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Lesson Plan
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\n\"Graphs\n\n
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\nEngageNY\n
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\nGraphs of Simple Nonlinear Functions\n

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\n\nFor Teachers\n\n8th\n\nStandards\n
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\nTime to move on to nonlinear functions. Scholars create input/output tables and use these to graph simple nonlinear functions. They calculate rates of change to distinguish between linear and nonlinear functions.\n
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Instructional Video5:38
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\n\"How\n\n
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\nCurated OER\n
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\nHow Can You Tell if a Function is Linear or Nonlinear From a Table?\n

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\n\nFor Teachers\n\n6th - 9th\n
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\nIs it possible to tell if a table of values represents a linear function or a nonlinear function? One way is to graph the ordered pairs to see if it makes a straight line. But, take a look at the rate of change in the table. If the rate...\n
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Lesson Plan
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\n\"Linear\n\n
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\nCurated OER\n
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\nLinear and Nonlinear Functions\n

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\n\nFor Teachers\n\n8th - 10th\n
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\nStudents identify properties of a line. In this algebra instructional activity, students differentiate between functions and nonfunctions. They use the slope and y intercept to graph their lines.\n
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Lesson Plan
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\n\"Increasing\n\n
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\nEngageNY\n
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\nIncreasing and Decreasing Functions 2\n

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\n\nFor Teachers\n\n8th\n\nStandards\n
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\nExplore linear and nonlinear models to help your class build their function skills. In a continuation of the previous lesson, learners continue to analyze and sketch functions that model real-world situations. They progress from linear...\n
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Lesson Plan
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\n\"Nonlinear\n\n
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\nEngageNY\n
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\nNonlinear Models in a Data Context\n

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\n\nFor Teachers\n\n8th\n\nStandards\n
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\nHow well does your garden grow? Model the growth of dahlias with nonlinear functions. In the lesson, scholars build on their understanding of mathematical models with nonlinear models. They look at dahlias growing in compost and...\n
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Workbook
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\n\"Functions\n\n
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\nUniversity of Utah\n
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\nFunctions\n

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\n\nFor Students\n\n8th\n\nStandards\n
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\nDefine, explore, compare, and analyze functions with the fourth chapter of a 10-part eighth-grade workbook series. After encountering the definition of a function, pupils begin to explore linear and nonlinear functions. They then...\n
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Activity
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\n\"Creating\n\n
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\nCreating a Polynomial Function to Fit a Table\n

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\n\nFor Students\n\n9th - 10th\n\nStandards\n
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\nDiscover relationships between linear and nonlinear functions. Initially, a set of data seems linear, but upon further exploration, pupils realize the data can model an infinite number of functions. Scholars use multiple representations...\n
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Handout
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\n\"Sketching\n\n
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\nCharleston School District\n
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\nSketching a Piecewise Function\n

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\n\nFor Students\n\n8th - 9th\n\nStandards\n
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\nHow do you combine linear and nonlinear functions? You piece them together! The lesson begins by analyzing given linear piecewise functions and then introduces nonlinear parts. Then the process is reversed to create graphs from given...\n
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Handout
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\n\"Graphing\n\n
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\nCharleston School District\n
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\nGraphing Functions\n

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\n\nFor Students\n\n8th\n\nStandards\n
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\nHow do letters and numbers create a picture? Scholars learn to create input/output tables to graph functions. They graph both linear and nonlinear functions by creating tables and plotting points. \n
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Lesson Plan
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\n\"Very\n\n
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\nCurated OER\n
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\nVery Varied - Inverse variation\n

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\n\nFor Teachers\n\n8th - 11th\n
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\nStudents identify inverse variations. In this inverse variation activity, students explore graphs and identify the inverse variation. They write equations for the inverse variation. Students compare and contrast the inverse variation...\n
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Worksheet
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\n\"Taylor's\n\n
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\nCurated OER\n
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\nTaylor's Theorem\n

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\n\nFor Students\n\nHigher Ed\n
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\nFor this Taylor's Theorem worksheet, students use the microscope approximation to determine the approximate value of a function. They rewrite expressions for the relative error, and observe changes in the relative error. They use...\n
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Lesson Plan
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\n\"The\n\n
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\nCurated OER\n
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\nThe Fractal Coast\n

