Gizmos for California - Mathematics: Mathematics II (California Standards adopted 2014)

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.

N-RN: : The Real Number System

N-RN.1: : Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

N-CN: : The Complex Number System

N-CN.1: : Know there is a complex number i such that i² = -1, and every complex number has the form a + bi with a and b real.

N-CN.2: : Use the relation i² = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

N-CN.7: : Solve quadratic equations with real coefficients that have complex solutions.

A-SSE: : Seeing Structure in Expressions

A-SSE.1: : Interpret expressions that represent a quantity in terms of its context.

A-SSE.1.a: : Interpret parts of an expression, such as terms, factors, and coefficients.

A-SSE.1.b: : Interpret complicated expressions by viewing one or more of their parts as a single entity.

A-SSE.2: : Use the structure of an expression to identify ways to rewrite it.

A-SSE.3: : Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

A-SSE.3.a: : Factor a quadratic expression to reveal the zeros of the function it defines.

A-APR: : Arithmetic with Polynomials and Rational Expressions

A-APR.1: : Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

A-CED: : Creating Equations

A-CED.1: : Create equations and inequalities in one variable including ones with absolute value and use them to solve problems.

A-CED.2: : Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

A-CED.4: : Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

A-REI: : Reasoning with Equations and Inequalities

A-REI.4: : Solve quadratic equations in one variable.

A-REI.4.b: : Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

F-IF: : Interpreting Functions

F-IF.4: : For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.

F-IF.5: : Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

F-IF.6: : Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

F-IF.7: : Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

F-IF.7.a: : Graph linear and quadratic functions and show intercepts, maxima, and minima.

F-IF.7.b: : Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

F-IF.8: : Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

F-IF.8.a: : Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

F-BF: : Building Functions

F-BF.1: : Write a function that describes a relationship between two quantities.

F-BF.1.a: : Determine an explicit expression, a recursive process, or steps for calculation from a context.

F-BF.3: : Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.

F-LE: : Linear, Quadratic, and Exponential Models

F-LE.6: : Apply quadratic functions to physical problems, such as the motion of an object under the force of gravity.

G-CO: : Congruence

G-CO.9: : Prove theorems about lines and angles.

G-CO.10: : Prove theorems about triangles.

G-CO.11: : Prove theorems about parallelograms.

G-SRT: : Similarity, Right Triangles, and Trigonometry

G-SRT.1: : Verify experimentally the properties of dilations given by a center and a scale factor:

G-SRT.1.b: : The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

G-SRT.2: : Given two figures, use the definition of similarity in terms of similarity transformations to decide if they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.

G-SRT.4: : Prove theorems about triangles.

G-SRT.5: : Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

G-SRT.6: : Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.

G-SRT.8: : Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.

G-SRT.8.1: : Derive and use the trigonometric ratios for special right triangles (30°,60°,90°and 45°,45°,90°).

G-C: : Circles

G-C.2: : Identify and describe relationships among inscribed angles, radii, and chords.

G-C.5: : Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Convert between degrees and radians.

G-GPE: : Expressing Geometric Properties with Equations

G-GPE.1: : Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.

G-GPE.2: : Derive the equation of a parabola given a focus and directrix.

G-GMD: : Geometric Measurement and Dimension

G-GMD.1: : Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone.

G-GMD.3: : Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

G-GMD.5: : Know that the effect of a scale factor k greater than zero on length, area, and volume is to multiply each by k, k², and k³, respectively; determine length, area and volume measures using scale factors.

S-CP: : Conditional Probability and the Rules of Probability

S-CP.1: : Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ('or,' 'and,' 'not').

S-CP.2: : Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

S-CP.3: : Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.

S-CP.9: : Use permutations and combinations to compute probabilities of compound events and solve problems.

S-MD: : Using Probability to Make Decisions

S-MD.6: : Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator).

S-MD.7: : Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game).

Correlation last revised: 12/27/2023

California - Mathematics: Mathematics II

California Standards | Adopted: 2014