few_shots: Example:
Problem/activity:
Stage 1: Money
Required Preparation
Materials to Copy
Blackline Masters
Would You Rather Stage 1 Spinner
Would You Rather Stage 1 Recording Sheet

Narrative
The first partner spins to get a group of coins. They write a question that compares the amount they spun to a different group of coins that they make up.


Mathematical concept/skill options: 
A. Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
B. Represent and interpret data.
C. Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
D. Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
E. Describe and compare measurable attributes.
F. Geometric measurement: understand concepts of angle and measure angles.
G. Convert like measurement units within a given measurement system.
H. Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
I. Measure and estimate lengths in standard units.
J. Classify objects and count the number of objects in each category.
K. Tell and write time.
L. Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
M. Measure lengths indirectly and by iterating length units.
N. Work with time and money.
O. Relate addition and subtraction to length.


Your response:
Thought: In this problem, students work with money in the form of coins.
Answer: N

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_center_000269

2
options: Analyze, compare, create, and compose shapes.

Prove geometric theorems.

Understand and apply the Pythagorean Theorem.

Define trigonometric ratios and solve problems involving right triangles.

Translate between the geometric description and the equation for a conic section.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Apply geometric concepts in modeling situations.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Use coordinates to prove simple geometric theorems algebraically.

Solve real-world and mathematical problems involving area, surface area, and volume.

Understand and apply theorems about circles.

Visualize relationships between two-dimensional and three-dimensional objects.

Understand similarity in terms of similarity transformations.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Make geometric constructions.

Prove theorems involving similarity.

Understand congruence in terms of rigid motions.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Reason with shapes and their attributes.

Explain volume formulas and use them to solve problems.

Experiment with transformations in the plane.

Draw, construct, and describe geometrical figures and describe the relationships between them.

Apply trigonometry to general triangles.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Find arc lengths and areas of sectors of circles.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Classify two-dimensional figures into categories based on their properties.
problem_activity: Task
The King of Syracuse reportedly requested Archimedes' advice for determining
if a crown was made with the appropriate mixture of gold and silver.   Archimedes
devised a method requiring the following measurements:
the volume $V$ of water displaced by the crown when it is submerged
in water,
the volume $V_1$ of water displaced by an equal mass (that is, equal to the
mass of the crown)  of gold when
submerged in the water,
the volume $V_2$ of water displaced by an equal mass of silver when
submerged in water.
How much water would a solid gold crown displace?  What about a solid
silver crown?  What if the crown is half gold (by volume) and half silver (by volume)?
If $p$ denotes the percentage of the crown, by volume, which comes from
gold, how much water will the crown displace?
Show that Archimedes' method can always determine the percentage of gold in the crown from its mass and volume.


correct_option_index: 6