options: Represent and solve equations and inequalities graphically.

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

Use polynomial identities to solve problems.

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

Solve equations and inequalities in one variable.

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

Multiply and divide within 100.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Gain familiarity with factors and multiples.

Analyze patterns and relationships.

Represent and solve problems involving multiplication and division.

Use properties of operations to generate equivalent expressions.

Create equations that describe numbers or relationships

Understand the relationship between zeros and factors of polynomials.

Rewrite rational expressions.

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

Use the four operations with whole numbers to solve problems.

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

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

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

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

Work with addition and subtraction equations.

Write expressions in equivalent forms to solve problems.

Reason about and solve one-variable equations and inequalities.

Add and subtract within 20.

Represent and solve problems involving addition and subtraction.

Interpret the structure of expressions.

Write and interpret numerical expressions.

Generate and analyze patterns.

Solve systems of equations.

Work with radicals and integer exponents.

Perform arithmetic operations on polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.
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: 4