… a problem solving strategy Tables & Patterns (3.7) … a problem solving strategy

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?

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

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

Sooo … One Pattern: … 24(100) + 23(50) + 22(50) + … + 1(50) = 16,200 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

Another Strategy: Systematic Lists A list generated through some kind of system. A System - Any procedure that allows you to do something (like organize info.) in a methodical way.

Loose Change: Leslie has 25¢ in her pocket but does not have a quarter. If you can tell her all possible combinations of coins she could have that add up to 25¢, she will give you the 25¢. Many systematic lists are in the form of a table whose columns are labeled with the info. given in the problem. The rows are used to indicate possible combinations. ? What’s the smallest # of dimes I can have ? … Let’s start there … Dimes Nickels Pennies

Loose Change: Leslie has 25¢ in her pocket but does not have a quarter. If you can tell her all possible combinations of coins she could have that add up to 25¢, she will give you the 25¢. There are 12 possibilities Dimes Nickels Pennies Remember that there is often more than one correct approach to producing systematic lists …