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

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

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-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.3: : Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options in a modeling context.

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.1: : Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

A-REI.3: : Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.

A-REI.3.1: : Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context.

A-REI.5: : Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.

A-REI.6: : Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.

A-REI.10: : Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).

A-REI.11: : Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

A-REI.12: : Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.

F-IF: : Interpreting Functions

F-IF.1: : Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

F-IF.2: : Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

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.e: : Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

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.2: : Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.

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.1: : Distinguish between situations that can be modeled with linear functions and with exponential functions.

F-LE.1.a: : Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.

F-LE.1.b: : Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.

F-LE.1.c: : Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.

F-LE.2: : 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).

F-LE.5: : Interpret the parameters in a linear or exponential function in terms of a context.

G-CO: : Congruence

G-CO.1: : Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.

G-CO.2: : Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

G-CO.4: : Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.

G-CO.5: : Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.

G-CO.6: : Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.

G-CO.8: : Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.

G-CO.12: : Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).

G-GPE: : Expressing Geometric Properties with Equations

G-GPE.7: : Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.

S-ID: : Interpreting Categorical and Quantitative Data

S-ID.1: : Represent data with plots on the real number line (dot plots, histograms, and box plots).

S-ID.2: : Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.

S-ID.3: : Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

S-ID.6: : Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.

S-ID.6.a: : Fit a function to the data; use functions fitted to data to solve problems in the context of the data.

S-ID.6.b: : Informally assess the fit of a function by plotting and analyzing residuals.

S-ID.6.c: : Fit a linear function for a scatter plot that suggests a linear association.

S-ID.7: : Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.

S-ID.8: : Compute (using technology) and interpret the correlation coefficient of a linear fit.

Correlation last revised: 12/27/2023

California - Mathematics: Mathematics I

California Standards | Adopted: 2014