California Common Core (CACC) - Integrated Pathway Mathematics 1 Skills Practice

Skills available for California Common Core (CACC) - Integrated Pathway Mathematics 1 Skills Practice
  1. Number and Quantity
  2. Algebra
  3. Functions
  4. Geometry
  5. Statistics and Probability
Number and Quantity
Reason quantitatively and use units to solve problems.
N-Q1 - Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays.
N-Q2 - Define appropriate quantities for the purpose of descriptive modeling.
N-Q3 - Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Seeing Structure in Expressions
Interpret the structure of expressions.
A-SSE1 - Interpret expressions that represent a quantity in terms of its context.
A-SSE1a - Interpret parts of an expression, such as terms, factors, and coefficients.
A-SSE1b - Interpret complicated expressions by viewing one or more of their parts as a single entity.
Creating Equations
Create equations that describe numbers or relationships.
A-CED1 - Create equations and inequalities in one variable including ones with absolute value and use them to solve problems.
A-CED2 - Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
A-CED3 - 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-CED4 - Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
Reasoning with Equations and Inequalities
Understand solving equations as a process of reasoning and explain the reasoning.
A-REI1 - 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.
Solve equations and inequalities in one variable.
A-REI3 - Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
A-REI3.1 - Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context.
Solve systems of equations.
A-REI5 - 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-REI6 - Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Represent and solve equations and inequalities graphically.
A-REI10 - 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-REI11 - 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).
A-REI12 - 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.
Interpreting Functions
Understand the concept of a function and use function notation.
F-IF1 - 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-IF2 - Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
F-IF3 - Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
Interpret functions that arise in applications in terms of context.
F-IF4 - 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-IF5 - Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
F-IF6 - 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.
Analyze functions using different representations.
F-IF7 - Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
F-IF7a - Graph linear and quadratic functions and show intercepts, maxima, and minima.
F-IF7e - Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
F-IF9 - Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
Building Functions
Build a function that models a relationship between two quantities.
F-BF1 - Write a function that describes a relationship between two quantities.
F-BF1a - Determine an explicit expression, a recursive process, or steps for calculation from a context.
F-BF1b - Combine standard function types using arithmetic operations.
F-BF2 - Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms
Build new functions from existing functions.
F-BF3 - Identify the effect on the graph of replacing f(x) by f(x) + k, kf(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.