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ONLINE PROJECTS are DUE by the end of each weekend.
Send Mr.Flisak an email when you're done:
flisakm@galileoweb.org

To complete each Weekly Online Project, COPY the title, the date, the Introduction, AND the Questions onto YOUR WEBPAGE.
Once all that is pasted onto YOUR webpage, answer each question by typing in your response.


ONLINE PROJECT 15 - May 26-June 6 - Exam Review

Introduction
:
Send Mr.Flisak an email when you're done: flisakm@galileoweb.org

This Project is a BIG one because it's part of your review for our Final Exam. You have TWO WEEKS to complete the Project -- do a bit every day over the next two weeks. Please complete it by Friday, June 6 and send me a message by that Friday evening to say you're done. Use that weekend to study for all your final exams so don't procrastinate this project until that last Friday or into that weekend.
Open a new Internet window, go to mathwithmrflisak, then to 'Online Math Help'. On the 'Online Math Help' page, click on the 'Explore Learning' logo to get to the Explore Learning website. As part of the review for our Final Exam,

PROJECT:

I've added 9 Gizmo's to our class page at Explore Learning beginning with one on Rational Expressions and ending with one on Hyperbolas. Launch the Gizmos one at a time, move the sliders, click on the checkboxes, watch what happens. In other words, use each Gizmo to learn about that math concept. If you think hard while using the Gizmo, you can learn a lot about the topic each concentrates on.

For each Gizmo, complete the Assessment Questions that are below it, make your multiple choice selections, then press the 'Check your answers' button. Your results will be submitted to me.

Send Mr.Flisak an email when you're done: flisakm@galileoweb.org



ONLINE PROJECT 14 - May 19-26 - Series

Introduction
:
Send Mr.Flisak an email when you're done: flisakm@galileoweb.org
To do this Project, you have to understand Sigma (Summation) Notation. This lesson will be on Tuesday and Wednesday this week.

PROJECT QUESTIONS:

Go to 'Math Help Online'. At the bottom of the 'Advanced Algebra' column of help links, you'll find a cell titled 'CH.11 - Sequences and Series'. Click on the link, in that cell, named 'Practice with Sigma Notation'. Answer the multiple choice questions.

How did you do?

Send Mr.Flisak an email when you're done: flisakm@galileoweb.org


ONLINE PROJECT 13 - May 12-18 - Arithmetic and Geometric Sequences

Introduction
:
Send Mr.Flisak an email when you're done: flisakm@galileoweb.org
To do this week's Online Project, you have to join a website called Explore Learning. Explore Learning is a great website for learning math and science using online games and activites called Gizmos. Some of you are already members. If you are NOT a member yet, click on this link for directions on how to join: How to Join Explore Learning

Once you've joined Explore Learning, go to 'Math Help Online' from the main page at mathwithmrflisak. Near the top of the 'Math Help Online' page, you'll see a graphical link for the Explore Learning website. Click on that link to get to Explore Learning. Click on the 'Log in' button on the top left side of the page.

PROJECT QUESTIONS:

Launch the first Gizmo called 'Arithmetic and Geometric Sequences' and answer the questions below.

Part 1: Arithmetic Sequences
1. Does changing the value of the first term change the pattern of an arithmetic sequence?
2. What happens to every value in an arithmetic sequence when you decrease the first term by 5?
3. When are the points in the sequence perfectly horizontal? Why?
4. What happens when you change the n value? Why?
5. Click on 'Table' above the graph. Move the sliders and observe what happens.
What kind of function produces the kind of data that follows an arithmetic sequence? What part of the equation of the function does the 'common difference' represent?

Part 2: Geometric Sequences
Change back to 'Graph' view and then, above the sliders, click on 'Geometric' to work with a Geometric Sequence.
6. What is the main difference between arithmetic and geometric sequences?
7. When is the geometric sequence of values perfectly horizontal? Why?
8. Which makes the geometric sequence rise faster -- raising the first term value OR raising the common ratio? WHY???

Part 3: Assessment
Use the Gizmo to help you answer the 5 Assessment Questions that are below the Gizmo. Choose a multiple choice response for each, then press the 'Check Your Answers' button at the bottom. I will automaticaly receive your results. You will not get a complete unless I get your results.

Send Mr.Flisak an email when you're done: flisakm@galileoweb.org


ONLINE PROJECT 12 - May 5-11 - Logarithmic Functions and Laws of Logarithms

Part 1: RATE Mr.Flisak and Your Other Teachers Online!

Follow the directions on the mathwithmrflisak main page to rate Mr.Flisak and other teachers at ratemyteachers.com.

Part 2: The Algebra Work...

