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Algebra Fundamentals

Supercharge your algebraic intuition and problem solving skills!

Explore how algebra works and why it matters, and build a strong foundation of skills across many algebra topics including equations, rates, ratios, and sequences.

By the end of this course, you’ll know both traditional algebraic techniques and many unique problem-solving approaches that aren’t typically covered in school. You'll also improve your algebraic intuition and hone your strategic thinking for approaching difficult problems.

Interactive
quizzes

38

Concepts and
exercises

355+
  1. 1

    Introduction

    Supercharge your algebraic intuition and problem solving skills!

    1. Scale and Lever Logic

      Warm up the skills and intuition that algebra requires by balancing scales and measuring weights.

    2. Magic Sum Puzzles

      How can numbers be arranged so that these three specific sets all sum to 12?

    3. Sequences

      Find and describe the patterns in these visual sequences.

  2. 2

    Simplifying Shortcuts

    Save time with this clever thinking.

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      Shortcuts 101

      Learn some clever techniques to simplify problems, saving yourself time and effort.

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      Guess, Check, and Revise

      In this strategic shortcut, use an easy number as a test case and then update to find the true answer.

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      Arithmetic Tricks I

      These problems can be quickly solved in your head if you find the trick to each of them.

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      Arithmetic Tricks II

      Practice using rearrangement of terms, factoring, distribution, canceling, and any other tricks you know!

  3. 3

    Arithmetic Logic and Magic

    Puzzles that are like Sudoku, but trickier!

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      Magic Rectangles Part I

      Is it possible to fill these grids so that the sums of the rows and columns are all correctly predicted?

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      Magic Rectangles Part II

      What if, instead of specific target sums, you only know that all of the sums need to match?

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      Magic Perimeters

      In this exploration, the digits need to be filled in around the perimeter of each shape.

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      Learn Calcdoku

      It's like Sudoku except that each specified region must obey a specific arithmetical rule.

  4. 4

    Balancing Scales

    The unification of logic and algebra.

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      Balancing Scales

      Explore several types of balance puzzles and learn some strategies for approaching them.

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      Elimination

      Simplify systems combining the shapes that balance on one scale with those that balance on another.

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      Substitution

      First isolate a shape on one side of a scale, then use this equivalency to make substitutions elsewhere.

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      Fraction-Related Strategies

      When fractional shapes or numbers are involved, a few additional steps are required to isolate variables.

  5. 5

    Sequences

    2, 5, 10, 17, 26... What comes next?

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      What Comes Next?

      Explore, describe, and then predict the patterns in these sequences.

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      Describing Sequences

      Practice describing sequences in three different ways: by property, recursively, and explicitly.

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      Arithmetic Sequences

      Focus in on this one sequence type and learn a few tricks that take advantage of its steady behavior.

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      Geometric Sequences

      Now focus in on these sequences that evolve using recursive multiplication instead of addition.

  6. 6

    Rates and Ratios

    If 4 cows make 4 gallons of milk in 4 days, how much milk do 8 cows make in 8 days?

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      Applying Rates and Ratios

      Explore rates and ratios in some of the real-life situations in which they show up.

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      Proportionality

      Hone your skills solving problems that employ proportionality and inverse proportionality.

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      Joint Proportionality

      In this exploration, multiple variables can change simultaneously, all contributing to an overall effect.

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      Scaling 3D Shapes

      Explore how scaling an object can counter-intuitively affect other properties of that object.