# Overview of Math Standards

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2 When appropriate: Manhattan-Ogden USD 383 Math Year at a Glance Algebra 1 Use multiple representations to enforce concepts (graph, table, equation). Model real life situations that compliment the mathematical techniques. Notes: Vocabulary terms are listed only in the unit they are first introduced. 1. Solving Linear Equations 1.1 Solving Simple Equations 1.2 Solving Multi-Step Equations 1.3 Solving Equations with Variables on Both Sides 1.4 Solving Absolute Value Equations 1.5 Rewriting Equations and Formulas 2. Solving Linear Inequalities 2.1 Writing & Graphing Inequalities 2.2 Solving Inequalities Using + and 2.3 Solving Inequalities Using x and 1 A-CED.A.1 A-REI.A.1 A-REI.B.3 N-Q.A.1 A-CED.A.4 A-CED.A.1 A-REI.B.3 Conjecture Rule Theorem Equation (linear) Solution Inverse operations Equivalent equations Identity Absolute value equation Extraneous solution Literal equation Formula Inequality Solution set Equivalent inequalities Compound inequality How can you use equations to solve real-life problems? How can you solve an equation with variables on both sides? How can you solve an absolute value equation? How can you use a formula for one measurement to write a formula for a different measurement? How can you use an inequality to describe a real-life statement? How can you solve simple and multi-step inequalities using the four basic operations? Solve simple and multi-step equations in one variable using the properties of equality. Solve equations containing an absolute value. Manipulate equations to solve for different variables. Write, graph, and solve single and multi-step linear inequalities using properties of inequalities Might be necessary to incorporate some review work including number sense and order of operations. Use inequality notation, ex. x < 3 but show how to read set builder, and if appropriate, show interval

3 2.4 Solving Multi-Step Inequalities 2.5 Solving Compound Inequalities 2.6 Solving Absolute Value Inequalities Absolute value inequality Absolute deviation How can you use inequalities to describe intervals on the real number line? How can you solve an absolute value inequality? Write, graph and solve compound inequalities using properties of inequalities notation for advanced classes Write, graph, and solve absolute value inequalities 3. Graphing Linear Functions 3.1 Functions 3.2 Linear Functions 3.3 Function Notation 3.4 Graphing Linear Equations in Standard Form 3.5 Graphing Linear Equations in Slope- Intercept Form 3.6 Transformations of Linear Functions 3.7 Graphing Absolute Value Functions 2 F-IF.A.1 A-CED.A.2 A-REI.C.10 F-IF.B.5 F-IF.C.7a F-LE.A.1b F-IF.A.2 F-IF.C.7a F-IF.C.9 F-IF.B.4 F-LE.B.5 F-BF.B.3 A-REI.D.10 F-IF.C.7b Relation Function Domain Range Independent variable Dependent variable Linear equation Linear function Nonlinear function Function notation x and y intercepts Slope (rise and run) Standard form Slope-intercept form Constant function Family of functions Parent function Transformation Translation Reflection What is a function? How can you determine whether a function is linear or nonlinear? How can you use function notation to represent a function? How can you describe the graph of a linear function in both slope-intercept and standard form? How is an absolute value function graphed? How do translations and reflections affect the parent Determine whether a relation is a function, and if so name its domain and range. Represent situations using function notation. Differentiate between linear and nonlinear functions. Graph and interpret linear functions when When teaching transformations, include only translations and reflections. Consider going over linear and absolute value graphs, and then do transformations on both at the same time (horizontal shifts are easier to see on absolute value functions)

4 Absolute value function Vertex Vertex form graph of a linear or absolute value function? presented in both standard and slopeintercept form. Graph and interpret an absolute value function in vertex form. Translate and reflect linear and absolute value functions to form many other graphs all related to the parent graph. 4. Writing Linear Functions 4.1 Writing Equations in Slope-Intercept Form 4.2 Writing Equations in Point-Slope Form 4.3 Writing Equations of Parallel & Perpendicular Lines 4.4 Scatter Plots & Lines of Best Fit 4.5 Analyzing Lines of Fit A-CED.A.2 F-BF.A.1a F-LE.A.1b F-LE.A.2 F-LE.B.5 S-ID.B.6a S-ID.B.6b S-ID.B.6c S-ID.C.7 S-ID.C.8 S.ID.C.9 Linear model Point-slope form Parallel lines Perpendicular lines Scatter plot Correlation Line of best fit Piecewise function (optional) When given information about a linear function, how can you write its equation? When are two lines parallel or perpendicular? How can you use a scatter plot and a line of best fit to make conclusions and predictions about data? Write an equation for a linear function in both pointslope and slopeintercept form. Determine when two lines are parallel or perpendicular. Stress pointslope form and the relationships between the various forms of a line. Students should be able to draw a line of best fit, and estimate its 3

5 4.7 Piecewise Functions (teacher discretion) F-If.A.3 F-BF.A.1a F-BF-A.2 A-REI.D.10 F-IF.C.7b Draw a line of best fit, find a suitable equation, and use it to interpret and predict. equation using point-slope techniques, understand the difference between positive, negative, and no correlation and make predictions based on the line of best fit. 5. Solving Systems of Linear Equations , 5.5 Solving Systems of Linear Equations by Graphing, Substitution, and Elimination A-CED.A.3 A-REI.C.6 A-REI.C.5 A-REI.D.11 A-REI.D.12 System of linear equations Substitution Elimination Half-plane How can a system of linear equations be solved? How many solutions can a system of linear equations have? Solve a linear system in two variables using the techniques of graphing, substitution, an elimination. 4.7 could be used to reinforce earlier concepts such as domain, range, but completely at teacher s discretion (not tested) More emphasis should be placed on systems of two lines, but absolute value functions 4

