07 Apr Algebra FoundationsRequired ResourcesRead/review t
Algebra FoundationsRequired ResourcesRead/review the following resources for this activity:OpenStax Textbook ReadingsLesson in CanvasAssignments in KnewtonUnit Conversions in the US SystemUnit Conversions in the Metric SystemUnit Conversion Between SystemsRewrite English Phrases into Algebraic ExpressionsAlgebraic Expressions and Applications with IntegersSolve Equations with the Subtraction and Addition Properties of EqualitySolve Equations with the Division and Multiplication Properties of EqualityDistance, Rate, and Time and Literal EquationsInitial Post InstructionsAs we jump into the world of Algebra, it is important to discuss how math, specifically Algebra, is used in the real-world.Search for videos from Ted Ed showing the real-world value of mathematics. Choose a video to watch and then provide a one-paragraph summary (3-4 sentences) of the video in your own words. Be sure to discuss the math concept used.Follow-Up Post InstructionsRespond to at least two peers in a substantive, content-specific way. Further the dialogue by providing more information and clarification.Week 2 DiscussionExploring factors and Factoring TrinomialsRequired ResourcesRead/review the following resources for this activity:OpenStax Textbook ReadingsLesson in CanvasAssignments in KnewtonAdding and Subtracting PolynomialsProduct Properties of ExponentsMultiplying PolynomialsSpecial Products of BinomialsQuotient Properties of Exponents and Dividing MonomialsDividing PolynomialsThe Greatest Common Factor and Factoring by GroupingInitial Post InstructionsWe start the week by introducing polynomials. We will learn how to identify and simplify polynomials. We will also learn how to find the greatest common factor (GCF) among them. As our knowledge of polynomials grows, we will then move on to factoring trinomials. For your first post, search online for an article or video that describes how polynomials can be used in the real world. Provide a one paragraph summary of the article or video in your own words.Follow-Up Post InstructionsRespond to at least two peers in a substantive, content-specific way. Further the dialogue by providing more information and clarification.Week 3 DiscussionSpecial Factoring StrategiesRequired ResourcesRead/review the following resources for this activity:OpenStax Textbook ReadingsLesson in CanvasAssignments in KnewtonFactoring Trinomials with a Leading Coefficient of 1Factoring Trinomials with a Leading Coefficient Other than 1Factoring Special ProductsChoosing a Factoring StrategySolving Quadratic Equations by FactoringSolving Polynomial Equations by FactoringInitial Post InstructionsThis week we continue our study of factoring. As you become more familiar with factoring, you will notice there are some special factoring problems that follow specific patterns. These patterns are known as:a difference of squares;a perfect square trinomial;a difference of cubes; anda sum of cubes.Choose two of the forms above and explain the pattern that allows you to recognize the binomial or trinomial as having special factors. Illustrate with examples of a binomial or trinomial expression that may be factored using the special techniques you are explaining. Make sure that you do not use the same example a classmate has already used!Follow-Up Post InstructionsRespond to at least two peers in a substantive, content-specific way. Further the dialogue by providing more information and clarification.Week 4 DiscussionGraphsRequired ResourcesRead/review the following resources for this activity:OpenStax Textbook ReadingsLesson in CanvasAssignments in KnewtonGraphing Linear EquationsSolving Systems of Linear Equations by GraphingSolving Systems of Linear Equations by SubstitutionSolving Systems of Linear Equations by EliminationInitial Post InstructionsBefore we begin graphing systems of equations, a good starting point is to review our knowledge of 2-D graphs. These graphs are known as 2-D because they have two axes. Find an online image of a graph to use as the foundation of your discussion. (This is easily accomplished by searching within Google Images.)Using your graph as the example:Select any two points on the graph and apply the slope formula, interpreting the result as a rate of change (units of measurement required); andUse rate of change (slope) to explain why your graph is linear (constant slope) or not linear (changing slopes).Embed the graph into the post by copying and pasting into the discussion. You must cite the source of the image. Also be sure to show the computations used to determine slope.Follow-Up Post InstructionsRespond to at least two peers in a substantive, content-specific way. Further the dialogue by providing more information and clarification.Week 5 DiscussionSystems of Equations in the Real WorldRequired ResourcesRead/review