Introduction
:
To do this week's Online Project, you have to join a website called Explore Learning. Explore Learning is a great website for learning math and science using online games and activites called Gizmos. Most of you have already joined Explore Learning. If you haven't, click on this link for directions on how to join: How to Join Explore Learning

Once you've joined Explore Learning, go to 'Math Help Online' from the main page at mathwithmrflisak. Near the top of the 'Math Help Online' page, you'll see a graphical link for the Explore Learning website. Click on that link to get to Explore Learning. Click on the 'Log in' button on the top left side of the page.

PROJECT QUESTIONS:

Graphs of Logarithms

Using Explore Learning, launch the first Gizmo called 'Logarithmic Functions - Activity A'. Experiment with the Gizmo, then answer the 4 Assessment Questions below the Gizmo. Make your choices, then press the 'Check Your Answers' button. When you press the button, I'll automatically get your results.

Laws of Logarithms

In a new Internet window, go to 'Math Help Online'. There, below the 'Advanced Algebra' heading, at the very bottom, you'll find a box with the 'CH.10: Exponential andn Log Functions' links. Click on the 'Laws of Logs Practice' link. On that page, there are 5 Examples and 4 Exercises. Write each example and exercise down on a piece of paper. Try to solve each. If you're stuck, click on the blue 'Answer' link below each question. To get points for this Project, you must hand in your answer page to me anytime this week or on Monday.



ONLINE PROJECT 11 - Apr.21-25 - Inverse Functions

Introduction: In a NEW Internet window, go to mathwithmrflisak, then click on the 'ONLINE Math Help' button. On the Math Help Online page, scroll down to see the table of links below. Look for the 'Advanced Algebra' heading and go to the very bottom of that column. There, you will find the cell with the 'CH.10 - Exponential and Log Functions' links. Click on the 'Manipulate Inverse Functions' link.

On that webpage, there are 6 functions to choose from. Start with the first one, the line. When you're done interacting with the line and once you've answered the question about line inverses, press the 'Set Function' button to get back the 6 functions main menu. You will eventually interact with the first 5 functions, in order, and answer one or two questions related to each one.

Questions:
1. The inverse of a function is........ across the line y =

Using the Inverse of a Line Grapher, move the 'a', 'b', 'h' and 'k' sliders around to see what a line and its inverse look like. Then, answer:
2. Can a line and it's inverse ever be parallel OR will they always intersect?
Using the Inverse of a Parabola Grapher, move the 'a', 'b', 'h' and 'k' sliders around to see what a parabola and its inverse look like. Then, answer:
3. Do a parabola and its inverse always intersect?
4. Is the inverse of a parabola a function?
Using the Inverse of a Cubic Grapher (the third one), move the 'a', 'b', 'h' and 'k' sliders around to see what a cubic and its inverse look like. Then, answer:
5. What is the maximum number of times a cubic and its inverse can intersect?
Using the Inverse of an Absolute Value Grapher, move the 'a', 'b', 'h' and 'k' sliders around to see what an absolute value and its inverse look like. Then, answer:
6. Do an absolute value function and its inverse behave the same way as a parabola? Why?
Using the Inverse of a Radical Grapher, move the 'a', 'b', 'h' and 'k' sliders around to see what a radical and its inverse look like. Then, answer:
7. Can a radical and its inverse ever be perpendicular to each other? What actually happens to the radical when this is true?


ONLINE PROJECT 10 - Apr.14-17 - Exponential Functions

DO NOT COPY ALL THE 'How to Join' Instructions to your webpage. Copy from where the Project Questions begin below.

HOW TO JOIN ExploreLearning.com

To become a member of OUR class at Explore Learning, go to the site by clicking on this link:
http:www.explorelearning.com

At the website, click on the 'Enroll in a Class Here' link as shown below:

explorelearning_banner_with_circle.jpg

Then, click on the 'click here to continue the enrollment..' purple link under 'No, I don't have a username and password':

explore2.jpg

I have created our class online so you need to enter this code where it asks for a 'Class Code': ES6APN4YUU
Hit the 'Enroll' button and you will be taken to a page where you have to create your username and password.
After that, you'll be logged in and will have access to the Gizmos that I have chosen for our class.

PROJECT QUESTIONS:

Part 1: Exponential Functions

On our Class Page on Explore Learning, open the 'Exponential Functions - Activity A Gizmo'.

Without moving the sliders, answer these questions:
1. What is the standard form of an exponential function's EQUATION?
2. What is the general shape of an exponential function's GRAPH? Describe the graph.
3. Look at the equation. Think about what y would be if x was 1, 2, 3, etc. Describe why the shape of the graph is what it is.

