| Lesson Plan ID: |
5230 |
| Title: |
You Mean ANYTHING To The Zero Power Is One? |
| Overview/Annotation: |
This lesson is a technology-based project to reinforce concepts related to the Exponential Function. It can be used in conjunction with any textbook practice set. Construction of computer models of several Exponential Functions will promote meaningful learning rather than memorization. |
| Content Standard(s): |
| MA(9-12) Algebra | 1. Simplify numerical expressions using properties of real numbers and order of operations, including those involving square roots, radical form, or decimal approximations. | | MA(9-12) Algebra | 3. Determine characteristics of a relation, including its domain, range, and whether it is a function, when given graphs, tables of values, mappings, or sets of ordered pairs. | | TC2(9-12) Computer Applications | 5. Utilize advanced features of spreadsheet software, including creating charts and graphs,
sorting and filtering data, creating formulas, and applying functions. |
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| Local/National Standards: |
Alabama Graduation Exam - Standard III, Objective 1: Identify Functions
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| Primary Learning Objective(s): |
Students will apply the concept that anything raised to the zero power is one. |
| Additional Learning Objective(s): |
Students will use the order of operations as other constants are multiplied by the power. Students will observe the effects of adding to the Exponential Function as well as the reflective properties of a negative constant similarly applied as a factor.
Students will be explore the concept of a limit by verifying the behavior of the function at zero. |
| Approximate Duration of the Lesson: |
31 to 60 Minutes |
| Materials and Equipment: |
Textbook and assigned problems from text, graph paper, teacher-developed guidelines
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| Technology Resources Needed: |
Computer with Internet access, Microsoft Excel or other spreadsheet software, printer. Optional: large screen presentation device such as TV scan converter or multimedia projector |
| Background/Preparation: |
The student must be able to construct a table of values and choose convenient values of x. |
| Procedures/Activities: |
1.)To graph an Exponential Function in Excel: The * symbol means multiply. ^ means exponent. + is the addition symbol and - is the negative or subtraction.
2.)In column A, list the x values starting with negative number, going through zero and on into positive numbers. List several values and experiment with intervals in Excel after becoming familiar with the process.
3.)Scroll down and highlight all the values in Column A. Find Insert on tool bar. Think INSERT NAME DEFINE. Define them as "x."
4.)In column B, you should write the exponential equation: "2 to the x" Determine how to state this equation mathematically. HINT: the equation should begin with = (an equal sign). These are your Y values. Scroll down and highlight column B. On the tool bar, find Edit. Think FILL DOWN. Output (answers) should be displayed.
5.)Highlight both columns. Go to Insert on the tool bar, find Chart and then Scatter Plot. Follow instructions to display graph.
6.)Proceed to Column C and use 3 as the base of your exponent.
(Or change the base to 3 in Column B rather than using another column.) Again, after the exponential equation has been defined, highlight both columns, insert chart--scatter plot and follow instruction to show chart on the screen.
7.)The purpose of the activity is to see that every graph "goes through" 1 on the y axis. Or every y-intercept is 1.
After several graphs have been constructed and the student is "convinced" there are follow-up activities ( Interactive Projects for Mathematics) Students who finish all problem should be directed to this web site which provides activities that practice function and algebra concepts.
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| Attachments:**Some files will display in a new window. Others will prompt you to download. |
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| Assessment Strategies: |
Any formal assessment provided in the textbook materials can be used for assessment. This activity may also be assessed through having students write a descriptive essay. Students can experiment with printing several functions on one graph and turning printouts in for assessment. |
| Extension: |
Parametric changes should be added by the addition or subtraction of constants. The effects of adding and subtraction constants can also be discovered with the same Excel processes previously described by adjusting the equation in Column B. Also, the multiplication of a factor by the power can be explored by the assignment of appropriate practice problems. This would involve another complete day of class time. These problems are routine types found in Algebra I textbooks.
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| Remediation: |
Pairing students at computers will be helpful. Students should work problems using their calculators and compare their answers to those obtained using Excel. |
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Each area below is a direct link to general teaching strategies/classroom
accommodations
for students with identified learning and/or behavior problems such as: reading
or math performance below grade level; test or classroom assignments/quizzes at
a failing level; failure to complete assignments independently; difficulty with
short-term memory, abstract concepts, staying on task, or following directions;
poor peer interaction or temper tantrums, and other learning or behavior problems.
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| Presentation of Material
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Environment |
| Time Demands |
Materials |
| Attention |
Using Groups and Peers |
| Assisting the Reluctant Starter
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Dealing with Inappropriate
Behavior |
Be sure to check the student's IEP for specific accommodations. |
| Variations Submitted by ALEX Users: |
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