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, in json format:
{
  "explanation": "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: Calculate expected values and use them to solve problems.

Summarize and describe distributions.

Draw informal comparative inferences about two populations.

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

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

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

Investigate patterns of association in bivariate data.

Use probability to evaluate outcomes of decisions.

Understand and evaluate random processes underlying statistical experiments.

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

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

Interpret linear models.

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

Develop understanding of statistical variability.

Use random sampling to draw inferences about a population.
problem_activity: In Class Launch
Use after Unit 3, Lesson 9
The US Department of Education does a survey of colleges every year. Students will use this data to test a conjecture they have about colleges. Tell students that these are some of the characteristics we have information on:
college ownership: public, private non-profit, or private for-profit
average SAT scores of admitted students
acceptance rate
number of enrolled students
average cost of attendance
median earnings 10 years after graduation
Task Statement 1 has four more categories (highest degree awarded, completion rate, percent of white students, and median ACT score), which can also be included in this discussion if students will be using that task statement.
Ask students to identify what type of data each of these is (for example, categorical, percent, mean, or count). Once all the types are identified, ask "Which of these characteristics might be related to each other? How are they related?" Write down each idea for all to see. Ask students why they think a pair of categories is related in the way they propose, to increase investment in finding the answer. However, students do not need to have well-supported reasons at this time.
If students are having trouble generating ideas, or they do not bring up a wide enough variety of ideas, introduce a few more. Here are some examples:
The more selective the college is, the higher the average SAT scores of the people who are accepted.
Private for-profit colleges cost more on average, but also have a wider range of costs, because they need to make money but also attract lots of students.
Public schools are larger than private schools.
Once enough ideas have been suggested, ask “If these relationships exist, how could we see them in the data? How could we present the data to show that they’re true?” Give students quiet think time and then invite them to share one of their ideas with a partner. Then ask students to share their ideas with the class. Ensure that a variety of ways of presenting data are discussed. Here are some examples:
The more selective the college is, the higher the average SAT scores of the people who are accepted: Make a scatter plot of admission rate vs. average SAT score.
Private for-profit colleges cost more on average, but also have a wider range of costs: Make a box-and-whisker plot of costs for each type of college.
Public schools are larger than private schools: Make a two-way frequency table of school ownership (public or private) vs school size (small, medium, and large, defined by ranges of numbers of enrolled students).
Teacher Instructions
The data provided is a spreadsheet of 200 schools, not all of which have information about each of the ten categories. Students will need access to technology such as Geogebra or Excel that will allow them to analyze and display the relationships that interest them.
If desired, the complete data set can be downloaded from the Department of Education website, and data can be curated in a different way. Different categories can be chosen based on the interests of the class, or the range of colleges can be narrowed down to those in the state. Historical data is also available. A few local colleges could be compared across time. If a customized data set is created, modify the launch accordingly.
Student-Facing Statement
Here are the characteristics of colleges that we have data about:
Choose two that might be related. What do you predict the relationship between them is?
college ownership: public, private non-profit, or private for-profit
average SAT score of admitted students
acceptance rate
number of enrolled students
average cost of attendance per year
median earnings 10 years after graduation
highest degree awarded
completion rate
percent of students who self-identify as white
median ACT score of admitted students
Take a look at the data in the spreadsheet. Before calculating, do some estimation based on the data. Can you tell if your hypothesis seems reasonable?
Use an appropriate display to summarize the data.
Analyze your graph or table and do any other calculations needed. Do your results confirm your prediction? If not, what do you think explains the results?
Here are some headlines. What analysis do you think the article describes? Give some examples of evidence that would support the headline or contradict it.
“Students from Selective Colleges Tend to Succeed”
“Isolation at Larger Colleges Leads to Higher Dropout Rates”
“High Cost of Private Colleges Not Outweighed by Lifetime Earnings”
Teacher Instructions
The data provided is a spreadsheet of 100 schools for which there is information about each of the six categories. Students will need access to technology such as Geogebra or Excel that will allow them to analyze and display the relationships that interest them.
If desired, the complete data set can be downloaded from the Department of Education website, and data can be curated in a different way. Different categories can be chosen based on the interests of the class, or the range of colleges can be narrowed down to those in the state. Historical data is also available. A few local colleges could be compared across time. If a customized data set is created, modify the launch accordingly.
Student-Facing Statement
Here are the characteristics of colleges that we have data about:
Choose two that might be related. What do you predict the relationship between them is?
college ownership: public, private non-profit, or private for-profit
average SAT score of admitted students
acceptance rate
number of enrolled students
average cost of attendance per year
median earnings 10 years after graduation
Take a look at the data in the spreadsheet. Before calculating, do some estimation based on the data. Can you tell if your hypothesis seems reasonable?
Use an appropriate display to summarize the data.
Analyze your graph or table and do any other calculations needed. Do your results confirm your prediction? If not, what do you think explains the results?
Here are some headlines. What analysis do you think the article describes? Give some examples of evidence that would support the headline or contradict it.
“Students from Selective Colleges Tend to Succeed”
“Isolation at Larger Colleges Leads to Higher Dropout Rates”
“High Cost of Private Colleges Not Outweighed by Lifetime Earnings”


correct_option_index: 3

5

11