Who Should Take This Course
This course efficiently provides all of the Algebraic foundation that is needed to start learning all of the branches of math in our systematic course series. Algebra is so fundamental (and so commonly occurring in middle school math competitions) that our course series splits it into two modules: Algebra Basics (Module 1) and Algebra Tools (Module 4). Algebra Basics focuses on some of the richest (and most confusing) concepts around ratios and fractions, revealing deeper perspectives than what is normally seen in standard K–12 curriculum.
To take this course, students should have a solid background in PreAlgebra and the willingness to concentrate on a single math problem for several minutes. A highly motivated student who has just completed PreAlgebra will find this course challenging, but manageable with effort. A student who is currently doing well in Algebra 1 will also learn a lot from the course and will discover some interesting facets of math that they had never realized before. Not recommended for students who can already score 12+ on AMC 8. Still not sure if this is the right course? Feel free to contact us at courseconsulting@poshenloh.com to discuss.
Syllabus

02
Day 1 Challenge: Fraction Gymnastics
Show Content Day 1: Something to Think About FREE PREVIEW
 Day 1: Challenge Explanation FREE PREVIEW
 Day 1: Your Turn FREE PREVIEW
 Day 1: Your Turn Explanation

03
Day 2 Challenge: Continued Fraction
Show Content Day 2: Something to Think About
 Day 2: Challenge Explanation
 Day 2: Your Turn
 Day 2: Your Turn Explanation

04
Day 3 Challenge: Comparing Fractions
Show Content Day 3: Something to Think About
 Day 3: Challenge Explanation
 Day 3: Your Turn
 Day 3: Your Turn Explanation

05
Day 4 Challenge: Sports Averages
Show Content Day 4: Something to Think About
 Day 4: Challenge Explanation
 Day 4: Your Turn
 Day 4: Your Turn Explanation

06
Week 1 Challenge
Show Content Week 1 Challenge: Try Your New Skills

07
What's Next
Show Content Week 1: Help Us Learn More About Your Learning Experience

08
Day 5 Challenge: Natural Proportion
Show Content Day 5: Something to Think About
 Day 5: Challenge Explanation
 Day 5: Your Turn
 Day 5: Your Turn Explanation

09
Day 6 Challenge: Keeping in Proportion
Show Content Day 6: Something to Think About
 Day 6: Challenge Explanation
 Day 6: Your Turn
 Day 6: Your Turn Explanation

10
Day 7 Challenge: Changing Percentages
Show Content Day 7: Something to Think About
 Day 7: Challenge Explanation
 Day 7: Your Turn
 Day 7: Your Turn Explanation

11
Day 8 Challenge: Undoing Percentages
Show Content Day 8: Something to Think About
 Day 8: Challenge Explanation
 Day 8: Your Turn
 Day 8: Your Turn Explanation

12
Week 2 Challenge
Show Content Week 2 Challenge: Try Your New Skills

13
What's Next
Show Content Week 2: Help Us Learn More About Your Learning Experience

14
Day 9 Challenge: Business Accounting
Show Content Day 9: Something to Think About
 Day 9: Challenge Explanation
 Day 9: Your Turn
 Day 9: Your Turn Explanation

15
Day 10 Challenge: Estimating Profit
Show Content Day 10: Something to Think About
 Day 10: Challenge Explanation
 Day 10: Your Turn
 Day 10: Your Turn Explanation

16
Day 11 Challenge: Gear Ratios
Show Content Day 11: Something to Think About
 Day 11: Challenge Explanation
 Day 11: Your Turn
 Day 11: Your Turn Explanation

17
Day 12 Challenge: Winning Ratios
Show Content Day 12: Something to Think About
 Day 12: Challenge Explanation
 Day 12: Your Turn
 Day 12: Your Turn Explanation

18
Week 3 Challenge
Show Content Week 3 Challenge: Try Your New Skills

19
What's Next
Show Content Week 3: Help Us Learn More About Your Learning Experience

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Day 13 Challenge: Working Together
Show Content Day 13: Something to Think About
 Day 13: Challenge Explanation
 Day 13: Your Turn
 Day 13: Your Turn Explanation

21
Day 14 Challenge: 100 Bottles
Show Content Day 14: Something to Think About
 Day 14: Challenge Explanation
 Day 14: Your Turn
 Day 14: Your Turn Explanation

22
Day 15 Challenge: Harmonic Mean
Show Content Day 15: Something to Think About
 Day 15: Challenge Explanation
 Day 15: Your Turn
 Day 15: Your Turn Explanation

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Day 16 Challenge: Changing Speed
Show Content Day 16: Something to Think About
 Day 16: Challenge Explanation
 Day 16: Your Turn
 Day 16: Your Turn Explanation

24
Week 4 Challenge
Show Content Week 4 Challenge: Try Your New Skills

25
What's Next
Show Content Congratulations on Completing This Course!
 Week 4: Help Us Learn More About Your Learning Experience
How To Use This Course
The best way to build creative thinking skills is to play with challenging new problems every day, especially those for which you don’t know how to start. This course, which can be finished in 1 month, constitutes of 16 Daily Challenges and 4 Weekly Challenges. Each Daily Challenge has two related math problems and their explanations. Don’t worry if they look unfamiliar. Just use the whole time during the problem videos (and hints) to think. You’ll get to invent your own strategies, which is the fun part!
Even if you figure out how to do a problem yourself, watching its explanation video is still very beneficial. It will show multiple interesting ways to do the problem, and introduce deeper ideas in math using everyday language. This brings advanced math down to earth.
There is only one practice problem in each Daily Challenge (the “Your Turn” problem), and there aren’t any homework problems. This is because the way to learn how to solve the widest variety of problems is to learn how to invent your own solution methods! So, we encourage you to solve new problems all on your own instead of working on repetitive exercises. You’ll spend the same time on fewer problems, every one of which needs fresh creativity.
After every four Daily Challenges, we revisit the topics (with some twists), through a Weekly Challenge problem set that lets you focus uninterrupted for 40 minutes, on a variety of specially designed questions. After doing the problems, please read the explanations, even for the problems you solved. There are a lot of fun math coincidences and insights hidden in the problems.
We recommend pacing the course so that you can play with this flavor of mathematical thinking for a bit of time almost every day.
The standard pace is to pick four days each week for four Daily Challenges, plus one hour on the weekend for the Weekly Challenge. If you think this pace is not challenging enough, feel free to double the pace, so that you can finish eight Daily Challenges and two Weekly Challenge each week.

Instructor
Loh draws from his experience as a mathematics professor at Carnegie Mellon University, and also as the national coach of the USA International Mathematical Olympiad team. His research and educational outreach takes him to cities across the world, reaching over 10,000 people annually through public lectures and inperson events, and he has featured in or cocreated videos totaling over 5 million YouTube views.
He has been continually involved in math competitions since he was a contestant in the late 1990's: when he ranked 3rd at the National MATHCOUNTS competition, and won a silver medal for the United States of America as a contestant at the International Mathematical Olympiad. He can be followed on Instagram (@poshenloh), Twitter (@poshenloh), WeChat (罗博深数学), and Weibo (poshenloh / 罗博深).PoShen Loh
Math Professor