calculus activity grab bag chris cunningham department of mathematics [email protected]
TRANSCRIPT
Calculus Activity Grab Bag
Chris CunninghamDepartment of Mathematics
Outline
• 5 Activities
For each Activity,• Activity Overview• Requirements for a Similar Activity• How Did it Go?
1. Experiments and Chaos
Activity Overview
(next year’s population) =
(parameter) *(this year’s population) * (1 – this year’s population)
Population ranges from 0.0 to 1.0.
The question for students: “How does this model behave?”
1. Experiments and Chaos
Activity Overview
Each student gets a different parameter value.
Using a calculator, each “sees what happens” starting with population 0.1.
Everyone plots results on the chalkboard until a general picture starts to emerge.
1. Experiments and Chaos
Requirements for a Similar Activity
• A “big picture”
• A lot of tedious work needed to see it
• A nice picture for the “big picture.”
1. Experiments and Chaos
How Did it Go?
1. Experiments and Chaos
How Did it Go?
1. Experiments and Chaos
How Did it Go?
• What are students actually doing during the activity?
• What are students going to “take away” from the activity?
• “Do we have to know this for the test?”
2. Relays
Activity Overview
• Students are organized into teams of 3• Student 1 gets a problem.• Student 2 gets a problem that is unsolvable
without the solution of problem 1.• Student 3 gets a problem that is unsolvable
without the solution of problem 2.
2. Relays
Activity Overview
1. Find (16 * 16 – 14 * 14).
2. Let N = TNYWR. Find (61 * 61 – N * N).
3. Let N = TNYWR. If someone's birthday is today and they are N years old, what year were they born?
2. Relays
Activity Overview
1. (16 * 16 – 14 * 14) = 60.
2. (61 * 61 – 60 * 60) = 121
3. Let N = TNYWR. If someone's birthday is today and they are N years old, what year were they born? 2012 – 121 = 1891.
2. Relays
Requirements for a Similar Activity
• Problems that are “partially solvable” even with partial information
• Problems that are expected to be solved quickly
2. Relays
How Did it Go?
• What are students actually doing during the activity?
• What are students going to “take away” from the activity?
• “Do we have to know this for the test?”
3. Logarithms
Activity Overview
Give them a toy to play with and “figure out.”
Ask questions about the toy.
Get them to build a better version of the toy.
3. Logarithms
Activity Overview
3. Logarithms
Requirements for a Similar Activity
• An “abstract” concept that has a nice physical interpretation
• A cool invention that is old enough to be forgotten by students
3. Logarithms
How Did it Go?
• What are students actually doing during the activity?
• What are students going to “take away” from the activity?
• “Do we have to know this for the test?”
4. Rosetta Stone
Activity Overview
• Students are given a mysterious packet.
• Students must decipher the code motivating them to solve the problems.
• Students know the prize is somewhere in the building waiting for them.
4. Rosetta Stone
Activity Overview
4. Rosetta Stone
Activity Overview
4. Rosetta Stone
Requirements for a Similar Activity
• The “answers” to the problems must be able to encode something
• Are the answers letters? Numbers? Words?
• This takes a lot of time to set up
• Prizes are needed
4. Rosetta Stone
How Did it Go?
• What are the students actually doing during the activity?
• What are the students going to “take away” from the activity?
• “Do we have to know this for the test?”
5. Astronomy
Activity Overview
5. Astronomy
Activity Overview
5. Astronomy
Activity Overview
!!!!!!!!
5. Astronomy
Requirements for a Similar Activity
• Almost any math or science topic could probably be the basis for a science fiction story…
• Requires some creative energy to put the problems together in this way.
5. Astronomy
How Did it Go?
• What are students actually doing during the activity?
• What are students going to “take away” from the activity?
• “Do we have to know this for the test?”
Wrap-Up
1. Experiments and Chaos2. Relays3. Logarithms4. Rosetta Stone5. Astronomy
• What are students actually doing during the activity?• What are students going to “take away” from the activity?• “Do we have to know this for the test?”
Contact me to collaborate/chat! [email protected]