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

Represent and solve equations and inequalities graphically.

Use properties of operations to generate equivalent expressions.

Work with radicals and integer exponents.

Understand the relationship between zeros and factors of polynomials.

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

Use polynomial identities to solve problems.

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

Create equations that describe numbers or relationships

Represent and solve problems involving addition and subtraction.

Work with addition and subtraction equations.

Represent and solve problems involving multiplication and division.

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

Reason about and solve one-variable equations and inequalities.

Solve equations and inequalities in one variable.

Multiply and divide within 100.

Perform arithmetic operations on polynomials.

Rewrite rational expressions.

Write expressions in equivalent forms to solve problems.

Analyze patterns and relationships.

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

Add and subtract within 20.

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

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

Represent and analyze quantitative relationships between dependent and independent variables.

Interpret the structure of expressions.

Write and interpret numerical expressions.

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

Gain familiarity with factors and multiples.

Solve systems of equations.

Use the four operations with whole numbers to solve problems.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Generate and analyze patterns.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
problem_activity: Task
Sara's doctor tells her she needs between 400 and 800 milligrams of folate per day, with part coming from her diet and part coming from a multi-vitamin. Each multi-vitamin contains 50 mg of folate, and because of the inclusion of other vitamins and minerals, she can only take a maximum of 8 tablets per day.
What are the possible combinations of $n$, number of vitamin tablets taken, and $a$, the amount of dietary folate, which will give Sarah exactly the minimum of 400 mg of folate each day? Express your answers in a table.
What are the possible combinations of vitamin tablets and dietary folate which give the maximum of 800 mg of folate each day?
Now use your tables from parts (i) and (ii) to express your answers as a system of three inequalities. Create a graph of $a$ versus $n$, and compare your graph to your tables from parts (i) and (ii).
Suppose instead of a multi-vitamin, Sara is given a powdered folate supplement she can add to water. She can drink any amount of the supplement she wants per day, as long as she does not exceed 400 mg per day. What are the possible combinations of folate she can ingest from her diet and from the powder? Graph your solution set. How does this graph compare to the graph from part (a)?


correct_option_index: 8