options: Solve systems of equations.

Multiply and divide within 100.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Write and interpret numerical expressions.

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

Work with addition and subtraction equations.

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

Add and subtract within 20.

Generate and analyze patterns.

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

Represent and solve problems involving multiplication and division.

Solve equations and inequalities in one variable.

Write expressions in equivalent forms to solve problems.

Use the four operations with whole numbers to solve problems.

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

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

Reason about and solve one-variable equations and inequalities.

Use properties of operations to generate equivalent expressions.

Create equations that describe numbers or relationships

Understand the relationship between zeros and factors of polynomials.

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

Interpret the structure of expressions.

Rewrite rational expressions.

Represent and solve problems involving addition and subtraction.

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

Gain familiarity with factors and multiples.

Work with radicals and integer exponents.

Represent and solve equations and inequalities graphically.

Analyze patterns and relationships.

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

Represent and analyze quantitative relationships between dependent and independent variables.

Perform arithmetic operations on polynomials.

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

Use polynomial identities to solve problems.
problem_activity: Given below are the graphs of two lines,
$${y = 0.5x + 5}$$
and
$${y = -1.25x + 8}$$
, and several regions and points are shown. Note that C is the region that appears completely white in the graph.
[IMG]
For each region and point, write a system of equations or inequalities that has the region or point as its solution set.
Verify that a point that lies in region A satisfies the system of inequalities that you wrote for region A.
Without choosing any specific numbers, explain how you know that all the points in quadrant 3 must satisfy the inequalities for region A.


correct_option_index: 18

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