Learning Resources

Alcumus on the Art of Problem Solving website

• (AoPS) Art of Problem Solving's "Alcumus" program lets you practice solving problems in Probability, Algebra, Geometry and Number Theory, and see your progress on dozens of sub-topics.  This is an AWESOME practice tool!!

• Coach can see how much you use it, and counts total usage towards qualifying for the Mathcounts team. (Qualifying = Scores on other contests + USAGE of Alcumus)

• SIGN UP with this link. If you do not sign through that specific link, the coach will not be able to see your progress. NOTE: Your username can be anything, but please use your real name when prompted for first and last names, or you won't get credit towards Mathcounts qualification.  Only your coach will see your real name.  Everyone else will see your username only.

• If you forget your password, don't create a 2nd account... email your coach, who can reset it (jonathan.a.mcintyre@gmail.com)

  • If you're under 13, stay with the regular "restricted" account.  Students 13 or older may take an extra step to get a full account, which just lets you take part in forums.

  • Your signup will put you into the "Pre-algebra" class.  The Math Team coach will then enroll you in 3 other topics (Geometry, Counting/Probability, Number Theory), which you can explore via the "Change Focus" button

  • Here are also some of the AoPS online books. These are usually very long, but there is a lot of information and can help you when doing alcumus :Volume 1,Introduction to algebra(Algebra 1 and 2 in school), Introduction to counting and probability

ClassMarker - our practice platform in Fall 2021.  We might not need it this year.  Still to be decided. 

Mathcounts Trainer app  This is the browser version. You can also download an app, great for practicing going fast on easier "sprint" problems.  Log in to your AoPS account first if you want to save your scores and progress.

"Saab" Mathcounts practice test generator - makes a test in whatever area of math you want to work on.  Auto-scores it and shows solutions when you finish.

Some past Mathcounts practice problems:

• Folder with 2017-18 weekly problems

• PDF with 2017-2018 Answers and Solutions (scroll down for solutions) to all of that year's "Workout" and "Warmup" practice problems

Brilliant -  Through our Mathcounts membership, we get access to Brilliant at no cost to you.   This is an excellent platform for learning concepts in a visual way, which fits well with our learning philosophy.  You can join our class here:  https://brilliant.org/classroom/join-v2/96867433-9130-4dd2-86a4-18761cadea61

You must use your real name, and must be a registered member of Math Team for me to permit you to keep an account there. 

Random Number Generator - Use this to make numbers in whatever range you want, then try to factor them (into their prime factors) as quickly as you can.  See how fast you can get.   

• This link will give you 3 integers between 100 and 499.

• Go here to reset the range and number of integers

Desmos  - This platform gives immediate graphical feedback on how equations relate to geometry.  It's outstanding for learning geometry concepts in a visual, interactive way.   Go to this address and try some activities

• • Geometry Sketcher

  • Graphing Practice

  • Our Group Activities on Desmos

Quizlet - Master important basics by signing up for a free Quizlet account, then using these:

• • Squares up to 40 (I don't like that it just shows the number, but it does go up to 40, which is very useful) 

  • Cubes up to 12 (these are the most important to learn)

  • Decimal fraction conversion:  https://quizlet.com/314165525/fraction-to-decimal-conversion-flash-cards/  

  • Estimating square roots:  https://quizlet.com/223172509/square-roots-estimating-square-roots-flash-cards/

  • Remember negative numbers!  https://quizlet.com/366515050/squares-and-cubes-flash-cards/

  • Here are some on graphing, with slopes and intercepts. Make sure you have these basics down:

    • https://quizlet.com/464949260/slope-flash-cards/ 

    • https://quizlet.com/339967447/slope-flash-cards/ 

    • https://quizlet.com/365622182/intercepts-flash-cards/ 

Here are places where you can learn about all the topics in middle school math, and the most common contest problem topics

Middle School Curriculum 

In your classes, some are using an excellent free resource called "Open-Up". The basics of all middle school math are covered here.  Check it out!

