## Description

- Overview:
- This lesson is for a math classroom, but can be adapted to fit any grade, subject, or content. In this lesson, students will use an iPad and its features: Keynote, Pages, Garageband, Numbers, Presentation, and iMovie. Students will use 3 of those features/programs to create a video lesson consisting of several examples from a topic of their choice. This project is in place of a term final, so their chosen topic should be from their current term.Image citation: The image is one I created.

- Remix of:
- Lesson Plan Template
- Subject:
- Secondary Mathematics
- Level:
- High School
- Material Type:
- Assessment
- Author:
- Tyrani Bevell
- Date Added:
- 02/26/2022

- License:
- Public Domain Dedication
- Language:
- English
- Media Format:
- Text/HTML

## Standards

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Learning Domain: Secondary Mathematics III

Standard: Understand that all polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

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Learning Domain: Secondary Mathematics III

Standard: 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).

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Learning Domain: Secondary Mathematics III

Standard: 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.

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Learning Domain: Secondary Mathematics III

Standard: Prove polynomial identities and use them to describe numerical relationships.

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Learning Domain: Secondary Mathematics III

Standard: Know and apply the Binomial Theorem for the expansion of (x + y)<sup>n</sup> in powers of x and y for a positive integer n, where x and y are any numbers.

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Learning Domain: Secondary Mathematics III

Standard: Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division or, for the more complicated examples, a computer algebra system.

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Learning Domain: Secondary Mathematics III

Standard: Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

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Learning Domain: Secondary Mathematics III

Standard: Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

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Learning Domain: Secondary Mathematics III

Standard: Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

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Learning Domain: Secondary Mathematics III

Standard: Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or non-viable options ina modeling context.

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Learning Domain: Secondary Mathematics III

Standard: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations.

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Learning Domain: Secondary Mathematics III

Standard: Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, for example, using technology to graph the functions, make tables of values, or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.

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Learning Domain: Secondary Mathematics III

Standard: Solve simple rational and radical equations in one variable, and give examples showing how extraneous solutions may arise.

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Learning Domain: Secondary Mathematics III

Standard: Interpret polynomial and rational expressions that represent a quantity in terms of its context.

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Learning Domain: Secondary Mathematics III

Standard: Interpret parts of an expression, such as terms, factors, and coefficients.

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Learning Domain: Secondary Mathematics III

Standard: Interpret complex expressions by viewing one or more of their parts as a single entity.

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Learning Domain: Secondary Mathematics III

Standard: Use the structure of an expression to identify ways to rewrite it.

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Learning Domain: Secondary Mathematics III

Standard: Understand the formula for the sum of a series and use the formula to solve problems.

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Learning Domain: Secondary Mathematics III

Standard: Derive the formula for the sum of an arithmetic series.

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Learning Domain: Secondary Mathematics III

Standard: Derive the formula for the sum of a geometric series, and use the formula to solve problems. Extend to infinite geometric series.

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Learning Domain: Secondary Mathematics III

Standard: Write a function that describes a relationship between two quantities.

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Learning Domain: Secondary Mathematics III

Standard: Combine standard function types using arithmetic operations.

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Learning Domain: Secondary Mathematics III

Standard: Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Note the effect of multiple transformations on a single function and the common effect of each transformation across function types. Include functions defined only by a graph. 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.

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Learning Domain: Secondary Mathematics III

Standard: Find inverse functions.

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Learning Domain: Secondary Mathematics III

Standard: 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. Include linear, quadratic, exponential, logarithmic, rational, square root, and cube root functions.

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Learning Domain: Secondary Mathematics III

Standard: 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.

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Learning Domain: Secondary Mathematics III

Standard: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

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Learning Domain: Secondary Mathematics III

Standard: Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

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Learning Domain: Secondary Mathematics III

Standard: Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

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Learning Domain: Secondary Mathematics III

Standard: Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions. Compare and contrast square root, cubed root, and step functions with all other functions.

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Learning Domain: Secondary Mathematics III

Standard: Graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior.

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Learning Domain: Secondary Mathematics III

Standard: Graph rational functions, identifying zeros and asymptotes when suitable factorizations are available, and showing end behavior.

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Learning Domain: Secondary Mathematics III

Standard: Graph exponential and logarithmic functions, showing intercepts and end behavior; and trigonometric functions, showing period, midline, and amplitude.

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Learning Domain: Secondary Mathematics III

Standard: Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

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Learning Domain: Secondary Mathematics III

Standard: Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

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Learning Domain: Secondary Mathematics III

Standard: Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quanitity increasing linearly, quadratically, or (more generally) as a polynomial function.

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Learning Domain: Secondary Mathematics III

Standard: For exponential models, express as a logarithm the solution to ab<sup>ct</sup> = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology. Include the relationship between properties of logarithms and properties of exponents, such as the connection between the properties of exponents and the basic logarithm property that log xy = logx + log y.

