few_shots: Example:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
[IMG]
Counters, 10 per pair of students
Decks of number cards 0-5 (with 4 of each number) or two 0-5 dice
Setup
This activity is done in pairs. The students sit side by side with 10-frame and deck of cards or dice. If they have cards, the cards are shuffled and placed face down in front of them.
Action
Player 1 flips a card or rolls the die. They place that many counters on the 10-frame. Player 2 flips a card or rolls the die. They place that many more counters on the 10-frame next to the counters already on the ten frame. The students count the total together.
A recording sheet can be added when the students have been introduced to equations and number sentences. For those students who can handle higher numbers, a deck of 0-10 cards and two 10-frames can be used.
This game can also be played alone.


Mathematical concept/skill options: 
A. Write and interpret numerical expressions.
B. Generate and analyze patterns.
C. Analyze patterns and relationships.
D. Use properties of operations to generate equivalent expressions.
E. Use the four operations with whole numbers to solve problems.
F. Work with radicals and integer exponents.
G. Solve systems of equations.
H. Represent and solve problems involving multiplication and division.
I. Perform arithmetic operations on polynomials.
J. Understand the relationship between zeros and factors of polynomials.
K. Understand properties of multiplication and the relationship between multiplication and division.
L. Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
M. Solve problems involving the four operations, and identify and explain patterns in arithmetic.
N. Use polynomial identities to solve problems.
O. Apply and extend previous understandings of arithmetic to algebraic expressions.
P. Rewrite rational expressions.
Q. Interpret the structure of expressions.
R. Add and subtract within 20.
S. Analyze and solve linear equations and pairs of simultaneous linear equations.
T. Represent and analyze quantitative relationships between dependent and independent variables.
U. Solve equations and inequalities in one variable.
V. Create equations that describe numbers or relationships
W. Reason about and solve one-variable equations and inequalities.
X. Represent and solve equations and inequalities graphically.
Y. Understand solving equations as a process of reasoning and explain the reasoning.
Z. Understand and apply properties of operations and the relationship between addition and subtraction.
AA. Gain familiarity with factors and multiples.
AB. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
AC. Work with addition and subtraction equations.
AD. Multiply and divide within 100.
AE. Work with equal groups of objects to gain foundations for multiplication.
AF. Represent and solve problems involving addition and subtraction.
AG. Write expressions in equivalent forms to solve problems.
AH. Understand the connections between proportional relationships, lines, and linear equations.


Your response:
AB

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_001477

K
options: Extend the domain of trigonometric functions using the unit circle.

Understand the concept of a function and use function notation.

Prove and apply trigonometric identities.

Interpret functions that arise in applications in terms of the context.

Analyze functions using different representations.

Build a function that models a relationship between two quantities.

Model periodic phenomena with trigonometric functions.

Define, evaluate, and compare functions.

Build new functions from existing functions.

Use functions to model relationships between quantities.

Construct and compare linear and exponential models and solve problems.

Interpret expressions for functions in terms of the situation they model.
problem_activity: Problem 1
A ball is thrown straight up from the top of a
$${48}$$
-foot tall building with an initial speed of
$${32}$$
feet per second. The height of the ball as a function of time can be modeled by the function
$$h(t)=-16t^2+{32}t+{48}$$
. Below is a graph and table of the function.
[IMG]
a. What are the solutions to this function? Interpret each solution in context of the situation.
b. What is the vertex of this function? Interpret the vertex in context of the situation.
Problem 2
The table below represents the value of Andrew’s stock portfolio, where
$$V$$
represents the value of the portfolio in hundreds of dollars and
$$t$$
is the time in months since he started investing. Answer the questions that follow based on the table of values.
| $$t$$                    (months) | $$V(t)$$                    (hundreds of dollars) |
|-----------------------------------|---------------------------------------------------|
|                 2                 |                        325                        |
|                 4                 |                        385                        |
|                 6                 |                        405                        |
|                 8                 |                        385                        |
|                10                 |                        325                        |
|                12                 |                        225                        |
|                14                 |                        85                         |
|                16                 |                        -95                        |
|                18                 |                       -315                        |
Assuming this data is quadratic, how much did Andrew invest in his stock initially? Explain how you arrived at this answer.
What is the maximum value of his stock and how long did it take to reach the maximum value?
After approximately how many months is Andrew’s stock portfolio valued at $0?
How fast is Andrew’s stock value decreasing between months 10 and 12? Find a two-month interval where the average rate of change is faster than it is between months 10 and 12 and explain why.
Problem 3
John is building a small rectangular pen for chickens. He wants the length to be 6 more feet than twice the width.
If the area of the pen is 36 square feet, what are the dimensions of the pen in feet?


correct_option_index: 3

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