By measuring the spacing of fossil footprints it is possible to estimate the speed of the trackmaker, but only after making several assumptions based on footprint size and the behavior of a wide range of living animals. A widely applied method for estimating speed from trackways was developed through the research of R. McNeill Alexander, an expert in biomechanics. This lab is a group exercise designed to lead students step-by-step through the methods and principles involved in estimating speed of movement from trackway data using Alexander's method. First students test the method on humans to see how accurate it is, and then they apply it to measurements taken from a variety of dinosaur trackways. This activity involves having students collect speed and footprint data on subjects while they are running and walking. The footprint data are analyzed and the speed estimates are compared to the actual measured speeds. Students then collect trackway measurements from published illustrations of dinosaur trackways to estimate dinosaur speeds. Students calculate the percent error for their experimental estimates and use this to interpret the results obtained from dinosaur trackways. Spreadsheets may be used to record and carry out the calculations in the analysis. Students are asked to discuss the significance of their results to ongoing debates over the physical capabilities of dinosaurs.

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With printouts of typical GPS velocity vectors found near different tectonic boundaries and models of a GPS station, demonstrate how GPS work to measure ground motion.GPS velocity vectors point in the direction that a GPS station moves as the ground it is anchored to moves. The length of a velocity vector corresponds to the rate of motion. GPS velocity vectors thus provide useful information for how Earth's crust deforms in different tectonic settings.

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This lesson teaches middle and high school students to understand the architecture of GPS -- from satellites to research quality stations on the ground. This is done with physical models and a presentation. Then students learn to interpret data for the station's position through time ("time series plots"). Students represent time series data as velocity vectors and add the vectors to create a total horizontal velocity vector. They apply their skills to discover that the Mid-Atlantic Ridge is rifting Iceland. They cement and expand their understanding of GPS data with an abstraction using cars and maps. Finally, they explore GPS vectors in the context of global plate tectonics.

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Because the campuses of the University of Kansas and the University of Houston are almost directly on a N-S line we can duplicate many aspects of the classic measurement of Eratosthenese in determining the circumference of the Earth. We use a web cast (backed up by cell phones) to communicate between the two campuses in real time. We measure the shadow of a 2 m stick in both locations at the same time and then go through the math required to calculate the size of the planet.

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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.

The calculation of the d-spacings, the angles between planes and zones, the bond lengths and angles and other important geometric relationships for a mineral can be a tedious task for the student and the instructor, particularly when completed with the large assortment of trigonometric identities and algebraic formulae that are available. However, such calculations are straightforward and relatively easy to do when completed with the metrical matrix and the interactive software MATOP. Several applications of the matrix are presented here, each of which is worked out in detail and which is designed to teach its use in the study of crystal geometry.

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This document is intended to provide practical guidelines for researchers to follow when examining their data for missingness and making decisions about how to handle that missingness. We primarily offer recommendations for multiple imputation, but also indicate where the same decisional guidelines are appropriate for other types of missing data procedures such as full information maximum likelihood (FIML). Streamlining procedures to address missing data and increasing the transparency of those procedures through consensus on reporting standards is inexorably linked to the goals of open scholarship (i.e., the endeavour to improve openness, integrity, social justice, diversity, equity, inclusivity and accessibility in all areas of scholarly activities, and by extension, academic fields beyond the sciences and academic activities; Pownall et al., 2021). Successfully implementing transparent and accessible guidelines for addressing missing data is also important for Diversity, Equity, Inclusion, and Accessibility (DEIA) improvement efforts (Randall et al., 2021). Structural barriers to participation in research can lead to participants from minoritized groups disproportionately dropping out of longitudinal, developmental studies or not completing measures (Randall et al., 2021). This selection effect can bias model estimates and confidence intervals, leading to unsubstantiated claims about equitable outcomes. In addition to often creating artificially small estimates of inequalities between groups, listwise deletion also limits statistical power for minoritized groups who are already underrepresented in many datasets.

