8th Grade Math: Unit 1

Unit 1 – Item 1
Joshua is saving money to attend the Atlanta Falcons game in Atlanta on November 3rd. He starts with an initial amount of $200 on October 4th and plans to save $50 each week. After w weeks, his total savings can be represented by the expression 200 + 50w.

1

What does the term 200 represent in context to Joshua’s savings? What does the term 50w represent? Explain your reasoning.

1

Model an expression that represents Joshua’s total savings after (w) weeks if Joshua decides to save $60 a week instead of $50 a week. Let this new expression equal T.

1

How many weeks will take Joshua to save $500 for his trip to attend the Atlanta Falcon’s game, if he saves $60 a week instead of $50 a week.

Unit 1 – Item 2
Dr. Middleton is trying to create a formula with his student, Jacobi, to solidify the fundraising goal for the Men of Excellence organization’s gala based on the number of gala attendees. The organization has raised $500 from pre-ticket sales. The tickets are selling for $10 a ticket. The total cost for the organization’s gala is represented by the equation C = 500 + 10n.

1

Interpret the equation that was given to you above. What does the C represent in the equation? What does n represent in the equation? Explain your reasoning.

1

Jacobi wants to ensure that the total cost for the gala does not exceed $800. Model and solve a linear inequality that represents the situation. What is the maximum number of attendees (n) that Jacobi can have while staying within budget?

1

Dr. Middleton and Jacobi decided that for the organization to be successful, they must have 30 attendees at the gala. Model and write an inequality that represents this requirement. What is the minimum amount that Jacobi and Dr. Middleton can spend to
help their fundraising goal if they have 30 members purchasing a ticket to the gala?

Unit 1 – Item 3
Jamauri and two of his friends are planning a college visit to Savannah State University, but they each need to rent a separate car. They need to know the total cost of renting a car from Travel Rental Car Company.

The total cost that Jamauri and his friends will pay altogether is modeled by the equation below which includes the daily amount and the down payment for each car:

𝐶 = 3(32.60𝑑 + 50)

1

What does the 3 from the equation represent within the context of the scenario?

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If d = 7, what would the total cost of the rental car be? Justify your answer.

Unit 1 – Item 4
Chris and Britney want to represent the problem below.

Imagine you are planning to buy small plants for your garden. Each plant costs $2, and you’ve also decided to buy a set of gardening gloves that cost $3. You have a total budget of $15 for this purchase. How many plants can you purchase?

1

Whose model of algebra tiles will help identify the number of plants that can be purchased?

How many plants can be purchased?

Unit 1 – Item 5
Darius and Amanda are having a discussion on the equation 3 (𝑥 + 4) + 2 = 5𝑥 − 10

1

Who is correct? Justify your answer through solving the equation in one-variable below based on algebraic properties and properties of real numbers.

1

When you arrive at your final answer, what does it tell you about the type of solution for this equation? Explain your answer.

1

Unit 1 – Item 6
Kennady is an aspiring botanist who dreams of having her own greenhouse to cultivate various plants. She's been studying different greenhouse designs and has come across a formula that calculates the area of a triangle, which is like the shape of the roof she wants for her greenhouse.

The formula she found is

where A represents the area, b represents the base of the triangle, and h represents the height.

Excitedly, Kennady starts sketching out her greenhouse design. She knows the height of the
triangular roof will be fixed at 10 feet, but she's unsure about the base length she'll need to cover the area she desires for her plants.

How can Kennedy rearrange the formula she found to find the area of her roof to find the base of her roof?

Unit 1 – Item 7
Alexis has been given the inequality 𝐶 ≤ 5𝑥 – 2, where C represents the total cost of
purchasing an item and x represents the number of items being purchased.

1

Alexis has $20 to go buy snacks from the store. The total cost is represented by the expression 5x – 2, where x is the number of snacks she intends to buy. Choose the number of snacks that would make the statement true (𝐶 ≤ 5𝑥 – 2).

1

Alexis decides to buy at least one but no more than four items? Would the total cost be less than the expression 5x – 2? Model a compound inequality to represent her situation.

Unit 1 – Item 8
Alex is saving money to buy a new bicycle. Alex already has $10 saved, and each week he saves a fixed amount.

1

Write an expression to represent the total amount of money Alex saves after a certain number of weeks. Let 𝑚 represent the number of weeks and 𝑤 represent the amount saved each week.

1

If Alex saves $7.50 each week, how many weeks will it take for Alex to save a total of $100? Create an equation and solve for 𝑚.

1

What does the term 200 represent in context to Joshua’s savings? What does the term 50w represent? Explain your reasoning.

Model an expression that represents Joshua’s total savings after (w) weeks if Joshua decides to save $60 a week instead of $50 a week. Let this new expression equal T.

How many weeks will take Joshua to save $500 for his trip to attend the Atlanta Falcon’s game, if he saves $60 a week instead of $50 a week.

Interpret the equation that was given to you above. What does the C represent in the equation? What does n represent in the equation? Explain your reasoning.

Jacobi wants to ensure that the total cost for the gala does not exceed $800. Model and solve a linear inequality that represents the situation. What is the maximum number of attendees (n) that Jacobi can have while staying within budget?

What does the 3 from the equation represent within the context of the scenario?

If d = 7, what would the total cost of the rental car be? Justify your answer.

Whose model of algebra tiles will help identify the number of plants that can be purchased?How many plants can be purchased?

Who is correct? Justify your answer through solving the equation in one-variable below based on algebraic properties and properties of real numbers.

When you arrive at your final answer, what does it tell you about the type of solution for this equation? Explain your answer.

Alexis has $20 to go buy snacks from the store. The total cost is represented by the expression 5x – 2, where x is the number of snacks she intends to buy. Choose the number of snacks that would make the statement true (𝐶 ≤ 5𝑥 – 2).

Alexis decides to buy at least one but no more than four items? Would the total cost be less than the expression 5x – 2? Model a compound inequality to represent her situation.

Write an expression to represent the total amount of money Alex saves after a certain number of weeks. Let 𝑚 represent the number of weeks and 𝑤 represent the amount saved each week.

If Alex saves $7.50 each week, how many weeks will it take for Alex to save a total of $100? Create an equation and solve for 𝑚.

Explain what the solution means in the context of Alex’s savings plan.

Whose model of algebra tiles will help identify the number of plants that can be purchased?

How many plants can be purchased?