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\n\nFor Teachers\n\n9th - 11th\n
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\nStudents investigate measuring as it relates to the real world. In this geometry lesson plan, students measure distances as they discuss fractals and how it relates to measuring. They measure both linear and non-linear distances.\n
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Instructional Video6:06
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\n\"What's\n\n
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\nWhat's an Exponential Function?\n

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\n\nFor Teachers\n\n10th - 12th\n
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\nThe instructor defines an exponential function as any expression or equation in which an exponent is a variable. She then gives several examples.\n
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Lesson Plan
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\n\"Composing\n\n
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\nCurated OER\n
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\nComposing Music Mathematically\n

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\n\nFor Teachers\n\n9th - 12th\n
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\nStudents recognize relationships between mathematics and music by identifying the frequency and volume of a pure tone. Students discover that sound can be represented as a function and collect pure tones to generate smooth curves.\n
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Instructional Video6:55
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\nWhat is a Quadratic Function?\n

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\n\nFor Teachers\n\n6th - 12th\n
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\nThis is an introductory video on how to identify a quadratic function. This video explains what a quadratic function is and what the graph of a quadratic function looks like. The instructor goes through 4 examples of quadratic functions...\n
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Instructional Video2:51
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\nWhat's a Polynomial?\n

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\n\nFor Teachers\n\n6th - 12th\n
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\nA polynomial is the sum of one or more monomials. They are identified by the number of terms they have. Monomials, binomials, trinomials, find out what these terms identify.\n
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Instructional Video2:27
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\nWhat's the Formula for the Square of a Difference?\n

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\n\nFor Teachers\n\n6th - 12th\n
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\nThe Difference Between Two Squares is an algebraic expression where two terms are perfect squares and one is negative. In this clip the Algebra teacher uses the FOIL method to factor a difference between two squares and prove the equation.\n
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Instructional Video2:09
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\nWhat's an Arithmetic Sequence?\n

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\n\nFor Teachers\n\n6th - 12th\n
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\n2, 4, 6, 8, who do we appreciate? Do the numbers in this sequence make it an arithmetic sequence? Watch this video and find out.\n
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Instructional Video5:41
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\nHow Do You Add Polynomials?\n

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\n\nFor Teachers\n\n6th - 12th\n
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\nSo you want to learn how to add polynomials? Here are the steps: Rewrite by removing the parentheses, identify the like terms, group like terms together, combine the like terms, and finally rewrite the simplified expression.\n
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Instructional Video2:46
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\nHow Do You Multiply Binomials Using FOIL?\n

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\n\nFor Teachers\n\n6th - 12th\n
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\nFOIL it! What? You want to multiply two binomials then use the FOIL method: First, Outside, Inside, Last. When you have done that, your final steps is to combine the like terms.\n
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Instructional Video4:18
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\nHow Do You Find the Additive Inverse of a Polynomial?\n

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\n\nFor Teachers\n\n6th - 12th\n
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\nFinding the additive inverse is not as complicated as you might think. The instructor demonstrates how to multiply each of the terms in the polynomial by -1 and explains how this works. But wait, there's a quicker way. What's that you...\n
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Instructional Video2:33
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\nHow Do You Solve a Word Problem by Subtracting Polynomials?\n

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\n\nFor Teachers\n\n6th - 12th\n
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\nIt's not a complicated word problem, but the picture frame just gives the problem a little context. So you are trying to find the difference, which means subtraction. The instructor reviews how to distribute the negative sign to the...\n
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Instructional Video3:51
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\nHow Do You Find the Degree of a Polynomial?\n

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\n\nFor Teachers\n\n6th - 12th\n
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\nHow do you determine the degree of a term? How do you determine the degree of a polynomial? Oh my! Observe the teacher as she shows you just how to figure out the degrees, first of terms, then of polynomials.\n
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Instructional Video4:54
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\nHow Do You Add Polynomials Vertically?\n

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\n\nFor Teachers\n\n6th - 12th\n
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\nThe instructor demonstrates how to line up two polynomials vertically to add them together. She emphasizes lining up the terms with the same powers. She also identifies some places where there is no term and shows how to write a...\n
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