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

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.

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

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

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

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

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.

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.

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 reinforce the distinction between statistical and non-statistical questions. Students write a statistical question and articulate why it qualifies as statistical. Students’ explanations should focus on the variability in the data used to answer the question. The context will be used again in the next activity, so this also gets students familiar with the object.
Launch
Arrange students in groups of 3–4. Give students 1 minute of quiet work time. Then, tell students to share their question and reasoning within their group. Tell the groups to decide if each question is statistical or non-statistical. If the group disagrees, discuss the question further and revise it until an agreement is reached.
Student Facing
Clare collects bottle caps and keeps them in plastic containers.
[IMG]
Write one statistical question that someone could ask Clare about her collection. Be prepared to explain your reasoning.
Student Response
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Activity Synthesis
The purpose of the discussion is to ensure students are comfortable constructing statistical and non-statistical questions.
Ask students to share their statistical questions and reasoning. If possible, ask students to refer back to the image as they share. Record and display their responses for all to see.
To involve more students in the conversation, consider asking some of the following questions:
“Were there any questions your group had in common?”
“Were there any questions your group could not agree were statistical? Why?”
“Were there any questions your group decided were non-statistical? What made that question non-statistical?”


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