# nctm 2006

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Category: Education

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### So What's the Problem? The Answer is the Natural Link Between Mathematics and Science" Jim Rubillo National Council of Teachers of Mathematics Reston, VA jrubillo@nctm.org:

So What's the Problem? The Answer is the Natural Link Between Mathematics and Science"Jim RubilloNational Council of Teachers of MathematicsReston, VAjrubillo@nctm.org

### The Purpose of Math & Science: The Adult World’s View:

The Purpose of Math & Science: The Adult World’s View Name Occupation Selma House Realtor Ivy Sticker Nurse Hugo First Paratrooper Walter Wall Carpet Installer G. Howie Shivers Refrigeration Specialist Phil Ovitt Politician Cindy Bag Express Line Supermarket Cashier Harry Fitabaldi Hair Club President & Client Too Howie Gettindere Locksmith Dewey, Cheatem & Howe Attorneys Sal Manella Toxic Food Expert

### Slide 5:

Is It Time for a Different Perspective? Say… What’s a mountain goat doing way up here in a cloud bank? Copyright: Gary Larsen

### PROBLEM SOLVING Engaging in an activity for which the method of solution is not known in advance. :

PROBLEM SOLVINGEngaging in an activity for which the method of solution is not known in advance.

### PROBLEM SOLVING NOT FORMALIZING (or memorizing) THE STEPS TO FIND THE ANSWERS TO WORD (or Story) PROBLEMS! :

PROBLEM SOLVINGNOT FORMALIZING (or memorizing)THE STEPS TO FIND THE ANSWERS TO WORD (or Story) PROBLEMS!

### A Fundamental Example I have quarters, dimes, and nickels in my pocket. If I take three coins out of my pocket, how much money could I have taken? :

A Fundamental ExampleI have quarters, dimes, and nickels in my pocket. If I take three coins out of my pocket, how much money could I have taken?

### Slide 9:

How many times in a 12-hour period will the digits on a digital clock have a sum of 10? Example: 12:34 1 + 2 + 3 + 4 = 10 Another Example

### Slide 10:

How many times in a 12-hour period will the digits on a digital clock have a sum of 10? At what time will the clock be the brightest?

### Get the Marble Out!:

Get the Marble Out! Problem?

### Get the Marble Out!:

Get the Marble Out! Problem? Exercise?

### Four Glasses and Three Knives:

Four Glasses and Three Knives Support One Glass Above the Others?

### How Did You Get That Result?:

How Did You Get That Result? © Stokes Publishing Co. www.stokesco.com

### Slide 19:

www.sudoku.com.au Sudoku is a popular form of applied reasoning and proof

### Slide 20:

www.sudoku.com.au Sudoku is a popular form of applied reasoning and proof 1 9 ?

### SPREADING, PEAKING, AND ENDING OF A FLU EPIDEMIC :

SPREADING, PEAKING, AND ENDING OF A FLU EPIDEMIC Every flu epidemic has a "population of opportunity." The epidemic is spread "randomly" until the maximum number of susceptible people contract the flu and the “epidemic is over."

### SPREADING, PEAKING, AND ENDING OF A FLU EPIDEMIC :

SPREADING, PEAKING, AND ENDING OF A FLU EPIDEMIC Everyone does not contract the flu. Only the “susceptible” people in the “population of opportunity” get sick.

### SPREADING, PEAKING, AND ENDING OF A FLU EPIDEMIC :

SPREADING, PEAKING, AND ENDING OF A FLU EPIDEMIC We take actions that attempt to reduce this "population of opportunity." Sample actions: immunization shots, isolation of infected people, sanitation, education on risk factors.

### Questions? :

Questions? How can we detect when the "growth of an uncontrolled epidemic" has peaked? How can we predict the maximum number of susceptible persons that will be infected?

### Slide 26:

www.nctm.org/mathnow

### Which graph (1, 2 or 3) best represents::

Which graph (1, 2 or 3) best represents: a car slowing down and then speeding up? 0

### Which graph (1, 2 or 3) best represents::

Which graph (1, 2 or 3) best represents: a speeding car crashing into a solid wall. 0

### The Graph Tells a Story!:

The Graph Tells a Story! You are at the movie and you buy a cup of popcorn. The graph shows the level of the popcorn in your cup. What happened?

### The Graph Tells a Story!:

The Graph Tells a Story! You are at the movie and you buy a cup of popcorn. The graph shows the level of the popcorn in your cup. What happened?

