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Algebra II Power Standards AMA ESD Based on MDE Algebra II course description revised 9-3-09 These power standards represent the most important mathematical ideas and skills of Algebra II, the concepts that all students need to learn for life (endurance) as well as for on-going education (leverage). Expressions and equations Expressions and equations Students in Algebra II represent real-world situations mathematically, evaluate expressions, and solve equations involving polynomials, rational expressions, and exponential and logarithmic expressions. I can put real-world situations into mathematical expressions and equations. (L1.2.1, A1.1.1) I can evaluate expressions for a given value of the variable. (A1.1.1) PS 1: Solve polynomial equations, equations involving I can solve polynomial equations, by adding, rational expressions, exponential equations and subtracting, multiplying, dividing and simplifying logarithmic equations. A1.2.5, A1.2.7 polynomials. (A1.2.5, A1.1.4, A1.1.5) Related content expectations: L1.2.1, A1.1.1, I can solve rational equations, by adding, subtracting, A1.1.4, A1.1.5, A1.1.6, A1.2.2, L2.1.3 (rules of multiplying and simplifying rational expressions. logarithms are post-MME) (A1.2.5, A1.1.4) PS 2: Solve an equation involving several variables I can solve exponential and logarithmic equations, by (with numerical or letter coefficients) for a designated transforming exponential and logarithmic expressions variable, and justify steps in the solution. A1.2.8 into equivalent forms using their properties and knowing that logarithms are the inverse of exponents. (A1.2.7, A1.1.6, A3.2.3 – logarithms are post-MME) I can solve equations by graphing the related function and finding the zeros. (A1.2.2) I can solve an equation that has several variables for a chosen variable. (A1.2.8) Functions Functions Students in Algebra II use exponential, logarithmic and rational functions to model real-world situations and solve problems. I understand logarithmic measurements scales such as the Richter scale, the pH scale, and decibel measurements, and I can solve problems that use these measuring scales. (L2.3.2 – post-MME.) PS 3: Describe and interpret logarithmic relationships in such measurement contexts as the Richter scale, the pH scale, or decibel measurements; solve applied problems. L2.3.2 – Real-world examples of logarithmic relationships are post-MME. I can decide which family of functions can be used to represent (model) a real-world situation. In Algebra I, those functions include linear, quadratic and exponential functions. In Algebra II they include exponential, logarithmic, and rational functions. PS 4: Identify the family of functions (exponential, logarithmic, rational) best suited for modeling a given (A2.4.1) real-world situation. Identify a function as a member I can look at a written function or graph and tell what of a family of functions from its symbolic form or family of functions it belongs to. (A2.3.1, A3.2.2) graph. A2.4.1, A2.3.1, A2.3.3, A3.2.2 (exponential I can write the general form of the function for each and logarithmic), A3.6.1 (rational) family of functions. (A2.3.3, A3.6.1) PS 5: Adapt the general symbolic form of a function to one that fits the specifications of a given situation by using the information to replace arbitrary constants with numbers, A2.4.2; identify and interpret the key features of a function from its graph or its formula(s); apply transformations to parent functions, A2.1.7, A2.2.2; solve problems with functions, A2.4.3. I know what each constant means in a general form for exponential functions. I can customize a general mathematical function to fit a specific real-world situation by using information from the situation to fill in each constant in the general function. (A2.4.2) Related content expectations: Exponential and Logarithmic functions: A3.2.2-3 – logarithmic functions are post-MME. Rational functions: A3.6.2 PS 6: Theory of functions: Interpret function notation (A2.1.2); is it a function? (A2.1.1); what are its zeros? (A2.1.6); where is it increasing/decreasing? (A2.1.6); combine functions (A2.2.1); find inverse of functions (A2.2.3) I can look at a graph and identify the key features of the function. (A2.1.7, A3.2.2, A3.6.2 – logarithmic functions are post-MME.) I can graph basic exponential, logarithmic and rational functions. (A2.1.3, A3.2.2, A3.6.1 – logarithmic functions are post-MME.) I can transform a function in different ways by changing its constants and I can show what that does to its graph. (A2.2.2) I can solve problems with functions. (A2.4.3) I understand recursive formulas for linear and PS 7: Relate sequences of values to recursive formulas exponential functions and I can relate them to for linear and exponential functions; find nth term. sequences of values. (L2.2.1 – post MME.) L2.2.1 – Sequences are post-MME. I can find the nth term of a sequence and the sum of Related content expectations: Sums of finite arithmetic and geometric sequences: L2.2.2 – post-MME PS 8: Use iterative processes in such examples as computing compound interest or applying approximation procedures. L2.2.3 – Iterative processes are post-MME. Statistics finite arithmetic and geometric sequences. (L2.2.1 – post MME.) I can use iterative processes for things like computing compound interest or approximating answers to complex problems. (L2.2.3 – post-MME.) Statistics Students in Algebra II represent and analyze data sets I can gather information from dot plots, histograms, related to real-world situations and identify sources of relative frequency histograms, bar graphs, basic bias. control charts, and box plots and I can make them, using appropriate labels and scales. (S1.1.1) PS 9: Construct and interpret dot plots, histograms, relative frequency histograms, bar graphs, basic control charts, and box plots with appropriate labels and scales; determine which kinds of plots are appropriate for different types of data; compare data sets and interpret differences based on graphs and summary statistics. S1.1.1 Related content expectations: Measures of center: S1.2.1 I can decide which kind of plot is the most appropriate to use for the given data. (S1.1.1) I can compare data sets and interpret differences based on graphs and summary statistics. (S1.1.1) I can find mean, median, mode and range of a data set. I can identify outliers. (S1.2.1) Probability Probability Students in Algebra II understand basic probability concepts and apply them to real-world situations. I can use counting techniques as needed. (L1.3.1 – post-MME) PS 10: Describe, explain, and apply various counting techniques; relate combinations to Pascal’s triangle; know when to use each technique. L1.3.1 – Counting techniques are post-MME. These topics are included in the HSCE document for Algebra II, but our criteria of endurance and leverage don’t apply to them, so they are not part of the power standards: Conic sections – G1.7.1 is recommended if there is time; G1.7.2 and G1.7.3 are extensions (pre-calculus). Conic sections are not tested on the MME. Complex numbers (L2.1.5) are “nice to know” and may appear as solutions to some polynomial equations. Complex numbers are not tested on the MME