The purpose of this task is for students to show their understanding of features of functions. This is a culminating task for modules 1 through 4 and asks students to describe features of specific functions, then to create two different functions when given specific features.

The purpose of this task is for students to solidify their understanding of piecewise functions using linear absolute value. Students will also learn how to graph, write, and create linear absolute value functions by looking at structure and making sense of piecewise defined functions.

The purpose of this task is to verify that the properties of exponents students know for integer exponents also work for rational exponents. In the context of writing exponential equations to represent the amount of interest earned over smaller intervals of time than annually, students will solidify their understanding of working with rational exponents in conjunction with the properties of exponents.

The purpose of this task is to examine the meaning and the arithmetic of irrational numbers, mainly non-rational radical numbers, as well as the meaning and arithmetic of complex numbers. Students will note similarities and differences in the rules of simplifying such expressions.

A Selected Response Item provided by Smarter Balanced as preliminary examples of the types of items that students might encounter on the summative assessment. The item contain a series of options from which to choose correct responses that extend the properties of exponents to rational exponents. MAT.HS.SR.1.00NRN.A.152

Sample Item provided by Smarter Balanced as preliminary examples of the types of items that students might encounter on the summative assessment. The item assesses whether students can explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational. MAT.HS.ER.3.00NRN.B.085

This lesson provides students with an introduction to exponential functions. The class first explores the world population since 1650. Students then conduct a simulation in which a population grows at a random yet predictable rate. Both situations are examples of exponential growth.

Euclid was right, we can’t make much progress in proving statements in geometry without a statement about parallelism. Euclid made an assumption related to parallelism—his frequently discussed and questioned 5th postulate. Non-Euclidean geometries resulted from mathematicians making different assumptions about parallelism. The purpose of this task is to establish some “parallel postulates” for transformational geometry. The authors of CCSS-M suggested some statements about parallelism that they would allow us to assume to be true in their development of the geometry standards: (1) rigid motion transformations “take parallel lines to parallel lines” (that is, parallelism, along with distance and angle measure, is preserved by rigid motion transformations—see 8.G.1), and (2) dilations “take a line not passing through the center of the dilation to a parallel line” (see G.SRT.1a). In this task we develop some additional statements about parallelism for the rigid motion transformations, which we will accept as postulates for our development of geometry: (1) After a translation, corresponding line segments in an image and its preimage are always parallel or lie along the same line; (2) After a rotation of 180°, corresponding line segments in an image and its pre-image are parallel or lie on the same line; (3) After a reflection, line segments in the pre-mage that are parallel to the line of reflection will be parallel to the corresponding line segments in the image. These statements about parallelism will lead to the proofs of theorems about relationships of angles relative to parallel lines crossed by a transversal.

The purpose of this task is to prove theorems about the properties of parallelograms that were surfaced in Mathematics I as students explored the rotational symmetry and line symmetry of various types of quadrilaterals. You may want to review this exploratory work with students. (See Symmetries of Quadrilaterals and Quadrilaterals—Beyond Definition in the Mathematics Vision Project, Secondary One curriculum.) Students will solidify that these properties of parallelograms are a consequence of the opposite sides of the quadrilateral being parallel to each other. That is, they will draw upon their theorems about parallel lines being cut by a transversal—with the diagonals of the parallelogram forming the transversals—to prove these additional properties of parallelograms.

In this task students use their techniques for changing the forms of quadratic expressions (i.e., factoring, completing the square to put the quadratic in vertex form, or using the quadratic formula to find the x-intercepts) as strategies for solving quadratic equations.

The purpose of this task is to develop a description of the essential features of a dilation:

a. Lines are taken to lines, and line segments to line segments of proportional length in the ratio given by the scale factor.
b. Angles are taken to angles of the same measure.
c. A line not passing through the center of dilation is taken to a parallel line, and lines passing through the center of dilation are unchanged.
d. To describe a mathematical dilation we need to specify a center of dilation and a scale factor. The center of dilation is a fixed point in the plane about which all points are expanded or contracted. It is the only invariant point under a dilation.
e. Dilations create similar figures—the image and pre-image are the same shape, but different sizes (unless the scale factor is 1, then the image and pre-image are congruent).

Students will draw on their foundation of the analogies between polynomial arithmetic and base-ten computation, focusing on properties of operations, particularly the distributive property. Students identify and make connections between zeros of polynomials and solutions of polynomial equations.

Students will continue to interpret expressions, create equations, rewrite equations and functions in different but equivalent forms, and graph and interpret functions, but this time using polynomial functions, and more specifically quadratic functions, as well as square root and cube root functions.

Susie is organizing the printing of tickets for a show. She has collected prices from several printers. Your task is to use graphs and algebra to advise Susie on how to choose the best printer.

This video includes four worked out examples dealing with probability. The video includes Addition Rule of Probability, Multiplication Rule and Conditional Probabilities.

Students use the addition rule to calculate the probability of a union of two events. Students interpret probabilities in context.

This lesson introduces the formulas for calculating the probability of the complement of an event, the probability of an intersection when events are independent, and conditional probabilities.

Students carry out an interactive, geometric "proof without words" for the algebraic technique of completing the square in this interactive. The page also includes directions and a link to the final solution.

Students are provided with information and notice that the original three points given seem to be midpoints of the sides of a newly formed triangle. Their task is to determine how they would prove this conjecture? 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.