the following resources for this activity:OpenStax Textbook ReadingsLesson in CanvasAssignments in KnewtonSystems of Linear Equations and Problem SolvingMixture Problems and Systems of EquationsInitial Post InstructionsIf you have a problem that has multiple variables, you can solve it using a system of equations. Think of a real-world example where you would need to solve using a system of equations. Write two or three sentences describing your example. Include the equations in your description, but do not solve the system. That will be left to your classmates.Follow-Up Post InstructionsRespond to at least two peers in a substantive, content-specific way. Further the dialogue by providing more information and clarification.Week 6 DiscussionSquare RootsRequired ResourcesRead/review the following resources for this activity:OpenStax Textbook ReadingsLesson in CanvasAssignments in KnewtonUnderstanding Square RootsSimplifying Square Root ExpressionsMultiplying Square Root ExpressionsDividing Square Root ExpressionsAdding and Subtracting Square Root ExpressionsTriangles and the Pythagorean TheoremSolving Radical EquationsInitial Post InstructionsOne of the most famous formulas in mathematics is the Pythagorean Theorem. It is based on a right triangle,and states the relationship among the lengths of the sides as a2+ b2= c2, where a and b refer to the legs of a right triangle and c refers to the hypotenuse. It has immeasurable uses in engineering, architecture, science, geometry, trigonometry, algebra, and in everyday applications. For your first post, search online for an article or video that describes how the Pythagorean Theorem can be used in the real world. Provide a one paragraph summary of the article or video in your own words. Be sure you cite the article and provide the link.Follow-Up Post InstructionsRespond to at least two peers in a substantive, content-specific way. Further the dialogue by providing more information and clarification.Week 7 DiscussionSolving Equations using Square Roots or the Quadratic FormulaRequired ResourcesRead/review the following resources for this activity:OpenStax Textbook ReadingsLesson in CanvasAssignments in KnewtonSolving Quadratic Equations Using the Square Root PropertySolving Quadratic Equations by Completing the SquareSolving Quadratic Equations with the Quadratic FormulaSolving Equations by using Quadratic MethodsProblem Solving with Quadratic EquationsInitial Post InstructionsFrom farmers to civil engineers, there are many jobs in which the quadratic equation could be utilized. To complete the Discussion activity, please do the following:Write a paragraph (3-4 sentences) answering the following questions:What is one possible field or profession you may be considering?What are ways the quadratic equation could be used in this chosen profession?Be very specific and include a practical example.Follow-Up Post InstructionsRespond to at least two peers in a substantive, content-specific way. Further the dialogue by providing more information and clarification.Week 8 DiscussionUnderstanding FunctionsRequired ResourcesRead/review the following resources for this activity:OpenStax Textbook ReadingsLesson in CanvasAssignments in KnewtonThe Vertical Line Test and Graphs of FunctionsGraph a Quadratic EquationRadical FunctionsInitial Post InstructionsIn the real world, functions are mathematical representations of input-output situations. A vending machine is one such example. The input is the money combined with the selected button. The output is the product.Here is another example: The formula for converting a temperature from Fahrenheit to Celsius is a function expressed as:C = (5/9)*(F – 32), where F is the Fahrenheit temperature and C is the Celsius temperature.If it is 77 degrees Fahrenheit in Phoenix Arizona, then what is the equivalent temperature on the Celsius thermometer?Our input is 77.C = (5/9)*(77 – 32)C = (5/9)*(45)C = 25The equivalent temperature is 25 degrees Celsius.To complete the Discussion activity, please do the following:Choose your own function or choose from the list below and then provide a unique example of a function and evaluate the function for a specific input (like the example above).Arm length is a function of height.The circumference of a circle is a function of diameter.The height of a tree is a function of its age.The length of person’s shadow on the ground is a function of his or her height.Weekly salary is a function of the hourly pay rate and the number of hours worked.Compound interest is a function of initial investment, interest rate, and time.Supply and demand: As price goes up, demand goes down.Follow-Up Post InstructionsRespond to at least two peers in a substantive, content-specific way. Further the dialogue by providing more information and clarification.
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