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 ninth card from the top of the deck. This will be 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 a Detailed Description

The Lesson:

Materials: 1 deck of cards per group, small sticky notes (or stickers)

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

Some possible student wonders:

• What if we chose 11, would it still work?
• Could we choose a number more than 20, or less than 10?
• Why does it (the number) have to be between 10 and 20?
• Where does the predicted card have to be at the start in order to make this work?

Whatever the student wonders, share on a class chart so students can refer to them as they work in small groups or at least with a partner to solve the problem. There is always at least one student who wonders about the range of numbers and this is an important part of the problem.

Before students begin, ask them what they think they might need to keep track of as they run through the trick. This can and should be a working list. Students may initially think they only need to keep track of the numbers they try (14, 17, 19). But as they do this, they may realize they need to know how the cards are changing positions because they need to know where cards are to find out the card that is predicted. So, as students discover another piece of information that they need to keep track of, they can add it to the list.

• the numbers they try
• the first 19 cards (20 can’t be used because the number must be between 10 and 20)
• the order of the cards.

The idea of keeping track of the cards is a big one. Students can solve the problem without keeping track of the cards, but it may be helpful.

Below is an example of how students might keep the information they collect organized.

Number	Sum of Digits
14	15
18	9
12	3

This is enough for students to get to the idea that the prediction card needs to start at the position ninth from the top. But, they may not be looking for patterns like that. Some possible “least helpful” questions might be useful here:

• What do you notice about the numbers you have recorded?
• What might this have to do with the predicted card?

As students work, make notes about their process and interesting strategies for solving the problem. Select groups to share in an order that will allow students to make connections to other strategies. For example, select groups to share base on efficiency. Students who marked the cards with numbered stickers might go first, followed by groups who just kept track of the different numbers possible. Facilitate a discussion that leads students to connect these two strategies.