options: Perform arithmetic operations on polynomials.

Represent and analyze quantitative relationships between dependent and independent variables.

Gain familiarity with factors and multiples.

Represent and solve equations and inequalities graphically.

Write and interpret numerical expressions.

Write expressions in equivalent forms to solve problems.

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

Solve equations and inequalities in one variable.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Create equations that describe numbers or relationships

Interpret the structure of expressions.

Use the four operations with whole numbers to solve problems.

Reason about and solve one-variable equations and inequalities.

Analyze patterns and relationships.

Use polynomial identities to solve problems.

Multiply and divide within 100.

Rewrite rational expressions.

Use properties of operations to generate equivalent expressions.

Work with radicals and integer exponents.

Work with addition and subtraction equations.

Understand the relationship between zeros and factors of polynomials.

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

Solve systems of equations.

Generate and analyze patterns.

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

Represent and solve problems involving multiplication and division.

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

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

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

Represent and solve problems involving addition and subtraction.

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

Add and subtract within 20.

Understand and apply properties of operations and the relationship between addition and subtraction.
problem_activity: Task
The population of a country is initially 2 million people and is increasing at 4% per year. The country's annual food supply is initially adequate for 4 million people and is increasing at a constant rate adequate for an additional 0.5 million people per year.
Based on these assumptions, in approximately what year will this country ﬁrst experience shortages of food?
If the country doubled its initial food supply and maintained a constant rate of increase in the supply adequate for an additional 0.5 million people per year, would shortages still occur?  In approximately which year?
If the country doubled the rate at which its food supply increases, in addition to doubling its initial food supply, would shortages still occur?


correct_option_index: 3