Deconstructing Number Tricks

Number tricks have been around about as long as I can remember. They usually occur in one of two varieties, ending with the number they begin with, or ending with a specific number.

Here is an example involving squares:

Example 1

And another example with basic operations:

Example 2

In both of the above cases the answer is 3, that is simply just a coincidence based on the examples I chose.

These types of puzzles make for excellent examples of simplifying expressions for an algebra class. The  puzzle involves a variable (number selected), and then a number of operations. By translating these puzzles into an expression, students can test out whether the answer will be consistent for any number picked.

Here is Example 1 again but translated into an algebraic expression:

Example 1 translated into an algebraic expression.

When students complete the expression in the last step the resulting solution will be 3. This proves any value for x will not affect the solution. Have students try it with negative numbers, with decimals, or even π.

When students get the hang of translating the puzzles into algebraic expressions and simplifying, have them attempt to create their own number tricks. I challenged a few of my students to end with numbers they began with, and end with a specific number I've chosen. They can then translate them into algebraic expressions and prove their number trick.

Here is an example a student created yesterday, "Kick In the Nuts".

And the corresponding algebraic expression.