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

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.

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.

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

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.

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

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

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: Activity
After organizing the data set into a frequency table in the warm-up, students now represent the information graphically. The drawing of the plot should be fairly straightforward. The emphasis here is on using a graphical representation to study and comment on the data distribution, and to reinforce how it allows us to make observations that are difficult to make by looking at lists and tables.
As students work, identify those who describe distributions not only in terms of individual categories or values (e.g. “four people did not order any toppings”) but also characterize them in broader terms (e.g. “almost all customers in the data set ordered 2 or fewer toppings”). Invite them to share during the discussion following the activity.
Launch
Keep students in groups of 2. Give students 4–5 minutes of quiet work time and 1–2 minutes to share their responses with a partner.
Action and Expression: Develop Expression and Communication.
Invite students to talk about their ideas with a partner before writing them down. Display sentence frames to support students when they explain their ideas. For example, “I notice that . . .,” or  “I know _____ because . . .”
Supports accessibility for: Language; Organization
Student Facing
Use the tables from the warm-up to display the number of toppings as a dot plot. Label your drawing clearly.
[IMG]
Use your dot plot to study the distribution for number of toppings. What do you notice about the number of toppings that this group of customers ordered? Write 2–3 sentences summarizing your observations.
Student Response
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Student Facing
Are you ready for more?
Think of a statistical question that can be answered with the data about the number of toppings ordered, as displayed on the dot plot. Then answer this question.
Student Response
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Activity Synthesis
Display a completed dot plot for all to see. Solicit as many observations or comments about the distribution as time permits. The goal of this discussion is to allow students to hear as many ways to describe distributions as possible. Be sure to select previously identified students to make observations that succinctly capture the distributions.


correct_option_index: 1