few_shots: Example:
Problem/activity:
Stage 1: Money
Required Preparation
Materials to Copy
Blackline Masters
Would You Rather Stage 1 Spinner
Would You Rather Stage 1 Recording Sheet

Narrative
The first partner spins to get a group of coins. They write a question that compares the amount they spun to a different group of coins that they make up.


Mathematical concept/skill options: 
A. Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
B. Represent and interpret data.
C. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
D. Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
E. Describe and compare measurable attributes.
F. Geometric measurement: understand concepts of angle and measure angles.
G. Convert like measurement units within a given measurement system.
H. Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
I. Measure and estimate lengths in standard units.
J. Classify objects and count the number of objects in each category.
K. Tell and write time.
L. Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
M. Measure lengths indirectly and by iterating length units.
N. Work with time and money.
O. Relate addition and subtraction to length.


Your response, in json format:
{
  "explanation": "In this problem, students work with money in the form of coins.",
  "answer": "N"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_center_000269

2
options: Understand the relationship between zeros and factors of polynomials.

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

Reason about and solve one-variable equations and inequalities.

Add and subtract within 20.

Multiply and divide within 100.

Interpret the structure of expressions.

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

Represent and solve problems involving addition and subtraction.

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

Use polynomial identities to solve problems.

Solve systems of equations.

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.

Generate and analyze patterns.

Create equations that describe numbers or relationships

Solve equations and inequalities in one variable.

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

Represent and solve problems involving multiplication and division.

Work with addition and subtraction equations.

Analyze patterns and relationships.

Represent and solve equations and inequalities graphically.

Work with radicals and integer exponents.

Use properties of operations to generate equivalent expressions.

Represent and analyze quantitative relationships between dependent and independent variables.

Write expressions in equivalent forms to solve problems.

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

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

Perform arithmetic operations on polynomials.

Gain familiarity with factors and multiples.

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

Use the four operations with whole numbers to solve problems.

Rewrite rational expressions.
problem_activity: Problem 1
A business is marketing its product and has collected data on sales and prices for the past few years. The company, through careful modeling, has determined that their profit is dependent upon the selling price of the item and that it follows a quadratic model.
The function below describes the profit,
$$P$$
, dependent upon the selling price,
$$s$$
, of its product.
$$P(s)=-20s^2+1,400s-12,000$$
a.  Write the function in intercept form and identify the roots.
b.  Explain what the roots mean in context of the situation.
c.  Write the function in vertex form and identify the vertex.
d.  Explain what the vertex means in context of the situation.
Problem 2
The height,
$$h$$
, in feet, of a projectile launched upward from a bridge is given by
$$ h=-16t^2+16t+96$$
, where
$$t$$
is time in seconds.
Write the equation in vertex form.
How long does it take for the projectile to reach maximum height?
What is the maximum height of the projectile?


correct_option_index: 25