with fun and challenging interactive explorations. All of their courses are crafted by award-winning teachers, researchers, and professionals from MIT, Caltech, Duke, Microsoft, Google, and more, with these principles of learning in mind.

Think Matrix (use this link to get 1 month free)  

Think Matrix uses AI technology to provide a self-adaptive learning platform. With over 10,000 practice questions in 29 modules and 70+ topics, students get unlimited practice and tests.

Best Books for Competition Math Math League Middle School Books Math League uses Lulu to handle sales of their books. Each year they prepare compilations of the material that was released at the contests the previous school year. Electronic versions of many of their tests are sold one test set at a time through the "test downloads"  link. The first ten years (1997-2007) of high school contests are also sold (for a limited time only!) bundled together through the "test downloads" link. MATHCOUNTS Books MATHCOUNTS provides a series of books with selected problems and their solutions from the contests. AlphaStar Academy AMC 8 PRACTICE TESTS: VOLUME 1 This book is for students who are preparing for middle school math competitions such as AMC 8 and MathCounts. It contains four AMC 8 practice exams with new problems not used in any past competitions and with insightful solutions.

Free Classes

Youth Conway

Youth Conway provides high quality, free, virtual instruction as well as engaging mathematical immersion activities in a time when many similar events have been canceled due to this global crisis.

Math Divulged Classes

Math Divulged is a COMPLETELY FREE online series of classes! They offer a diverse set of topics and levels and participants have complete control over the classes they choose to attend, allowing them to craft their dream schedule. Math Divulged is composed of dedicated competitive math veterans, including MathCounts National Champion, MOPpers, IMO Gold Medal winner, etc

Everaise Academy

Everaise provides 5 week STEM outreach program for middle and high school students that seeks to challenge participants through engaging courses in mathematics, physics, astronomy, linguistics, and biology. ​

Euclid's Orchard

Euclid's Orchard serves to provide high quality handouts to teach those who are interested in a variety of subjects.

Trinity School NYC Math Team Classes

TrinMAC offered free, virtual math camp ​ during the summer of 2020.

Mallstars Classes

MoTown All Stars Mathematics Team is a team of motivated students dedicated to improving the mathematics community. They offer a number of classes from middle school to Olympiad level.

Pai d Classes ​

If you are looking for paid Math classes, here is a list of the most popular paid classes.

AlphaStar Academy​

AlphaStar Academy offers extensive training programs for gifted students towards national and international Math and Science competitions such as MathCounts, American Mathematics Competitions, USA Math Olympiads, USA Computing Olympiads, F=ma, and USA Physics Olympiads.

Art of Problem Solving

Since 2003, the AoPS online school has provided a unique learning experience carefully designed for outstanding students studying online. We offer a full math curriculum for middle and high school, introductory programming courses, and specialty courses to prepare students for particular math and science competitions. Most of our courses meet weekly for live sessions, and have a variety of types of weekly homework.

Daily Challenge By Po Shen-Loh  

One of the best online courses for middle school competition math! Prof. Loh's ability to design problems, along with his engaging and thorough explanations makes their courses are extremely efficient in helping students with little competition math experience advance to a much higher level!

Momentum Learning

Momentum Learning provides tutoring services to elementary and high school students in the Sugar Land, Texas area. Their comprehensive services cover the critical subject areas for educational success in these grades. They provide weekly classes covering a variety of subjects including school math, contest math, coding, science, English, and public speaking.

MathLeague.org

Mathleague offers a number of services designed to promote math and problem solving abilities in individual or group settings. Instructors at mathleague.org run short-term classes to help prepare students for math competitions and develop their problem-solving skills. Classes will be held throughout the school year in person and online. 

Awesome Math

AwesomeMath is devoted to providing enriching experiences in mathematics for intellectually curious learners. Through summer camps, publications, curriculum, and competitions AwesomeMath fosters a community that values critical thinking, creativity, passionate problem solving, and lifetime mathematical learning.

AMC Advantage

AMC Advantage is a collection of problems designed to improve problem-solving skills and get students ready or the competition.

RSM AMC Classes

Russian School of Math's selective and tiered competitions program prepares students for the full array of national and international math Olympiads.

John Hopkins CTY Competitive Math Prep

This course is designed to extend skills in problem solving taught in MathCounts, to foster mathematical creativity, and to prepare students for competitions similar to the American Mathematics Competition (AMC 8, 10).

MyMathCounts Classes

They have online classes, preparation books, private tutoring, and other math materials.

Achievable (save 25%)

Achievable provides AMC 8 and AMC 10/12 courses through their memory-reinforcing platform which automatically prioritizes the material students need and then trains them to remember it more effectively on test day.

MyMathCounts Books

* these books often have typos and errors.