OK 8th Grade Math Curriculum

OK 8th Grade Math Curriculum

• CC.HSN.RN.B.3Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
  • Rational vs. Irrational numbers
  • Solving radical equations
  • Converting repeating decimals to fractions
• CC.HSN.Q.A.1Use 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.
  • Metric systems
  • Imperial systems
  • Scale diagrams
  • Conversions involving squares and cubic
• CC.HSN.Q.A.2Define appropriate quantities for the purpose of descriptive modeling.
  • Conversions between metric and imperial systems
  • Squares and square roots
  • Pythagorean theorem
  • Estimating square roots
  • Using the pythagorean relationship
  • Applications of pythagorean theorem
• CC.HSA.SSE.A.1Interpret expressions that represent a quantity in terms of its context.
  • What is a polynomial?
  • Applications of linear equations
• CC.HSA.SSE.A.2Use the structure of an expression to identify ways to rewrite it.
  • Polynomial components
  • Simplifying rational expressions and restrictions
  • Applications of polynomials
  • Find the difference of squares: (a - b)(a + b) = (a^2 - b^2)
• CC.HSA.SSE.B.3Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
  • Common factors of polynomials
  • Adding and subtracting rational expressions
  • Evaluating polynomials
  • Using algebra tiles to factor polynomials
  • Solving polynomial equations
• CC.HSA.CED.A.1Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.
  • Introduction to linear equations
  • Solving rational equations
  • Solving exponential equations using exponent rules
• CC.HSA.CED.A.2Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
  • Slope intercept form: y = mx + b
  • Graphs of rational functions
  • Applications of rational equations
  • Simplifying complex fractions
  • Partial fraction decomposition
• CC.HSA.CED.A.3Represent 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.
  • Determining number of solutions to linear equations
  • Linear programming word problems
  • Graphing reciprocals of linear functions
  • Graphing reciprocals of quadratic functions
• CC.HSA.CED.A.4Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.
  • Point-slope form: y - y_1 = m(x - x_1)
  • Graphing quadratic inequalities in two variables
  • Graphing systems of quadratic inequalities
• CC.HSA.REI.A.1Explain 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.
  • Combination of both parallel and perpendicular line equations
  • Applications of inequalities
  • What is linear programming?
• CC.HSA.REI.B.3Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
  • Solving one-step linear inequalities
  • Solving multi-step linear inequalities
  • Converting radicals to mixed radicals
  • Converting radicals to entire radicals
  • Adding and subtracting radicals
• CC.HSA.REI.C.5Prove 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.
  • Shortcut: Vertex formula
  • Graphing quadratic functions: General form VS. Vertex form
  • Finding the quadratic functions for given parabolas
• CC.HSA.REI.C.6Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
  • Solving systems of linear equations by elimination
  • System of linear equations
• CC.HSA.REI.D.10Understand 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).
  • Solving systems of linear equations by graphing
  • Solving a linear system with matrices using Gaussian elimination
  • The determinant of a 2 x 2 matrix
  • The determinant of a 3 x 3 matrix (General & Shortcut Method)
• CC.HSA.REI.D.11Explain 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.
  • Graphing linear functions using table of values
  • Graphing exponential functions
  • Graphing logarithmic functions
  • The inverse of 3 x 3 matrices with matrix row operations
  • The inverse of 3 x 3 matrix with determinants and adjugate
• CC.HSA.REI.D.12Graph 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.
  • Inequalities of combined functions
  • Graphing linear inequalities in two variables
  • Graphing systems of linear inequalities
  • 2 x 2 invertible matrix
  • Solving linear systems using Cramer's Rule
• CC.HSF.IF.A.1Understand 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).
  • Domain and range of a function
  • Function notation (advanced)
  • Identifying functions
• CC.HSF.IF.A.2Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
  • Function notation
  • Difference quotient: applications of functions
• CC.HSF.IF.A.3Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers.
  • Greatest common factors (GCF)
  • Introduction to sequences
  • Sigma notation
• CC.HSF.IF.B.4For 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.
  • Word problems of graphing linear functions
  • Characteristics of quadratic functions
  • Relationship between two variables
  • Understand relations between x- and y-intercepts
  • Combining transformations of functions
  • Reflection across the y-axis: y = f(-x)
  • Reflection across the x-axis: y = -f(x)
  • Transformations of functions: Horizontal stretches
  • Transformations of functions: Vertical stretches
• CC.HSF.IF.B.5Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
  • Point of discontinuity
  • Even and odd functions
• CC.HSF.IF.B.6Calculate 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.
  • Rate of change
  • Direct variation
• CC.HSF.IF.C.7Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
  • Graphing linear functions using a single point and slope
  • Graphing quadratic functions: General form VS. Vertex form
  • Graphing exponential functions
  • Graphing logarithmic functions
  • Graphing from slope-intercept form y=mx+b
  • Graphing transformations of exponential functions
  • Graphing transformations of logarithmic functions
  • Sine graph: y = sin x
  • Cosine graph: y = cos x
  • Tangent graph: y = tan x
  • Cotangent graph: y = cot x
  • Secant graph: y = sec x
  • Cosecant graph: y = csc x
• CC.HSF.IF.C.8Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
  • Slope intercept form: y = mx + b
  • General form: Ax + By + C = 0
  • Point-slope form: y - y_1 = m(x - x_1)
  • Converting from general to vertex form by completing the square
  • Adding functions
  • Subtracting functions
  • Multiplying functions
  • Dividing functions
  • Operations with functions
• CC.HSF.IF.C.9Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
  • Parallel and perpendicular lines in linear functions
  • Graphs of rational functions
  • Inequalities of combined functions
• CC.HSF.BF.A.1Write a function that describes a relationship between two quantities.
  • Applications of linear relations
  • Finding an exponential function given its graph
  • Finding a logarithmic function given its graph
• CC.HSF.BF.A.2Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms.
  • Arithmetic sequences
  • Geometric sequences
  • Arithmetic series
  • Geometric series
  • Infinite geometric series
• CC.HSF.BF.B.3Identify 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.
  • Transformations of quadratic functions
  • Transformations of functions: Horizontal translations
  • Transformations of functions: Vertical translations
• CC.HSF.LE.A.1Distinguish between situations that can be modeled with linear functions and with exponential functions.
  • Introduction to nonlinear equations
  • Solving exponential equations using exponent rules
  • Exponential decay: Half-life
  • Exponential growth and decay by percentage
• CC.HSF.LE.A.2Construct 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).
  • Graphing linear functions using table of values
• CC.HSG.GPE.B.7Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula.
  • Distance formula: $d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
• CC.HSS.ID.A.1Represent data with plots on the real number line (dot plots, histograms, and box plots).
  • Reading and drawing histograms
  • Box-and-whisker plots and scatter plots
  • Frequency tables and dot plots
  • Frequency distribution and histograms
• CC.HSS.ID.A.2Use 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.
  • Median and mode
  • Mean
  • Range and outliers
  • Center of a data set: mean, median, mode
  • Spread of a data set - standard deviation & variance
• CC.HSS.ID.A.3Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).
  • Application of averages
  • Shapes of distributions
• CC.HSS.ID.B.5Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.
  • Reading and drawing Venn diagrams
  • Probability with Venn diagrams
• CC.HSS.ID.B.6Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.
  • Reading and drawing line graphs
  • Bivariate, scatter plots and correlation