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.
Measuring the dimensions of nano-circuits requires an expensive, high-resolution microscope with integrated video camera and a computer with sophisticated imaging software, but in this activity, students measure nano-circuits using a typical classroom computer and (the free-to-download) GeoGebra geometry software. Inserting (provided) circuit pictures from a high-resolution microscope as backgrounds in GeoGebra's graphing window, students use the application's tools to measure lengths and widths of circuit elements. To simplify the conversion from the on-screen units to the real circuits' units and the manipulation of the pictures, a GeoGebra measuring interface is provided. Students export their data from GeoGebra to Microsoft® Excel® for graphing and analysis. They test the statistical significance of the difference in circuit dimensions, as well as obtain a correlation between average changes in original vs. printed circuits' widths. This activity and its associated lesson are suitable for use during the last six weeks of the AP Statistics course; see the topics and timing note below for details.
This learning video deals with a question of geometrical probability. A key idea presented is the fact that a linear equation in three dimensions produces a plane. The video focuses on random triangles that are defined by their three respective angles. These angles are chosen randomly subject to a constraint that they must sum to 180 degrees. An example of the types of in-class activities for between segments of the video is: Ask six students for numbers and make those numbers the coordinates x,y of three points. Then have the class try to figure out how to decide if the triangle with those corners is acute or obtuse.
Students act as R&D entrepreneurs, learning ways to research variables affecting the market of their proposed (hypothetical) products. They learn how to obtain numeric data using a variety of Internet tools and resources, sort and analyze the data using Excel and other software, and discover patterns and relationships that influence and guide decisions related to launching their products. First, student pairs research and collect pertinent consumer data, importing the data into spreadsheets. Then they clean, organize, chart and analyze the data to inform their product production and marketing plans. They calculate related statistics and gain proficiency in obtaining and finding relationships between variables, which is important in the work of engineers as well as for general technical literacy and decision-making. They summarize their work by suggesting product launch strategies and reporting their findings and conclusions in class presentations. A finding data tips handout, project/presentation grading rubric and alternative self-guided activity worksheet are provided. This activity is ideal for a high school statistics class.
Living in a big city like New York can be very challenging. City planning is an interdisciplinary enterprise where social scientists, humanists, psychologists, scientists, statisticians, citizens, politicians, etc. come together to offer solutions to improve quality of life in the city. To find such solutions, these people need clear and reliable (qualitative and quantitative) information about specific challenges that residents and visitors face For the variety of stakeholders in the city, many different things might be considered worthy of study, depending on their interests and needs regarding, e.g., employment, financial status, family size, healthcare, mobility, and education.
For example, do you know whether your neighborhood issufficiently protected from a fire? What about other neighborhoods in the city? To what extent does a CUNY degree help a person gain employment in the City? In which ways do race or gender or sexual preference play a role in how people experience city life? Can these be quantified in dollar terms? Once you have identified a problem, write an essay that describes a question
about city life that you believe is worthy of a statistical study.
As if they are environmental engineers, student pairs are challenged to use Google Earth Pro (free) GIS software to view and examine past data on hurricanes and tornados in order to (hypothetically) advise their state government on how to proceed with its next-year budget—to answer the question: should we reduce funding for natural disaster relief? To do this, students learn about maps, geographic information systems (GIS) and the global positioning system (GPS), and how they are used to deepen the way maps are used to examine and analyze data. Then they put their knowledge to work by using the GIS software to explore historical severe storm (tornado, hurricane) data in depth. Student pairs confer with other teams, conduct Internet research on specific storms and conclude by presenting their recommendations to the class. Students gain practice and perspective on making evidence-based decisions. A slide presentation as well as a student worksheet with instructions and questions are provided.
Students groups create scientific research posters to professionally present the results of their AQ-IQ research projects, which serves as a conclusion to the unit. (This activity is also suitable to be conducted independently from its unit—for students to make posters for any type of project they have completed.) First, students critically examine example posters to gain an understanding of what they contain and how they can be made most effective for viewers. Then they are prompted to analyze and interpret their data, including what statistics and plots to use in their posters. Finally, groups are given a guide that aids them in making their posters by suggesting all the key components one would find in any research paper or presentation. This activity is suitable for presenting final project posters to classmates or to a wider audience in a symposium or expo environment. In addition to the poster-making guide, three worksheets, six example posters, a rubric and a post-unit survey are provided.
- Physical Science
- Statistics and Probability
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- Ashley Collier
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Students learn about the role engineers and mathematicians play in developing the perfect bungee cord length by simulating and experimenting with bungee jumping using washers and rubber bands. Working as if they are engineers for a (hypothetical) amusement park, students are challenged to develop a show-stopping bungee jumping ride that is safe. To do this, they must find the maximum length of the bungee cord that permits jumpers (such as brave Washy!) to get as close to the ground as possible without going "splat"! This requires them to learn about force and displacement and run an experiment. Student teams collect and plot displacement data and calculate the slope, linear equation of the line of best fit and spring constant using Hooke's law. Students make hypotheses, interpret scatter plots looking for correlations, and consider possible sources of error. An activity worksheet, pre/post quizzes and a PowerPoint® presentation are included.
In this lesson, students learn that sound is energy and has the ability to do work. Students discover that sound is produced by a vibration and they observe soundwaves and how they travel through mediums. They understand that sound can be absorbed, reflected or transmitted. Through associated activities, videos and a PowerPoint presentation led by the teacher, students further their exploration of sound through discussions in order to build background knowledge.
