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Fortune Teller

In this simple symmetry illusion, magically point the arrow wherever you choose.

Ages: 4+ (with help)
Players:
Time: 10-20 Minutes
Type: curiosities
Location: tabletop
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Ages: 4+ (with help)
Players:
Time: 10-20 Minutes
Type: curiosities
Location: tabletop

Instructions

First, make the arrow. Cut a small square of cardboard that is small enough for a little magician's hands to hold opposite corners easily. The trick is also easier if the cardboard is sturdy.

Square of cardboard, a marker, and scissors

Next, add the arrows. You can draw them with a marker, or glue on arrows cut out of paper as we did in the video.

You've got to add the arrows carefully for the trick to work. On the front, draw the arrow facing up.

An arrow drawn on a square of cardboard

Turn the cardboard over so that the arrow is still pointing up on the back. Then draw an arrow pointing to the right. It's important that the arrow on the back is pointing up (even though you can't see it) and the arrow on the front is pointing to the right. Here is a picture of the arrows on a thin piece of paper, with the marker bleeding through the paper a bit, so that you can see how they are both oriented.

An arrow drawn on a square of paper
The first arrow, pointing up.
An arrow drawn on the back of the square of paper
The second arrow, pointing right (along with the first, showing through the paper).

Actually, it would also be fine if the back arrow were pointing down, or the front arrow were pointing left. The important thing is that one of the arrows be up/down, and the other left/right.

Now that you've got your fortune teller made, it's time to figure out how to use it. Hold the square on opposite corners and flip it over.

Turning over the square of cardboard

Flip several times. Is your arrow always pointing in the same direction, or is it switching back and forth?

Now hold your square on the other pair of opposite corners and flip it over. Whatever it was doing previously (always pointing the same way, or switching back and forth), now it will be doing the other.

In other words, you control whether the arrow alternates directions or not by which pair of opposite corners you hold! (Try not to make this too obvious when performing the trick. Though, for young magicians, it doesn't really matter of course.)

It will definitely take some practice to perform this trick. Before you start the trick, note whether the corners you are holding cause the arrow to alternate or not. As you ask questions, you need to keep track of whether you are in "alternating" mode or "same direction" mode. If the arrow is pointing at you and you want it to point at you again when flipped, make sure you hold the "same direction" corners of the square. If you want it to instead point away from you, make sure you hold the "alternating" corners of the square.

See the Learning Notes below for some insights into how this trick works.

Don't forget: it's Beast Academy Playground, not Beast Academy Study Hall. Change the rules, be silly, make mistakes, and try again. The Variations and Learning Notes are here for you if you want to dive deeper, but not all of them apply to learners of every age. The most important thing is to have fun.

Variations d

Broken Arrow:

Fortune telling is only one way to present this magical arrow. Can you think of others? Here is an idea: Tell a friend that you tried to make a "One-Way" arrow sign for your model train set (or as a clue in a treasure hunt, or to help you remember which way is up... whatever you can think of). Show them that your sign is broken because the arrow changes direction each time you flip it. Then ask them to wave their hand over the arrow and say the magic word. Then flip the arrow again (this time holding the opposite corners). The arrow now points the same direction when flipped. Be sure to act very surprised at your friend's magical abilities!

Classroom Tips d

Make this surprisingly effective little trick when learning about symmetry, or just as a fun craft between units or before a break.

Discussion Questions

  • How many lines of symmetry does an arrow have?
  • What capital letters have reflectional symmetry?
  • Which capital letter has the most lines of symmetry?
  • If you draw the arrows show they show through the paper (so you can see both at once), at what angle do they meet?

Alignment with Beast Academy Curriculum

  • Level 4, Chapter 1: Shapes

See Variations and Learning Notes for more ideas on how to adapt this activity and incorporate it into your classroom.

Learning Notes d

Symmetry:

When something is symmetrical, it can be flipped over a line (called the line of symmetry) and still look the same. Think of flipping the letter A over this line. It wouldn't change.

The letter A with a dotted line drawn vertically down the center

The letter P has no such line. It isn't symmetrical. (This reflectional symmetry is actually only one kind of symmetry. There are others too, including rotational symmetry, where an object can be spun around a point and still look the same.)

To understand the math behind the "magic" of the Fortune Teller, visualize both arrows at once, as if you could see through the piece of cardboard. To actually see this, use a dark marker on a thin piece of paper.

An arrow showing through a square of paper, with another arrow drawn on the front

Do these two arrows together have a line of symmetry? They do!

The arrows pointing to the top left and top right, with a vertical dotted line through the center

The line of symmetry goes through two opposite corners. When flipped over this line, the image doesn't change, which means both arrows continue to point in the same direction. These opposite corners are the ones that do not alternate the arrows.

If we draw a line through the other pair of opposite corners, we see that this line is not a line of symmetry. The picture of the arrows isn't the same on both sides of the line.

The arrows pointing to the top left and bottom left, with a vertical dotted line through the center

When we flip the arrows over this line, each of them ends up pointing in the opposite direction. These opposite corners are the ones that cause the arrow to alternate!

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Materials
  • cardboard
  • marker
Learning Goals
  • symmetry
  • wonder
Common Core Standards
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Recommended Videos

Image of Ms. Q

Ready to level up?

Keep problem solving with Beast Academy’s full math curriculum for students ages 7–13. Check out our captivating comic book series and immersive online platform.

LEARN MORE

Bring problem-solving to your classroom

Keep your entire class engaged with a full book and online math curriculum, for students ages 7–13. 98% of teachers say they’re satisfied with Beast Academy.

LEARN MORE
Image of a BA book