Both of the questions in this task are solved by the division problem 12Ö3 but what happens to the ribbon is different in each case.
In this task, we are given the graph of two lines including the coordinates of the intersection point and the coordinates of the two vertical intercepts, and are asked for the corresponding equations of the lines. It is a very straightforward task that connects graphs and equations and solutions and intersection points.
This task provides an opportunity for students to construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
This task provides an opportunity for students to construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
This classroom task is meant to elicit a variety of different methods of solving a quadratic equation (A-REI.4).
This task combines two skills from domain G-C: making use of the relationship between a tangent segment to a circle and the radius touching that tangent segment (G-C.2), and computing lengths of circular arcs given the radii and central angles (G-C.5). It also requires students to create additional structure within the given problem, producing and solving a right triangle to compute the required central angles (G-SRT.8).
This task presents an opportunity to explore a more general and non-algebraic view of functions.
The purpose of this task is to construct and use inverse functions to model a a real-life context. Students choose a linear function to model the given data, and then use the inverse function to interpolate a data point.
This task focuses on the fact that exponential functions are characterized by equal successive quotients over equal intervals. This task can be used alongside F-LE Equal Factors over Equal Intervals.
This task focuses on the fact that linear functions are characterized by constant differences over equal intervals. It could be used alongside to F-LE Equal Differences over Equal Intervals I & II.
Students learn about ultrasound and how it can be used to determine the shapes and contours of unseen objects. Using a one-dimensional ultrasound imaging device (either prepared by the teacher or put together by the students) that incorporates a LEGO(TM) MINDSTORMS(TM) NXT intelligent brick and ultrasonic sensor, they measure and plot the shape of an unknown object covered by a box. Looking at the plotted data, they make inferences about the shape of the object and guess what it is. Students also learn how engineers use high-frequency waves in the design of medical imaging devices, the analysis of materials and oceanographic exploration. Pre/post quizzes, a worksheet and a LEGO rbt program are provided.
The airplanes unit begins with a lesson on how airplanes create lift, which involves a discussion of air pressure and how wings use Bernoulli's principle to change air pressure. Next, students explore the other three forces acting on airplanes thrust, weight and drag. Following these lessons, students learn how airplanes are controlled and use paper airplanes to demonstrate these principles. The final lessons addresses societal and technological impacts that airplanes have had on our world. Students learn about different kinds of airplanes and then design and build their own balsa wood airplanes based on what they have learned.
This task presents a context that leads students toward discovery of the formula for calculating the volume of a sphere. Students who are given this task must be familiar with the formula for the volume of a cylinder, the formula for the volume of a cone, and CavalieriŐs principle.
The goal of this task is to provide examples for comparing two fractions by finding a benchmark fraction which lies in between the two.
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.