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**Grades 9-12.**

**For your Common Core curriculum.**

These Common Core Standards supplements have been revised to tighten alignment and better reflect current interpretations of CCSS content and practices, based on implementation experience. Each book contains a collection of activity sets focusing on Number and Quantity, Algebra, Functions, and Statistics and Probability. Each activity set consists of 4 different stations (10-15 minutes each) where students work in small groups on multiple sets of activities, moving from station to station once their activities are complete. A debrief discussion follows the station activities. Uses readily available materials and manipulatives (not included). Includes teacher support with discussion guides, answer keys, and materials lists. 238 pages.

**CCSS Product Alignment**

**Math High School: Number and Quantity**

**HSN.CN.1** Know there is a complex number *i* such that *i*2 = -1, and every complex number has the form *a + bi* with *a* and *b* real.

**HSN.CN.2** Use the relation *i*2 = -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

**HSN.CN.3** (+) Find the conjugate of a complex number, use conjugates to find moduli and quotients of complex numbers.

**HSN.CN.7** Solve quadratic equations with real coefficients that have complex solutions.

**HSN.CN.9** (+) Know the Fundamental Theorem of Algebra, show that it is true for quadratic polynomials.

**Math High School: Algebra**

**HSA.SSE.2** Use the structure of an expression to identify ways to rewrite it. *For example, see x ^{4} - y^{4} as (x2)2 - (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 - y2)(x2 + y2).*

**HSA.SSE.3a** Factor a quadratic expression to reveal the zeros of the function it defines.

**HSA.SSE.3b** Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

**HSA.SSE.3c** Use the properties of exponents to transform expressions for exponential functions. *For example the expression 1.15 ^{t} can be rewritten as (1.15^{1/12})^{12t} 8776, 1.012^{12t} to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.*

**HSA.APR.2** Know and apply the Remainder Theorem: For a polynomial *p*(*x*) and a number *a*, the remainder on division by *x - a* is *p*(*a*), so *p*(*a*) = 0 if and only if (*x - a*) is a factor of *p* (*x*).

**HSA.APR.3** Identify zeros of polynomials when suitable factorizations are available, and use the zeros to construct a rough graph of the function defined by the polynomial.

**HSA.CED.2** Create equations in two or more variables to represent relationships between quantities, graph equations on coordinate axes with labels and scales.

**HSA.CED.3** Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. *For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.*

**HSA.REI.4a** Use the method of completing the square to transform any quadratic equation in *x* into an equation of the form (*x* - *p*)2 = *q* that has the same solutions. Derive the quadratic formula from this form.

**HSA.REI.4b** Solve quadratic equations by inspection (e.g., for *x*2 = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as *a* 177, *bi* for real numbers *a* and *b*.

**Math High School: Functions**

**HSF.IF.2** Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

**HSF.IF.3** Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. *For example, the Fibonacci sequence is defined recursively by 131,(0) = 131,(1) = 1, 131,(n+1) = 131,(n) + 131,(n-1) for n 8805, 1.*

**HSF.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. *Key features include: intercepts, intervals where the function is increasing, decreasing, positive, or negative, relative maximums and minimums, symmetries, end behavior, and periodicity.*

**HSF.IF.5** Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. *For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.*

**HSF.IF.7a** Graph linear and quadratic functions and show intercepts, maxima, and minima.

**HSF.IF.7b** Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.

**HSF.IF.7c** Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

**HSF.IF.7d** (+) Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

**HSF.IF.7e** Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.

**HSF.IF.8a** Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

**HSF.IF.8b** Use the properties of exponents to interpret expressions for exponential functions. For example, identify percent rate of change in functions such as y = (1.02)^{t}, y = (0.97)^{t}, y = (1.01)12^{t}, y = (1.2)^{t}/10, and classify them as representing exponential growth or decay.

**HSF.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.

**HSF.BF.3** Identify the effect on the graph of replacing 131,(*x*) by 131,(*x*) + *k, k *131,(*x*), 131,(*kx*), and 131, (*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. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

**HSF.BF.4a** Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an expression for the inverse. *For example, f(x) =2 x179, or f(x) = (x+1)/(x-1) for x 1.*

**HSF.BF.4b** (+) Verify by composition that one function is the inverse of another.

**HSF.BF.4c** (+) Read values of an inverse function from a graph or a table, given that the function has an inverse.

**HSF.BF.4d** (+) Produce an invertible function from a non-invertible function by restricting the domain.

**HSF.BF.5** (+) Understand the inverse relationship between exponents and logarithms and use this relationship to solve problems involving logarithms and exponents.

**HSF.TF.2** Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers, interpreted as radian measures of angles traversed counterclockwise around the unit circle.

**HSF.TF.4** (+) Use the unit circle to explain symmetry (odd and even) and periodicity of trigonometric functions.

**Math High School: Geometry**

**HSG.GPE.1** Derive the equation of a circle of given center and radius using the Pythagorean Theorem, complete the square to find the center and radius of a circle given by an equation.

**HSG.GPE.2** Derive the equation of a parabola given a focus and directrix.

**HSG.GPE.3** (+) Derive the equations of ellipses and hyperbolas given the foci, using the fact that the sum or difference of distances from the foci is constant.

**Math High School: Statistics and Probability**

**HSS.ID.2** Use 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.

**HSS.ID.4** Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve.

**HSS.ID.6a** Fit a function to the data, use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.

**HSS.ID.6b** Informally assess the fit of a function by plotting and analyzing residuals.

**HSS.ID.6c** Fit a linear function for a scatter plot that suggests a linear association.

**HSS.ID.9** Distinguish between correlation and causation.

**HSS.CP.1** Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (or, and, not).

**HSS.CP.2** Understand that two events *A* and *B* are independent if the probability of *A* and *B* occurring together is the product of their probabilities, and use this characterization to determine if they are independent.

**HSS.CP.3** Understand the conditional probability of *A* given *B* as *P*(*A* and *B*)/*P*(*B*), and interpret independence of *A* and *B* as saying that the conditional probability of *A* given *B* is the same as the probability of *A*, and the conditional probability of *B* given *A* is the same as the probability of *B*.

**HSS.CP.7** Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.

**HSS.CP.8** (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B A) = P(B)P(A B), and interpret the answer in terms of the model.

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