This is an exploration activity for students to visually see the graph of trig functions and understand about sin and cos functions and understand the concept of amplitude.

This is an exploration activity for students to visually see the graph of trig functions and understand about sin and cos functions and understand the concept of amplitude.Section 2 of this activity allows students to explore the period and vertical shift in trig functions.

The purpose of this task is to develop strategies for transforming the Ferris wheel functions so that the function and graphs represent different initial starting positions for the rider. Students have already considered vertical translations by moving the center of the Ferris wheel up or down, resulting in the midline of the graph being translated vertically. They have also considered horizontal and vertical dilations of the graph by changing the radius of the Ferris wheel or the speed of rotation, resulting in varying the amplitude or the period of the graph. In this task, horizontal translations of the graph are considered. Students may also note that sine and cosine graphs are interchangeable, as long as the graph is shifted horizontally by an appropriate amount.

In this task students solidify their understanding of using trigonometric functions to model periodic behavior by applying trigonometry to a context that is periodic (high and low tides), but not circular motion. They learn how to interpret amplitude and period in terms of this new context. They also consider using inverse trigonometric functions to answer questions about the time at which the tide reaches various heights. Students answer these inverse questions both graphically and algebraically.

The purpose of this task is to practice working with geometric and arithmetic sequences.
This is the final task in the module and is intended to help students develop fluency in using various
representations for sequences. This task could be used as a performance assessment.

This resource contains exercises where students can be assessed on identifying properties in complex polynomial equations.

Students are challenged with the following task: If two sheets of 8.5 by 11 inch paper are rolled into a short cylinder and a tall cylinder, does one hold more than the other?

Students are provided with a scenario and asked to determine which amounts of postage is it impossible to make using only five-cent and seven-cent stamps? 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.

Students visualize radian measures of angles traversed counter clockwise around the unit circle in this interactive resource.

The purpose of this task is for students to become more fluent in finding inverses and to increase their flexibility in thinking about inverse functions using tables, graphs, equations, and verbal descriptions.

The purpose of this task is to solidify student understanding of how the degree of the polynomial function impacts the rate of change and end behavior. By comparing the values of expressions with ‘extreme’ values, students will be able to:
• Understand that the degree of the polynomial is the highest valued whole number exponent and that this term determines the end behavior (regardless of the other terms in the expression).
• Determine that the higher the degree of a polynomial, the greater the value as F approaches infinity. Understand that while the highest degree polynomial has the greatest value as F → ∞, that exponential functions have the greatest rate of change, and therefore the greatest value when F becomes very large.
• Identify differences between even and odd degree functions. In this task, students will know the end behavior for odd degree functions (as F → −∞, H(F) → −∞ and that both even and odd degree polynomial functions as F → ∞, H(F) → ∞) as long as the co-efficient is positive and realize that the opposite is true if the co-efficient is negative.

The purpose of this task is for students to surface comparisons between polynomials and whole numbers and use these comparisons to add and subtract polynomials algebraically. Students will also add and subtract polynomials given only graphically, adding corresponding points on the two graphs to obtain a sum. Students will make and test conjectures about the sum and differences of polynomials, such as “the sum of two quadratics is quadratic.”

The purpose of this task is for students to learn to add, subtract, multiply and divide rational expressions. The task is designed so that students, again, connect operations with rational numbers to operations with rational expressions.

In this lesson, students construct a table of logarithms base 10 and observe patterns that indicate properties of logarithms.

In this lesson, students construct a table of logarithms base 10 and observe patterns that indicate properties of logarithms.

In this lesson, students understand how to change logarithms from one base to another. Students calculate logarithms with any base using a calculator that computes only logarithms base 10 and base ??. Students justify properties of logarithms with any base.

In this lesson, students differentiate between a population and a sample. Students differentiate between a population characteristic and a sample statistic. Students recognize statistical questions that are answered by estimating a population mean or a population proportion.

In this lesson, students distinguish between observational studies, surveys, and experiments. Students explain why random selection is an important consideration in observational studies and surveys and why random assignment is an important consideration in experiments. Students recognize when it is reasonable to generalize the results of an observational study or survey to some larger population and when it is reasonable to reach a cause-and-effect conclusion about the relationship between two variables.

Students use logarithm tables to calculate products and quotients of multi-digit numbers without technology. Students understand that logarithms were developed to speed up arithmetic calculations by reducing multiplication and division to the simpler operations of addition and subtraction. Students solve logarithmic equations of the form log(??) = log(??) by equating ?? and ??.

In this lesson, students use data from a random sample to estimate a population proportion. Students calculate and interpret margin of error in context. Students know the relationship between sample size and margin of error in the context of estimating a population proportion.