This is a good problem-solving task to use to teach students perseverance. The mathematics involved is not difficult, but it is hidden well within the trick itself. So, it may take a bit of perseverance to solve this neat little puzzle of a trick.

Click the video below to watch how this might be presented.

This is a self-working trick with just a tiny set-up. Before presenting this, make note of the nineteenth card from the face of the deck. This can be done in front of students as you look through the cards to make sure they are all there. The 19th card from the face is your prediction, so write it on a piece of paper, fold it up, and place it in full view.

The rest of the trick is presented exactly as you saw in the video above. Click Here for Detailed Instructions

No matter which three cards are selected, 30 cards will be dealt from the top of the deck. Those 30 cards, plus the three that were selected from the top half of the deck, effectively remove 33 cards, leaving the 34th card from the top of the original deck now on top of what is left of the deck in the student’s hand. The 34th card from the top is also the 19th card from the face.

The Lesson:

Materials: 1 deck of cards per group

They may want to see it done again. If so, casually note the nineteenth card from the face of the deck, write it down as your prediction, and do the trick again. After presenting the trick to students, ask them what they noticed and what they are wondering and have them share with a partner before asking them to share with the class.

Some things students may notice:

• cards were selected from the top half of the deck
• cards were dealt from the top
• cards were dealt based on the value of each card minus 10
• cards were dealt based on the total value of the three cards

Some possible student wonders:

• What if we chose 3 different cards?
• Do the three cards matter?
• Where does the predicted card have to be at the start in order to make this work?
• Is the subtraction (from 10) important?

For younger students, the goal is to figure out that no matter which three cards are selected, 30 cards will be dealt. Those 30 cards, plus the three that were selected, effectively remove 33 cards, leaving the 34th card at the top of what is left of the deck in the student’s hand. So, no which three cards are selected, 33 cards are taken from the top half of the deck every time.

More advanced students may assign variables to the three selected cards (x, y, and z) to discover why this works. This is the same idea as for younger students – just a more formal algebraic proof. If the values of the cards are x, y, and z, then the number of cards dealt will be:

(10 – x) + (10 – y) + (10 – z) + x + y + z = 10 + 10 + 10 – x – y – z + x + y + z = 30

Students will need to follow the steps of this trick without knowing about the 19th card from the bottom. So, they will be following the steps of the trick with no surprise at the end.

Students may do this several times without collecting any data. Encourage students to record everything they can about each time they do this trick as a group. The patterns will emerge and they will be able to solve this problem. I believe in them and you.