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:
Thought: 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: Understand and evaluate random processes underlying statistical experiments.

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

Interpret linear models.

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

Use probability to evaluate outcomes of decisions.

Summarize and describe distributions.

Investigate patterns of association in bivariate data.

Calculate expected values and use them to solve problems.

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

Use random sampling to draw inferences about a population.

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.

Draw informal comparative inferences about two populations.

Develop understanding of statistical variability.

Make inferences and justify conclusions from sample surveys, experiments, and observational studies.
problem_activity: Problem 1
At a particular diner, everyone drinks coffee. However, some people drink their coffee with sugar, some with cream, some with both, and some with neither.
Describe the coffee preferences of the 30 people in the diner in the Venn diagram below. Be sure to label the circles appropriately.
10 people just like cream in their coffee.
13 people like sugar in their coffee; 8 of these people also like cream.
7 people like neither cream nor sugar in their coffee.
[IMG]
Problem 2
Below is a diagram that shows all of the members of the student council at a particular high school. Each member is represented by a labeled point. The students that are in circle “
$$J$$
” are juniors and the students in circle “
$$M$$
” are male.
[IMG]
Find
$$P(J)$$
.
Find
$$P(M)$$
.
Find
$$P(J \space and \space M)$$
.
Find
$$P(J \space or \space M)$$
.
Why does
$$ P(J \space or \space M)≠P(J)+P(M)$$
? Design a formula to calculate
$$P(J \space or \space M)$$
using any of the probability found in (a) through (c).


correct_option_index: 8

10