few_shots: Example:
Problem/activity:
Task
 Arrange the fractions in order from least to greatest. Explain your answer with a picture.
 $\frac{1}{5}, \frac{1}{7}, \frac{1}{3} $
 $\frac{2}{5}, \frac{2}{7}, \frac{2}{3} $
 $\frac{5}{6}, \frac{3}{6}, \frac{1}{6} $
 $\frac{5}{12}, \frac{8}{12}, \frac{4}{12} $

Mathematical concept/skill options: 
A. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
C. Use equivalent fractions as a strategy to add and subtract fractions.
D. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
E. Understand decimal notation for fractions, and compare decimal fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
F. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.


Your response:
Thought: This problem involves understanding fractions as numbers by comparing their quantities.
Answer: F

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_000157

3
options: Reason with shapes and their attributes.

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

Prove geometric theorems.

Experiment with transformations in the plane.

Apply trigonometry to general triangles.

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

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

Make geometric constructions.

Understand and apply the Pythagorean Theorem.

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

Understand similarity in terms of similarity transformations.

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

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

Understand and apply theorems about circles.

Analyze, compare, create, and compose shapes.

Prove theorems involving similarity.

Use coordinates to prove simple geometric theorems algebraically.

Explain volume formulas and use them to solve problems.

Define trigonometric ratios and solve problems involving right triangles.

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

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

Apply geometric concepts in modeling situations.

Understand congruence in terms of rigid motions.

Find arc lengths and areas of sectors of circles.

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

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

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
problem_activity: Optional activity
In this Fermi problem, students estimate the total volume occupied by all of the breakfast cereal purchased in a year in the United States.
Monitor for different approaches to solving the problem, and select students to share during the discussion. In particular, look for:
A range of estimates
Different levels of precision in reporting the final estimate
Different arrangements of boxes
Launch
Arrange students in groups of 1–4. Provide access to four-function calculators. If students are doing their own research, provide access to internet-enabled devices. If conducting a gallery walk at the end, provide access to tools for making a visual display.
Before starting, ask students to come up with a guess about the answer and poll the class. Record all guesses.
Ask students to brainstorm the information they need to answer the question. Give the information provided when students ask for it, or provide access to internet-enabled devices so that students can find the information they need.
Vital information to have on hand includes:
Every year, people in the U.S. buy 2.7 billion boxes of breakfast cereal.
A “typical” cereal box has dimensions of 2.5 inches by 7.75 inches by 11.75 inches.
Representation: Internalize Comprehension.
Represent the same information through different modalities by using physical objects to represent abstract concepts. Some students may benefit by starting with an image, video, or a typical size cereal box to support visualization.
Supports accessibility for: Conceptual processing; Visual-spatial processing
Student Facing
Imagine a warehouse that has a rectangular floor and that contains all of the boxes of breakfast cereal bought in the United States in one year.
If the warehouse is 10 feet tall, what could the side lengths of the floor be?
Student Response
Teachers with a valid work email address can
click here to register or sign in
for free access to Student Response.
Anticipated Misconceptions
Students may not think about
how
the boxes are packed. That is, they may make a volume calculation and then perform division. (Ask these students to think about how the boxes are placed in the warehouse.)
Students may struggle with unit conversions. (Encourage them to go step by step: How many inches are in a foot? How many square inches are in a square foot? How many cubic inches are in a cubic foot?)
Activity Synthesis
Invite students or groups to share different solution approaches. Consider asking students to create a visual display and conducting a gallery walk. Highlight strategies that include keeping careful track of the information used including:
What is the volume of each box?
How are the boxes arranged for storage?
How are the dimensions of the warehouse floor determined?
Make sure to discuss why different people have different estimates.
Some students may just calculate volume and not think of how the boxes are packed. (This is OK as the amount of empty space will not be large unless the boxes are placed haphazardly.)
Students may place the boxes in a different way.
Students may or may not take account of the small amount of space in the warehouse that is not filled by the boxes.
There are an infinite number of rectangles with suitable area to serve as the floor of the warehouse. Note, however, that having an appropriate area (e.g., 36,000,000 square feet) is
not
sufficient. For example, we could not have a warehouse that is 1 inch wide and 432,000,000 feet long. In general, if one of the dimensions is too small, it increases the amount of wasted space.


correct_option_index: 5