Lesson 1

Discover

 

Sometimes numbers have a somewhat magical quality. But rest assured, there are mathematical concepts behind that magic. Try the puzzle in the Try This activity to see if you can figure out the math behind the magic.

 

Try This 1

 

Follow the steps in Table 1.

 

TABLE 1
Step	Instruction
1	Pick any number.
2	Square the number.
3	Subtract 4 from the result.
4	Divide the result by 2 more than the original number.

1. How does the final result compare to the original number?
2. Repeat the procedure three times with a different starting number each time. What do you notice?
3. Copy Table 1. Then add a third column, as shown, called “Expression.” Write an expression for each step in the table, beginning with the expression x.
   
   

   TABLE 2
   Step	Instruction	Expression
   1	Pick any number.	x
   2	Square the number.
   3	Subtract 4 from the result.
   4	Divide the result by 2 more than the original number.

4. Based on your answers to questions 1 and 2, what is another expression that could be used to represent the final result?
5. There is one starting number that does not yield a similar result to the other ones. Can you determine this number?

Save your responses in your course folder. You will need to retrieve these results later in the lesson in order to check your work and to share what you have learned with a partner.