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, in json format:
{
  "explanation": "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: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
problem_activity: Activity
The purpose of this activity is for students to apply the formula for area of a circle to solve a problem in context. The diameter of the circle is given, so students must first determine the radius.
Launch
Display this image of table top for all to see. Ask students, “What do you notice? What do  you wonder?”
[IMG]
Quiet work time followed by a whole-class discussion.
Student Facing
Elena wants to tile the top of a circular table. The diameter of the table top is 28 inches. What is its area?
Student Response
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Student Facing
Are you ready for more?
A box contains 20 square tiles that are 2 inches on each side. How many boxes of tiles will Elena need to tile the table?
Student Response
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for free access to Extension Student Response.
Anticipated Misconceptions
Students may square the diameter, forgetting that they need to determine the radius first.
Activity Synthesis
Invite students to share their strategies for finding the area of the tabletop. After 3 students have shared their strategies, ask the class what formula all of the students used for finding the area of a circle. Record and display this formula,
\(A = \pi r^2\)
, for all to see. Here,
\(A\)
is the area of the circle, and
\(r\)
is the radius of the circle.
Engagement: Develop Effort and Persistence.
Encourage and support opportunities for peer interactions. Prior to the whole-class discussion, invite students to share their work with a partner. Display sentence frames to support student conversation such as: “First, I _____ because….”, “I noticed _____ so I….”, “Why did you...?”, and “I agree/disagree because….”
Supports accessibility for: Language; Social-emotional skills


correct_option_index: 1