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

Represent and solve equations and inequalities graphically.

Generate and analyze patterns.

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

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

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

Represent and solve problems involving multiplication and division.

Use properties of operations to generate equivalent expressions.

Understand properties of multiplication and the relationship between multiplication and division.

Use the four operations with whole numbers to solve problems.

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

Understand the relationship between zeros and factors of polynomials.

Reason about and solve one-variable equations and inequalities.

Analyze patterns and relationships.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Perform arithmetic operations on polynomials.

Gain familiarity with factors and multiples.

Use polynomial identities to solve problems.

Multiply and divide within 100.

Work with addition and subtraction equations.

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

Solve systems of equations.

Write expressions in equivalent forms to solve problems.

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.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Add and subtract within 20.

Rewrite rational expressions.

Interpret the structure of expressions.

Create equations that describe numbers or relationships

Write and interpret numerical expressions.

Work with radicals and integer exponents.
problem_activity: Task
Suppose $f$ is a quadratic function given by the equation $f(x) = ax^2 + bx + c$
where $a,b,c$ are real numbers and $a$ is non-zero.
Explain why $f$ can have at most two roots; that is explain why there can be at most two distinct real numbers $r_1,r_2$ so that $f(r_1) = f(r_2) = 0$.
Give examples to show that it is possible for $f$ to have zero, one, or two
real roots.


correct_option_index: 11