few_shots: Example:
Problem/activity:
Problem 1
Solve using the standard algorithm. If you get stuck, use an area model and/or the partial products algorithm to help. Then assess the reasonableness of your answer.
a.
$$5,803\times46$$
b.
$$63\times2,116$$
Problem 2
Dunkin' introduced a croissant doughnut in 2014. In the first three months of its debut, they sold 7,870 dozen of them per day. How many croissant doughnuts were sold in the first three months?


Mathematical concept/skill options: 
A. Use place value understanding and properties of operations to perform multi-digit arithmetic. (A range of algorithms may be used.)
B. Understand place value.
C. Understand the place value system.
D. Extend the counting sequence.
E. Work with numbers 11–19 to gain foundations for place value.
F. Use place value understanding and properties of operations to perform multi-digit arithmetic.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
G. Perform operations with multi-digit whole numbers and with decimals to hundredths.
H. Generalize place value understanding for multi-digit whole numbers.
Grade 4 expectations in this domain are limited to whole numbers less than or equal to 1,000,000.
I. Use place value understanding and properties of operations to add and subtract.


Your response:
Thought: This set of problems asks students to perform multiplication, which is an operation, on multi-digit whole numbers.
Answer: G

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_000674

5
options: Prove geometric theorems.

Understand and apply the Pythagorean Theorem.

Make geometric constructions.

Use coordinates to prove simple geometric theorems algebraically.

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

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

Explain volume formulas and use them to solve problems.

Experiment with transformations in the plane.

Prove theorems involving similarity.

Understand and apply theorems about circles.

Apply geometric concepts in modeling situations.

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

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

Understand congruence in terms of rigid motions.

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

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

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

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

Find arc lengths and areas of sectors of circles.

Analyze, compare, create, and compose shapes.

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

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

Define trigonometric ratios and solve problems involving right triangles.

Reason with shapes and their attributes.

Understand similarity in terms of similarity transformations.

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

Apply trigonometry to general triangles.
problem_activity: Optional activity
In this activity, students compute the length of a figure that is composed of half-circles and straight line segments. For the first question, they are given the length of the line segments and the diameter of the circle. For the second question, students have to compute the diameter of the circle.
As students work, monitor for students who decomposed the figure in different ways and used different approximations of
\(\pi\)
. The discussion focuses on whether the differences lead to meaningful differences in the estimate for the distance around the track.
Launch
If desired, introduce the context of a running track. Allow students to choose what approximation to use for
\(\pi\)
. Quiet work time followed by partner discussion.
Action and Expression: Internalize Executive Functions.
Provide students with a graphic organizer to organize the information provided in the problem and to structure their problem-solving strategy. The graphic organizer should include the prompts: “What do I need to find out?”, “What do I need to do?”, and “How I solved the problem.”
Supports accessibility for: Language; Organization
Speaking, Writing: MLR5 Co-Craft Questions.
To help students understand the situation, display the image of the running track, and ask students to write down possible mathematical questions they could ask. Listen for, and amplify language students use to describe different parts of the track (inside and outside), half-circles, straight line segments, etc. Then, invite pairs to share their questions with the class. This will help students produce the language of mathematical questions, and support common understanding of the situation.
Design Principle(s): Maximize meta-awareness; Support sense-making
Student Facing
The field inside a running track is made up of a rectangle that is 84.39 m long and 73 m wide, together with a half-circle at each end.
[IMG]
What is the distance around the inside of the track? Explain or show your reasoning.
The track is 9.76 m wide all the way around. What is the distance around the outside of the track? Explain or show your reasoning.
Student Response
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for free access to Student Response.
Student Facing
Are you ready for more?
This size running track is usually called a 400-meter track. However, if a person ran as close to the “inside” as possible on the track, they would run less than 400 meters in one lap. How far away from the inside border would someone have to run to make one lap equal exactly 400 meters?
Student Response
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click here to register or sign in
for free access to Extension Student Response.
Anticipated Misconceptions
If students have trouble seeing the circle and rectangle that compose the figure, suggest that they draw additional lines to decompose the figure.
Students might apply the formula for the circumference of a circle to find the circumference of the oval-shaped field and track. If this happens, remind students that the track is not in the shape of a circle. Ask if they see a way to form a circle and a rectangle within the space.
Students who are familiar with the fact that this size track is referred to as a 400-meter track may be confused when their answer does not equal 400 meters. Explain that a runner does not run right on the edge of the track and possibly direct the student to look at the extension.
Activity Synthesis
Most of the discussion will occur in small groups. However, the whole class can debrief on the following questions:
“In what ways did you decompose the figure into different shapes?”
“Why did you choose a particular approximation for
\(\pi\)
, and what was the resulting answer?”
“How are different students’ answers related, and are they all reasonable lengths for this situation?”
Students who use more digits for their approximation of
\(\pi\)
may come up with a slightly different answer, such as 398.1. In general, when making calculations, if only an estimate is desired, then using 3.14 for
\(\pi\)
is usually good enough. In a situation like this, where the given measurements are quite precise, it can be worth trying more digits in the expansion of
\(\pi\)
, but it turns out not to make much difference in this case.


correct_option_index: 17