few_shots: Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Mathematical concept/skill options: 
A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
B. Reason quantitatively and use units to solve problems.
C. Apply and extend previous understandings of numbers to the system of rational numbers.
D. Represent complex numbers and their operations on the complex plane.
E. Perform arithmetic operations with complex numbers.
F. Compute fluently with multi-digit numbers and find common factors and multiples.
G. Represent and model with vector quantities.
H. Perform operations on vectors.
I. Use properties of rational and irrational numbers.
J. Use complex numbers in polynomial identities and equations.
K. Extend the properties of exponents to rational exponents.
L. Know that there are numbers that are not rational, and approximate them by rational numbers.
M. Perform operations on matrices and use matrices in applications.
N. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.


Your response:
Thought: This problem involves understanding fractions, multiplication, and division.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001097

7
options: Understand and apply the Pythagorean Theorem.

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

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

Explain volume formulas and use them to solve problems.

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

Understand and apply theorems about circles.

Understand congruence in terms of rigid motions.

Prove theorems involving similarity.

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

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

Use coordinates to prove simple geometric theorems algebraically.

Analyze, compare, create, and compose shapes.

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

Find arc lengths and areas of sectors of circles.

Understand similarity in terms of similarity transformations.

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

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

Make geometric constructions.

Experiment with transformations in the plane.

Define trigonometric ratios and solve problems involving right triangles.

Apply trigonometry to general triangles.

Reason with shapes and their attributes.

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

Apply geometric concepts in modeling situations.

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

Prove geometric theorems.

Graph points on the coordinate plane to solve real-world and mathematical problems.
problem_activity: Problem 1
Subway has a giant sub. They cut it into eight pieces, as shown below.
[IMG]
Is this a fair share of the sub? If so, how much of the sub is each piece? If not, how would you make the share more fair?
Problem 2
Your teacher will give you some paper strips. Each strip represents 1. Fold each strip so that the parts represent each of the following:
a.   Halves
b.   Fourths
c.   Eighths
d.   Thirds
e.   Sixths
Problem 3
a.   Partition the rectangle into equal-sized parts. Shade one of the parts.
[IMG]
b.   Trade rectangles with a partner. If the whole rectangle is 1, what number represents the shaded part? Explain your reasoning.


correct_option_index: 21