The purpose of this task is to surface alternative ways of measuring a central angle of a circle: in degrees, as a fraction of a complete rotation, or in radians. In this context, students will practice using right triangle trigonometry to find the coordinates of points on a circle. Students will also become more familiar with radian measurement and have a deeper understanding of the relationship between arc length measurements and radian angle measurements. In Secondary Math II, students encountered the idea that the length of the arc intercepted by an angle is proportional to the radius, and have defined the radian measure of the angle as the constant of proportionality (G.C.5). Part 1 of this task will surface what students understand about these concepts and whether they can connect them to the context of the problem. Part 2 of this task will continue to reinforce students’ understanding about right triangle trigonometry from Secondary Math II and show to what extent they are seeing right triangles within the circle, as explored in the previous learning cycle of this module. Part 3 points students’ attention towards the radian definition of angle measurement.

Students determine how far a brother and sister travel before they catch up with one another. The mathematics task is intended to be a problem or question that encourages the use of mathematical practices. The dialogue is meant to show how students might engage in the mathematical practices as they work on the task.

The purpose of this task is to reinforce students’ prior knowledge of factoring and to introduce polynomial long division. The task draws connections between polynomial long division and division of whole numbers to support students in understanding the procedure. Students will write remainders in two ways to create equivalent polynomial expressions and determine whether a given expression is a factor according to the Polynomial Remainder Theorem. Both factoring and long division will be used in upcoming tasks to write polynomials in factored form and to find their roots

Website link that provides 8 modalities on the topic "Division of Rational Expressions". Students may review the topic by reading notes and examples, using flashcards, watching a video, or through the use of a student-created study guide.

Students read and comment on examples from the media (newspaper and Internet) that involve estimating a population proportion or a population mean. Students calculate the margin of error and compare their calculations with the published results. In addition, students interpret the margin of error in the context of the article and comment on how the survey was conducted.

Students read and comment on examples from the media that involve statistical experiments that compare two treatments.

This lesson plan explores the basic principals behind designing and building a home, and the many variations and unique qualities that go into it. Students will have the opportunity to design their own homes and furniture while understanding coding and planning limitations.

Given a description of a statistical experiment, students identify the response variable and the treatments. Students recognize the different purposes of random selection and of random assignment.cStudents recognize the importance of random assignment in statistical experiments.

Students will be able to have a better understanding of the slope of a line, the y intercept, and parallel lines.

Lesson plan using a Cyberchase activity, students are introduced to a problem that gives them a sense of how quickly exponential growth accrues in the classic problem about a chess board and grains of rice. The context is extended to consider applications using money growth and chain letters. They are introduced to the algebraic representation for exponential growth.

The purpose of this task is to build on students’ understanding of a logarithmic function as the inverse of an exponential function and their previous work in determining values for logarithmic expressions to find the graphs of logarithmic functions of various bases. Students use technology to explore transformations with log graphs in base 10 and then generalize the transformations to other bases.

This resource provides problems to justify a solution method and to explain each step of the process using mathematical reasoning.

The purpose of this task is to extend students’ understanding of inverse functions to include quadratic functions and square roots. In the task, students are given the equation of a quadratic function for braking distance and asked to think about the distance needed to stop safely for a given speed. The logic is then turned around and students are asked to model the speed the car was going for a given braking distance. After students have worked with the inverse relationships with the limited domain [0, 217] (assuming that 217 is the maximum speed of the car), then students are asked to consider the quadratic function and its inverse on the entire domain. This is to elicit a discussion of when and under what conditions the inverse of a function is also a function.

Students see how well they understand function expressions by trying to match the function graph to a generated graph. They may choose from several function types or select random and let the computer choose.

In this task, you must design a cylindrical drink can that uses the least aluminum for a given volume of drink.

Students create scale drawings of polygonal figures by the Ratio Method.
Given a figure and a scale drawing from the Ratio Method, students answer questions about the scale factor and the center.

Students understand that parallel lines cut transversals into proportional segments. They use ratios between corresponding line segments in different transversals and ratios within line segments on the same transversal.
Students understand Eratosthenes’ method for measuring the earth and solve related problems.

Students understand how the Greeks measured the distance from the earth to the moon and solve related problems.

Inscribe a rectangle in a circle.
Understand the symmetries of inscribed rectangles across a diameter.

Explore the relationship between inscribed angles and central angles and their intercepted arcs.