This is a task from the Illustrative Mathematics website that is one part of a complete illustration of the standard to which it is aligned. Each task has at least one solution and some commentary that addresses important asects of the task and its potential use. Here are the first few lines of the commentary for this task: A seven-year-old boy has a favorite treat, Super Fruity Fruit Snax. These "Fruit Snax" come in pouches of 10 snack pieces per pouch, and the pouches ar...

A full AP® Statistics curriculum that explores relevant data in social issues, economics, medicine, sports, and more. The sequence works well in conjunction with the course CED and the most widely-used AP® Statistics textbooks.

Students build a formal understanding of probability, considering complex events such as unions, intersections, and complements as well as the concept of independence and conditional probability.  The idea of using a smooth curve to model a data distribution is introduced along with using tables and technology to find areas under a normal curve.  Students make inferences and justify conclusions from sample surveys, experiments, and observational studies.  Data is used from random samples to estimate a population mean or proportion.  Students calculate margin of error and interpret it in context.  Given data from a statistical experiment, students use simulation to create a randomization distribution and use it to determine if there is a significant difference between two treatments.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

(Nota: Esta es una traducción de un recurso educativo abierto creado por el Departamento de Educación del Estado de Nueva York (NYSED) como parte del proyecto "EngageNY" en 2013. Aunque el recurso real fue traducido por personas, la siguiente descripción se tradujo del inglés original usando Google Translate para ayudar a los usuarios potenciales a decidir si se adapta a sus necesidades y puede contener errores gramaticales o lingüísticos. La descripción original en inglés también se proporciona a continuación.)

Los estudiantes crean una comprensión formal de la probabilidad, considerando eventos complejos como sindicatos, intersecciones y complementos, así como el concepto de independencia y probabilidad condicional. La idea de usar una curva suave para modelar una distribución de datos se introduce junto con el uso de tablas y tecnología para encontrar áreas bajo una curva normal. Los estudiantes hacen inferencias y justifican conclusiones de encuestas de muestra, experimentos y estudios de observación. Los datos se usan de muestras aleatorias para estimar una media o proporción de población. Los estudiantes calculan el margen de error y lo interpretan en contexto. Dados los datos de un experimento estadístico, los estudiantes usan la simulación para crear una distribución de aleatorización y lo usan para determinar si hay una diferencia significativa entre dos tratamientos.

Encuentre el resto de los recursos matemáticos de Engageny en https://archive.org/details/engageny-mathematics.

English Description:
Students build a formal understanding of probability, considering complex events such as unions, intersections, and complements as well as the concept of independence and conditional probability.  The idea of using a smooth curve to model a data distribution is introduced along with using tables and technology to find areas under a normal curve.  Students make inferences and justify conclusions from sample surveys, experiments, and observational studies.  Data is used from random samples to estimate a population mean or proportion.  Students calculate margin of error and interpret it in context.  Given data from a statistical experiment, students use simulation to create a randomization distribution and use it to determine if there is a significant difference between two treatments.

Find the rest of the EngageNY Mathematics resources at https://archive.org/details/engageny-mathematics.

Students toss coins to determine what traits a set of mouse parents possess, such as fur color, body size, heat tolerance, and running speed. Then they use coin tossing to determine the traits a mouse pup born to these parents possesses. Then they compare these physical features to features that would be most adaptive in several different environmental conditions. Finally, students consider what would happen to the mouse offspring if those environmental conditions were to change: which mice would be most likely to survive and produce the next generation?

The purpose of this task is to assess a student's ability to explain the meaning of independence in a simple context.

This lesson unit is intended to help teachers assess how well students are able to: make sense of a real life situation and decide what math to apply to the problem; understand and calculate the conditional probability of an event A, given an event B, and interpret the answer in terms of a model; represent events as a subset of a sample space using tables, tree diagrams, and Venn diagrams; and interpret the results and communicate their reasoning clearly.

Students explore the relationships between genetics, biodiversity, and evolution through a simple activity involving hypothetical wild mouse populations. First, students toss coins to determine what traits a set of mouse parents possesses, such as fur color, body size, heat tolerance, and running speed. Next they use coin tossing to determine the traits a mouse pup born to these parents possesses. These physical features are then compared to features that would be most adaptive in several different environmental conditions. Finally, students consider what would happen to the mouse offspring if those environmental conditions were to change: which mice would be most likely to survive and produce the next generation?

This lesson unit is intended to help teachers assess how well students are able to: Understand conditional probability; represent events as a subset of a sample space using tables and tree diagrams; and communicate their reasoning clearly.

This lesson unit is intended to help teachers assess how well students understand conditional probability, and, in particular, to help teachers identify and assist students who have the following difficulties: representing events as a subset of a sample space using tables and tree diagrams; and understanding when conditional probabilities are equal for particular and general situations.

The intent of clarifying statements is to provide additional guidance for educators to communicate the intent of the standard to support the future development of curricular resources and assessments aligned to the 2021 math standards.  Clarifying statements can be in the form of succinct sentences or paragraphs that attend to one of four types of clarifications: (1) Student Experiences; (2) Examples; (3) Boundaries; and (4) Connection to Math Practices.

This task uses the same situation to explore different concepts of probability theory.

This task lets students explore the concepts of probability as a fraction of outcomes, and using two-way tables of data. The special emphasis is on developing their understanding of conditional probability and independence. This task could be used as a group activity where students cooperate to formulate a plan of how to answer each question and calculate the appropriate probabilities. The task could lead to extended class discussions about the different ways of using probability to justify general claims.

This is a very open ended task. It poses the question, but the students have to formulate a plan to answer it, and use the two-way table of data to find all the necessary probabilities. The special emphasis is on developing their understanding of conditional probability and independence. This task could be used as a group activity where students cooperate to formulate a plan of how to answer the question and calculate the appropriate probabilities. The task could lead to extended class discussions about the different ways of using probability to justify general claims.

This resource is geared for teacher use. It is loosely linked to the Secondary Math II, Mathematics Vision Project curriculum.