The purpose of the task is to explicitly identify a common error made by many students, when they make use of the "identity" f(x+h)=f(x)+f(h). A function f cannot in general be distributed over a sum of inputs.

This activity is an inquiry based field investigation where students measure and map a small stream and then develop an understanding of the formation of a variety of small stream features.

This activity is a teacher-guided inquiry activity of the sorting or grouping of Minnesota critters according to student driven criteria or purpose of their groupings. Teacher/student questions and discussion should be encouraged after this activity to emphasize that awareness of the criteria or purpose of certain groupings may be important before beginning an investigation.

Students focus on the testing phase of the design process by considering how they have tested computer programs in the past and learning about a new method called JUnit to test programs in the future. JUnit is a testing method that is included with NetBeans (Java) installs or can be downloaded from the web and included in the Java build. Students design tests using JUnit and implement those tests.

Learning Assistants are used to facilitate student discussion in peer instruction during clicker questions (i.e., classroom response systems), by asking Socratic questions, emphasizing reasoning, and probing student thinking.

This unit on nanoparticles engages students with a hypothetical Grand Challenge Question that asks about the skin cancer risk for someone living in Australia, given the local UV index and the condition of the region's ozone layer. The question asks how nanoparticles might be used to help detect, treat and protect people from skin cancer. Through three lessons, students learn about the science of electromagnetic radiation and energy waves, human skin and its response to ultraviolet radiation, and the state of medical nanotechnology related to skin cancer. Through three hands-on activities, students perform flame tests to become familiar with the transfer of energy in quantum form, design and conduct their own quality-control experiments to test sun protection factors (SPFs), and write nanotechnology grant proposals.

A variation of the think-pair-share technique is used to reinforce understanding of the income and substitution effects associated with a price change.

This is a guided inquiry investigation where students record and gather visual information of what the moon phases look like.

This activity demonstrates geo-demographic consumer segment lifestyle consumption patterns. The information available on the site is relevant to segmentation and targeting strategies used by marketers.

Labs and tutorials that use equipment such as circuits can be modified to use PhET simulations instead. Research shows that substituting the PhET Circuit Construction Kit simulation for real equipment in a variety of contexts leads to improved conceptual learning in the best cases, and the same conceptual learning in the worst cases. There are many advantages to using PhET simulations over real equipment: They are easy to use, so students can play around and modify the experiment quickly and easily without fear of breaking the equipment. They have productive constraints to focus attention on the most important aspects of the experiment (e.g. bulb brightness and current flow) rather than on irrelevant aspects (e.g. wire color and length). Finally, if real equipment is not available, PhET simulations provide the opportunity to do multiple experiments with a single piece of equipment: a computer.

These labs provide examples of using very open-ended questions to guide students in exploring a simulation and designing their own experiments. These labs can lead to a high level of quantitative thinking about data analysis.

This task highlights a slightly different aspect of place value as it relates to decimal notation. More than simply being comfortable with decimal notation, the point is for students to be able to move fluidly between and among the different ways that a single value can be represented and to understand the relative size of the numbers in each place.

An inquiry activity for students to test physical properties of several compounds to analyze data and determine if the compound is ionic or covalent. This is ideal for an introduction to ionic and molecular compound nomenclature.

Students use authentic spectral data from the Cassini mission of Saturn and Saturn's moon, Titan, gathered by instrumentation developed by engineers. Taking these unknown data, and comparing it with known data, students determine the chemical composition of Saturn's rings and Titan's atmosphere.

In this individual research project, a senior thesis student conducts a regression analysis that explores whether high school GPA or standardized test scores are better predictors of the cumulative GPAs of college graduates at her own university. The data are easily obtainable from the Office of Institutional Research. The project can be modified to be a group research project in a Research Methods Class or a Special Topics Upper Level Economics class.

Students use the spectrograph from the "Building a Fancy Spectrograph" activity to gather data about different light sources. Using the data, they make comparisons between the light sources and make conjectures about the composition of these sources.

Students will utilize an applet to further expand their knowledge of confidence intervals.

This visualization activity combines student data collection with the use of an applet to enhance the understanding of the distributions of mean square treatment (MST), mean square error (MSE) as well as their ratio, an F-distribution. Students will see theoretical distributions of the mean square treatment, mean square error and their ratio and how they compare to the histograms generated by the simulated data.

This activity allows students to investigate classification and create their own dichotomous key. Discussion will include classification of items in everyday life.

This peer review of writing tool helps students improve their writing by asking their peers in the class to provide feedback in a constructive manner.