Students will examine tables of data from the 1820 Census to understand the implications of the Missouri Compromise, specifically in Maine and Missouri.

The purpose of this activity is to introduce students to the Missouri Compromise and the issues associated with the expansion of slavery in the Antebellum period of United States history. Students will begin the activity by creating a map that represents the Missouri Compromise’s impact on the United States. This map will serve as a backdrop for the activity while introducing students to political and cultural sectionalism (northern and southern states and the issue of slavery) in the early 1800s. After students complete the map, they will answer several questions using it. Students will also be prompted to examine aggregated data from the 1820 Census and a map titled “Mapping Slavery in the Nineteenth Century” to make comparisons and draw conclusions about slavery, specifically in Missouri.

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.

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.

A basic introduction to data modeling

Word Count: 2073

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Students use the STELLA program to create hierarchies of models of increasing complexity to understand the absorption of solar energy by the Earth and its radiation of that energy back to space.

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Students use a variety of tools to explore the interior of the Earth in this inquiry activity.

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Students will learn why families are important social institutions and how family structures, household sizes, and living arrangements have changed substantially since the 1970s. In part 1, students will work in groups of three to four to analyze census data so that they may understand these changes. In part 2, students will watch a clip from the show “Modern Family” and compare their observations with census data.

Methylmercury contamination within fish populations is an important toxin that affect human, animal, and environmental health, serving as a carcinogen (cancer-causing agent) and endocrine-disruptor (compounds that in some way alter the signaling of the hormone system. The impacts of exceeding safe dietary methylmercury levels were tragically made clear in Ontario, Canada, where a First Nations community in Grassy Narrows are living with the consequences of methylmercury poisoning in the fish supply. The fish were contaminated due to the dumping of mercury in the traditional waterways of the First Nation community. In 2016, there were highly publicized protests in Muskrat Falls, Labrador, Canada, where the Inuit people raised direct concerns about the potential for a proposed Nalcor Energy hydroelectric dam, to increase mercury levels in fish in those waters, which are an integral part of their traditional diet. Despite significant protests, the project was completed in 2019 and 41 km were flooded. This module uses these real-world examples as a jumping-off point for exercises that will guide case-study driven discussion on mathematical, biological and ethical concerns.

Methylmercury contamination within fish populations is an important toxin that affect human, animal, and environmental health, serving as a carcinogen (cancer-causing agent) and endocrine-disruptor (compounds that in some way alter the signaling of the hormone system. The impacts of exceeding safe dietary methylmercury levels were tragically made clear in Ontario, Canada, where a First Nations community in Grassy Narrows are living with the consequences of methylmercury poisoning in the fish supply. The fish were contaminated due to the dumping of mercury in the traditional waterways of the First Nation community. In 2016, there were highly publicized protests in Muskrat Falls, Labrador, Canada, where the Inuit people raised direct concerns about the potential for a proposed Nalcor Energy hydroelectric dam, to increase mercury levels in fish in those waters, which are an integral part of their traditional diet. Despite significant protests, the project was completed in 2019 and 41 km were flooded. This module uses these real-world examples as a jumping-off point for exercises that will guide case-study driven discussion on mathematical, biological and ethical concerns.

Students learn the physical properties of sound, how it travels and how noise impacts human health—including the quality of student learning. They learn different techniques that engineers use in industry to monitor noise level exposure and then put their knowledge to work by using a smart phone noise meter app to measure the noise level at an area of interest, such as busy roadways near the school. They devise an experimental procedure to measure sound levels in their classroom, at the source of loud noise (such as a busy road or construction site), and in between. Teams collect data using smart phones/tablets, microphones and noise apps. They calculate wave properties, including frequency, wavelength and amplitude. A PowerPoint® presentation, three worksheets and a quiz are provided.

This resource consists of a Java applet and expository text. The applet is a simulation of the Monty Hall experiment: a car is behind one door, goats are behind the other two doors. The player chooses a door and then the host opens another door. The player is given the option of switching to the remaining door. The stochastic behavior of the host and the probability of the player switching can be specified.