Ingham County Power Standards and Related Learning Targets for Algebra II
based on Michigan High School Content Expectations
Power Standards are the enduring understandings and key skills of the subject. They are the culmination
of a student’s work at that grade. They give students power to confront real world problems and leverage
for learning more advanced content.
The power standards for Algebra II are combinations of the main headings (strands) in the subject and
some of the most comprehensive and overarching content expectations within those strands. We did not
simply choose a small number of the content expectations as power standards. The remaining content
expectations that are foundational for the power standards are included in this document as “related
learning targets.” They are the steps students take in their conceptual and computational mastery of the
power standards.
Power Standard 1: Solve equations and inequalities – Write, simplify, and find solutions of complex
equations that represent mathematical or applied situations.
Related Learning Targets – Students will:
1) Translate between verbal and symbolic descriptions of expressions and evaluate expressions for
given values of the variable; expressions can include exponents, logarithms and trig functions.
(A1.1.1)
2) Associate a given equation with a function whose zeros are the solutions of the equation. (A1.2.2)
3) Solve an equation involving several variables (with numerical or letter coefficients) for a
designated variable, and justify steps in the solution. (A1.2.8)
4) Know common formulas and apply appropriately in contextual situations. (A1.2.9)
5) Add, subtract, multiply, and simplify polynomials and rational expressions; divide a polynomial
by a monomial. (A1.1.4, A1.1.5)
6) Solve polynomial equations and equations involving rational expressions and justify steps in the
solution. (A1.2.5)
7) Transform exponential and logarithmic expressions into equivalent forms using the properties of
exponents and logarithms, including the inverse relationship between exponents and logarithms.
(A1.1.6, A3.2.3)
8) Solve exponential and logarithmic equations and justify steps in the solution. (A1.2.7)
9) Use special values of the inverse trigonometric functions to solve trigonometric equations over
specific intervals. (A1.2.10)
5/25/2009
For more information, contact Theron Blakeslee, Ingham Intermediate School District
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Power Standard 2: Translate among representations of functions – Represent, recognize and analyze
the key features of functions in symbols, graphs, tables, diagrams or words and translate among
representations. (A2.1.3, A2.1.7)
Related Learning Targets – Students will:
1) Read, interpret, and use function notation and evaluate a function at a value in its domain.
(A2.1.2)
2) Determine whether a relationship (given in contextual, symbolic, tabular, or graphical form) is a
function, and identify its domain and range. (A2.1.1)
3) Identify the zeros of a function, the intervals where the values of a function are positive or
negative, and describe the behavior of a function as x approaches positive or negative infinity,
given the symbolic and graphical representation. (A2.1.6)
4) Combine functions by addition, subtraction, multiplication, and division. (A2.2.1)
5) Recognize whether a function (given in tabular or graphical form) has an inverse that is a
function, and recognize simple inverse pairs. (A2.2.3)
6) Distinguish among exponential, logarithmic and trigonometric functions by their verbal
descriptions: Recognize exponential functions as situations such as compound interest, population
growth, radioactive decay, etc. (A3.2.5); recognize logarithmic functions as representing physical
situations such as sound intensity (decibel scale), Earthquake intensity (Richter scale), and the pH
scale used for acid and base strength (L2.3.2); recognize trigonometric functions as situations
involving simple harmonic motion and other cyclical situations.
7) Interpret the symbolic forms and recognize (sketch) the graphs of exponential and logarithmic
functions (A3.2.2), simple rational functions (A3.6.1), and trigonometric functions (A3.7.4).
 Analyze graphs of simple rational functions and understand the relationship between the zeros
of the numerator and denominator, and the function’s intercepts, asymptotes, and domain
(A3.6.2)
 Graph the sine and cosine functions; analyze graphs by noting domain, range, period,
amplitude, and location of maxima and minima. (A3.7.4)
 Use the unit circle to define sine and cosine; approximate values of sine and cosine; use
sine and cosine to define the remaining trigonometric functions; explain why the
trigonometric functions are periodic. (A3.7.1)
 Use the relationship between degree and radian measures to solve problems. (A3.7.2)
 Use the unit circle to determine the exact values of sine and cosine, for integer multiples of
/6 and /4. (A3.7.3)
 Graph transformations of basic trigonometric functions (involving changes in period,
amplitude, phase, and midline) and understand the relationship between constants in the
formula and the transformed graph. (A3.7.5, A2.2.2)
5/25/2009
For more information, contact Theron Blakeslee, Ingham Intermediate School District
2
Power Standard 3: Model real-world situations using functions – Choose the appropriate family of
functions to model a real-world situation, write the symbolic form of the function, and use the specific
function to draw conclusions about the situation. (A2.4.1, A2.4.2, A2.4.3, A2.3.1, A2.3.3)
Related Learning Targets – Students will:
1) Recognize exponential functions as situations such as compound interest, population growth,
radioactive decay, etc. (A3.2.5); recognize logarithmic functions such as sound intensity (decibel
scale), Earthquake intensity (Richter scale), and the pH scale used for acid and base strength
(L2.3.2); recognize trigonometric functions as situations involving simple harmonic motion and
other cyclical situations.
2) Write the symbolic forms of exponential, logarithmic and trigonometric functions given
appropriate information (see PS 2, RLT 7 above).
3) Use the specific symbolic form of the function to find values that answer questions about the
situation modeled by the function. (A2.4.3)
Power Standard 4: Examine statistics and determine probabilities – Collect, display, analyze, and
describe data; compute and apply probabilities. Use statistics and probabilities to make predictions and
informed decisions.
Related Learning Targets – Students will:
1) Describe data collection techniques and evaluate the appropriateness of each for a given situation,
determining ways to minimize bias.
2) Choose and construct an appropriate plot for displaying data, including dot plots, histograms, bar
graphs, and box plots, and use it to describe the data and compare data sets.
3) Calculate and interpret measures of center and variation.
4) Use distributions, including normal distribution, to describe a data set and relate the distribution
to the measures of center and variation as well as z-scores. Use properties of the distribution,
including z-scores, to make informed decisions.
We consider the following topics to be extensions of the core of Algebra II:
 Calculations involving complex numbers (L2.1.5)
 Sequences and iteration (L2.2.1, L2.2.2, L2.2.3)
 Conic sections (G1.7.1, G1.7.2, G1.7.3)
The work presented here is the result of a process of a committee of mathematics teachers in Ingham County.
5/25/2009
For more information, contact Theron Blakeslee, Ingham Intermediate School District
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