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

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Number and Quantity
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Quantities
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.
Practice
N-Q2
Define appropriate quantities for the purpose of descriptive modeling.
Practice
N-Q3
Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Practice
Algebra
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Seeing Structure in Expressions
Interpret the structure of expressions.
A-SSE1
Interpret expressions that represent a quantity in terms of its context.
Practice
A-SSE1a
Interpret parts of an expression, such as terms, factors, and coefficients.
Practice
A-SSE1b
Interpret complicated expressions by viewing one or more of their parts as a single entity.
Practice
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.
Practice
A-CED2
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
Practice
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.
Practice
A-CED4
Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
Practice
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.
Practice
Solve equations and inequalities in one variable.
A-REI3
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Practice
A-REI3.1
Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context.
Practice
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.
Practice
A-REI6
Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Practice
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).
Practice
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).
Practice
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.
Practice
Functions
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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).
Practice
F-IF2
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
Practice
F-IF3
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
Practice
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.
Practice
F-IF5
Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
Practice
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.
Practice
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.
Practice
F-IF7a
Graph linear and quadratic functions and show intercepts, maxima, and minima.
Practice
F-IF7e
Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
Practice
F-IF9
Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
Practice
Building Functions
Build a function that models a relationship between two quantities.
F-BF1
Write a function that describes a relationship between two quantities.
Practice
F-BF1a
Determine an explicit expression, a recursive process, or steps for calculation from a context.
Practice
F-BF1b
Combine standard function types using arithmetic operations.
Practice
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
No resources for this standard yet.
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.
Practice
Linear, Quadratic, and Exponential Models
Construct and compare linear, quadratic, and exponential models and solve problems.
F-LE1
Distinguish between situations that can be modeled with linear functions and with exponential functions.
Practice
F-LE1a
Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
Practice
F-LE1b
Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
Practice
F-LE1c
Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
Practice
F-LE2
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).
Practice
F-LE3
Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
Practice
Interpret expressions for functions in terms of the situation they model.
F-LE5
Interpret the parameters in a linear or exponential function in terms of a context.
Practice
• How to Contextually Interpret the Parameters of an Exponential Function Given in f(x)=b^x+k Form - Content coming soon
Geometry
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Congruence
Experiment with transformations on the plane.
G-CO1
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.
Practice
G-CO2
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).
Practice