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10 Big Ideas
by Doug McG - Wednesday, October 24, 2007, 04:49 PM
After reviewing the unit, use the reply button to post what you think are the 10 big math content ideas in "High Dive."
Picture of Peter Sullivan
Re: 10 Big Ideas
by Peter Sullivan - Wednesday, October 24, 2007, 06:50 PM

1) Trigonometry: using sine and cosine to find lengths and height of diver.

2)  Creating generic formula for falling time from rest.

3) Combining height of diver with generic falling time to create diver falling time.

4) Creating simplified x-coordinate formulas for diver (using just trig) and cart ( using falling time times speed) and then solving for w.

5) Converting between polar and standard co-ordinates.

6) Solving quadratic equations by hand and with formula.

7) Plugging in falling time with a vertical force formula to quadratic formula to create new falling time formula.

8) Seperating out vertical and horizontal components of velocity through trig with vectors.

9) Creating the two new x-coordinate equations using new falling time and factoring in the horizontal push from ferris wheel

10) Solving for the intersection on the calculator.   


Picture of Martin Kessler
Re: 10 Big Ideas
by Martin Kessler - Wednesday, October 24, 2007, 08:15 PM

1. Using trig, especically sine and cosine, to find triangle's side lengths. 

2. Learning that sine and cosine can work without a right angle. The angle can be negative and even greater than 360 degrees.

3. Distance can be calculated by multiplying average speed by time.

4. Any object that falls is affected by gravity by the same force and therefore accelerates at the same rate.

5. How long it takes an object to hit the ground is different if it starts from rest or not.

6. Not all the functions in the y equals have to be graphed and the calculator can find the intersection point of two functions.

7. Polar coordinates and rectangular coordinates are two way of describing position on a graph.

8. An object's falling time is not affected by its horizontal velocity.

9. Horizontal movement is calculated by multiplying horizontal velocity by time.

10. Inverse sine and cosine can be used to calculate angles when side lengths are given.

11. IMP will trick you.

Picture of Mikko Harvey
Re: 10 Big Ideas
by Mikko Harvey - Wednesday, October 24, 2007, 10:50 PM
IMP will not harm you.
Picture of Peter Ryan
Re: 10 Big Ideas
by Peter Ryan - Wednesday, October 24, 2007, 10:10 PM
This will probably get repetetive because both Peter and Martin have made very thorough lists.

1. Trigonometry...the use of sine, cosine, and tanget to find lengths of sides of triangles.

2. Becoming comfortable with using the sine and cosine functions and learning when to use which.

3. Learn about how to calculate speed, distance, and time. Speed=Distance/Time, Distance=Speed*Time, Time=Distance/Speed.

4. Learn to work with circles and learn what the different points of release are and so on.

5. Falling objects are affected by things such as gravity and what their initial speed is when falling.

6. When an object is falling off a moving ferris wheel, it will fall differently than if it was falling just off a platform.

7. As we learned with the bullet/gun example, the horizontal movement of an object does not effect how long it takes for it to fall.

8. Figuring out equations for different parts of the situation: falling time, wheel time, and so on.

9. Seperating vertical and horizontal components of a falling object.

10. Have fun? Be aware of the different measurements in the unit problem.
Picture of Mikko Harvey
Re: 10 Big Ideas
by Mikko Harvey - Wednesday, October 24, 2007, 10:51 PM
10) General quadratic equation saves lots of time.

9) Instantaneous/average speed with accelerating, dropping object.

8) Falling Time equations

7) Trigonometry

6) Pulling together several equations so solve a larger problem

5) Falling time is not changed by horizontal velocity

3) General circle work…How to find certain angles, lengths, similar triangles within/outside circle

4) Polar coordinates

2) Gravity’s affect on falling time

1) Angular speed
Picture of Ryan Prothro
Re: 10 Big Ideas
by Ryan Prothro - Wednesday, October 24, 2007, 11:35 PM
1- Understanding the meaning of sine, cosine, and tangent in terms of both a right-angled triangle as well as in terms of “y” and “r”
2- Learning and getting practice with working with circles and being able to find angles within them
3- Leaning how to put together equations using many different equations to make and solve for the final result (=the unit problem0
4- Understanding more closely and extensively how sin and cosine are related and how to see this relationship
5- Learning how to find the intersection of two lines more accurately (with a graphing calculator)
6- Getting practice with and understanding how to calculate the falling time as well as why the falling time equation works
7- Learning the quadratic formula equation = b+-(√ b2+4ac)/ 2a
8- Learning how to use inverse sine what the inverse sine is and what the answer gives you
9- Knowing how the push of the wheel and gravity effects the falling time and acceleration of the diver
10- Learning how to convert polar coordinates to standard coordinates and vise versa

Picture of jonah vorspan-stein
Re: 10 Big Ideas
by jonah vorspan-stein - Thursday, October 25, 2007, 07:15 PM
1. Inverse trigonometry
2. Quadratic equation
3. Falling time
4. Trigonometry
5. Triangles within cirlces
5. Angular speed
6. Figuring out angular percent of a circle
7. Horizontal/Vertical speed component
8. Gravity pulls at a constant regardless of vertical motion
9. Falling time with force given by wheel
10. Points of intersection