Move the 'b' slider around. 'b' is the base of the exponential function. Watch what happens to the EQUATION and the GRAPH.
4. What point does the exponential graph almost always pass through?
5. Why does y = 1 when x = 0, NO MATTER what the base (b) of the exponential function is?
4. What happens when 'b', the base of the exponential function, gets bigger? Why?
5. What happens when 'b', the base of the exponential function, gets smaller but remains larger than 1? Why?
6. What happens when the base is 1? Why?
7. What happens when the base is between 0 and 1?

Move the 'a' slider around and watch what happens. 'a' is the coefficient, or number, in front of the exponential base.
8. What happens when 'a' gets bigger?
9. What happens when 'a' gets smaller?
10. What happens when 'a' becomes negative?
11. Make 'a' equal to -2.3. Where does the graph intercept the y-axis. Therefore, the 'a' value represents the -.
12. Does changing 'b' change the effect that 'a' has on the graph?

Below the graphing Gizmo are 4 'Assessment Questions'. If necessary, use the Grapher to help you answer the questions. Choose answers you're certain about. Then, click the 'Check your Answers' button on the bottom. Your answers will be sent to me by email.

Part 2: Logarithmic (Log) Functions

Press back and go back to our Class Page on Explore Learning, open the 'Logarithmic Functions - Activity A Gizmo'.

Without moving the slider, look at the equation and graph and answer:
1. What does the general shape of the log function look like?

Move the 'a' slider around. 'a' represents what is called the base of the log.
2. What happens to the graph when 'a' gets larger?
3. What happens to the graph when 'a' gets smaller?
4. Just like the exponential graph, the log function graph always passes through a certain point too. What is the point?

Click in the check boxes that say 'Show associated exponential' and 'show line y=x'. Move the 'a' slider around and see what happens.
5. Looking at that, explain how an exponential function and a logarithmic function are related?


ONLINE PROJECT 9 - Apr.7-11 - Conics Review

Introduction: In a NEW Internet window, go to mathwithmrflisak, then click on the 'ONLINE Math Help' button. On the Math Help Online page, scroll down to see the table of links below. Look for the 'Advanced Algebra' heading and go to the very bottom of that column. There, you will find the box with the 'CH.9 - Conic Sections' links.

Questions:
Click on the 'Examples of Conics' link, then list real life examples of each conic below:
1. Examples of Ellipses:
2. Examples of Parabolas:
3. Examples of Hyperbolas:

Back at 'Math Help Online', click on the 'Identifying Conics Quiz' link. On that webpage, there are 6 different equations. On a piece of paper, re-arrange each equation so that all terms are on one side and so that 0 is on the other side. Then, complete the square (twice sometimes) in order to get a standard equation. Look at your standard equation and recognize it as either a line, parabola, ellipse, circle, hyperbola, OR none of them. Type in your standard equations and the name of the curve below (use '^' for 'squared'):

4. Equation: Type of curve:
5. Equation: Type of curve:
6. Equation: Type of curve:
7. Equation: Type of curve:
8. Equation: Type of curve:
9. Equation: Type of curve:

Back on the website, check to see if you were correct, by moving the boxes with the curve names in them into the yellow spaces.
True or False will appear to let you know if you're right or wrong.

10. How did you do?

Email: flisakm@galileoweb.org when you're done.


ONLINE PROJECT 8: Mar.17-20 - Conics: The Parabola

Introduction: In a NEW Internet window, go to mathwithmrflisak, then click on the 'ONLINE Math Help' button. On the Math Help Online page, scroll down to see the table of links below. Look for the 'Advanced Algebra' heading and go to the very bottom of that column. There, you will find the box with the 'CH.9 - Conic Sections' links. Click on the second link, 'Graphing Conics'. The java applet that opens allows you to change the values in the equations of circles, parabolas, ellipses, and hyperbolas. This week, you'll work with the Parabola. Check the 'Light Grid Marks' option on the right side to help you answer the questions below.
Then, use the drop down menu to change the graph from 'Circle' to 'Vertical Parabola'.
Below the graph are sliders that you can use to change the values of 'a', 'h', and 'k'.

Questions:

1. Type in the general equation of a vertical parabola (it's written on the webpage under the drop down menu box).
2. Use the drop down menu to switch to a 'horizontal parabola'. Type in the general equation of a vertical parabola.
3. How are the graphs of a horizontal and vertical parabola different?
4. How are the equations of a horizontal and vertical parabola different?
5. Does the co-ordinate (h,k) represent the same part of each type of parabola?
6. The co-ordinate (h,k) is what part of a parabola?
7. Does changing the 'a' value have the same effect on both types of parabolas? What happens when 'a' changes?
8. Does changing 'h' and 'k' have the same effect on both types of parabolas?
9. What is the equation of a parabola that opens to the left and has a vertex at (2, 5)? Type in your equation and check to see if you're correct by using the applet.
10. What is the equation of a parabola that opens down and has a vertex at (-3, -7)? Type in your equation and check to see if you're correct by using the applet.

