options: Represent and solve equations and inequalities graphically.

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

Solve systems of equations.

Create equations that describe numbers or relationships

Perform arithmetic operations on polynomials.

Generate and analyze patterns.

Solve equations and inequalities in one variable.

Write and interpret numerical expressions.

Write expressions in equivalent forms to solve problems.

Add and subtract within 20.

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

Multiply and divide within 100.

Use properties of operations to generate equivalent expressions.

Analyze patterns and relationships.

Rewrite rational expressions.

Use the four operations with whole numbers to solve problems.

Work with radicals and integer exponents.

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

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

Gain familiarity with factors and multiples.

Work with addition and subtraction equations.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Represent and analyze quantitative relationships between dependent and independent variables.

Reason about and solve one-variable equations and inequalities.

Represent and solve problems involving multiplication and division.

Understand the relationship between zeros and factors of polynomials.

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

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

Represent and solve problems involving addition and subtraction.

Interpret the structure of expressions.

Use polynomial identities to solve problems.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.
problem_activity: Task
A government buys $x$ fighter planes at $z$ dollars each,
and $y$ tons of wheat at $w$ dollars each. It spends a total of $B$
dollars, where $B = xz + yw$. In (a)–(c), write an
equation whose solution is the given quantity.
The number of tons of wheat the government can afford to buy if it
spends a total of \$100 million, wheat costs  \$300 per ton, and it must
buy 5 fighter planes at \$15 million each.
The price of fighter planes if the government bought 3 of them, in addition to $10,\!000$ tons of wheat at \$500 a ton, for a total of \$50 million.
The price of a ton of wheat, given that a fighter plane costs $100,\!000$ times as much as a ton of wheat, and that the government bought 20 fighter planes
and $15,\!000$ tons of wheat for a total cost of
\$90 million.


correct_option_index: 3