• • Grade 6 Math Topics at Open-Up

  • Grade 7 Math Topics at Open-Up

  • Grade 8 Math Topics at Open-Up

Math Contest Curriculum

This is the Math Team's self-developed library of the most common middle school math contest problem types, and the most useful facts to learn to help you with them.  It includes:

• Our Math Club Google Drive Folder - Contains all our materials, including past handouts, past contest info, and the main learning resources subfolder described below.

• Learning Resources   Start by reading the README file.  Has all kinds of good stuff to learn, including basic facts to memorize, high level strategies for problem solving, and instruction on specific topics (see "Topic Sheets" below).

• Topic Sheets - This has the bulk of what you'll need to learn.  This is "Level 3" learning.  Make sure you also cover levels 1, 2 and 4 in the Learning Resources subfolders.

• Summary of Topic Sheets   A 2-page synopsis of the main facts explained in the topic sheets.  Make sure you know everything on this if you want to do well in math competitions.

• Mathcounts Video-Based topic sheets

• Math Organization Document - This document is like an index to all our written and video resources, organized by topic.  It links to our writeups on topics, plus AoPS videos and mathcount minis along with their stretches.  If you want to find a lot on one specific topic, go here! 

AoPS Videos

See these described in the "Outside Videos" section below.  Their "Counting", "Pre-Algebra" and "Algebra 1" categories cover those topics fairly thoroughly.

See a version of this with pictures at the end of our Orientation Guide

When using Alcumus, if you don't "set focus", you'll only get Pre Algebra problems, so you'll miss out on Geometry, Probability and Number Theory.

While in Alcumus, you'll see a "Focus" panel in the upper right.  Sitting there, barely noticeable at the lower left of that panel is the "Change Focus" button.  

This is an important button! 

Pick "Change Focus", and you'll see a window with many lines going across, one for each Pre Algebra subtopic.  It shows your progress on each topic under Pre Algebra 

(See this same writeup at the bottom of our Orientation Guide to see images of what's being described.)

Your goal for earning points is to get as many categories from the red stage through the orange stage and up to green. 

It will automatically push you to the next topic once you reach green.  

If you "Change Focus" back to a green topic you can do a little more on it to get it to blue. 

Once you're at blue you won't earn many more points in that category. 

It's best to just get as many greens as you can. Don't worry about getting blues, unless you really want to work on that topic a lot.

Once you've had enough of Pre Algebra, try a different topic!   Pick the "Prealgebra" button in the upper right, and you'll see a list of 7 or 8 topics.

Avoid choosing Algebra, Intermediate Algebra or Precalculus, as we don't look at those for Mathcounts.

Choose one of "Number Theory", "Counting & Probability", or "Geometry".  

To sum up:  If you get tired of a type of problem, "Set Focus".  If there's an area you know you need more work on, choose "Set Focus" and work on it! 

Note, to finish setting focus, pick on the category you want, then scroll down to click the "Play" button at the bottom right. 

Also note that you can go to "Settings" (on the left) to adjust problem difficulty and whether it auto-advances the topic when you reach Green (the default), or only after you reach Blue. 

Review 

Look in the "Our Meetings" section above for videos of our lessons, and our contest problem reviews.

Below are libraries of good videos from other sources, thoroughly covering all topics you'll need to know to excel at Mathcounts, AMC 8 and other middle school contests.  Master the content in these and you'll be a top scorer! 

"Mathcounts Minis" videos    By Art of Problem Solving (AoPS) founder Richard Rusczyk.  Highly recommended, especially for newer students.  These focus on Mathcounts problems, and are somewhat random in order.

"Art of Problem Solving" Videos  More Richard Rusczyk videos covering almost all middle school math topics!  These are more "ordered", going from basic to more advanced topics within each major category.  Try these categories:

• Counting and Probability

• Pre-Algebra

• Algebra 1

• Mathcounts State Competition Problem Review    These are more advanced problems, for when you need more challenge.

