options: Counting & Cardinality: students learn to know number names and the count sequence, count to tell the number of objects, and compare numbers.

Number & Operations in Base Ten: students learn to work with the base-ten system and build place value understanding.

Operations & Algebra: students learn to solve problems using algebraic thinking and operations such as addition, subtraction, multiplication, and division. They may learn to identify and explain arithmetic patterns, evaluate or manipulate numerical expressions, and reason with equations and inequalities.

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.

Measurement & Data: students learn to work with data and measure attributes such as time, money, length, area, and volume. They may learn to compare measurements to operations and convert between different units of measure.

Number & Operations - Fractions: students learn to understand fractions as numbers and may work with them using addition, subtraction, multiplication, and division.

Statistics & Probability: students learn to analyze and produce data distributions, and build understanding of univariate and bivariate data. They learn to interpret data, make statistical inferences, justify conclusions, understand rules of probability, and use probability to make decisions.

Ratios & Proportional Relationships: students learn to recognize, describe, represent, and reason with ratios, rates, proportional relationships, and percent.

Number Systems and Quantity: students learn to understand the complex number system and reason quantitatively.

Geometry: students learn to classify geometric figures by their properties, and understand and compare the relationships between them. Students develop and use formulas to compute lengths, areas, and volumes, and they use transformations to generate new shapes and compare existing ones. Geometry can be studied with and without coordinates.

Modeling: students learn to choose and use appropriate mathematics and statistics to analyze real-world empirical situations, improve decisions, and report on their conclusions and the reasoning behind them.
problem_activity: Warm-up
The purpose of this warm-up is to elicit the idea that an increase in sample size is associated with a decrease in margin of error, which will be useful when students investigate the relationship between margin of error and sample size in a later activity. While students may notice and wonder many things about these images, the relationship between sample size and margin of error is the important discussion point. This prompt gives students opportunities to see and make use of structure (MP7). The specific structure they might notice is that the margin of error decreases as the sample size increases.
Launch
Tell students that their job is to think of at least one thing they notice and at least one thing they wonder. Display the table for all to see. Give students 1 minute of quiet think time, and then 1 minute to discuss the things they notice with their partner, followed by a whole-class discussion.
Student Facing
Five students wanted to see how many children’s movies have female lead characters. They each took a sample of children’s movies, found the proportion of movies that had female lead characters, then used their results to simulate 100 additional samples. The table shows some of the findings based on the original sample and the simulations.
What do you notice? What do you wonder?
{"table": [{"_attributes": {"border": "1"}, "thead": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "_value": "student"}, {"_attributes": {"scope": "col"}, "_value": "number of movies used in the original random sample"}, {"_attributes": {"scope": "col"}, "_value": "estimated proportion"}, {"_attributes": {"scope": "col"}, "_value": "margin of error"}]}]}], "tbody": [{"tr": [{"th": [{"_attributes": {"scope": "row"}, "_value": "A"}], "td": [{"_value": "20"}, {"_value": "0.273"}, {"_value": "0.204"}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "B"}], "td": [{"_value": "20"}, {"_value": "0.205"}, {"_value": "0.189"}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "C"}], "td": [{"_value": "30"}, {"_value": "0.280"}, {"_value": "0.180"}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "D"}], "td": [{"_value": "30"}, {"_value": "0.232"}, {"_value": "0.157"}]}, {"th": [{"_attributes": {"scope": "row"}, "_value": "E"}], "td": [{"_value": "50"}, {"_value": "0.205"}, {"_value": "0.115"}]}]}]}]}
Student Response
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Activity Synthesis
The purpose of the discussion is to notice that the margin of error tends to decrease when a greater number of things are used in the sample. Ask students to share the things they noticed and wondered. Record and display their responses for all to see. If possible, record the relevant reasoning on or near the table. After all responses have been recorded without commentary or editing, ask students, “Is there anything on this list that you are wondering about?” Encourage students to respectfully disagree, ask for clarification or point out contradicting information. If the relationship between the margin of error and sample size does not come up during the conversation, ask students to discuss this idea.


correct_option_index: 6