Learning Designer: Rachelle Babcock
Course: College Algebra
Start
Title: Polynomial Functions Recommendations for instructional design strategies for effective and engaging delivery:
I would apply the Constructivist Approach. Students would be provided with interactive opportunities to learn; students will think back on concepts and utilize those concepts in a present process and develop ways to apply the concept in the future. Students will be active in their learning by engaging in various activities on the LMS. Giving the students various forms of media within the course is essential. My suggestion and approach would be to use mixed media and practice activities throughout this module and course. Incorporating step-by-step instructional practice activities that are interactive will assist the students in learning this concept. In addition, creating an interactive digital lesson would be beneficial-we will check for learning throughout the lesson with pop-up questions and feedback.
Setting the Stage
First, start the lesson by setting the stage-giving simple imagery that discusses the concept. Items the student can relate to. I would start with this activity so that the students can start thinking about the concept without having the lecture and reading completed. I would also ask open-ended questions to the students, such as: Think of the examples. Have you ever considered polynomials as factors before seeing the infographic? How might you use polynomials in the future? Note: This could also be turned into a survey where students are asked questions like the above and compare answers.
Interactive Videos
I would suggest an interactive video. The video could be created by the instructor and questions would pop up throughout the video: questions can be multiple choice, highlighting, fill in the blank, as well as drag and drop format.
Here is an example for the instructor:
Interactive Link: Algebra Basics: What Are Polynomials? - Math Antics
I would follow the interactive video with an instructional lesson that is interactive-a simulated classroom lesson.
Project Plan
Below is a detailed Project Plan I would present to the developing faculty member.
*click on the computer below to view the project plan.
Project Plan
Suggested Practice Activity/Assessment:
Example: Discussion could relate back to the setting the stage since the student has now learned the concept. Example: We saw the everyday uses of linear equations in the past modules. Polynomial expressions are used in many areas of study, but they may not be as readily observed. In Physics, Economics, Calculus and many other areas of scientific studies, polynomial equations are used to describe relationships. One great example is the projectile motion of a ball in the air.
Go online and research the topic of polynomial equations. Find an application of using polynomial equations or polynomial functions. Describe the example and how it is used. Make sure that you cite your sources correctly.
Degree, Leading Terms, Leading Coefficient
Practice Activity
Start
1/4
Let's start with answering what is Polynomial? Pick the answer you think is the best matches.
Sums (and differences) of polynomial "terms". For an expression to be a polynomial term, any variables in the expression must have whole-number powers (or else the "understood" power of 1, as in x1, which is normally written as x).
An expression with a variable with negative or fractional exponents, division by a variable, or a variable inside a radical.
Has variables in the denominator and the variable is also inside a radical.
right answer
Great job! A plain number can also be a polynomial term.
2/4
A plain number can also be a polynomial term. In particular, for an expression to be a polynomial term, it must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions. Review the examples below and pick the polynomial term:
1/x2
6x-2
4x2
right answer
Great job! This is correct-because it obeys all the rules.
3/4
For the given polynomial function, find the degree, the leading term, and the leading coefficient. f(x)=11x5-2x+3x7-100x3+x4-12 Let's work on the first step. Pick the answer you think is the best matches.
Answer 2 degree=highest power =>degree=7 leading term: the term with the =>LT=3X7 highest power Leading coefficient:the coefficient of =>LC=3 the leading term
Answer 1 degree=highest power =>degree=3 leading term: the term with the =>LT=3X7 highest powerLeading coefficient:the coefficient of =>LC=3 the leading term
Answer 3 degree=highest power =>degree=3 leading term: the term with the =>LT=3X7 highest powerLeading coefficient:the coefficient of =>LC=7 the leading term
right answer
Great start! Lets move onto the next step!
4/4
Now, let's move on to the polynomial graphed end behavior. What is the end behavior of the graph of the following polynomial function? f(x)=-4x5-8x3-3x2+7x Pick the answer you think is the best matches.
Rises left, falls right
Falls left, rises right
Rises left, rises right
right answer
We have the highest power is odd which is 5 and then the coefficient of the highest degree is negative, therefore the left tail will rise and the right tail will fall.