One of our favorites is this video on figuring out whether a number is prime:  https://artofproblemsolving.com/videos/prealgebra/chapter3/50   In Math Team we'll show you an advanced prime factoring technique to skip the long division!

OmegaLearn videos   on "AMC 8 Fundamentals".  Not nearly as good as AoPS videos, but these take less time than watching all the AoPS videos, and give a good overview of all the major types of problems.   10 videos, about 57 minutes each.

Some of our lessons on basic and advanced techniques in solving problems are recorded so you can review them 2 or 3 times until you get it down. 

• Calculation shortcuts

• Calculation shortcuts, Part 3  (didn't record Part 2)

• Right Triangles

• Arithmetic Series

• Geometric Series

• Counting Combinations

• Stars & Bars (balls in bins) and Pascal's Triangle

• Factoring (GCD, simplified radicals, etc.) and Ratios
  
  

Or, you can just go to our Drive folder of all the above videos and more.

We often review the AMC 8 and Mathcounts (school) contest problems.   This is a great way to learn how to solve the hard problems, and go faster on the others.

• 2024 AMC 8 (January), problems 1-15

• 2023 Mathcounts Chapter Contest Sprint Round, 1-13

• 2023 Mathcounts Chapter Contest Sprint Round, 14-23

• 2023 Mathcounts Chapter Contest Sprint Round, 24-30

• Jan 2023 AMC 8 problem review, 1 - 15

• Jan 2023 AMC 8 problem review, 16 - 25

• 2022 Mathcounts Chapter Sprint, 1-18

• 2022 Mathcounts Chapter Sprint, 19-30

• Jan 2022  AMC 8 problem review

• Nov 2021 AMC 10A problem review

Or, you can just go to our Drive folder of all the above videos and more.

Simplification!   Convert every problem into an easier-to-solve problem

Strategy examples

For a good discussion of problem solving strategy, see Coach McIntyre's free e-book about stategies to solve every problem on the 2017 AMC 8

Strategy handouts

See the "Level 4 - Strategy: Attacking Hard Problems" subfolder under our Google Drive's "Learning Resources: Handouts & Videos" folder. 

See the 10 Strategies list at MAA's Curriculum Inspirations page. 

Free programs you must apply for

• MIT Primes STEP - Year-long weekly program.  Requires a recommendation letter, and application to be accepted.

Misc Online Learning

• MAA Curriculum Inspirations - Videos and more giving excellent problem solving advice from the makers of the AMC tests.

• Proofs Without Words - From "Art of Problem Solving".  Helps you experience visual problem solving.

• Math Open Reference - excellent site with interactive displays to help you really get a feel for the concepts.

• https://mathcounts.nextthought.com - Interactive Mathcounts problems and solutions from the past 3 years, with a discussion forum.  Ask your parents to help you set up an account.

• Avoiding Silly Mistakes (in competitions) - Excellent suggestions on how to cut out avoidable mistakes.

Ottoson Math Links

• ACE Coordinator's Math Enrichment page

  • IXL Math Grade 7 - practice problems, 10 free per day

  • IXL Math Grade 8 - practice problems, 10 free per day

At Gibbs

Look for these games in the media center

If you want to spend some money to get some quality coaching and training, here are some options.

We provide this list for your convenience.   There's no expectation that you try any of these, but they're good options for those who want to even more. 

Online and In Person (all of these have in person classes in this area during non-pandemic times, and also have a good selection of online classes):

• Art of Problem Solving  https://artofproblemsolving.com/school/schedule

• Idea Math   https://www.ideamath.education/landing/overview

• Russian School of Math  https://www.russianschool.com/programs/competition

In Person (normally)

• Frost Math (Lexington)   http://www.frostmath.com/