few_shots: Example:
Problem/activity:
Task
Cruz and Erica were both getting ready for soccer.
Cruz ran 1 lap around the school.
Erica ran 3 laps around the playground.
Erica said,
I ran more laps, so I ran farther.
Cruz said,
4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. My laps are much longer, so I ran farther.
Who is right? Draw a picture to help you explain your answer.


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. Develop Understanding of fractions as numbers.
Grade 3 expectations in this domain are limited to fractions with denominators 2, 3, 4, 6, and 8.
E. Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
F. 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.


Your response, in json format:
{
  "explanation": "In this problem, students learn to recognize equivalent fractions. That is, three laps around the playground is 3/12 mile, which is equivalent to 1/4, which is one lap around the school.",
  "answer": "B"
}

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_task_000212

4
options: Find arc lengths and areas of sectors of circles.

Define trigonometric ratios and solve problems involving right triangles.

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

Explain volume formulas and use them to solve problems.

Prove geometric theorems.

Understand similarity in terms of similarity transformations.

Apply trigonometry to general triangles.

Experiment with transformations in the plane.

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

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

Make geometric constructions.

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

Use coordinates to prove simple geometric theorems algebraically.

Understand and apply theorems about circles.

Understand and apply the Pythagorean Theorem.

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

Prove theorems involving similarity.

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

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).

Analyze, compare, create, and compose shapes.

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

Apply geometric concepts in modeling situations.

Understand congruence in terms of rigid motions.

Reason with shapes and their attributes.

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

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
problem_activity: Activity
This activity is comprised of two major parts: finding the total wall area to be painted and estimating needed supplies and associated costs. Students use a floor plan of a bedroom and a list of its features and measurements to calculate the room’s total wall area. They then use the square footage to make purchasing decisions and estimate costs.
Because of the variations in the bedroom’s walls and features, keeping track of the shapes to be included or excluded from the area calculation may be challenging to students. Look out for likely omissions or missed steps. For examples, students may neglect to:
Include the 3 square feet of wall space above the door.
Account for the south face of the small wall at one end of the closet. (At 0.5 feet wide and 8 feet tall, it accounts for 4 square feet of paintable surface area.)
Account for the area above or below the window.
Convert lengths to a common unit before determining area or before adding areas of different faces of the room. As students work, notice those who organize their work methodically and those who may need organizational support.
Launch
Since students may not be familiar with floor plans, consider spending a few minutes making sense of one as a class before working on the task. Display a floor plan of the classroom and identify where and how different features of the classroom (doors, windows, closets, etc.) are represented on the the plan.
Give students 2–3 minutes to read the task statement individually and to note any questions that come to mind. Afterwards, ask a couple of students to restate the task in their own words, and spend a few minutes answering any clarifying questions students may have.
Arrange students in groups of 2. Give students approximately 15 minutes of quiet think time to complete the first question (determining the total wall area to be painted). Ask students to discuss their work with their partner afterwards, and to pause for a whole-class debrief before moving on to the rest of the task.
Select a few students to share their strategies and solutions for the total wall area. Discuss any disagreements or questions in the shared calculation or approach. Make sure that the class agrees on the total square feet before instructing students to complete the rest of the task individually.
Engagement: Internalize Self Regulation.
Provide a project checklist that chunks the various steps of the project into a set of manageable tasks.
Supports accessibility for: Organization; Attention
Reading: MLR6 Three Reads.
Use this routine to help students make sense of the diagram and the accompanying text before unveiling the task questions. In the first read, students read the floor plan as well as the problem and with the goal of comprehending the situation (e.g., We need to repaint all the walls in a bedroom, except for a door and window.). In the second read, ask students to identify important quantities (e.g., The east wall is 3 yards long; the window is 5 feet long by 3 feet wide; the ceiling is 8 feet high). Use a visual display to help students make connections to the text by adding details to the floor plan. In the third read, reveal the questions and ask students to brainstorm possible solution strategies that connect to the important floor plan details and quantities they have listed. This routine supports students’ reading comprehension, without solving the problem for them.
Design Principle(s): Support sense-making; Maximize meta-awareness
Student Facing
Here is the floor plan for a bedroom:
[IMG]
Imagine you are planning to repaint all the walls in this room, including inside the closet.
The east wall is 3 yards long.
The south wall is 10 feet long but has a window, 5 feet by 3 feet, that does not need to be painted.
The west wall is 3 yards long but has a door, 7 feet tall and 3 feet wide, that does not need to be painted.
The north wall includes a closet, 6.5 feet wide, with floor-to-ceiling mirrored doors that do not need to be painted. There is, however, a smaller wall between the west wall and the closet that does need to be painted on all sides. The wall is 0.5 feet wide and extends 2 feet into the room.
The ceiling in this room is 8 feet high.
All of the corners are right angles.
If you paint all the walls in the room, how many square feet do you need to cover?
An advertisement about the paint that you want to use reads: “Just 2 quarts covers 175 square feet!” If you need to apply two coats of paint on all the walls, how much paint do you need to buy?
Paint can only be purchased in 1-quart, 1-gallon, and 5-gallon containers. How much will all supplies for the project cost if the cans of paint cost
$
10.90 for a quart,
$
34.90 for a gallon, and
$
165.00 for 5 gallons?
You have a coupon for 20% off all quart-sized paint cans. How does that affect the cost of the project?
Student Response
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Activity Synthesis
Begin by asking 1–2 students to explain their calculations on how much paint is needed. Students should see that using the total wall area alone to find the volume of paint to purchase is not going to be adequate, since two full coats are needed, and paint can only be purchased in specific quantities. How students account for these factors in their decisions and calculations may vary. For example, some students may prefer buying fewer containers of a larger quantity while others may prefer buying more containers of a smaller quantity. Some may choose to have as little extra paint as possible, while other may choose otherwise. (To have enough paint, students may choose to purchase 7 quart-sized containers, 2 gallon-sized containers, or 3 quart-sized and 1 gallon-sized containers.)
Once students have a chance to discuss the various ways students chose to purchase paint, discuss their cost estimates. Consider setting up a few ranges of costs (e.g.,
$
80–
$
84.99,
$
85–
$
89.99,
$
90–
$
94.99,
$
95–
$
99.99,
$
100 or more, etc.) and polling students on where their cost estimates land. Their estimates vary depending on the containers chosen, supplies included, and other assumptions or decisions they made.
Ask, “Can all of these values be correct?” Give students a moment of quiet think time before selecting 2–3 to respond and to share how they calculated their estimates. Record and display students’ responses to help everyone make sense of how the different costs are possible. For example, students who decided that a minimum of 7 total quarts of paint are needed may have reasoned as follows: Cost of painting supplies + cost for 1 gallon container + cost of 3 quart containers = total cost.
$
For the final question of the activity, select a student with a successful strategy to share how they applied the coupon. Consider wrapping up the activity by asking how to purchase the paint and use the coupon to get the best deal.


correct_option_index: 11