Email: flisakm@galileoweb.org when you're done.


ONLINE PROJECT 7: Mar.10-16 - Conics: The Circle

Introduction: In a NEW Internet window, go to mathwithmrflisak, then click on the 'ONLINE Math Help' button. On the Math Help Online page, scroll down to see the table of links below. Look for the 'Advanced Algebra' heading and go to the very bottom of that column. There, you will find the box with the 'CH.9 - Conic Sections' links. Click on the second link, 'Graphing Conics'. The java applet that opens allows you to change the values in the equations of circles, parabolas, ellipses, and hyperbolas. This week, you'll work with the Circle. Check the 'Light Grid Marks' option on the right side to help you answer the questions below. Below the circle graph are 3 sliders. One slider changes the r (radius) value, and the other 2 change the 'h' and 'k' values.

Questions:

1. Move the 'r' slider around. Explain clearly what 'r' represents in the equation of a circle.
2. If a circle has a radius of 13, what will the value on the right side of the circle equation be? Why?
3. Move the 'h' slider around. Explain clearly what the 'h' value represents in the equation of a circle.
4. Move the 'k' slider around. Explain clearly what the 'k' value represents in the equation of a circle.
5. What would the equation of a circle with center at (-4, 7) and radius of 8 be? Use what you learned above and the sliders on the applet to check if your equation is correct. Did you get it right? Write your equation here:

Email: flisakm@galileoweb.org when you're done.


ONLINE PROJECT 6: Mar.3-10 - Completing the Square

Introduction: In a NEW Internet window, go to mathwithmrflisak, then click on the 'ONLINE Math Help' button. On the Math Help Online page, scroll down to see the table of links below. Look for the 'Advanced Algebra' heading and go to the very bottom of that column. There, you will find the box with the 'CH.7 - Quadratic Functions' links. Click on the 'Completing the Square: PRACTICE' link. Use the java applet to complete the square of 5 different quadratic functions. To type fractions, use the '/' key on your keyboard and press <ENTER> when you are done filling one box in. On your webpage, type in the standard form equation AND the vertex form equation for each of the 5 equations you complete the square on. Set yours up like the example given.

Equations:

Example: y= x^2 - 6x - 3 changes to y = (x-3)^2 - 12

Your Equations:
1.
2.
3.
4.
5.


ONLINE PROJECT 5: Feb.25 - Mar.2 - Imaginary Numbers

Introduction: In a NEW Internet window, go to mathwithmrflisak, then click on the 'ONLINE Math Help' button. On the Math Help Online page, scroll down to see the table of links below. Look for the 'Advanced Algebra' heading and go to the very bottom of that column. There, you will find the box with the 'CH.6 - Radicals Complex #s' links. Click on the link title: 'What are Imaginary Numbers?'. Answer the questions below using the information on that webpage.

Questions:
1. Why was the imaginary unit created in math?
2. Imaginary numbers are NOT really 'imaginary'. Who is to blame for making us think that they are imaginary?
3. Open the link: http://library.thinkquest.org/20991/alg2/cn.html Go to the very bottom of the webpage where it says 'Graphing Complex Numbers'. Look at how the 4 complex numbers are graphed. Explain how to graph complex numbers.


ONLINE PROJECT 4: Feb.19-22 - Simplifying Radicals

Introduction: In a NEW Internet window, go to mathwithmrflisak, then click on the 'ONLINE Math Help' button. On the Math Help Online page, scroll down to see the table of links below. Look for the 'Geometry' heading and go to the very bottom of that column. There, you will find the box with the 'Pythagorean Theorem' links.

Questions:
1. Click on the 'Roots Practice' link. Simplify each of the 10 roots on a piece of paper. When you have an answer, select the option from the given choices on the webpage. How did you do?

2. Use 'Grapher 2' from the 'Online Math Help' page to graph the following 4 radical equations. Use the 'root button' to make a radical equation AND use the 'trace' bar under the graph to move the blue dot to see where at what x-value and y-value the graph begins.
Capture1.jpg
Answer the following:
a.) What is the general shape of a Radical Equation? (hint: it resembles the shape of a letter)
b.) How does the number UNDER the radical sign with x change the graph?
c.) How does the number OUTSIDE the radical sign change the graph?


