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X-Ray Dice

Use addition and subtraction to magically predict the number on the bottom of a die.

Ages: 4-9
Players: 1
Time: Under 10 Minutes
Type: curiosities
Location: tabletop
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Ages: 4-9
Players: 1
Time: Under 10 Minutes
Type: curiosities
Location: tabletop

Instructions

Teach this trick to your young magician. (And then magically forget the trick so you can be impressed every time they perform it for you!) First, some background information: opposite faces of a standard 6-sided die always add to 7. So if you roll a 4, the opposite side must be a 3, because 4 + 3 = 7. Or if you roll a 1, the opposite side must be a 6, because 1 + 6 = 7. You get the idea.

To perform the trick, the magician should: Ask an audience member (grandparents are excellent for this) to roll a die, then magically announce what number is on the bottom of the die.

For younger math beasts, figuring out the number will take some practice. See Learning Notes below for some ideas on how to help them think about this math.

Help your child come up with some good banter for their performance! Maybe something like, "Did you know my glasses are actually equipped with X-ray vision?" or "When I touch my nose, I can actually see through this die!"

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

Two Dice:

The magician gives an audience member two dice, then puts on a blindfold (or closes their eyes really tightly!). The audience member rolls the dice and announces the sum. The magician then predicts the sum of the numbers on the bottom of the dice. (The trick: Using the fact that opposite faces of a die add to 7, we know the opposite faces of two dice must add to 14. Subtract the top sum from 14 to predict the sum of the bottom faces.)

Classroom Tips d

Teach this trick when practicing simple addition or subtraction up to 10. Then let your students go home and amaze their families! If you have blank cubes, let students pick their own target number and fill in opposite sides of the die with pairs that add to their number.

Discussion Questions

  • How many different pairs of numbers can you find that add to 7? (There's also an extra pair that isn't on dice: 0 + 7.)
  • Show me 7 - 4 = 3 with tokens. Show me 3 + 4 with tokens. How are these related?

Alignment with Beast Academy Curriculum

  • None (until BA Level 1 is released!)

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

Learning Notes d

Counting Up:

One way for younger kids to figure out the number on the bottom of the die is to count up on their fingers. Say a 4 is showing on the top. Help your child count up to 7 starting on the next number after 4. Each time they count up, they can hold up a finger. So your child can say, "5, 6, 7," and hold up a finger for each of these numbers: 3 fingers all together. That means the number on the bottom of the die is a 3! Counting up is a way of figuring out how many more are needed to get to 7, and lays the foundation for addition and subtraction.

Taking Away:

Another idea for helping younger kids, similar to the "Counting Up" strategy above, is to start with 7 fingers held up, then take away the number showing on the die. So if a 4 is rolled, your child can put down 4 of their fingers. 3 fingers are still held up. That means the number on the bottom of the die is a 3.

If fingers are too tricky to hold up and put down one at a time, use coins or tokens of some kind. Count out 7 coins on the table. Then take away the number showing on the die.

Fact Families:

Kids who are already comfortable with addition up to 10 can probably perform this trick without fingers or tokens. Ask them to explain how they figured out the math, then take the opportunity to verbalize the arithmetic in different ways. If the die shows 4, your child will need to ask themselves, "4 plus what number equals 7?" Or they can ask, "7 minus 4 equals what number?" This helps build the understanding that addition and subtraction are related. In fact four different equations can be made wit 3, 4, and 7: 3 + 4 = 7, 4 + 3 = 7, 7 - 4 = 3, and 7 - 3 = 4.

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Materials
  • a standard 6-sided die
Learning Goals
  • addition
  • subtraction
Common Core Standards
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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