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# Algebra through Puzzles

## 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

#### Calculating Cleverly

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.

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#### Arithmetic Tricks

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

4. Included with

#### More Arithmetic Tricks

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

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

2. Included with

#### More Magic Rectangles

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.

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.

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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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