6 5.4 Solving Special Systems of Linear Equations 5.6 Graphing Linear Inequalities in Two Variables 5.7 Systems of Linear Inequalities **SEMESTER BREAK** How can a linear inequality or system of linear inequalities be solved? Realize how many solutions are possible just by looking at the equations of the system (ex. two lines could intersect once, infinitely many times, or not at all. should be used as well. May choose to combine or change order of sections to best suit class needs/teaching style. Interpret a special solution (infinite or no solutions). Solve a single linear inequality or a system of linear inequalities by graphing. Stress multiple ways to solve systems; encourage efficiency, but ultimately the correct solution (by whichever method) is most important. 6. Exponential Functions and Sequences 6.1 Properties of Exponents 6.2 Radicals & Rational Exponents N-RN.A.2 N-RN.A.1 A-CED.A.2 F-If.B.4 F-IF.C.7e F-IF.C.9 F-BF.A.1a n th root Radical Index of radical Exponential function Exponential growth, decay Exponential equation What are the basic rules of exponents? How are roots and powers used to make a rational exponent? Apply the basic rules of exponents to expressions containing numbers and variables. 6.1 will require thorough review and time. Students should understand that a rational 5

7 6.3 Exponential Functions 6.4 Exponential Growth & Decay 6.5 Solving Exponential Equations F-BF.B.3 F-LE.A.1a F-LE.A.2 A-SSE.B.3c F-IF.C.8b F-LE.A.1c A-CED.A.1 A-REI.A.1 A-REI.D.11 F-IF.A.3 F-BF.A.2 What are the characteristics of an exponential function, and how is it like and different from a linear function? What is the difference between exponential growth and exponential decay? How is an exponential equation solved? Convert between roots/powers and rational exponents. Graph exponential growth and decay functions and transform them using translations and reflections. Solve an exponential equations with like bases. exponent is another way of writing a root and a power; can limit to square and cube roots. Students should recognize and understand a very basic exponential function, both growth and decay, with previously learned transformations applied. Students should be able to solve an exponential equation with LIKE bases; teachers can experiment with unlike bases if applicable to their students. 6

8 7. Polynomial Equations and Factoring Algebra A-APR. A.1: Understand that polynomials form a system similar to integers in being closed. A-APR.B.3: Identify zeros of polynomials in factored form. A-REI.B.4b: Solve quadratic equations in one variable by inspection-example x 2 =49, quadratic formula, factoring. A-SSE.A.2: Use the structure of an expression to identify ways to rewrite it. A-REI.B.3a: Solve linear equations and inequalities in one variable including equations with coefficients represented by letters. Polynomial (also monomial, binomial, trinomial) Degree Factored form Standard form Zero-product property Leading coefficient FOIL method (special case of distribution) Root (also repeated root) Closed How are polynomials added, subtracted, multiplied and divided? How is a polynomial equation solved? How is factoring used to break a trinomial into a product of two binomials? How do you recognize and factor special products? Perform the four basic operations on polynomial expressions (including long and synthetic division). Solve a polynomial equation through factoring and application of the zeroproduct property and recognize the the solutions are the x- intercepts o the polynomial equation. Factor a polynomial expression Consider breaking the unit into two parts and testing separately (operations and then factoring). Review factoring out a GCF from a polynomial. Spend plenty of time factoring as it is an important component for many algebra 2 skills. 7

10 functions represented in a different way (algebraically, graphically, numerically in tables, or by verbal description) F-IF.B.4: Interpret and sketch graphs. F-BF.A.1: Write a function that describes a relationship between two quantities. A-SSE.B.3: Factor a quadratic to find zeros. A-APR.B.3: Identify zeros of polynomials when factored and use zeros to construct a rough graph. A-CED.A.2: Create equations to represent relationships, graph 9

12 9.5 Solving Quadratic Equations by the Quadratic Formula 9.6 Systems on Non- Linear Equations system on non-linear equations? Determine the number of real solutions to a quadratic equation through graphing or evaluating the discriminant. Determine how many solutions exist when given the graph of a nonlinear system. variables and numbers). Stress multiple ways to solve quadratic equations; encourage efficiency, but ultimately the correct solution (by whichever method) is most important. Students are not expected to solve a system of nonlinear equations, only note the number of possible solutions and understand why; you might discuss how to solve, but the expectation is not to carry out 11

13 substitution or elimination for specific solution sets. 10. Radical Functions and Equations 10.1 Graphing Square Root Functions 10.3 Solving Square Root Equations A-CED.A.2 F-IF.B.4 F.IF.B.6 F-IF.C.7b F.IF.C.9 A-CED.A.1 Square root function What are some characteristics of the graph of a square root function? How can you solve an equation involving square roots? Graph and describe a square root function, including ones that have been transformed. If time allows, introduce the square root function (graphs and equations) Solve an equation containing a square root. 11. Data Analysis and Displays 11.1 Measures of Center and Variation 11.2 Box-and-Whisker Plots S-ID.A.3 S-ID.A.1 Mean Median Mode Range Interquartile range Outlier Quartile Box-and-whisker plot How can you describe the center and variation of a data set? How can a box-and-whisker plot be used to describe a data set? I can choose an appropriate measure of center. I can use a box-and-whisker plot to interpret a data set. If time allows and teacher feels there is a need, students should be able to use the three measures of center, range as a measure of variation, and displaying onevariable data in box-and- 12

14 whisker (or other) plots. 13

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