This task deals with a student error that may occur while students are completing F-IF Average Cost.

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.

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.

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.

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.

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.

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 develop a physical understanding for the meaning of equality by trying to find equal lengths using rods.

For this task, Minitab software was used to generate 100 random samples of size 16 from a population where the probability of obtaining a success in one draw is 33.6% (Bernoulli). Given that multiple samples of the same size have been generated, students should note that there can be quite a bit of variability among the estimates from random samples and that on average, the center of the distribution of such estimates is at the actual population value and most of the estimates themselves tend to cluster around the actual population value.

This task helps students broaden and deepen their understanding of the equals sign and equality.

In this task students interpret two graphs that look the same but show very different quantities. The first graph gives information about how fast a car is moving while the second graph gives information about the position of the car. This problem works well to generate a class or small group discussion. Students learn that graphs tell stories and have to be interpreted by carefully thinking about the quantities shown.

This task could be used in instructional activities designed to build understandings of fraction division. With teacher guidance, it could be used to develop knowledge of the common denominator approach and the underlying rationale.

In this lesson, the electromagnetic spectrum is explained and students learn that visible light makes up only a portion of this wide spectrum. Students also learn that engineers use electromagnetic waves for many different applications.

Students learn the value of writing and art in science and engineering. They acquire vocabulary that is appropriate for explaining visual art and learn about visual design principles (contrast, alignment, repetition and proximity) and elements (lines, color, texture, shape, size, value and space) that are helpful when making visual aids. A PowerPoint(TM) presentation heightens students' awareness of the connection between art and engineering in order to improve the presentation of results, findings, concepts, information and prototype designs. Students also learn about the science and engineering research funding process that relies on effective proposal presentations, as well as some thermal conductivity / heat flow basics including the real-world example of a heat sink which prepares them for the associated activity in which they focus on creating diagrams to communicate their own collected experimental data.

Students make simple spectroscopes (prisms) to look at different light sources. The spectroscopes allow students to see differing spectral distributions of different light sources. Students also shine a light source through different materials with varying properties and compare the differences.

This problem is the fifth in a series of seven about ratios. In the first problem students define the simple ratios that exist among the three candidates. It opens an opportunity to introduce unit rates. The subsequent problems are more complex. In the second problem, students apply their understanding of ratios to combine two pools of voters to determine a new ratio. In the third problem, students apply a known ratio to a new, larger pool of voters to determine the number of votes that would be garnered.

This is the sixth problem in a series of seven that use the context of a classroom election. While it still deals with simple ratios and easily managed numbers, the mathematics surrounding the ratios are increasingly complex.