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Learning Domain: Secondary Mathematics III

Standard: Interpret the parameters in a linear, quadratic, and exponential functions in terms of a context.

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Learning Domain: Secondary Mathematics III

Standard: Understand radian measure of an angle as the length of the arc on the unit circle subtended by the angle.

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Learning Domain: Secondary Mathematics III

Standard: 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.

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Learning Domain: Secondary Mathematics III

Standard: Use special triangles to determine geometrically the values of sine, cosine, tangent for π/3, π/4 and π6, and use the unit circle to express the values of sine, cosine, and tangent for π – x, π + x, and 2π – x in terms of their values for x, where x is any real number.

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Learning Domain: Secondary Mathematics III

Standard: Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

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Learning Domain: Secondary Mathematics III

Standard: Use inverse functions to solve trignometric equations that arise in modeling context; evaluate the solutions using technology and interpret them in terms of context. Limit solutions to a given interval.

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Learning Domain: Secondary Mathematics III

Standard: Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of twodimensional objects.

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Learning Domain: Secondary Mathematics III

Standard: Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

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Learning Domain: Secondary Mathematics III

Standard: Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).

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Learning Domain: Secondary Mathematics III

Standard: Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

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Learning Domain: Secondary Mathematics III

Standard: Prove the Laws of Sines and Cosines and use them to solve problems.

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Learning Domain: Secondary Mathematics III

Standard: Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

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Learning Domain: Secondary Mathematics III

Standard: Derive the formula A = ½ ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

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Learning Domain: Secondary Mathematics III

Standard: Extend polynomial identities to the complex numbers.

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Learning Domain: Secondary Mathematics III

Standard: Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials. Limit to polynomials with real coefficients.

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Learning Domain: Secondary Mathematics III

Standard: Understand that statistics allow inferences to be made about population parameters based on a random sample from that population.

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Learning Domain: Secondary Mathematics III

Standard: Recognize the purposes of and differences among sample surveys, experiments, and observational studies; explain how randomization relates to each.

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Learning Domain: Secondary Mathematics III

Standard: Use data from a sample survey to estimate a population mean or proportion; develop a margin of error through the use of simulation models for random sampling.

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Learning Domain: Secondary Mathematics III

Standard: Evaluate reports based on data.

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Learning Domain: Secondary Mathematics III

Standard: 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.

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Learning Domain: Secondary Mathematics III

Standard: Make sense of problems and persevere in solving them. Explain the meaning of a problem and look for entry points to its solution. Analyze givens, constraints, relationships, and goals. Make conjectures about the form and meaning of the solution, plan a solution pathway, and continually monitor progress asking, "Does this make sense?" Consider analogous problems, make connections between multiple representations, identify the correspondence between different approaches, look for trends, and transform algebraic expressions to highlight meaningful mathematics. Check answers to problems using a different method.

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Learning Domain: Secondary Mathematics III

Standard: Reason abstractly and quantitatively. Make sense of the quantities and their relationships in problem situations. Translate between context and algebraic representations by contextualizing and decontextualizing quantitative relationships. This includes the ability to decontextualize a given situation, representing it algebraically and manipulating symbols fluently as well as the ability to contextualize algebraic representations to make sense of the problem.

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Learning Domain: Secondary Mathematics III

Standard: Construct viable arguments and critique the reasoning of others. Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Make conjectures and build a logical progression of statements to explore the truth of their conjectures. Justify conclusions and communicate them to others. Respond to the arguments of others by listening, asking clarifying questions, and critiquing the reasoning of others.

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Learning Domain: Secondary Mathematics III

Standard: Model with mathematics. Apply mathematics to solve problems arising in everyday life, society, and the workplace. Make assumptions and approximations, identifying important quantities to construct a mathematical model. Routinely interpret mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose.

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Learning Domain: Secondary Mathematics III

Standard: Use appropriate tools strategically. Consider the available tools and be sufficiently familiar with them to make sound decisions about when each tool might be helpful, recognizing both the insight to be gained as well as the limitations. Identify relevant external mathematical resources and use them to pose or solve problems. Use tools to explore and deepen their understanding of concepts.

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Learning Domain: Secondary Mathematics III

Standard: Attend to precision. Communicate precisely to others. Use explicit definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose. Specify units of measure and label axes to clarify the correspondence with quantities in a problem. Calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context.

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Learning Domain: Secondary Mathematics III

Standard: Look for and make use of structure. Look closely at mathematical relationships to identify the underlying structure by recognizing a simple structure within a more complicated structure. See complicated things, such as some algebraic expressions, as single objects or as being composed of several objects.

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Learning Domain: Secondary Mathematics III

Standard: Look for and express regularity in repeated reasoning. Notice if reasoning is repeated, and look for both generalizations and shortcuts. Evaluate the reasonableness of intermediate results by maintaining oversight of the process while attending to the details.

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