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:
Thought: 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: Use polynomial identities to solve problems.

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

Perform arithmetic operations on polynomials.

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

Represent and analyze quantitative relationships between dependent and independent variables.

Apply and extend previous understandings of arithmetic to algebraic expressions.

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

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

Write and interpret numerical expressions.

Gain familiarity with factors and multiples.

Use the four operations with whole numbers to solve problems.

Represent and solve problems involving addition and subtraction.

Add and subtract within 20.

Multiply and divide within 100.

Use properties of operations to generate equivalent expressions.

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

Rewrite rational expressions.

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

Reason about and solve one-variable equations and inequalities.

Represent and solve problems involving multiplication and division.

Create equations that describe numbers or relationships

Represent and solve equations and inequalities graphically.

Analyze patterns and relationships.

Write expressions in equivalent forms to solve problems.

Work with radicals and integer exponents.

Understand the relationship between zeros and factors of polynomials.

Solve systems of equations.

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

Work with addition and subtraction equations.

Solve equations and inequalities in one variable.

Interpret the structure of expressions.

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

Generate and analyze patterns.

Understand the connections between proportional relationships, lines, and linear equations.
problem_activity: Problem 1
A quadratic equation is shown below.
$${x^2=(2x-9)^2}$$
a.  Solve this equation by expanding and then factoring.
b.  Solve this equation by taking the square root of each side.
Problem 2
A physics teacher put a ball at the top of a ramp and let it roll down toward the floor. The class determined that the height of the ball could be represented by the equation
$${h=-16t^2+4}$$
, where the height,
$$h$$
, is measured in feet from the ground and time,
$$t$$
, is measured in seconds.
[IMG]
What do you notice about the structure of the quadratic expression in this problem?
In the equation, explain what the
$$4$$
represents.
Determine the time it takes for the ball to reach the floor. Interpret your solution(s) in context of the problem.


correct_option_index: 29