All Lessons
Solve Equations with Unknown Coefficients
(A) Solve linear equations in one variable, including those for which the application of the distributive property is necessary and for which variables are included on both sides
A1.12.E(E) Solve mathematic and scientific formulas, and other literal equations, for a specified variable.
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Add, Subtract, and Multiply Polynomials
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Solve Multi-Step Linear Inequalities
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Factor Quadratic Expressions - Part 1
(8) Quadratic functions and equations. The student applies the mathematical process standards to solve, with and without technology, quadratic equations and evaluate the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.
A1.8.A(A) Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula
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Factor Quadratic Expressions - Part 2
(8) Quadratic functions and equations. The student applies the mathematical process standards to solve, with and without technology, quadratic equations and evaluate the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.
A1.8.A(A) Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula
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Solve Exponential Equations
(C) Write exponential functions in the form f(x) = abx (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay
A2.5.D(D) Solve exponential equations of the form y = abx where a is a nonzero real number and b is greater than zero and not equal to one and single logarithmic equations having real solutions
PCAL.5.I(I) Generate and solve exponential equations in mathematical and real-world problems
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Solve Quadratic Equations by Completing the Square
(7) Quadratic functions and equations. The student applies the mathematical process standards when using graphs of quadratic functions and their related transformations to represent in multiple ways and determine, with and without technology, the solutions to equations.
A1.7.A(A) Graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry
A1.7.B(B) Describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions
A1.7.C(C) Determine the effects on the graph of the parent function f(x) = x2 when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d.
A1.8(8) Quadratic functions and equations. The student applies the mathematical process standards to solve, with and without technology, quadratic equations and evaluate the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.
A1.8.A(A) Solve quadratic equations having real solutions by factoring, taking square roots, completing the square, and applying the quadratic formula
A1.8.B(B) Write, using technology, quadratic functions that provide a reasonable fit to data to estimate solutions and make predictions for real-world problems.
A1.9(9) Exponential functions and equations. The student applies the mathematical process standards when using properties of exponential functions and their related transformations to write, graph, and represent in multiple ways exponential equations and evaluate, with and without technology, the reasonableness of their solutions. The student formulates statistical relationships and evaluates their reasonableness based on real-world data.
A1.9.A(A) Determine the domain and range of exponential functions of the form f(x) = abx and represent the domain and range using inequalities
A1.9.B(B) Interpret the meaning of the values of a and b in exponential functions of the form f(x) = abx in real-world problems
A1.9.C(C) Write exponential functions in the form f(x) = abx (where b is a rational number) to describe problems arising from mathematical and real-world situations, including growth and decay
A1.9.D(D) Graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical and real-world problems
A1.9.E(E) Write, using technology, exponential functions that provide a reasonable fit to data and make predictions for real-world problems.
HSF.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
HSF.IF.8.AHSF.IF.8.A 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.8.BHSF.IF.8.B 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)áµ—, y = (0.97)áµ—, y = (1.01)12áµ—, y = (1.2)áµ—/10, and classify them as representing exponential growth or decay.
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Solve Quadratic Equations by Factoring
(10) Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to rewrite in equivalent forms and perform operations on polynomial expressions.
A1.10.A(A) Add and subtract polynomials of degree one and degree two
A1.10.B(B) Multiply polynomials of degree one and degree two
A1.10.C(C) Determine the quotient of a polynomial of degree one and polynomial of degree two when divided by a polynomial of degree one and polynomial of degree two when the degree of the divisor does not exceed the degree of the dividend
A1.10.D(D) Rewrite polynomial expressions of degree one and degree two in equivalent forms using the distributive property
A1.10.E(E) Factor, if possible, trinomials with real factors in the form ax2 + bx + c, including perfect square trinomials of degree two
A1.10.F(F) Decide if a binomial can be written as the difference of two squares and, if possible, use the structure of a difference of two squares to rewrite the binomial.
A1.11(11) Number and algebraic methods. The student applies the mathematical process standards and algebraic methods to rewrite algebraic expressions into equivalent forms.
A1.11.A(A) Simplify numerical radical expressions involving square roots
A1.11.B(B) Simplify numeric and algebraic expressions using the laws of exponents, including integral and rational exponents.
HSF.IF.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
HSF.IF.8.AHSF.IF.8.A 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.8.BHSF.IF.8.B 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)áµ—, y = (0.97)áµ—, y = (1.01)12áµ—, y = (1.2)áµ—/10, and classify them as representing exponential growth or decay.
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Graph Linear Functions by Plotting Ordered Pairs
(C) Contrast bivariate sets of data that suggest a linear relationship with bivariate sets of data that do not suggest a linear relationship from a graphical representation
A1.3.C(C) Graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical and real-world problems
8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
HSA.REI.10HSA.REI.10 Understand 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).
HSF.IF.7.AHSF.IF.7.A Graph linear and quadratic functions and show intercepts, maxima, and minima.
This expressions and equations lesson teaches students how to graph linear functions by plotting ordered pairs. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students will plot ordered pairs from a linear function on the coordinate plane.
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Identify Quadratic Function Graphs
(7) Quadratic functions and equations. The student applies the mathematical process standards when using graphs of quadratic functions and their related transformations to represent in multiple ways and determine, with and without technology, the solutions to equations.
A1.7.A(A) Graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept, zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry
A1.7.B(B) Describe the relationship between the linear factors of quadratic expressions and the zeros of their associated quadratic functions
A1.7.C(C) Determine the effects on the graph of the parent function f(x) = x2 when f(x) is replaced by af(x), f(x) + d, f(x - c), f(bx) for specific values of a, b, c, and d.
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Find the Input Value of a Function Given the Output
HSF.IF.1 Understand 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).
HSF.IF.2HSF.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
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Identify Function Types
This interpreting functions lesson teaches students how to identify different types of functions. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students will identify the attributes of a function and its graph to determine which type of function it is.
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Plot Function Types
HSF.IF.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.*
HSF.IF.7.AHSF.IF.7.A Graph linear and quadratic functions and show intercepts, maxima, and minima.
HSF.IF.7.CHSF.IF.7.C Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.
HSF.IF.7.EHSF.IF.7.E Graph exponential and logarithmic functions, showing intercepts and end behavior, and trigonometric functions, showing period, midline, and amplitude.
This interpreting functions lesson teaches students how to plot different types of functions on the coordinate plane. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students will determine the type of function, evaluate the function for a variety of values, and plot the results onto the coordinate plane.
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Convert Between Linear Function Notation and x-y Notation
This interpreting functions lesson teaches students how to convert between linear function notation and x-y notation. The lesson includes research-based strategies and strategic questions that prepare students for assessments. In this lesson, students will rewrite functions using different notations. Students will also demonstrate that the two notations describe the same line.