Engineers create and use new materials, as well as new combinations of existing materials to design innovative new products and technologies—all based upon the chemical and physical properties of given substances. In this activity, students act as materials engineers as they learn about and use chemical and physical properties including tessellated geometric designs and shape to build better smartphone cases. Guided by the steps of the engineering design process, they analyze various materials and substances for their properties, design/test/improve a prototype model, and create a dot plot of their prototype testing results.

This lesson is about the estimation of the value of Pi. Based on previous knowledge, the students try to estimate Pi value using different methods, such as: direct physical measurements; a geometric probability model; and computer technology. This lesson is designed to stimulate the learning interests of students, to enrich their experience of solving practical problems, and to develop their critical thinking ability. To understand this lesson, students should have some mathematic knowledge about circles, coordinate systems, and geometric probability. They may also need to know something about Excel. To estimate Pi value by direct physical measurements, the students can use any round or cylindrical shaped objects around them, such as round cups or water bottles. When estimating Pi value by a geometric probability model, a dartboard and darts should be prepared before the class. You can also use other games to substitute the dart throwing game. For example, you can throw marbles to the target drawn on the floor. This lesson is about 45-50 minutes. If the students know little about Excel, the teacher may need one more lesson to explain and demonstrate how to use the computer to estimate Pi value. Downloadable from the website is a video demonstration about how to use Excel for estimating Pi.

Students measure and analyze forces that act on vehicles pulling heavy objects while moving at a constant speed on a frictional surface. They study how the cars interact with their environments through forces, and discover which parameters in the design of the cars and environments could be altered to improve vehicles' pulling power. This LEGO® MINDSTORMS® based activity is geared towards, but not limited to, physics students.

In this lesson, students will learn how great navigators of the past stayed on course that is, the historical methods of navigation. The concepts of dead reckoning and celestial navigation are discussed.

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.

Student teams design, build and test small-sized gliders to maximize flight distance and an aerodynamic ratio, applying their knowledge of fluid dynamics to its role in flight. Students experience the entire engineering design process, from brainstorming to CAD (or by hand) drafting, including researching (physics of aerodynamics and glider components that take advantage of that science), creating materials lists, constructing, testing and evaluating—all within constraints (works with a launcher, budget limitation, maximizing flight distance to mass ratio), and concluding with a summary final report. Numerous handouts and rubrics are provided.

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 video motion capture technology, becoming familiar with concepts such as vector components, magnitudes and directions, position, velocity, and acceleration. They use a (free) classroom data collection and processing tool—the ARK Mirror—to visualize and record 3-D motion. The Augmented Reality Kinematics (ARK) Mirror software collects data via a motion detector. Using an Orbbec Astra Pro 3D camera or Microsoft Kinect (see note below), students can visualize and record a robust set of data and interpret them using statistical and graphical methods. This lesson introduces students to just one possible application of the ARK Mirror software—in the context of a high school physics class. Note: The ARK Mirror is ported to operate on an Orbbec platform. It may also be used with a Microsoft Kinect, although that Microsoft hardware has been discontinued. Refer to the Using ARK Mirror and Microsoft Kinect attachment for how to use the ARK MIrror software with Microsoft Kinect.

This learning video addresses a particular problem of selection bias, a statistical bias in which there is an error in choosing the individuals or groups to make broader inferences. Rather than delve into this broad topic via formal statistics, we investigate how it may appear in our everyday lives, sometimes distorting our perceptions of people, places and events, unless we are careful. When people are picked at random from two groups of different sizes, most of those selected usually come from the bigger group. That means we will hear more about the experience of the bigger group than that of the smaller one. This isn't always a bad thing, but it isn't always a good thing either. Because big groups ''speak louder,'' we have to be careful when we write mathematical formulas about what happened in the two groups. We think about this issue in this video, with examples that involve theaters, buses, and lemons. The prerequisite for this video lesson is a familiarity with algebra. It will take about one hour to complete, and the only materials needed are a blackboard and chalk.

Students design a cooler and monitor the effectiveness of its ability to keep a bottle of ice water cold in comparison to a bottle of ice water left at room temperature. Students have the opportunity to brainstorm a design of their cooler and its attributes. They then choose from the materials provided to create a prototype. They have the opportunity to test their prototype by measuring the room temperature, the starting temperature of the water and graphing and monitoring the change in temperature over increments time in comparison to the room temperature water.

Students learn how roadways are designed and constructed, and discuss the advantages and limitations of the current roadway construction process. They look at current practices of roadway monitoring, discuss the limitations, and consider ways to further road monitoring research. To conclude, student groups compete to design smooth, cost-efficient and sound model road bases using gravel, sand, water and rubber (representing asphalt). This lesson prepares students for the associated activity in which they act as civil engineers hired by USDOT to research through their own model experimentation how to best use piezoelectric materials to detect road damage by showing how piezoelectric transducers can indicate road damage.

Up to this point in Grade K, students have worked intensively within 10 and have often counted to 30 using the Rekenrek during fluency practice. This work sets the stage for this module where students clarify the meaning of the 10 ones and some ones within a teen number and extend that understanding to count to 100.

Module 1 of the Kindergarten curriculum in A Story of Units.  In Topics A and B, classification activities allow students to analyze and observe their world and articulate their observations.  Reasoning and dialogue begin immediately.  In Topics C, D, E, and F, students order, count, and write up to ten objects to answer “how many?” questions from linear, to array, to circular, and finally to scattered configurations wherein they must devise a path through the objects as they count.  In Topics G and H, students use their understanding of relationships between numbers and know that each successive number name refers to a quantity that is one greater and that the number before is one less.

Students use a LEGO® ball shooter to demonstrate and analyze the motion of a projectile through use of a line graph. This activity involves using a method of data organization and trend observation with respect to dynamic experimentation with a complex machine. Also, the topic of line data graphing is covered. The main objective is to introduce students graphs in terms of observing and demonstrating their usefulness in scientific and engineering inquiries. During the activity, students point out trends in the data and the overall relationship that can be deduced from plotting data derived from test trials with the ball shooter.

The learning of linear functions is pervasive in most algebra classrooms. Linear functions are vital in laying the foundation for understanding the concept of modeling. This unit gives students the opportunity to make use of linear models in order to make predictions based on real-world data, and see how engineers address incredible and important design challenges through the use of linear modeling. Student groups act as engineering teams by conducting experiments to collect data and model the relationship between the wall thickness of the latex tubes and their corresponding strength under pressure (to the point of explosion). Students learn to graph variables with linear relationships and use collected data from their designed experiment to make important decisions regarding the feasibility of hydraulic systems in hybrid vehicles and the necessary tube size to make it viable.

Students explore in detail how the Romans built aqueducts using arches—and the geometry involved in doing so. Building on what they learned in the associated lesson about how innovative Roman arches enabled the creation of magnificent structures such as aqueducts, students use trigonometry to complete worksheet problem calculations to determine semicircular arch construction details using trapezoidal-shaped and cube-shaped blocks. Then student groups use hot glue and half-inch wooden cube blocks to build model aqueducts, doing all the calculations to design and build the arches necessary to support a water-carrying channel over a three-foot span. They calculate the slope of the small-sized aqueduct based on what was typical for Roman aqueducts at the time, aiming to construct the ideal slope over a specified distance in order to achieve a water flow that is not spilling over or stagnant. They test their model aqueducts with water and then reflect on their performance.