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Transcript
Learning Designer: Rachelle Babcock Course: College Algebra
Start
Title: Polynomial Functions Recommendations for instructional design strategies for effective and engaging delivery: I would apply the Constructivist Approach. Students would be provided with interactive opportunities to learn; students will think back on concepts and utilize those concepts in a present process and develop ways to apply the concept in the future. Students will be active in their learning by engaging in various activities on the LMS. Giving the students various forms of media within the course is essential. My suggestion and approach would be to use mixed media and practice activities throughout this module and course. Incorporating step-by-step instructional practice activities that are interactive will assist the students in learning this concept. In addition, creating an interactive digital lesson would be beneficial-we will check for learning throughout the lesson with pop-up questions and feedback.
Setting the Stage
First, start the lesson by setting the stage-giving simple imagery that discusses the concept. Items the student can relate to. I would start with this activity so that the students can start thinking about the concept without having the lecture and reading completed. I would also ask open-ended questions to the students, such as: Think of the examples. Have you ever considered polynomials as factors before seeing the infographic? How might you use polynomials in the future? Note: This could also be turned into a survey where students are asked questions like the above and compare answers.
Interactive Videos
I would suggest an interactive video. The video could be created by the instructor and questions would pop up throughout the video: questions can be multiple choice, highlighting, fill in the blank, as well as drag and drop format. Here is an example for the instructor: Interactive Link: Algebra Basics: What Are Polynomials? - Math Antics I would follow the interactive video with an instructional lesson that is interactive-a simulated classroom lesson.
Project Plan
Below is a detailed Project Plan I would present to the developing faculty member. *click on the computer below to view the project plan.
Project Plan
Suggested Practice Activity/Assessment:
Example: Discussion could relate back to the setting the stage since the student has now learned the concept. Example: We saw the everyday uses of linear equations in the past modules. Polynomial expressions are used in many areas of study, but they may not be as readily observed. In Physics, Economics, Calculus and many other areas of scientific studies, polynomial equations are used to describe relationships. One great example is the projectile motion of a ball in the air. Go online and research the topic of polynomial equations. Find an application of using polynomial equations or polynomial functions. Describe the example and how it is used. Make sure that you cite your sources correctly.
Degree, Leading Terms, Leading Coefficient
Practice Activity
Start
1/4
Let's start with answering what is Polynomial? Pick the answer you think is the best matches.
Sums (and differences) of polynomial "terms". For an expression to be a polynomial term, any variables in the expression must have whole-number powers (or else the "understood" power of 1, as in x1, which is normally written as x).
An expression with a variable with negative or fractional exponents, division by a variable, or a variable inside a radical.
Has variables in the denominator and the variable is also inside a radical.
right answer
Great job! A plain number can also be a polynomial term.
2/4
A plain number can also be a polynomial term. In particular, for an expression to be a polynomial term, it must contain no square roots of variables, no fractional or negative powers on the variables, and no variables in the denominators of any fractions. Review the examples below and pick the polynomial term:
1/x2
6x-2
4x2
right answer
Great job! This is correct-because it obeys all the rules.
3/4
For the given polynomial function, find the degree, the leading term, and the leading coefficient. f(x)=11x5-2x+3x7-100x3+x4-12 Let's work on the first step. Pick the answer you think is the best matches.
Answer 2 degree=highest power =>degree=7 leading term: the term with the =>LT=3X7 highest power Leading coefficient:the coefficient of =>LC=3 the leading term
Answer 1 degree=highest power =>degree=3 leading term: the term with the =>LT=3X7 highest powerLeading coefficient:the coefficient of =>LC=3 the leading term
Answer 3 degree=highest power =>degree=3 leading term: the term with the =>LT=3X7 highest powerLeading coefficient:the coefficient of =>LC=7 the leading term
right answer
Great start! Lets move onto the next step!
4/4
Now, let's move on to the polynomial graphed end behavior. What is the end behavior of the graph of the following polynomial function? f(x)=-4x5-8x3-3x2+7x Pick the answer you think is the best matches.
Rises left, falls right
Falls left, rises right
Rises left, rises right
right answer
We have the highest power is odd which is 5 and then the coefficient of the highest degree is negative, therefore the left tail will rise and the right tail will fall.
congrats You have completed the activity!
Try again!
wrong
Try again