few_shots: Example:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Mathematical concept/skill options: 
A. Analyze proportional relationships and use them to solve real-world and mathematical problems.
B. Understand ratio concepts and use ratio reasoning to solve problems.


Your response:
Thought: This problem focuses on the ratio between two ingredients. Students do not have to analyze proportional relationships in-depth, which is reserved for a higher grade level, but rather use ratios to find missing values.
Answer: B

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_000972

6
options: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Write and interpret numerical expressions.

Multiply and divide within 100.

Perform arithmetic operations on polynomials.

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

Represent and solve problems involving addition and subtraction.

Generate and analyze patterns.

Work with addition and subtraction equations.

Use polynomial identities to solve problems.

Work with radicals and integer exponents.

Add and subtract within 20.

Create equations that describe numbers or relationships

Gain familiarity with factors and multiples.

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

Solve equations and inequalities in one variable.

Use the four operations with whole numbers to solve problems.

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

Analyze patterns and relationships.

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

Represent and solve equations and inequalities graphically.

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

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

Understand the relationship between zeros and factors of polynomials.

Write expressions in equivalent forms to solve problems.

Reason about and solve one-variable equations and inequalities.

Represent and solve problems involving multiplication and division.

Rewrite rational expressions.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

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

Solve systems of equations.

Represent and analyze quantitative relationships between dependent and independent variables.

Interpret the structure of expressions.

Use properties of operations to generate equivalent 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: 11