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.

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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.

1. Included with

Shortcuts 101

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

2. Included with

Guess, Check, and Revise

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

3. Included with

Arithmetic Tricks I

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

4. Included with

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!

1. Included with

Magic Rectangles Part I

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

2. Included with

Magic Rectangles Part II

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

3. Included with

Magic Perimeters

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

4. Included with

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.

1. Included with

Balancing Scales

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

2. Included with

Elimination

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

3. Included with

Substitution

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

4. Included with

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?

1. Included with

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.

3. Included with

Arithmetic Sequences

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

4. Included with

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?

1. Included with

Applying Rates and Ratios

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

2. Included with

Proportionality

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

3. Included with