MAT 116 Complete Course
What is the difference between an equation and an expression? Include an example of each. Can you solve for a variable in an expression? Explain your answer. Can you solve for a variable in an equation? Explain your answer. Write a mathematical phrase or sentence for your classmates to translate.
What are the steps of the order of operations? Why is it important that you follow the steps rather than solve the problem from left to right?
Groupings (parenthesis, brackets, or braces)
Multiplication or division
Addition or subtraction
Please Excuse My Dear Aunt Sally and P-E-M-D-A-S are mnemonic devices for what? What do the underlines help remind you to do in P-E-M-D-A-S? Why is it important to be able to remove parentheses? Why is it important to be able to combine like terms? Provide examples that illustrate both of these processes.
Exercise: Week Two Concept Check
Assignment: Expressions and Equations
Why does the inequality sign change when both sides are multiplied or divided by a negative number? Does this happen with equations? Why or why not? Write an inequality for your classmates to solve. In your inequality, use both the multiplication and addition properties of inequalities. Consider solving your classmates’ inequalities. Explain how you arrived at your answers. Also, help other students who may be having difficulty solving inequalities. Ask clarifying questions if you need additional assistance.
How do you know if a value is a solution for an inequality? How is this different from determining if a value is a solution to an equation? If you replace the equal sign of an equation with an inequality sign, is there ever a time when the same value will be a solution to both the equation and the inequality? Write an inequality and provide a value that may or may not be a solution to the inequality. Consider responding to a classmate by determining whether or not the solution provided is a solution to the inequality. If the value he or she provides is a solution, provide a value that is not a solution. If the value is not a solution, provide a value that is a solution.
Describe in your own words how to solve a linear equation using the equality properties. Demonstrate the process with an example. Next, replace the equal sign in your example with an inequality by using the less than or greater than sign. Then solve the inequality.
Why should we clear fractions when solving linear equations and inequalities? Demonstrate how this is done with an example. Why should we clear decimals when solving linear equations and inequalities? Demonstrate how this is done with an example.
Exercise: Week Four Concept Check
Assignment: Solving Inequalities and Graphing Equations
What similarities and differences do you see between functions and linear equations studied in Ch. 3? Are all linear equations functions? Is there an instance when a linear equation is not a function? Support your answer. Create an equation of a nonlinear function and provide two inputs for your classmates to evaluate.
What is the difference between domain and range? Describe a real-life situation that could be modeled by a function. Describe the values for x that may not be appropriate values even when they are defined by your classmates’ function. A function could, for example, indicate the amount of bone strength (y) in a living human body over time in years (x). It would not make sense to look at negative years, because the person would not yet be born. Likewise, looking beyond 100 years might not make sense, as many people do not live to be 100.
What is a function, in your own words? Give an example of a function using the variable x and explain how we evaluate a function for a given value of x.
Provide an example of at least five ordered pairs that do not model a function. The domain will be any five integers between 0 and 20. The range will be any five integers between -10 and 10. Your example must not be the same as those of other students or the textbook. Why does your example not model a function? Explain the domain and range of a function. Under what circumstances would the domain be something other than all real numbers? Provide an example. Consider participating by providing feedback about your classmates’ answers, commenting on your classmate’s example, providing an additional example for your classmates to solve or adding additional information on this concept.
Exercise: Week Six Concept Check
Assignment: Functions and their Graphs
Systems of equations can be solved by graphing or by using substitution or elimination. What are the pros and cons of each method? Which method do you like best? Why? What circumstances would cause you to use a different method? Consider responding to your classmates by indicating pros and cons they may not have considered or persuading them to see the value of the method you like best (if you chose different methods). Describe situations in which you might use their methods of solving.
Review examples 2, 3, and 4 in section 8.4 of the text. How does the author determine what the first equation should be? What about the second equation? How are these examples similar? How are they different? Find a problem in the text that is similar to examples 2, 3, and 4. Post the problem for your classmates to solve. Consider responding to your classmates by asking clarifying questions or by expanding a classmate’s response. Also, help students solve the problem you posted by providing feedback or hints if necessary. You may also want to provide an explanation for your solution after a sufficient number of students have replied.
Sometimes it is very obvious which method is most efficient to solve a system of equations because of the way the problem is set up. To be efficient, under what conditions would you use graphing? Elimination? Substitution? Provide an example of each.
In your own words, what does it mean for a system to be consistent or inconsistent? Type an equation for g(x) that results, with f(x), in an inconsistent system: How else can you describe the two lines in this inconsistent system?
Provide an example that uses the elimination method to solve two linear equations. Participate by checking the work of your classmates, and comment on whether it is correct or provide another example for your classmates to solve using the elimination method.
Provide an example that uses the substitution method to solve two linear equations. Participate by checking the work of your classmates and comment on whether it is correct or provide another example for your classmates to solve using the substitution method.
Exercise: Week Eight Concept Check
Assignment: Systems of Equations and Inequalities
Post your response to the following: Has the content in this course allowed you to think of math as a useful tool? If so, how? What concepts investigated in this course can apply to your personal and professional life? In what ways did you use MyMathLab® for extra support?
“I teach on-site and online math courses, and I must say that students who take online math courses have more available resources, more help, and more time to learn the material than on-site students.” Do you agree? Explain why or why not? How do you feel?
Create a list of three to five important suggestions for students starting a new MAT/116 section on Monday. These suggestions can also be applied in MAT/117. Write your suggestions to help a fellow student succeed in this course using short sentences, and arrange them in decreasing order from greatest to least important.
**bold**, to write a math equation use, for example,