Students are presented with the following challenge: their new school is under construction and the architect accidentally put the music room next to the library. Students need to design a room that will absorb the most amount of sound so that the music does not disturb the library. Students use a box as a proxy for the room need to create a design that will decrease the sound that is coming from the outside of the box. To evaluate this challenge, students use a speaker within the box and a decibel meter outside the box to measure the effectiveness of their design.
Students experiment with various ways to naturally dye materials using sources found in nature—roots, leaves, seeds, spices, etc.—as well as the method of extracting dyes. Then they analyze various materials using statistical methods and tackle an engineering design challenge—to find dyes that best suit the needs of a startup sustainable clothing company.
Students apply what they know about light polarization and attenuation (learned in the associated lesson) to design, build, test, refine and then advertise their prototypes for more effective sunglasses. Presented as a hypothetical design scenario, students act as engineers who are challenged to create improved sunglasses that reduce glare and lower light intensity while increasing eye protection from UVA and UVB radiation compared to an existing model of sunglasses—and make them as inexpensive as possible. They use a light meter to measure and compare light intensities through the commercial sunglasses and their prototype lenses. They consider the project requirements and constraints in their designs. They brainstorm and evaluate possible design ideas. They keep track of materials costs. They create and present advertisements to the class that promote the sunglasses benefits, using collected data to justify their claims. A grading rubric and reflection handout are provided.
In this module, students move from simply representing data into analysis of data. Students begin to think and reason statistically, first by recognizing a statistical question as one that can be answered by collecting data. Students learn that the data collected to answer a statistical question has a distribution that is often summarized in terms of center, variability, and shape. Throughout the module, students see and represent data distributions using dot plots and histograms. They study quantitative ways to summarize numerical data sets in relation to their context and to the shape of the distribution. As the module ends, students synthesize what they have learned as they connect the graphical, verbal, and numerical summaries to each other within situational contexts, culminating with a major project.
In this module, students begin their study of probability, learning how to interpret probabilities and how to compute probabilities in simple settings. They also learn how to estimate probabilities empirically. Probability provides a foundation for the inferential reasoning developed in the second half of this module. Additionally, students build on their knowledge of data distributions that they studied in Grade 6, compare data distributions of two or more populations, and are introduced to the idea of drawing informal inferences based on data from random samples.
Using thermometers, cotton balls, string and water, students make simple psychrometers—a tool that measures humidity. They learn the difference between relative humidity (the ratio of water vapor content to water vapor carrying capacity) and dew point (the temperature at which dew forms). Teams collect data using their homemade psychrometers and then calculate relative humidity inside and outside, comparing their results to an off-the-shelf psychrometer (if available). A lab worksheet is provided for data collection and calculation. As a real-world connection, students learn that humidity and air density is taken into consideration by engineers for many design projects. To conclude, they answer and discuss analysis and application questions.
Introductory Business Statistics is designed to meet the scope and sequence requirements of the one-semester statistics course for business, economics, and related majors. Core statistical concepts and skills have been augmented with practical business examples, scenarios, and exercises. The result is a meaningful understanding of the discipline, which will serve students in their business careers and real-world experiences.
The book "Introductory Business Statistics" by Thomas K. Tiemann explores the basic ideas behind statistics, such as populations, samples, the difference between data and information, and most importantly sampling distributions. The author covers topics including descriptive statistics and frequency distributions, normal and t-distributions, hypothesis testing, t-tests, f-tests, analysis of variance, non-parametric tests, and regression basics. Using real-world examples throughout the text, the author hopes to help students understand how statistics works, not just how to "get the right number."
Introductory Business Statistics with Interactive Spreadsheets - 1st Canadian Edition is an adaptation of Thomas K. Tiemann's book, "Introductory Business Statistics". In addition to covering basics such as populations, samples, the difference between data and information, and sampling distributions, descriptive statistics and frequency distributions, normal and t-distributions, hypothesis testing, t-tests, f-tests, analysis of variance, non-parametric tests, and regression basics, the following information has been added: the chi-square test and categorical variables, null and alternative hypotheses for the test of independence, simple linear regression model, least squares method, coefficient of determination, confidence interval for the average of the dependent variable, and prediction interval for a specific value of the dependent variable. This new edition also allows readers to learn the basic and most commonly applied statistical techniques in business in an interactive way -- when using the web version -- through interactive Excel spreadsheets. All information has been revised to reflect Canadian content.
Introductory Statistics follows scope and sequence requirements of a one-semester introduction to statistics course and is geared toward students majoring in fields other than math or engineering. The text assumes some knowledge of intermediate algebra and focuses on statistics application over theory. Introductory Statistics includes innovative practical applications that make the text relevant and accessible, as well as collaborative exercises, technology integration problems, and statistics labs.
Students learn about life-cycle assessment and how engineers use this technique to determine the environmental impact of everyday products and processes. As they examine what’s involved in making and consuming cupcakes, a snack enjoyed by millions of people every year, students learn about the production, use and disposal phases of an object’s life cycle. With the class organized into six teams, students calculate data for each phase of a cupcake’s life cycle—wet ingredients, dry ingredients, baking materials, oven baking, frosting, liner disposal—and calculate energy usage and greenhouse gases emitted from making one cupcake. They use ratios and fractions, and compare options for some of the life-cycle stages, such as different paper wrapper endings (disposal to landfills or composting) in order to make a life-cycle plan with a lower environmental impact. This activity opens students’ eyes to see the energy use in the cradle-to-grave lives of everyday products. Pre/post-quizzes, worksheets, activity cards, Excel® workbook and visual aids are provided.