### Can Learning a Concept Out of Context Lead to Confusion? or Why Do Americans Focus on being “Average?”:

Can Learning a Concept Out of Context Lead to Confusion?or Why Do Americans Focus on being “Average?”

### Washington and Old Dominion Trail :

Washington and Old Dominion Trail http://wodfriends.org/elevations.html

### What is the Rate of Change between Milepost 5.5 and Milepost 29?:

What is the Rate of Change between Milepost 5.5 and Milepost 29?

### What is the Rate of Change between Milepost 5.5 and Milepost 29?:

What is the Rate of Change between Milepost 5.5 and Milepost 29? Milepost 5.5: 336 feet Change in elevation = -2 ft/23.5 miles = -0.085 ft/mile Milepost 29: 334 feet -1.02 inches/mile

### Almost Level? What Has Been Missed?:

Almost Level? What Has Been Missed? Milepost 5.5: 336 feet Change in elevation = -2 ft/23.5 miles = -.085 ft/mile Milepost 29.5: 334 feet -1.02 inches/mile

### What are the Rates of Change between Milepost 11, Milepost 14 and Milepost 16.5?:

What are the Rates of Change between Milepost 11, Milepost 14 and Milepost 16.5? Milepost 11: 447 feet Milepost 14: 237 feet Change = -210 ft/ 3 miles = - 70 ft/mile Milepost 14: 237 feet Milepost 16.5: 384 feet Change = 147 ft/ 2.5 miles = +58.8 ft/mile Milepost 11: 447 feet Milepost 16.5: 384 feet Change = -63 ft/ 5.5 miles = - 11.5 ft/mile

### What percentage of the numbers in Pascal’s Triangle are even?:

What percentage of the numbers in Pascal’s Triangle are even? 1 1 1 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 7 21 35 35 21 7 1

### Pascal’s Triangle E + O = O, O + E = O, E + E = E, O + O = E:

Pascal’s TriangleE + O = O, O + E = O, E + E = E, O + O = E O O O O E O O O O O O E E E O O O E E O O O E O E O E O O O O O O O O O

### Rows Proportion (evens):

Rows Proportion (evens) 8 9/36 = .250 16 55/136 = .404 32 285/528 = .539 64 1351/2080 = .650 128 6069/8256 = .735 256 26335/32896 = .801 512 111645/131328 = .850

### Rows Proportion (evens):

Rows Proportion (evens) 1024 465751/524800 = .888 2048 1921029/2098176 = .916 4096 7859215/8390656 = .937 8192 31964205/33558528 = .953 16384 129442951/134225920 = .964 32768 522538389/536887296 = .973 65536 2104469695/2147516416 = .980

### Rows Proportion (evens):

Rows Proportion (evens) 1024 465751/524800 = .888 2048 1921029/2098176 = .916 4096 7859215/8390656 = .937 8192 31964205/33558528 = .953 16384 129442951/134225920 = .964 32768 522538389/536887296 = .973 65536 2104469695/2147516416 = .980

### Rows Proportion (evens) Based upon a geometric estimate:

Rows Proportion (evens) Based upon a geometric estimate 131072 8460859965/8590000128 = .985 262144 33972448951/34359869440 = .989 524288* = .991 1048576* = .994

### Slide 46:

I Have a Cube of Material It Measures One Cubic Foot (Length = 12 inches, Width = 12 inches, Depth = 12 inches) The surface area of the cube is 6 square feet

### Slide 47:

I Have a Cube of Material It Measures One Cubic Foot (Length = 12 inches, Width = 12 inches, Depth = 12 inches) The surface area of the cube is 6 square feet A gallon can of wall paint covers 400 square feet of surface area

### Slide 48:

We Will Cut the Cube into “Little Cubes” Each Dimension Will Be One-Thousandth of an Inch (Each Cube Length= 0.001 inch, Width = 0.001 inch, Depth = 0.001 inch) That’s (12000)3 little cubes Each small cube has 6 surfaces

### Slide 49:

How Many Gallons of Paint Are Required to Paint the Surfaces of All of the Little Cubes? All (12000)3 little cubes!

### Slide 51:

What’s the Point? Volume is always one cubic foot, but as the dimensions of each small cube decreases, the surface area goes to infinity!

### PROBLEM SOLVING requires us to provide students with a continuing series of unique and engaging experiences. :

PROBLEM SOLVINGrequires us to provide students with a continuing series of unique and engaging experiences.

### Nine (or Rather Twelve) Inch Nails?:

Nine (or Rather Twelve) Inch Nails? Balance Ten Nails on One Nail?