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 dont 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 mens
  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 Hoosiers 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, Jordans 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.topliterat
  ure.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)