Interactive course — Foundational Math

Mathematical Fundamentals

The essential tools for mastering algebra, probability, and logic!

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Overview

In this course, we'll develop the foundational math that touches algebra, probability, and logic — but not by handing you facts to memorize. Math isn't about memorizing formulas, it's about problem solving.

This course covers many traditional logic, algebra, and probability techniques. Each exploration is designed to push your mindset and mathematical skills to the next level! In short: you'll need to think for yourself, think creatively, and think strategically — that's what real problem solving requires.

Topics covered

  • Algebraic Expressions
  • Arithmetic Operators
  • Cryptogram Puzzles
  • Discount Finance
  • Divisibility
  • Divisibility Rules
  • Expected Value
  • Logic Fundamentals
  • Rates and Ratios
  • Sequences
  • The Distributive Property
  • Variables

Interactive quizzes

38

Concepts and exercises

365+

Course map

Prerequisites and Next Steps

  1. 1

    Introduction

    Explore the foundations of algebra and logic without any rote memorization.

    1. Cryptograms

      These fun puzzles will help you develop patterns and tricks to solve algebra problems faster and more skillfully.

      1
    2. Is It Possible?

      Figure out what operations are needed in each challenge, or prove that the goal is impossible!

      2
    3. Challenge Set

      Limber up with some warm-ups, and then give your brain a workout with three tougher challenges.

      3
  2. 2

    Digits & Divisibility

    Divisibility rules, cryptograms, and other digit magic.

    1. Divisibility

      Apply the divisibility rules for 1, 2, 5, and 10, and summarize why this set is special.

      4
    2. Last Digits Rules

      What's different about the divisibility rules for 4 and 8?

      5
    3. More Divisibility Rules

      The rules for 3, 6, 7, and 9, are a fair bit stranger than what you've seen so far.

      6
    4. Cryptograms Solved By Divisibility

      Apply your understanding of divisibility rules to cracking cryptogram puzzles!

      7
    5. Cryptogram Addition Puzzles

      Creatively extend your cryptogram solving strategies to handle a different operation.

      8
    6. Cryptogram Variety Pack

      Each of these challenges will require the skillful and elegant application of logic, number theory, and algebra.

      9
  3. 3

    Patterns & Variables

    Find the pattern, then make predictions.

    1. Seeing Patterns

      Is there order, repetition, or regularity in these visual patterns?

      10
    2. Describing Patterns

      Understand and create recursive and explicit descriptions of patterns.

      11
    3. Find the Formula

      Find and interpret the algebraic descriptions of patterns.

      12
    4. Using Variables

      Use variables to describe interrelated unknowns.

      13
    5. Always-Sometimes-Never

      Are these statements provable, or can you think of counterexamples?

      14
    6. The Distributive Property

      Explore and understand this algebraic property using geometric visualizations.

      15
  4. 4

    Mathematical Logic

    Logic shows you how to win!

    1. Logic Warmups

      Get your analytical and critical thinking skills warmed-up and ready for some strenuous exercise!

      16
    2. Humans and Werewolves

      Apply logic to determine the secret identities of the entities in each challenge.

      17
    3. Implication

      Understand the behavior of "If...then..." statements within the framework of formal logic.

      18
    4. Find the Order

      Are the small clues in each of these challenges enough information to figure out the whole situation?

      19
    5. Hat Color Mysteries

      Extend your strategic, logical thinking to challenges that require several separate stages of reasoning.

      20
  5. 5

    Ratios & Percentages

    The mathematics of comparisons: ratios, percentages, and fractions.

    1. Exploring Ratios

      Learn how to use rewriting fractions as a problem-solving shortcut.

      21
    2. Rates

      It's easy to answer these rate and speed questions incorrectly if you're not careful!

      22
    3. Percent Applications

      Use these problems to expose and correct a few common misconceptions about percentages.

      23
    4. Percent Puzzles

      Put your intuition for ratios and percentages to the test in some tricky scenarios!

      24
    5. Comparing Ratios

      Explore powerful, intuitive shortcuts for comparing the magnitudes of ratios.

      25
    6. Fraction Sense

      Extend your skill using fractions to these challenging, subtle cases where multiple variables are involved.

      26
  6. 6

    Probability

    What are the odds of getting all these problems right?

    1. Using Outcomes

      Strengthen your intuition for probabilistic math by thinking systematically about outcomes.

      27
    2. Outcome Distributions

      Learn how to create and use distribution charts to tackle challenging problems.

      28
    3. Complements

      Learn how and when to switch perspectives and ask, "When does this event NOT happen?".

      29
    4. Common Fallacies

      Use these problems to expose and correct some common misconceptions about probability.

      30
    5. Expected Value

      Practice making smart, strategic decisions, even when the outcomes are uncertain.

      31
    6. Games & Gambling

      Analyze lotteries, coin flips, and other games of chance to learn how probability can help you avoid costly mistakes.

      32
  7. 7

    When It Gets Tough

    Demonstrate what you've learned with these difficult problems.

    1. When It Gets Tough

      Break down and tackle difficult problems that require the creative, coordinated use of multiple techniques.

      33
    2. Matchsticks and Coins

      Get ready to first solve these manipulation challenges, and then to prove that your solutions are ideal.

      34
    3. Logical Arithmetic

      These advanced cryptograms are more difficult than any you've seen in this course so far!

      35
    4. The Arithmetic-Algebra Connection

      Extend basic arithmetic into surprising, beautiful, and useful patterns.

      36
    5. From Arithmetic to Algebra 2

      Dive deeper into exploring the properties of large sums of consecutive numbers.

      37
    6. Advanced Challenges

      Review a sample of the major topics covered in this course: algebra, number theory, logic, and probability.

      38