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

Represent and solve problems involving addition and subtraction.

Work with radicals and integer exponents.

Generate and analyze patterns.

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

Use polynomial identities to solve problems.

Write and interpret numerical expressions.

Work with addition and subtraction equations.

Add and subtract within 20.

Use the four operations with whole numbers to solve problems.

Reason about and solve one-variable equations and inequalities.

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

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

Gain familiarity with factors and multiples.

Use properties of operations to generate equivalent expressions.

Solve equations and inequalities in one variable.

Solve systems of equations.

Multiply and divide within 100.

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

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

Interpret the structure of expressions.

Understand the relationship between zeros and factors of polynomials.

Write expressions in equivalent forms to solve problems.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Perform arithmetic operations on polynomials.

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

Represent and solve problems involving multiplication and division.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Represent and solve equations and inequalities graphically.

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

Analyze patterns and relationships.

Rewrite rational expressions.

Create equations that describe numbers or relationships
problem_activity: Problem 1
A quadratic equation is shown below.
$${x^2=(2x-9)^2}$$
a.  Solve this equation by expanding and then factoring.
b.  Solve this equation by taking the square root of each side.
Problem 2
A physics teacher put a ball at the top of a ramp and let it roll down toward the floor. The class determined that the height of the ball could be represented by the equation
$${h=-16t^2+4}$$
, where the height,
$$h$$
, is measured in feet from the ground and time,
$$t$$
, is measured in seconds.
[IMG]
What do you notice about the structure of the quadratic expression in this problem?
In the equation, explain what the
$$4$$
represents.
Determine the time it takes for the ball to reach the floor. Interpret your solution(s) in context of the problem.


correct_option_index: 15