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: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

Explain and use the relationship between the sine and cosine of complementary angles.

Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
problem_activity: Problem 1
Brandon and Madison use different triangles to determine the slope of the line shown below.
[IMG]
Brandon started at (0,-1) and drew a right triangle going up 2 units and right 3 units.
Madison started at (-3,-3) and drew a right triangle going up 6 units and right 9 units.
Draw and label both triangles on the graph.
How can Brandon and Madison use their triangles to find the slope?
What trigonometric ratio do Brandon and Madison use to find the slope?
Problem 2
Below is a line segment on a coordinate grid.
[IMG]
Draw the right triangle that you can use to find the length of this line segment.
Find the length of the line segment.
Find the measure of all of the angles of the triangle formed.
Problem 3
Standing on the gallery of a lighthouse (the deck at the top of a lighthouse), a person spots a ship at an angle of depression of 20°. The lighthouse is 28 meters tall and sits on a cliff 45 meters tall as measured from sea level.  What is the horizontal distance between the lighthouse and the ship?


correct_option_index: 0