Mathematical Thinking
Learn to wield important tools in algebra, geometry, and number theory.
Finding Half
Combining Parts
Splitting Parts
Splitting and Combining
Equal Parts
Sixths and Twelfths
Eighths and Sixteenths
Making Equivalent Fractions
Simplifying Fractions
Equivalent Fractions
Identifying Equivalents
Fraction Bars
Fractions on a Line
Equivalent Fractions on Number Lines
Fractions Greater Than One
Addition on Number Lines
Comparing Fractions
Comparing Speeds
Ratios in Recipes
Fractions and Fractals
Compounding Growth
Everyday Percents
Percents of a Whole
Percent Increase
Percent Decrease
Compare the Pair
Compound Interest with Percents
Building Blocks of Numbers
Division and Remainders
Divisible by Three
Divisible by Nine
Number Building Puzzles
Rearranging Sums
Staircases
Averages
Introducing Exponents
The Product Rule
Powers of Ten
Exponential Growth
Scientific Notation
Negative Exponents
Using Scientific Notation
Generalizing
Magical Variables
Reverse Engineering Arithmetic
Sums and Symmetry
How Much Altogether?
Introduction to Cryptograms
Cryptogram Challenges
Up next
Infinity
Expand your mind with the paradoxes and beauties of infinity.
Course description
In this course, we'll introduce the foundational ideas of algebra, number theory, and geometry that come up in nearly every topic across STEM. You'll learn many essential problem solving techniques and you'll need to think creatively and strategically to solve each challenge. Each exploration is designed to push your mathematical skills to the next level. Math isn't about memorizing formulas, it's about problem solving. It's about looking at patterns and predicting the future of those patterns, and it's about solving complex problems by using deductive reasoning to turn them into simple ones.
Topics covered
- Algebraic Expressions
- Arithmetic Operators
- Cryptogram Puzzles
- Discount Finance
- Divisibility
- Divisibility Rules
- Logic Fundamentals
- Rates and Ratios
- Sequences
- The Distributive Property
- Variables
Prerequisites and next steps
This course is for anyone who remembers middle school math (basic algebra and fractions), and is ready for a refresher and new challenges on core mathematical concepts.