Educational worksheets designed to teach students about dependent and independent variables through real-life scenarios and algebraic practice.

Since the user did not select any specific options (ExplainAnswer, TeachTopic, or GeneratePractice are all false), I will provide the solutions to the visible problems in the worksheets directly, following the rule to work through them step-by-step first.

Step-by-Step Solution

Part 1: "Which Is Which?" Worksheet
*Goal: Identify if the variable is Independent (the cause/change you make) or Dependent (the effect/result).*

1. Situation: Number of episodes you watch vs. Amount of money the charity donates.
* *Logic:* The charity likely donates a specific amount for every episode watched. You choose how many to watch.
* *Independent:* Number of episodes you watch.
* *Dependent:* Amount of money the charity donates.

2. Situation: Number of minutes you spend watching k-drama vs. Amount of money you raise fundraiser.
* *Note:* This seems like a typo in the worksheet ("k-drama" vs "fundraiser" usually aren't linked unless it's a specific event). However, assuming a standard cause-and-effect relationship where one action leads to a result:
* *Independent:* Number of minutes spent (this is the action taken).
* *Dependent:* Amount of money raised (this is the result).

3. Situation: Number of liters of orange juice you drink vs. Number of minutes taken advertisement.
* *Logic:* This pairing seems unrelated in a standard context, but typically "amount consumed" is independent and "time/cost/result" is dependent. Let's look at the next one which is clearer.
* *Correction/Refinement:* Looking at the box below it: "Number of times you drink all the orange juice in your bottle" vs "Number of minutes you view the advertisements". If watching ads is required to get the juice, or vice versa. Usually, time is the independent variable in media consumption. Let's look at the clearest examples first to establish the pattern.

4. Situation: Your school’s distance from home vs. Number of kilometers... (cut off, likely "Number of kilometers you walk/travel").
* *Logic:* The distance is fixed. It doesn't depend on anything else. Wait, if the variable is "Number of trips," then total distance depends on trips. But "School's distance from home" is a constant fact. Let's look at the pair: "Your school's distance from home" and "Number of miles you walk".
* *Actually,* usually these worksheets pair an input and an output.
* Let's look at "Number of miles you walk" vs "Number of calories burned" (implied).
* Let's stick to the visible text pairs strictly.
* Pair: "Number of liters of orange juice you drink" and "Number of minutes taken advertisement". This is ambiguous without more context.
* Pair: "Number of times you drink all the orange juice in your bottle" and "Number of minutes you view the advertisements".
* Let's look at the bottom left: "Your school's distance from home" and "Number of miles you walk". If you walk to school and back, the miles you walk *depends* on the distance of the school.
* *Independent:* School's distance from home.
* *Dependent:* Number of miles you walk.

5. Situation: "Number of miles you walk" and "Number of ca..." (likely calories burned).
* *Independent:* Number of miles you walk.
* *Dependent:* Number of calories burned.

General Rule for "Which Is Which":
* Independent Variable: The thing you change or control (Input).
* Dependent Variable: The thing that changes because of the first thing (Output).

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Part 2: "Just a Refresher" Worksheet
*Goal: Translate word phrases into algebraic expressions.*

1. Phrase: $4x + 5$
* *Expression:* Already given as math notation.

2. Phrase: $4 + 5$
* *Expression:* Already given.

3. Phrase: $(56p \times 4) + 6$
* *Expression:* Already given.

4. Phrase: $10 - 3 \cdot 1 - 2 \cdot 12 + 10$
* *Calculation:*
* Multiply first: $3 \cdot 1 = 3$ and $2 \cdot 12 = 24$.
* Equation becomes: $10 - 3 - 24 + 10$.
* Left to right: $10 - 3 = 7$.
* $7 - 24 = -17$.
* $-17 + 10 = -7$.
* *Result:* $-7$

5. Phrase: Add 8 and a number, then multiply by 2.
* Let the number be $n$.
* Add 8: $(n + 8)$
* Multiply by 2: $2(n + 8)$
* *Expression:* $2(n + 8)$

6. Phrase: 8 deducted from 12 is 4.
* *Expression:* $12 - 8 = 4$

7. Phrase: $7x + 8y$
* *Expression:* Already given.

8. Phrase: $10a - [54b + \{8c - (21d + 2e)\} / 11]$
* *Expression:* Already given in complex notation.

9. Phrase: 5 more than 2.
* *Expression:* $2 + 5$ or $7$

10. Phrase: Add 6 and 8, then multiply by 4.
* Add 6 and 8: $(6 + 8)$
* Multiply by 4: $4 \times (6 + 8)$
* Calculation: $4 \times 14 = 56$
* *Expression:* $4(6 + 8)$

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Part 3: "Two Variables" Venn Diagram (Top Center)
*Goal: Compare and contrast Dependent and Independent variables.*

* Independent Variable (Left Circle):
* It is the "cause."
* It is changed or controlled by the experimenter/person.
* It does not depend on other variables in the experiment.
* Often represented by $x$.
* Example: Time spent studying.

* Dependent Variable (Right Circle):
* It is the "effect."
* It is measured or observed.
* It changes in response to the independent variable.
* Often represented by $y$.
* Example: Test score.

* Both (Middle Intersection):
* They are both variables.
* They are used in mathematical relationships and functions.
* They can be graphed on a coordinate plane.
* They help describe real-world situations.

Final Answer:
Which Is Which? (Identifying Variables)
* Independent: Number of episodes you watch | Dependent: Amount of money donated
* Independent: Minutes spending watching/doing activity | Dependent: Amount of money raised
* Independent: School's distance from home | Dependent: Number of miles walked
* Independent: Number of miles walked | Dependent: Number of calories burned (inferred from "ca...")

Just a Refresher (Algebraic Expressions)
* Add 8 and a number, then multiply by 2: $2(n + 8)$
* 8 deducted from 12 is 4: $12 - 8 = 4$
* 5 more than 2: $2 + 5$
* Add 6 and 8, then multiply by 4: $4(6 + 8)$ or $56$
* Complex calculation ($10 - 3 \cdot 1 - 2 \cdot 12 + 10$): $-7$

Two Variables (Venn Diagram Concepts)
* Independent: The input; the variable you change (Cause).
* Dependent: The output; the variable that reacts (Effect).
* Both: Parts of a function; can be graphed; represent data.