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

Gain familiarity with factors and multiples.

Represent and solve problems involving addition and subtraction.

Solve systems of equations.

Represent and solve equations and inequalities graphically.

Multiply and divide within 100.

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

Rewrite rational expressions.

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

Write expressions in equivalent forms to solve problems.

Represent and analyze quantitative relationships between dependent and independent variables.

Represent and solve problems involving multiplication and division.

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

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

Generate and analyze patterns.

Work with radicals and integer exponents.

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

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

Write and interpret numerical expressions.

Create equations that describe numbers or relationships

Understand the relationship between zeros and factors of polynomials.

Use the four operations with whole numbers to solve problems.

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

Reason about and solve one-variable equations and inequalities.

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

Interpret the structure of expressions.

Add and subtract within 20.

Use properties of operations to generate equivalent expressions.

Analyze patterns and relationships.

Solve equations and inequalities in one variable.

Perform arithmetic operations on polynomials.

Work with addition and subtraction equations.

Use polynomial identities to solve problems.

Apply and extend previous understandings of arithmetic to algebraic expressions.
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: 4