# 4 Math for Elementary Education teachers problems

1) Look at the growing pattern below. How many squares will it take to make the *n*th figure in this pattern?

2) What if we made a pattern by joining pentagons? If the length of each side of the pentagon is 3 units, then what would be the perimeter of *nth *pentagons joined together? *Note:* The perimeter is the distance around the outside of the figure.

3) Variations of this problem have appeared in many places. Jack and Jill decide to start a rumor that there will be no school on the following Monday. What if each person tells exactly 2 people? How long will it take now? Assume that the rate for telling the next 2 people is 1 hour. That is, initially Jack and Jill know; after 1 hour, 2 more people know; after 2 hours, 4 more people know, . . . .

4) Consider the following table of numbers.

x |
y |

1 | 3 |

2 | 6 |

3 | 9 |

4 | 12 |

5 | 15 |

6 | 18 |

7 | 21 |

(a) Describe the pattern in your own words.

(b) Find the value of *y* when *x* is 100.

(c) Find a general expression for finding the *n*th term in your own words.

(d) Translate part (c) into function notation. *f*(*x*) =