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Grade 9 Math Courses - California Curriculum

Discover California's Grade 9 Math courses: Algebra I and Mathematics I. Explore fundamental concepts, problem-solving skills, and prepare for advanced math studies in high school.

CA Grade 9 Math Curriculum - Algebra I and Math I Topics

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ID
Standard
StudyPug Topic
A1.N.RN.1
CA.A1.N.RN.1: Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents

Convert between radicals and rational exponents

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Exponent rules

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Order of operations with exponents

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A1.N.RN.2
CA.A1.N.RN.2: Rewrite expressions involving radicals and rational exponents using the properties of exponents
A1.N.RN.3
CA.A1.N.RN.3: Explain why the sum or product of two rational numbers is rational; why the sum of a rational number and an irrational number is irrational
A1.N.Q.1
CA.A1.N.Q.1: Use units as a way to understand problems and to guide the solution of multi-step problems
A1.N.Q.2
CA.A1.N.Q.2: Define appropriate quantities for the purpose of descriptive modeling

Rates

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Proportions

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A1.N.Q.3
CA.A1.N.Q.3: Choose a level of accuracy appropriate to limitations on measurement when reporting quantities

Upper and lower bound

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Rounding numbers

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A1.A.SSE.1
CA.A1.A.SSE.1: Interpret expressions that represent a quantity in terms of its context

What is a polynomial?

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A1.A.SSE.3
CA.A1.A.SSE.3: Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression
A1.A.APR.1
CA.A1.A.APR.1: Understand that polynomials form a system analogous to the integers, namely, they are closed under certain operations
A1.A.CED.1
CA.A1.A.CED.1: Create equations and inequalities in one variable and use them to solve problems
A1.A.CED.2
CA.A1.A.CED.2: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales
A1.A.CED.3
CA.A1.A.CED.3: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options
A1.A.CED.4
CA.A1.A.CED.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations
A1.A.REI.3
CA.A1.A.REI.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters
A1.A.REI.3.1
CA.A1.A.REI.3.1: Solve one-variable equations and inequalities involving absolute value, graphing the solutions and interpreting them in context
A1.A.REI.4
CA.A1.A.REI.4: Solve quadratic equations in one variable using various methods
A1.A.REI.5
CA.A1.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
A1.A.REI.6
CA.A1.A.REI.6: Solve systems of linear equations exactly and approximately, focusing on pairs of linear equations in two variables
A1.A.REI.7
CA.A1.A.REI.7: Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically
A1.A.REI.10
CA.A1.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
A1.A.REI.11
CA.A1.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)
A1.A.REI.12
CA.A1.A.REI.12: Graph the solutions to a linear inequality in two variables as a half-plane, and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes
A1.F.IF.1
CA.A1.F.IF.1: Understand that a function from one set (domain) to another set (range) assigns to each element of the domain exactly one element of the range

Identifying functions

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A1.F.IF.2
CA.A1.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

Function notation

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One to one functions

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A1.F.IF.3
CA.A1.F.IF.3: Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers
A1.F.IF.4
CA.A1.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
A1.F.IF.5
CA.A1.F.IF.5: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes
A1.F.IF.6
CA.A1.F.IF.6: Calculate and interpret the average rate of change of a function over a specified interval

Rate of change

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A1.F.IF.7
CA.A1.F.IF.7: Graph functions expressed symbolically and show key features of the graph
A1.F.IF.8
CA.A1.F.IF.8: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function

Adding functions

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Subtracting functions

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Multiplying functions

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Dividing functions

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A1.F.IF.9
CA.A1.F.IF.9: Compare properties of two functions each represented in a different way
A1.F.BF.1
CA.A1.F.BF.1: Write a function that describes a relationship between two quantities
A1.F.BF.2
CA.A1.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
A1.F.BF.3
CA.A1.F.BF.3: 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
A1.F.BF.4
CA.A1.F.BF.4: Find inverse functions

Inverse functions

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A1.F.LE.3
CA.A1.F.LE.3: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function

Evaluating polynomials

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A1.F.LE.6
CA.A1.F.LE.6: Apply quadratic functions to physical problems, such as the motion of an object under the force of gravity
A1.S.ID.1
CA.A1.S.ID.1: Represent data with plots on the real number line (dot plots, histograms, and box plots)
A1.S.ID.2
CA.A1.S.ID.2: Use statistics appropriate to the shape of the data distribution to compare center and spread of two or more different data sets

Median and mode

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Mean

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Range and outliers

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Application of averages

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A1.S.ID.5
CA.A1.S.ID.5: Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data
A1.S.ID.7
CA.A1.S.ID.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data
A1.S.ID.8
CA.A1.S.ID.8: Compute (using technology) and interpret the correlation coefficient of a linear fit

Probability

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