Patterns (1.2)

1. Patterns (1.2) … a problem solving strategy

2. Patterns (1.2) • Sequence Ordered string of numbers tied together by a consistent rule • Term An individual member of a sequence Note: It is possible that some sequences have more than one answer.

3. Mix & Match … EXAMPLE: EXAMPLE:

4. Example (try at your seats): Dodger Stadium: Radio broadcasters joke about the number of people who start leaving Dodger Stadium during the seventh inning of baseball games. One evening, during a particularly boring baseball game in which the Dodgers were trailing 6 runs after 6 innings, the fans began to leave at a record pace. After the first out in the top of the seventh inning, 100 fans left. After the second out, 150 fans left. After the third out, 200 fans left. The pattern continued in this way, with 50 more fans leaving after each out than had left after the previous out. The ridiculous thing was, the Dodgers tied up the game in the bottom of the ninth inning, and people still kept leaving early. The game lasted 10 innings (the Dodgers lost anyway) and the pattern continued through the bottom of the tenth inning. How many fans left early?

5. Let’s organize the data … 4 innings x 6 outs/inning = 24 outs TOTAL First thought … People leaving Total People that left so far Out This could take a while …

6. Second thought … (have a student fill in this chart on the side board) Keep filling in the data … Out # 1 2 3 Total Base fans leaving 100 100 100 Additional fans 50 50 Additional fans 50

7. Sooo … One Pattern: … 24(100) + 23(50) + 22(50) + … + 1(50) = 16,200 Another Pattern: … 24(100) + (23 + 22 + 21 + … + 1)50 = 16, 200 One thing we’re missing… What about the fans that left after the third out at the bottom of the tenth? Are they leaving EARLY? 16, 200 – 1,250 = 14,950 100 + 23(50) = 1,250