A WebQuest for 9th Grade (Mathematics). Math
Designed by
Zahra Idris Adam
zhraaishag@yahoo.com
To download this work(office 2007 format) click Here
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What is a WebQuest?
A WebQuest is an inquiry-oriented lesson format in which most or all the information that learners work with comes from the web http://webquest.org/index.php
Tools of webQuest
Introduction
Mathematics is an abstract subject constructed by the human mind. It interests on ideas, methods and human patterns of thinking. In the last period, the mathematical branches had been developed and expanded and their c contents became very complicated. So recently it became difficult for many learners to understand the concepts and theories of math, especially when using traditional methods of teaching. Therefore it becomes necessary to use modern sources of learning and to make full utility out of vast potential of computer in teaching the complex mathematical branches.
Thus , here I used the WebQuest to introduce activity which uses the internet as the primary resource. This WebQuest is designed to help you learn:
· What sin, cosine and tangent functions are?
· How can be they calculated?
· How to find the sin, cosine and tangent functions of special angles? Historical background
http://zhraaishag.blogspot.com/
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Task
1. What do we call a plane surface bounded by straight line?
2. The rectilinear figure bounded by three straight lines are called ……
3. What are the kinds of triangles according to their sides?
4. What are the kinds of triangles according to their angles?To answer these question s
http://www.quia.com/quiz/1861140.html
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Process
Now, each group will have to take one activity and search about it…
Send the answer by e-mail
Activity 1
Before answering the questions First read the text about sine cosine and tangent functions then answer these questions
http://www.youtube.com/watch?v=OURcodVdH3k
Definition of sine, cosine and tangent
http://wright.nasa.gov/airplane/trig.html
The Law of Sines
http://www.mathsisfun.com/algebra/trig-sine-law.html
The Law of Cosines
http://www.mathsisfun.com/algebra/trig-cosine-law.html
What are sine, cosine and tangent?
Why are these functions important?
Drawing the graph of sine and cosine?Click here to see more graphs of sine and cosine
http://www.walter-fendt.de/m14e/sincostan_e.htm
Here more information about sine, cosine and tangent
http://www.staff.vu.edu.au/mcaonline/units/trig/ratios.html
Here is more graphic of sine and cosine
http://www3.0zz0.com/2009/06/29/07/144797188.png
http://www3.0zz0.com/2009/06/29/07/379636989.png
http://www3.0zz0.com/2009/06/29/07/960155447.png
Or
http://www.facebook.com/album.php?aid=3046&id=1835516930&saved
Activity 2
First: read about sine, cosine and tangent function of the special angles then answer these questions….
http://www.youtube.com/watch?v=hFNCijzfCmM
What is the value of each angle?
What the value of angle BAC
What do call side AB?
Side BD = 1 unit, calculate length of AD?
Ok to see the graphic click here
Exercises:
1/what are the sine, cosine and tangent of 30°? The classic 30° triangle has a hypotenuse of length 2 units, an opposite side of length 1 unit and an adjacent side of √ (3) unit
2/what are the sine , cosine and tangent of 45°?
The classic 45° triangle has two sides of 1 unit each and hence, a hypotenuse of √ (2) unit:
Ok let’s go to find the answer
Assimment
Exercise
Try this paper –based exercis
http://www.mathsisfun.com/sine-graph-exercise.html
Where can you calculate the sine function for all angles from 0° to 360°, and then graph the result. It will help you to understand these relatively simple functions
Sine Function
First, read our page on Sine, Cosine and Tangent
Now you will know that the sine of any angle is simply the length of the far side of the triangle (the "opposite") divided by the long side (the "hypotenuse"):
Draw Triangles
To make the graph, we need to calculate the sine for different angles, then put those points on a graph, and then "join the dots".
Step 1: Draw the Angled Lines
Place a mark at the center of a piece of paper, then, using a protractor, mark every 15 degrees from 0° to 180° in a semi-circle. Then rotate the protractor and mark from 180° around to the start again. Then draw lines radiating from the center to each of your marks so that you end up with an illustration like this:
Lines at 15°
Or, you can click on the above illustration, and then print out the result.
Step 2: Draw and Measure the Triangles
We can now turn each of those lines into a triangle, example:
Measure Triangles
When you have completed each triangle, it is simply a matter of measuring the lines. Remember that the sine is the length of the line opposite the angle divided by the hypotenuse (which should all be the same length if you have drawn it well)
Write all your measurements in a table. This is what I got, but your measurements may be different:
You can print a table ready to fill in here.
Important: When the "opposite" line goes downwards it is negative.
Tip: if you have drawn it well, you can take advantage of the symmetry of 0-90, 90-180, 180-270 and 270-360.
Graph The Results
Get some graph paper and prepare it by scaling off 0 to 360 in 15 increments along the x-axis, and scaling off -1 to +1 on the y-axis. You can use your own graph paper, or print out this graph paper
Now plot each point from the table on the graph.
Then join the dots as neatly as you can.
Result
The result should look something like the graph at the very top.
But you have done much more than draw a nice curve. You have :
learned about one of the most important functions in mathematics
Learned that you don't have to believe what people say - you can try it for yourself.
had experience plotting graphs
learned how symmetry can save effort
Hope you enjoyed!
Activity 3
First, read our page on special angle then answer these questions:
http://www.youtube.com/watch?v=-6sbejE0iYQ
What do we call the point A?
How can are calculate sine, cosine and tangent of special angle?
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Evaluation
Your work on each task will be weighed as follows:
1/ If you answer all the questions by using tools gives (10 point)
2/ If you answer some of questions by using tools gives (5 point)
3/ If you answer the all questions without tools gives (2.5 point)
Congratulation of all ……………….
Conclusion
WebQuest help the learner more to understand the sin , cosine and tangent function of special angles. Whose can be difficult understood by traditional methods.
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References
http://www.mashpee.k12.ma.us/Donohue%20webpage/wqtest.htm
http://math2.eku.edu/greenwell/MAT303/WEBQUEST/
http://www.mhcbe.ab.ca/ict/CurrSup/Wheels/wheels.htm
http://www.0zz0.com/index.php?sid=ba8348b6b7ddbef49f2560d4046914aa
To download this work (office 2007 format ) click Here
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The Asses
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