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.

Using paper, paper clips and tape, student teams design flying/falling devices to stay in the air as long as possible and land as close as possible to a given target. Student teams use the steps of the engineering design process to guide them through the initial conception, evaluation, testing and re-design stages. The activity culminates with a classroom competition and scoring to evaluate how each team's design performed.

Student teams measure voltage and current in order to determine the power output of a photovoltaic (PV) panel. They vary the resistance in a simple circuit connected to the panel to demonstrate the effects on voltage, current, and power output. After collecting data, they calculate power for each resistance setting, creating a graph of current vs. voltage, and indentifying the maximum power point.

Students use balloons (a polymer) to explore preconditioning a viscoelastic material behavior that is important to understand when designing biomedical devices. They improve their understanding of preconditioning by measuring the force needed to stretch a balloon to the same displacement multiple times. Students gain experience in data collection and graph interpretation.

Students are introduced to the physical concept of the colors of rainbows as light energy in the form of waves with distinct wavelengths, but in a different manner than traditional kaleidoscopes. Looking at different quantum dot solutions, they make observations and measurements, and graph their data. They come to understand how nanoparticles interact with absorbing photons to produce colors. They learn the dependence of particle size and color wavelength and learn about real-world applications for using these colorful liquids.

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: Jane wants to sell her Subaru Forester, but doesn’t know what the listing price should be. She checks on craigslist.com and finds 22 Subarus listed. Th...

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: Jerry forgot to plug in his laptop before he went to bed. He wants to take the laptop to his friend's house with a full battery. The pictures below sho...

Students are introduced to various types of energy with a focus on thermal energy and types of heat transfer as they are challenged to design a better travel thermos that is cost efficient, aesthetically pleasing and meets the design objective of keeping liquids hot. They base their design decisions on material properties such thermal conductivity, cost and function. These engineering and science concepts are paired with student experiences to build an understanding of heat transfer as it plays a role in their day-to-day lives. While this introduction only shows the top-level concepts surrounding the mathematics associated with heat transfer; the skills become immediately useful as students apply what they know to solve an engineering challenge.

Students build on their existing air quality knowledge and a description of a data set to each develop a hypothesis around how and why air pollutants vary on a daily and seasonal basis. Then they are guided by a worksheet through an Excel-based analysis of the data. This includes entering formulas to calculate statistics and creating plots of the data. As students complete each phase of the analysis, reflection questions guide their understanding of what new information the analysis reveals. At activity end, students evaluate their original hypotheses and “put all of the pieces together.” The activity includes one carbon dioxide worksheet/data set and one ozone worksheet/data set; providing students and/or instructors with a content option. The activity also serves as a good standalone introduction to using Excel.

Students measure the effectiveness of water filters in purifying contaminated water. They prepare test water by creating different concentrations of bleach (chlorine-contaminated) water. After passing the contaminated water through commercially available Brita® water filters designed to purify drinking water, students determine the chlorine concentration of the purified water using chlorine test strips and measure the adsorption of chlorine onto activated carbon over time. They graph and analyze their results to determine the effectiveness of the filters. The household active carbon filters used are one example of engineer-designed water purification systems.

Students use conductivity meters to measure various salt and water solutions, as indicated by the number of LEDs (light emitting diodes) that illuminate on the meter. Students create calibration curves using known amounts of table salt dissolved in water and their corresponding conductivity readings. Using their calibration curves, students estimate the total equivalent amount of salt contained in Gatorade (or other sports drinks and/or unknown salt solutions). This activity reinforces electrical engineering concepts, such as the relationship between electrical potential, current and resistance, as well as the typical circuitry components that represent these phenomena. The concept of conductors is extended to ions that are dissolved in solution to illustrate why electrolytic solutions support the passage of currents.

In addition to the associated lesson, this activity functions as a summative assessment for the Using Stress and Strain to Detect Cancer unit. In this activity, students will create a 1-D strain plot in Microsoft Excel depicting the location of a breast tumor amidst healthy tissue. The results of this activity will function as proof of the accuracy and reliability of the students' breast cancer detection design.

(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.)

En este módulo, los estudiantes reconectan y profundizan su comprensión de las estadísticas y los conceptos de probabilidad introducidos por primera vez en los grados 6, 7 y 8. Los estudiantes desarrollan un conjunto de herramientas para comprender e interpretar la variabilidad en los datos, y comienzan a tomar decisiones más informadas de los datos . Trabajan con distribuciones de datos de varias formas, centros y diferenciales. Los estudiantes se basan en su experiencia con datos cuantitativos bivariados del grado 8. Este módulo prepara el escenario para un trabajo más extenso con muestreo e inferencia en calificaciones posteriores.

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

English Description:
In this module, students reconnect with and deepen their understanding of statistics and probability concepts first introduced in Grades 6, 7, and 8. Students develop a set of tools for understanding and interpreting variability in data, and begin to make more informed decisions from data. They work with data distributions of various shapes, centers, and spreads. Students build on their experience with bivariate quantitative data from Grade 8. This module sets the stage for more extensive work with sampling and inference in later grades.

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