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Introduction to Algebra

Supercharge your thinking with the language of algebra.

Explore graphs of equations, exponents, counting problems, and more, emphasizing intuition and understanding over just finding an answer.

This course will deepen your knowledge of basic algebra and introduce you to some surprisingly useful applications of this powerful mathematical tool.

Interactive
quizzes

28

Concepts and
exercises

280+
  1. 1

    Introduction

    Describe the world with the language of algebra.

    1. Writing Algebra

      Use algebra to trace the relationships between multiple unknown quantities.

    2. Calculation Shortcuts

      Sometimes asking a simpler question can produce the same answer for less.

    3. Graphical Reasoning

      Graphs can reveal surprising relationships and bypass calculation.

  2. 2

    Graphing

    See the structure of algebraic relationships.

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      Creating Points

      Coordinates give us the tools to describe locations with precision.

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      Connect the Dots

      Reason about equations to uncover their properties and patterns.

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      Graph Menagerie

      Take a tour of the variety of shapes that equations can form.

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      Interpreting Graphs

      Use graphs to solve problems that resist algebraic unpacking.

  3. 3

    Equations and Unknowns

    Sometimes x is unknown, and sometimes it's unknowable.

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      Combination Locks

      How much information is needed to pin down the exact combination?

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      Equations and Variables

      How does the number of variables affect what can be known about the equations?

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      Scaling and Adding Equations

      Practice solving multi-equation problems.

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      Graphing Equations

      Explore the connections between lines and the equations that generate them.

  4. 4

    Algebra in Motion

    Mostly, we just want to see the collisions!

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      Distance, Rate, and Time

      Explore the algebra that describes motion and change.

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      Stunt Driving and Collisions

      Use these dangerous motion problems to practice and strengthen your skills!

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      The Harmonic Average

      Learn how to calculate the average of two speeds.

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      Boats

      Speed becomes more complicated when what you're travelling in (a river) is also moving.

  5. 5

    Common Misconceptions

    You'd be surprised how many contest these algebraic facts.

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      The Basics

      Identify and repair the mistakes in thinking that lead to these common errors.

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      Ordering and Reordering

      The order in which you evaluate the parts of a calculation can have a huge impact on the outcome.

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      Two Ways to Cancel

      Understanding the ideas behind "cancelling" will keep you from making some common errors.

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      The Distributive Property

      Test the limits of your understanding of addition, multiplication, and how they interact!