calculus activity grab bag chris cunningham department of mathematics [email protected]

28
Calculus Activity Grab Bag Chris Cunningham Department of Mathematics [email protected]

Upload: robert-garrett

Post on 16-Jan-2016

224 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

Calculus Activity Grab Bag

Chris CunninghamDepartment of Mathematics

[email protected]

Page 2: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

Outline

• 5 Activities

For each Activity,• Activity Overview• Requirements for a Similar Activity• How Did it Go?

Page 3: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

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?”

Page 4: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

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.

Page 5: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

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.”

Page 6: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

1. Experiments and Chaos

How Did it Go?

Page 7: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

1. Experiments and Chaos

How Did it Go?

Page 8: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

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?”

Page 9: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

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.

Page 10: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

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?

Page 11: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

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.

Page 12: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

2. Relays

Requirements for a Similar Activity

• Problems that are “partially solvable” even with partial information

• Problems that are expected to be solved quickly

Page 13: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

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?”

Page 14: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

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.

Page 15: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

3. Logarithms

Activity Overview

Page 16: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

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

Page 17: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

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?”

Page 18: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

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.

Page 19: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

4. Rosetta Stone

Activity Overview

Page 20: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

4. Rosetta Stone

Activity Overview

Page 21: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

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

Page 22: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

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?”

Page 23: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

5. Astronomy

Activity Overview

Page 24: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

5. Astronomy

Activity Overview

Page 25: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

5. Astronomy

Activity Overview

!!!!!!!!

Page 26: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

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.

Page 27: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

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?”

Page 28: Calculus Activity Grab Bag Chris Cunningham Department of Mathematics ccccc@illinois.edu

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]