few_shots: Example:
Problem/activity:
Narrative
The purpose of this activity is for students to create composite shapes and compose new shapes from composite shapes. For example, students may find that a rectangular prism can be made from four triangular prisms or from eight smaller cubes. Students then discover that they can combine two of the composed rectangular prisms to make a new rectangular prism.
Required Materials
Materials to Gather
Geoblocks
Launch
Groups of 4
Give each group geoblocks.
Display a large cube.
“This cube can be built from other shapes. See how many ways you can build a cube using other shapes.”
3 minutes: partner work time
Share responses.
Activity
“Choose a different shape. Try to find smaller shapes you can use to build that shape.”
5 minutes: partner work time
Student Response
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Activity Synthesis
Display a cube and a composite cube—for example, a cube composed of four small cubes and one rectangular prism.
Demonstrate putting the shapes together.
“What new shape did I make with the cube and the cube I made?”
“Put your shapes together to make a rectangular prism.”
Display a rectangular prism and two triangular prisms.
“Find these shapes. Put them together. What new shape can you make?” (a cube, a rectangular block)


Mathematical concept/skill options: 
A. Reason with shapes and their attributes.
B. Understand similarity in terms of similarity transformations.
C. Use coordinates to prove simple geometric theorems algebraically.
D. Translate between the geometric description and the equation for a conic section.
E. Understand congruence and similarity using physical models, transparencies, or geometry software.
F. Analyze, compare, create, and compose shapes.
G. Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).
H. Understand congruence in terms of rigid motions.
I. Classify two-dimensional figures into categories based on their properties.
J. Draw, construct, and describe geometrical figures and describe the relationships between them.
K. Explain volume formulas and use them to solve problems.
L. Prove theorems involving similarity.
M. Prove geometric theorems.
N. Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
O. Define trigonometric ratios and solve problems involving right triangles.
P. Apply trigonometry to general triangles.
Q. Visualize relationships between two-dimensional and three-dimensional objects.
R. Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
S. Make geometric constructions.
T. Apply geometric concepts in modeling situations.
U. Solve real-world and mathematical problems involving area, surface area, and volume.
V. Graph points on the coordinate plane to solve real-world and mathematical problems.
W. Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
X. Understand and apply theorems about circles.
Y. Understand and apply the Pythagorean Theorem.
Z. Experiment with transformations in the plane.
AA. Find arc lengths and areas of sectors of circles.


Your response:
A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: im_lesson_009431

1
options: Draw informal comparative inferences about two populations.

Develop understanding of statistical variability.

Understand and evaluate random processes underlying statistical experiments.

Summarize and describe distributions.

Investigate patterns of association in bivariate data.

Use random sampling to draw inferences about a population.

Summarize, represent, and interpret data on a single count or measurement variable.

Make inferences and justify conclusions from sample surveys, experiments, and observational studies.

Investigate chance processes and develop, use, and evaluate probability models.

Summarize, represent, and interpret data on two categorical and quantitative variables.

Calculate expected values and use them to solve problems.

Use the rules of probability to compute probabilities of compound events in a uniform probability model.

Interpret linear models.

Understand independence and conditional probability and use them to interpret data.

Use probability to evaluate outcomes of decisions.
problem_activity: Problem 1
You would like to know whether the number of minutes that a train is delayed correlates to the number of violent acts that occur on the platform or in the train.
Which would result in the most reliable data?
Delay trains, on purpose, by 5 minutes, 10 minutes, and 20 minutes and track the number of violent acts reported to the MBTA police. Compare this information to when the trains are not delayed.
Use data about delayed trains and look at the report data for the MBTA police—connecting the times of each.
Ask a sample of ridership about number of violent acts witnessed and ask respondents to identify the station and the approximate time these acts took place.
Which of these is an observational study, which is a survey, and which is an experiment? How do you know?
Problem 2
To determine if higher speed limits cause more traffic fatalities, researchers compared the number of traffic deaths on randomly selected stretches of highway within 65 mph speed limits to the number of traffic deaths on an equal number of randomly selected stretches of highway with 75 mph speed limits.
Problem 3
For each part below, determine 1) if the type of study described is a survey, observational study, or experimental study, and 2) if the study is good or bad, and why.
Why are students missing so much school in the district? A district administrator selects 300 student names at random from the enrollment list and sends a letter to each student’s home. The letter includes a page to be returned to their school signed by a parent or guardian. The page asks, “How many days has your student missed school this year?” and “What are the reasons for missing school on those days?”
Why are students missing so much school in the district? A district administrator chooses one of the elementary schools in the district and asks the principal to provide information about the number of absences and the excuse notes provided to the school.
Do voters in the district favor a sales tax increase of 1% to fund the parks and recreation department? A politician sends a letter to 300 voters in the district asking, “Would you pay extra money on your essential groceries to hire more government workers to plant flowers around the town?”
Do voters in the district favor a sales tax increase of 1% to fund the parks and recreation department? A politician sends a letter to 300 voters selected at random in the district asking, “Would you be in favor of a 1% increase in sales tax to fund the parks and recreation department in town?”


correct_option_index: 7