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: Understand and evaluate random processes underlying statistical experiments.

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

Interpret linear models.

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

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

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

Investigate patterns of association in bivariate data.

Use random sampling to draw inferences about a population.

Calculate expected values and use them to solve problems.

Develop understanding of statistical variability.

Use probability to evaluate outcomes of decisions.

Draw informal comparative inferences about two populations.

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

Summarize and describe distributions.

Summarize, represent, and interpret data on a single count or measurement variable.
problem_activity: Activity
The last activity in this lesson moves one more step closer to quantifying likelihood of scenarios by ordering them individually rather than into groups. Some of the scenarios have a numerical probability expressed as a percentage, some in decimal form, some as a fraction, and some do not have a numerical probability given (MP7). This gives students the opportunity to work with probabilities expressed as percentages, decimals, and fractions.
You will need the blackline master for this activity.
Launch
Arrange students in groups of 3. Distribute one copy of the blackline master for each group.
Tell students to take turns ordering the cards by beginning with one card, then adding in additional cards one at a time before, after, or between cards as needed.
Give students 5 minutes for group work followed by a whole-class discussion.
Student Facing
Your teacher will give you some cards that describe events. Order the events from least likely to most likely.
After ordering the first set of cards, pause here so your teacher can review your work. Then, your teacher will give you a second set of cards.
Add the new set of cards to the first set so that all of the cards are ordered from least likely to most likely.
Student Response
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Anticipated Misconceptions
Students may have trouble understanding the Rock, Paper, Scissors context. Tell these students that a player randomly chooses one of the three items to play in each round. If students still struggle, tell them that each of the three items are expected to be played with equal likelihood.
Activity Synthesis
The purpose of the discussion is for students to talk about the methods they used to sort the cards and compare likelihood of different situations.
Some questions for discussion:
"How were the numerical values of the likelihoods written?" (Some were written as percentages, some as fractions, and some as decimal values.)
"How did you compare them when there was a mix of percentages, fractions, and decimals?"
"Some of the cards did not have a percentage, fraction, or decimal. How did you determine where those cards would go in the order?"
Speaking, Listening: MLR7 Compare and Connect.
Ask students to prepare a visual display of their sorted cards. Students should consider how to display their cards so that another student can interpret the reasoning behind the order they selected. Some students may wish to add notes or details to their displays to help communicate their thinking. Invite students to investigate each other’s work, ask students to compare the order between displays. Listen for and amplify any comments about the use of percentages, fractions, and decimals to compare the likelihood of different situations. Then encourage students to make connections between the various ways to quantify the likelihood of a situation. Listen for and amplify language students use to explain that the percentage, fraction, and decimal used to quantify the likelihood of the same scenario are all equivalent. This will foster students’ meta-awareness and support constructive conversations as they compare and connect quantities that represent the likelihood of a situation.
Design Principle(s): Cultivate conversation; Maximize meta-awareness


correct_option_index: 5