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

Analyze patterns and relationships.

Generate and analyze patterns.

Use polynomial identities to solve problems.

Add and subtract within 20.

Create equations that describe numbers or relationships

Write expressions in equivalent forms to solve problems.

Represent and analyze quantitative relationships between dependent and independent variables.

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

Multiply and divide within 100.

Understand the relationship between zeros and factors of polynomials.

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

Rewrite rational expressions.

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.

Solve equations and inequalities in one variable.

Represent and solve problems involving multiplication and division.

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

Represent and solve problems involving addition and subtraction.

Work with radicals and integer exponents.

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

Reason about and solve one-variable equations and inequalities.

Write and interpret numerical expressions.

Represent and solve equations and inequalities graphically.

Use the four operations with whole numbers to solve problems.

Solve systems of equations.

Perform arithmetic operations on polynomials.

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

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

Interpret the structure of expressions.

Use properties of operations to generate equivalent expressions.

Gain familiarity with factors and multiples.
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: 5