Students can use this worksheet to practice distinguishing between independent and dependent variables in various mathematical scenarios.

To solve the problem of identifying independent and dependent variables in each scenario, we need to understand the relationship between the variables. The independent variable is the one that is manipulated or changed, while the dependent variable is the one that is observed or measured as a result of the change in the independent variable.

Let's analyze each scenario step by step:

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1. The number of students in a class, \( s \), and the number of desks needed, \( d \).

- Independent variable: \( s \) (number of students in a class)
- Dependent variable: \( d \) (number of desks needed)
- Explanation: The number of desks needed (\( d \)) depends on the number of students (\( s \)). If the number of students changes, the number of desks required will also change.

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2. The number of candles on a birthday cake, \( c \), and that person’s age, \( a \).

- Independent variable: \( a \) (person’s age)
- Dependent variable: \( c \) (number of candles on a birthday cake)
- Explanation: The number of candles (\( c \)) on a birthday cake is typically equal to the person’s age (\( a \)). Therefore, the number of candles depends on the person’s age.

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3. The height of a sunflower in inches, \( h \), and the number of days since it was planted, \( d \).

- Independent variable: \( d \) (number of days since it was planted)
- Dependent variable: \( h \) (height of the sunflower in inches)
- Explanation: The height of the sunflower (\( h \)) grows over time, depending on the number of days (\( d \)) since it was planted. The height is influenced by the passage of time.

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4. The number of gallons of paint needed, \( g \), and the size of a room in square feet, \( s \).

- Independent variable: \( s \) (size of the room in square feet)
- Dependent variable: \( g \) (number of gallons of paint needed)
- Explanation: The amount of paint needed (\( g \)) depends on the size of the room (\( s \)). A larger room requires more paint.

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5. The number of eggs Davia has, \( e \), and the number of batches of muffins he can bake, \( b \).

- Independent variable: \( e \) (number of eggs Davia has)
- Dependent variable: \( b \) (number of batches of muffins he can bake)
- Explanation: The number of batches of muffins (\( b \)) Davia can bake depends on the number of eggs (\( e \)) he has. More eggs allow him to bake more batches.

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6. The amount of money Isabella earns, \( m \), and the number of hours she works, \( h \).

- Independent variable: \( h \) (number of hours she works)
- Dependent variable: \( m \) (amount of money Isabella earns)
- Explanation: The amount of money earned (\( m \)) depends on the number of hours worked (\( h \)). More hours worked generally lead to more earnings.

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7. The number of T-shirts a basketball team orders, \( t \), and the number of players on the team, \( p \).

- Independent variable: \( p \) (number of players on the team)
- Dependent variable: \( t \) (number of T-shirts ordered)
- Explanation: The number of T-shirts ordered (\( t \)) depends on the number of players (\( p \)). Each player typically needs one T-shirt.

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8. The number of miles Terrance has driven, \( m \), and the amount of gas he has used, \( g \).

- Independent variable: \( m \) (number of miles driven)
- Dependent variable: \( g \) (amount of gas used)
- Explanation: The amount of gas used (\( g \)) depends on the number of miles driven (\( m \)). Driving more miles consumes more gas.

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Final Answer:

1. Independent variable: \( s \); Dependent variable: \( d \)
2. Independent variable: \( a \); Dependent variable: \( c \)
3. Independent variable: \( d \); Dependent variable: \( h \)
4. Independent variable: \( s \); Dependent variable: \( g \)
5. Independent variable: \( e \); Dependent variable: \( b \)
6. Independent variable: \( h \); Dependent variable: \( m \)
7. Independent variable: \( p \); Dependent variable: \( t \)
8. Independent variable: \( m \); Dependent variable: \( g \)

\[
\boxed{
\begin{array}{ll}
1. & \text{Independent variable: } s, \text{ Dependent variable: } d \\
2. & \text{Independent variable: } a, \text{ Dependent variable: } c \\
3. & \text{Independent variable: } d, \text{ Dependent variable: } h \\
4. & \text{Independent variable: } s, \text{ Dependent variable: } g \\
5. & \text{Independent variable: } e, \text{ Dependent variable: } b \\
6. & \text{Independent variable: } h, \text{ Dependent variable: } m \\
7. & \text{Independent variable: } p, \text{ Dependent variable: } t \\
8. & \text{Independent variable: } m, \text{ Dependent variable: } g \\
\end{array}
}
\]