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A Hidden secret

When we practice magic we have the pleasure of seeing the result. If I cast an enlargement spell, my item grows. If I cast an invisibility charm, what was seen is now unseen. But for most Slants, math homework isn't nearly as exciting. You do the work, get a grade, and then it probably goes through the shredder in the teacher's lounge. 

Not anymore. As you practice your skills you will be rewarded. You will see how your dedication transforms into something new and spectacular. And if you can perfect your skills. . . you'll reveal what is hidden. 

Marco the Great and the Mystery of Phaseville

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The content on this page is supplementary material for Marco the Great and the Mystery of Phaseville

Open book with a page bent

Have you ever bent the page of a book to mark your spot? Commonly called a "dog-ear", these inconspicuous marks grace the pages of texts around the world. Here's the secret: fold just right and you can reveal the invisible; amazing hidden messages and images will come to life in front of your eyes. 


Open book with multiple pages folded over


Each fold is one piece of the puzzle. Once all pieces have been collected, the hidden will be revealed. Folds do not require any cutting. If you ever wish to conceal the secret, unfold each page and place your book under a heavy item for a few days. Depending on the sharpness of your creases, the ghosts of your folds may still remain. 


At the bottom of each page is a clue. Solve the clue to uncover a march (a line in the form y=ax+b). Use the vertical number line on the right to mark b, the y-intercept. Then use the slope, a, to graph the line. Finally, fold the page along the line you created. 

Both lines should be marked on the right page. See videos below for step-by-step instructions. 

Not sure the line you found is correct? Need some help in decoding a clue? First, check out the back of the book. Information on how to decode the clues presented in each chapter is provided to get you off on the right foot. Next, scroll down to the Hints and Tips section for an interactive applet to help with each and every page. 


How to Videos


Jump-start your journey with these how-to videos. 

Phaseville Folds

Phaseville Folds

Phaseville Folds
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Introduction to Folding

Introduction to Folding

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How to Fold

How to Fold

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Tips and Tricks

Tips and Tricks

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Pace Yourself

There is no "right way" to go about the page folds. Some of our readers completed the clues as they read, and at the very end sat down and folded each page. It took them about 2 hours. Others folded at the end of each chapter, uncovering the secret as they went. It's totally up to you!

It Doesn't Have to be Perfect

Readers have mixed up the slope, not folded perfectly, and even sent Zero to the wrong station! They still ended up with an amazing outcome and were able to uncover the mysteries of Phaseville. When you complete your folds you will be able to see if any pages don't quite seem to fit. You can go back, check those clues, and adjust. 

These nuggets will help you on your journey!


Keep Track

As you solve the clues, grab a journal or even a blank page in the book to keep a growing list of your findings. This will make it easy to check your lines, slopes, and intercepts. You can even use our interactive program to check your work!

Confused stick figure

Common Mistakes

Mixing Up the Slopes

Slope is Δy over Δx. If your slope is 1/2 you want to go up 1 over 2. This is different than up 2 over 1! Read the slope as "number over number", the "over" then helps you to head in the right direction. A slope of 3/4 can be read "3 over 4" to remind you to go up three over four. 

Wrong Station!

Even if you find the right Station to send Zero to, your folding may not hit that station! This is generally because we place the bookmark, ruler, or straight-edge directly on the line. That makes the fold end up a little below where we want it to be. To combat this, place your bookmark or ruler slightly above your points for a positive slope and slightly below your points for a negative slope. Then, when you fold, the crease will land directly on the correct stations. 

Where am I?

NEGATIVES!! They can get us every time. We've seen mistakes like marking –9 instead of –11 because the reader identified –10 and moved up (you know because 10,11,12,...). If negatives get you confused, try starting at 0 and counting down, then you can more easily see why –11 is lower than –10. You could also flip the book upside down which has the effect of making the negative part of the number line look and act more like positive values we might be more used to. 

It's So Steep!

Steep slopes like ±2 and ±3 are the hardest folds. This is because the very tip is just a sliver. To avoid a steep-slope mistake, take your time with these and make sure the tip of the fold is creased correctly. 

Explore our How-To Videos for more tips & tricks!

Hints & Tips


Our decoding bookmark is super versatile! You can use it to help make the folds, check your slopes, and more. 

If you didn't snag one in our preorder special – not to worry! Order yours today to help you solve the mystery.


Not sure if your order is correct? Need additional help in decoding a clue? We've got you! Explore our interactive decoder below. You can enter the page number you are working on to see if your march is correct, or enter the clue you are trying to decode for an extra boost!

©MathBait created with GeoGebra

© MathBait

Ready to start your adventure?

Grab your copy and jump into the pages with a mathematical learning experience like never before!

Want more games, explorations, and math done the fun way? Enroll in our online program, The Kryptografima, today!

Marco the Great and the Mystery of Phaseville
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