Algebra for Sports Fans

1. Algebra for Sports Fans Making connections between sports and math concepts

2. The challenge for some math students A certain percentage of students have difficulty learning algebra concepts. Students become frustrated. They convince themselves that they don�t like math. If the student does not absorb algebra concepts, they cannot advance to upper level math classes easily. Ultimately, they will need to review algebra to succeed.

3. A possible solution Students succeed when they can connect math concepts to topics they already know. Many students are sports fans. They play, watch or follow sports. Sports can connect the student to math concepts. As a result, learning math is more interesting. Remember the math by recalling the connection to sports!

4. Evaluating an Expression Variable: A letter that is used to represent one or more numbers. Numbers are the values of the expression. Examples: 8y means �8 times y�. The operation is multiplication. 16 means �16 divided by b� (division) b (Algebra One, Larson, 2004 pg 3)

5. Evaluating an Expression: 100 Meter Dash Usain Bolt of Jamaica holds the current men�s world record in the 100 meter dash. His time at the �08 Beijing Olympic Games was 9.69 seconds (Wikipedia). One meter equals 1.09 yards. Bolt ran 109 yards in 9.69 seconds. Bolt is six-foot-five, possibly the tallest world class sprinter in history. He takes about 41 strides in a 100-meter (109 yard) race (Slate.com, 8/17/08). How long is each stride? Let x equal the length of each stride: 109 = 41, 109 = x, x= 2.66 yards x 41 (Adapted: Algebra One, Larson, 2007, pg 7, #53)

6. Order of Operations: T-Shirt Sales (1 of 2) We use order of operations when we have to evaluate an expression with more than one operation. First, we perform any calculations inside grouping symbols (brackets). Next, perform multiplication and division moving from left to right. Finally, perform addition and subtraction. Hank the Hoosier is selling T-Shirts at the NCAA basketball tournament. Hank is a big Indiana fan. Half the T-Shirts, which say �Go Hoosiers�, were purchased from a supplier for $5.95 each. The second half, which say �Hoosiers Rule!�, were bought for $6.15 each. Question: What is Hank the Hoosier�s average cost for the T-Shirts? (After all, Hank needs to know his cost so he can price the T-Shirts to make a profit).

7. Order of Operations: T-Shirt Sales (2 of 2) Formula: Average Cost of T-Shirts: (5.95 + 6.15) 2 Steps: * Add the amounts inside the brackets. * Divide that answer by 2 (the denominator) Result: $12.10 / 2 = 6.05 (His average cost is $6.05 per T-Shirt) (Adapted: Algebra One, Larson, 2007, pg 11, #34)

8. Writing Expressions: Indy 500 Race Expressions are used to compute rates, such as rate of speed. A product is an expression that uses multiplication. A quotient uses division. A quotient can be used to compute miles per hour. In 1990, Arie Luyendyk set the record for the fastest finishing time at the Indianapolis 500 auto race. His time was an average of 186 miles per hour. How long did it take him to finish the 500 mile race? (Indy500.com). Basic Formula: Rate = (Distance)/ (Time) 186 = 500/ x, where x equals time to finish in hours x * 186 = 500 (Multiply both sides by x) x = 500/ 186 (Divide both sides by 186) x = 2.69 hours

9. Equations: Basketball/ Average Points per Game (1 of 2) An Open Sentence is an equation that contains one or more variables. You learned earlier (slide 4) that a variable is a letter used to represent one or more numbers. Assume our equation contains one variable. If the number we enter into the variable makes the statement true, the number is a solution of the equation. Michael Jordan holds the NBA record for highest scoring average in the NBA playoffs. Jordan averaged 33.4 points per game in 179 career playoff games (nba.com). How is average points per game calculated?

10. Equations: Basketball/ Average Points per Game (2 of 2) Jordan has played the first 10 games of the season. He has averaged 16 points per game. He has scored 160 total points (10 * 16) = 160. Over the first 20 games, Jordan�s coach would like him to average 25 points per game. Jordan will need to score 500 total points (20 * 25) = 500 in the first 20 games. Question: How many points would Jordan have to score in the next 10 games to average 25 points over the first 20 games? Points (1st 10 games) + Points (2nd 10 games) = Total Points (20 Games) 160 + X = 500 X = 500 � 160 X = 340 Since 340 makes the equation true, it is a solution 340 points/ 10 games = 34 points per game needed over next 10 games (Adapted- Algebra 1, Larson, Bowell, Kanold, Stiff, 2004, page 24)

11. Problem Solving Using Models / Rafting Trip (1 of 2) To translate phrases into algebra, look for words that indicate operation. Example: Four times a number is expressed as 4x You are considering two rivers for a summer rafting trip, each in different parts of the country. In order to plan for food and lodging, you need to know the length of each river. Your research indicates that the Colorado River is three times the length of the Connecticut River, plus 229 miles. What equation could you use to model this equation? In other words, what equation would give you the length of the Colorado River?

12. Problem Solving Using Models / Rafting Trip (1 of 2) Equation for the length of the Colorado River: Assume r = Length of the Connecticut River Equation: 3r + 229 The Connecticut River is 407 miles long (http://encyclopedia.topliterature.com) The Colorado River is: 3 (407) + 229 = 1,450 miles long (answers.com) (Adapted- Algebra 1, Larson, Bowell, Kanold, Stiff, 2004, page 36, #41)