ONLINE PROJECT 3: Feb.11-15 - Asymptotes of Rational Expressions

Introduction: In a NEW Internet window, go to mathwithmrflisak, then click on the 'ONLINE Math Help' button. On the Math Help Online page, scroll down to see the table of links below. Look for the 'Advanced Algebra' heading and go to the very bottom of that column. There, in the 'CH.5 - Rational Expressions' box, you will find a link named: 'Graphing Rational Equations'. Click on this link. On the new page, scroll down just a little until you see a button that says 'click here to start'. Click on this button. The Grapher that opens will help you understand asymptotes and graphing rational equations.

Questions:
Before starting the questions, move the 'c' dial SLOWLY and CAREFULLY until c = 1.0. If you move it too much or too fast, and c = 0.0, then your computer will freeze.
1. Move the 'd' dial until d = a negative whole number. Write the equation for your rational function by using the format given on the top left of the graphing applet. Substitute numbers for a,b,c, and d. One example is: y = (x+2)/(x-5).
2. For this same function, where is the vertical asymptote? At x = _
3. Move the 'd' dial around and watch how the vertical asymptote changes. What is your conclusion about the relationship between the solution of x in the denominator and the location of the vertical asymptote?
4. Move the 'a' dial around and watch what happens to the horizontal asymptote. What is your conclusion about the relationship between the value of the coefficient in the numerator and the location of the horizontal asymptote?
5. Write the equation of a function after making the changes in #4. Where is the horizontal asymptote and how does it relate to this function?
6. Move the 'c' dial around and watch how the horizontal asymptote changes. Stop moving 'c' around and write your new equation. Write the location of the horizontal asymptote too as y = __.
7. Look at your equation in #6 and look at the location of the horizontal asymptote. What is your conclusion about the relationship between the value of the coefficient in the numerator and the value of the coefficient in the denominator AND the location of the horizontal asymptote?

ONLINE PROJECT 2: Jan.14-18 - Rational Expressions

Introduction: Rational Expressions and Equations are fractions in algebraic form. In other words, rational expressions are fractions that include variables.

STEPS:
To complete this project, Open a New Internet Window, and go to mathwithmrflisak again. From the main page, click on the button for 'Online Math Help'. Look for the 'Advanced Algebra' heading in the table and scroll to the bottom of that column. At the bottom, you'll find links for Chapter 5.

Click on the link that says: 'Simplify Rational Expres. 1'.

Take Notes in your Math Notebook with the Title: 'Simplifying Rational Expressions'. Add Example 1 to your notes (you don't have to write the explanatory sentences into your notes, just the numbers). Think about what can be cancelled in the fraction, THEN type your answer into the open box on the website. Use the '/' symbol to represent a fraction.

Do the same for examples 2,3, and 4. Add each to your notes and type your answer into the box. When you're done with all 4, click the 'Check your Answers' button at the bottom. Write the four answers into your notebook under each example.

Questions:
1. What is the technique for simplifying rational expressions? Write the steps you would take to simplify a fraction with variables.
2. When would the simplified form of a rational expression no longer be a fraction?
3. When would the simplified form of a rational expression be equal to zero?
4. What do you think you would need to do first if you were adding two rational expressions?

ONLINE PROJECT 1: Jan.7-11 - PARABOLAS

Introduction: Use the online parabola grapher at: http://www-groups.dcs.st-and.ac.uk/~history/Java/Parabola.html to answer the questions below ON YOUR WEBPAGE. Open the Parabola Grapher in a separate window.

    • REMEMBER: we use the letters 'a', 'b', and 'c' to represent the coefficients in a parabola's equation.

For example, given: 3x^2 + 5x - 10 a=3, b=2, c=10
  • the '^' means that 2 is the exponent

Questions:
1. What happens to a parabola when 'a' gets larger? Write the equation of a parabola like this. You can use the '^' symbol above the number '6' on your keyboard to express and exponent.
2. What happens to a parabola when 'a' is less than 1 but greater than 0? Write the equation of a parabola like this.
3. What happens to a parabola when 'a' is 0. WHY?????? Write the equation of a parabola like this.
4. What happens to a parabola when 'a' is less than 0? Write the equation of a parabola like this.
5. What happens to a parabola when 'b' changes (positive or negative)? Change 'b' quickly to see if you can explain the shape of the path that the vertex of the parabola makes when changing 'b'.
6. What happens to the parabola when 'c' gets larger in the positive direction? Write the equation of a parabola like this.
7. What happens to the parabola when 'c' gets larger in the negative direction? Write the equation of a parabola like this.
8. 'c' represents what?