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, in json format:
{
  "explanation": "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: Model periodic phenomena with trigonometric functions.

Build new functions from existing functions.

Prove and apply trigonometric identities.

Construct and compare linear and exponential models and solve problems.

Extend the domain of trigonometric functions using the unit circle.

Build a function that models a relationship between two quantities.

Analyze functions using different representations.

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

Understand the concept of a function and use function notation.

Interpret expressions for functions in terms of the situation they model.

Define, evaluate, and compare functions.

Use functions to model relationships between quantities.
problem_activity: Problem 1
Four sequences are shown below. Which one does not belong and why?
|  $${4, 8, 12, 16, 20 ...}$$  |    $${50, 46, 42, 38, 34, ...}$$    |
|------------------------------|-------------------------------------|
| $${1, 4, 16, 64, 216, ...}$$ | $${1600, 400, 100, 25, 12.5, ...}$$ |
Problem 2
Complete each sequence by filling in the missing terms. Then identify each sequence as arithmetic or geometric and name the common difference or common ratio.
a.
$${-2}$$
,
$$4$$
, ___, ___, ___,
$${28}$$
, ...
b.
$${{1\over2}}$$
, ___, ___,
$$4$$
,
$$8$$
, ___, …
c.
$$5$$
, ___, ___, ___,
$${2{1\over3}}$$
,
$${1{2\over3}}$$
, ...
d.   ___,
$$3$$
,
$${-9}$$
, ___,
$$-81$$
, ___, …
Problem 3
Write a recursive formula for each sequence.
a.
$${11, \space14,\space 17,\space 20,\space 23, …}$$
b.
$${{1\over9},\space {1\over3},\space1,\space 3,\space 9,\space …}$$
c.
$${32,\space 16,\space 8,\space 4,\space 2,\space …}$$


correct_option_index: 3

5