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

Use polynomial identities to solve problems.

Perform arithmetic operations on polynomials.

Represent and solve problems involving multiplication and division.

Analyze patterns and relationships.

Reason about and solve one-variable equations and inequalities.

Use properties of operations to generate equivalent expressions.

Write expressions in equivalent forms to solve problems.

Represent and solve problems involving addition and subtraction.

Rewrite rational expressions.

Gain familiarity with factors and multiples.

Represent and solve equations and inequalities graphically.

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

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

Solve equations and inequalities in one variable.

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.

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

Create equations that describe numbers or relationships

Add and subtract within 20.

Interpret the structure of expressions.

Use the four operations with whole numbers to solve problems.

Write and interpret numerical expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Understand the relationship between zeros and factors of polynomials.

Solve systems of equations.

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

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

Generate and analyze patterns.

Multiply and divide within 100.

Work with addition and subtraction equations.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.
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: 19