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?


Standard options: 
A. Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities. For example, “The ratio of wings to beaks in the bird house at the zoo was 2:1, because for every 2 wings there was 1 beak.” “For every vote candidate A received, candidate C received nearly three votes.”
B. Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
C. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠0, and use rate language in the context of a ratio relationship. For example, “This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.” (Expectations for unit rates in this grade are limited to non-complex fractions.)


Your response:
Thought: This problem solves a real-world problem involving mixing ingredients for cookies. A student doing this problem would need to reason about equivalent ratios of butter amounts to sugar amounts.
Answer: B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: fl_problem_000972

6
options: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.  For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
problem_activity: Problem 1
Below is the parent function of a quadratic function:
[IMG]
Given the equation in vertex form and the corresponding graph, identify the transformations to each function.
| **           Equation          ** |                             **           Graph          **                              | **           Transformation(s)          ** |
|-----------------------------------|-----------------------------------------------------------------------------------------|--------------------------------------------|
|       $${g(x)=(x+1)^2+3}$$        | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap1b.png |                                            |
|       $${r(x)=-2(x-1)^2}$$        | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap1c.png |                                            |
|        $${t(x)=(2x-1)^2}$$        | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap1d.png |                                            |
Problem 2
A quadratic equation is
decreasing over the interval
$${-\infty < x < 3}$$
increasing over the interval
$${3 < x < \infty}$$
and has a rate of change of zero at
$${x=3}$$
.
Describe how each of the three graphs below fit this description.
| .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap2a.png | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap2b.png | .. image:: https://d37su8u1z9ynie.cloudfront.net/uploads/2017/08/18/alg2_u2_l4_ap2c.png |
|-----------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------|-----------------------------------------------------------------------------------------|


correct_option_index: 2