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

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

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.

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.

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.

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

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.

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

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.

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

Functions: students learn to define, use, and evaluate functions to model relationships between quantities.
problem_activity: Activity
In this activity, students extend their thinking about distribution shapes to using the shape to justify making a decison from a set of repesentations. In previous lessons, students matched distribution shapes to situations. Students practice applying the situations when they choose a representation and are able to eliminate the others. This activity prepares students to compare specific measures of several distribution shapes in a later lesson.
Student Facing
Restaurant A
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Restaurant B
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Restaurant C
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Restaurant D
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Each histogram represents the number of star ratings for a different restaurant. The ratings range from 0–4, with 0 representing a very poor experience and 4 representing an excellent experience. For each question, explain your reasoning.
Which restaurant do reviewers like the most?
Which restaurant do reviewers like the least?
Which restaurant received mostly mixed reviews?
Which restaurant would you choose to try?
Student Response
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Activity Synthesis
Discuss how students use the data distribution shapes to choose their answers. Here are sample questions to promote class discussion:
“How did you determine at which restaurant you would eat?” (I thought the restaurant with the highest ratings is the one at which I would want to eat.)
“How can you tell which restaurant has the best ratings?” (I can tell which one has the best ratings by looking for the histogram with the greatest frequency of 4 or 4-star ratings indicated by tall bars on the right side of the histogram.)
“How does shape influence your decisions?” (Shape influences my decisions because as I am looking for the amount of ratings, I am looking at how tall the bars are on each histogram. The skewed histograms show me that reviewers tend to agree that the restaurant is either very good or very bad. The uniform shape shows me that the restaurant has an equal amount of each rating, which might mean the experience is somewhat random. The bimodal shape shows me that reviewers are split on the restaurant, with some rating the quality very good while others are rating it as very poor.)


correct_option_index: 4