$14$

Chapter $1-$ Thinking Critically

Activity $6$: Magic Number Tricks

PURPOSE Translate verbal phrases into algebraic expressions and reinforce the work backward problem$-$solving strategy.

COMMON CORE SMP

SMP $1,$ SMP $2,$ SMP $8$

MATERIALS Other: Calculator

GROUPING Work individually.

Dr$.$ Wonderful, the Mathematical Magician, astounds crowds with his amazing ability to read people's minds. Here are the directions that he gives to five people in the crowd. Follow Dr$.$ Wonderful's directions and complete the table below. Choose a different number for each person.

PERSON

Pick any number.

Multiply by $3.$

Add $30.$

Divide by $3.$

$1$

$2$

$3$

$4$

$5$

Subtract your original number. $$

$q,q,q,q,q,q,q,q,q,$

Dr$.$ Wonderful tells the people to write their answers on a sheet of paper but not to reveal them to anyone else. He closes his eyes, concentrates deeply, and then claims that he knows each person's answer. Suppose you picked $239.$ What do you think Dr$.$ Wonderful would say your answer is$?$ Why?

To learn why the trick works, let $n$ be the number. Write an algebraic expression for each step and record it below.

Step $1$:

Step $2$:

Step $3$:

Step $4$:

Step $5$:

The result is