options: Gain familiarity with factors and multiples.

Interpret the structure of expressions.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Solve systems of equations.

Understand solving equations as a process of reasoning and explain the reasoning.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Analyze patterns and relationships.

Use polynomial identities to solve problems.

Use the four operations with whole numbers to solve problems.

Work with equal groups of objects to gain foundations for multiplication.

Work with addition and subtraction equations.

Work with radicals and integer exponents.

Represent and solve equations and inequalities graphically.

Reason about and solve one-variable equations and inequalities.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Multiply and divide within 100.

Understand the relationship between zeros and factors of polynomials.

Create equations that describe numbers or relationships

Represent and solve problems involving multiplication and division.

Represent and analyze quantitative relationships between dependent and independent variables.

Add and subtract within 20.

Understand the connections between proportional relationships, lines, and linear equations.

Generate and analyze patterns.

Understand and apply properties of operations and the relationship between addition and subtraction.

Represent and solve problems involving addition and subtraction.

Solve equations and inequalities in one variable.

Write expressions in equivalent forms to solve problems.

Rewrite rational expressions.

Use properties of operations to generate equivalent expressions.

Perform arithmetic operations on polynomials.

Write and interpret numerical expressions.

Understand properties of multiplication and the relationship between multiplication and division.
problem_activity: Problem 1
A ball is thrown straight up from the top of a
$${48}$$
-foot tall building with an initial speed of
$${32}$$
feet per second. The height of the ball as a function of time can be modeled by the function
$$h(t)=-16t^2+{32}t+{48}$$
. Below is a graph and table of the function.
[IMG]
a. What are the solutions to this function? Interpret each solution in context of the situation.
b. What is the vertex of this function? Interpret the vertex in context of the situation.
Problem 2
The table below represents the value of Andrew’s stock portfolio, where
$$V$$
represents the value of the portfolio in hundreds of dollars and
$$t$$
is the time in months since he started investing. Answer the questions that follow based on the table of values.
| $$t$$                    (months) | $$V(t)$$                    (hundreds of dollars) |
|-----------------------------------|---------------------------------------------------|
|                 2                 |                        325                        |
|                 4                 |                        385                        |
|                 6                 |                        405                        |
|                 8                 |                        385                        |
|                10                 |                        325                        |
|                12                 |                        225                        |
|                14                 |                        85                         |
|                16                 |                        -95                        |
|                18                 |                       -315                        |
Assuming this data is quadratic, how much did Andrew invest in his stock initially? Explain how you arrived at this answer.
What is the maximum value of his stock and how long did it take to reach the maximum value?
After approximately how many months is Andrew’s stock portfolio valued at $0?
How fast is Andrew’s stock value decreasing between months 10 and 12? Find a two-month interval where the average rate of change is faster than it is between months 10 and 12 and explain why.
Problem 3
John is building a small rectangular pen for chickens. He wants the length to be 6 more feet than twice the width.
If the area of the pen is 36 square feet, what are the dimensions of the pen in feet?


correct_option_index: 19