Football Math: Understanding Coefficients

Coefficient | The Great "Multiplier"

Welcome to today's math lesson where we'll explore coefficients through the exciting world of football. Grab your playbook - we're about to make math as exciting as game day!

A coefficient is simply a number that multiplies avariable. Think of it as the "multiplier" in football math.

Let's start with scoring. In football, every scoring play has its own coefficient. When we write 6t, the 6 is our coefficient, and 't' represents touchdowns.

If a team scores 3 touchdowns, we multiply: 6 times 3, giving us 18 points.

Field goals work similarly. We write 3f, where 3 is the coefficient and 'f' represents the number of field goals.

Penalties | Subtraction

Now, let's tackle penalties. A holding penalty is written as -10h. The coefficient is -10 because you lose 10 yards.

That minus sign is crucial - it tells us we're moving backward, not forward.

Run the Ball!

Running plays have coefficients too. A team averaging 4.5 yards per run is written as 4.5r, where 'r' is the number of rushing attempts.

If a team runs the ball 5 times, that's 4.5 times 5, or 22.5 yards.

Game Day Scenario | 20 yard line

1st Down

Line of Scrimmage is 20 yard line

Result of play 1: rush for +5 yards

20 yard line + 5 yards = 25 yard line

2nd Down

Line of Scrimmage is 25 yard line

Result of play 2: rush for +5 yards

25 yard line + 5 yards = 30 yard line

Be Efficient!

The total yards gained from plays 1 and 2 is correct, but there is a more efficient way to calculate the total yards gained.

The most efficient way to calculate the number of yards gained for two or more rush attempts is to multiply.

Why are we allowed to multiply instead of using addition? Because, we gained the same number of yards for each rush attempt.

Rush for 5 yards + Rush for 5 yards is the same as 2 Rushes(5 yards).

5 + 5 = 10 | 2(5) = 10

Both rush attempts = 10 yards gained

Don't forget to follow the rules for PEMDAS

3rd Down

Line of Scrimmage is 30 yard line

Result of play 3: 15-yard penalty

A penalty is a loss of yards previously gained.

A loss is calculated by subtracting the penalty yards from the starting point.

15-yard penalty: subtracts 15

30 yard line - a 15 yard penalty = ball moved back to the 15 yard line

4th Down

Line of Scrimmage is 15 yard line

Play 4 result: 12 yard pass completion

A pass completion of 12 yards represents a gain (addition) of 12 yards from the line of scrimmage.

15 yard line + 12 yard pass completion = ball moved forward
to 27 yard line

One 12-yard pass: adds 12

Final position: 27-yard line

Math 1

Identifying Arithmetic Sequences

A sequence of numbers is just that, a list of numbers in order.

It can be a short list, such as the number of points earned on each assignment in a class, such as {10, 10, 8, 9, 10, 6, 10}.

Or it can be a longer list, even infinitely long, such as the list of prime numbers.

For example, here’s a sequence of numbers, specifically, the squares of the first 12 natural numbers.

{1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144}

Each value in the sequence is called a term.

Terms in the list are often referred to by their location in the sequence, as in the nth term (pronounced enth).

For the sequence {1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144}, the first term of the sequence is 1, the fourth term is 16, and so on.

In the sequence of assignment scores {10, 10, 8, 9, 10, 6, 10}, the first term is 10 and the third term is 8.

Touchdown with Arithmetic Sequences: Football Scoring Patterns

Learning Objective:

Students will identify arithmetic sequences using football-themed examples and determine common differences between terms.

Imagine tracking a football team's scoring pattern throughout a game.

If they score exactly 7 points (touchdown + extra point) every quarter, they're creating an arithmetic sequence!

Key Concepts: An arithmetic sequence is a pattern where each number increases or decreases by the same amount.

Common difference = the constant difference between consecutive terms

Each term is found by adding the common difference to the previous term

Football-Themed Examples:

Field Position Sequence:

A team starts at their own 20 yard line and gains exactly 5 yards on each play.

Field position sequence: 20, 25, 30, 35, 40, 45, 50

Common difference = 5 yards

Score Tracking:

A team scores a field goal (3 points) in each quarter.

Score sequence: 3, 6, 9, 12

Common difference = 3 points