few_shots: Example:
Problem/activity:
Task
Materials
One 10-frame per pair of students (see example below)
[IMG]
Counters, 10 per pair of students
Decks of number cards 0-5 (with 4 of each number) or two 0-5 dice
Setup
This activity is done in pairs. The students sit side by side with 10-frame and deck of cards or dice. If they have cards, the cards are shuffled and placed face down in front of them.
Action
Player 1 flips a card or rolls the die. They place that many counters on the 10-frame. Player 2 flips a card or rolls the die. They place that many more counters on the 10-frame next to the counters already on the ten frame. The students count the total together.
A recording sheet can be added when the students have been introduced to equations and number sentences. For those students who can handle higher numbers, a deck of 0-10 cards and two 10-frames can be used.
This game can also be played alone.


Mathematical concept/skill options: 
A. Write and interpret numerical expressions.
B. Generate and analyze patterns.
C. Analyze patterns and relationships.
D. Use properties of operations to generate equivalent expressions.
E. Use the four operations with whole numbers to solve problems.
F. Work with radicals and integer exponents.
G. Solve systems of equations.
H. Represent and solve problems involving multiplication and division.
I. Perform arithmetic operations on polynomials.
J. Understand the relationship between zeros and factors of polynomials.
K. Understand properties of multiplication and the relationship between multiplication and division.
L. Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
M. Solve problems involving the four operations, and identify and explain patterns in arithmetic.
N. Use polynomial identities to solve problems.
O. Apply and extend previous understandings of arithmetic to algebraic expressions.
P. Rewrite rational expressions.
Q. Interpret the structure of expressions.
R. Add and subtract within 20.
S. Analyze and solve linear equations and pairs of simultaneous linear equations.
T. Represent and analyze quantitative relationships between dependent and independent variables.
U. Solve equations and inequalities in one variable.
V. Create equations that describe numbers or relationships
W. Reason about and solve one-variable equations and inequalities.
X. Represent and solve equations and inequalities graphically.
Y. Understand solving equations as a process of reasoning and explain the reasoning.
Z. Understand and apply properties of operations and the relationship between addition and subtraction.
AA. Gain familiarity with factors and multiples.
AB. Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.
AC. Work with addition and subtraction equations.
AD. Multiply and divide within 100.
AE. Work with equal groups of objects to gain foundations for multiplication.
AF. Represent and solve problems involving addition and subtraction.
AG. Write expressions in equivalent forms to solve problems.
AH. Understand the connections between proportional relationships, lines, and linear equations.


Your response, in json format:
{
  "explanation": "This task teaches students to understand addition as putting together counters, or adding to already placed counters.",
  "answer": "AB"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_001477

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

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

Use coordinates to prove simple geometric theorems algebraically.

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

Make geometric constructions.

Explain volume formulas and use them to solve problems.

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

Prove theorems involving similarity.

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

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

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

Understand similarity in terms of similarity transformations.

Understand congruence in terms of rigid motions.

Analyze, compare, create, and compose shapes.

Find arc lengths and areas of sectors of circles.

Apply geometric concepts in modeling situations.

Reason with shapes and their attributes.

Understand and apply the Pythagorean Theorem.

Experiment with transformations in the plane.

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

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

Classify two-dimensional figures into categories based on their properties.

Understand and apply theorems about circles.

Prove geometric theorems.

Define trigonometric ratios and solve problems involving right triangles.

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

Apply trigonometry to general triangles.
problem_activity: Warm-up
In this warm-up, students reason about the volume and dimensions of a cylinder based on information given about a sphere of the same height. The purpose of this warm-up is for students to recognize when they do not have enough information to reach a single answer. While they can determine the height of the cylinder, the radius is completely undefined, which means the volume of the cylinder could be anything.
Launch
Give students quiet work time followed by a whole-class discussion.
Student Facing
A cylinder and sphere have the same height.
If the sphere has a volume of
\(36\pi\)
cubic units, what is the height of the cylinder?
What is a possible volume for the cylinder? Be prepared to explain your reasoning.
Student Response
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Anticipated Misconceptions
Some students may not understand why the second problem talks about “possible” volumes if they assume the radius of the cylinder is the same as the sphere. Ask these students to explain how they found the radius of the cylinder to help them notice that the problem never gives that information.
Activity Synthesis
Ask students to share how they calculated the height of the cylinder. If any students made a sketch, display these for all to see.
Select at least 5 students to give a possible volume for the cylinder and record these for all to see. Ask students,
“Why do we not know what the volume of the cylinder is?” (We don’t know the radius, only the height, so the volume could be anything.)
“Is knowing the height of a sphere enough information to determine the volume?” (Yes. The volume of a sphere is based on the radius, which is half the height.)
Tell students that in the next activity, they will investigate how changes to the radius of a sphere changes the volume of the sphere.


correct_option_index: 10