INTEGRATED SCIENCE, MATH AND TECHNOLOGY ACTIVITIES:

The following example of an integrated activity is provided to show possible Science/Math/Technology connections to the challenges introduced earlier.

The concepts of forces and Newton’s Laws could be important for any S/M/T connection that involves "mass and movement." The following is an example that students may use to better understand that  "motion that is caused by a constant force"—in this case gravitational force.  This example builds upon the story (or myth) of the "apple falling and hitting Issac Newton on the head" and the insight he gained about gravity and force.

Unit of force = newton  = approximately 1/5 of a pound or 3.2 ounces or 100 grams

Consider that five medium-size apples weigh approximately one (1) pound.

In common language we could describe a newton (N) as approximately the weight of one (1) medium-size apple, (or the force created by the weight (3.2 ozs.) of a medium-size apple here on Earth). If we are using metric measurements, we would describe a newton as being about equal to the weight of 100 grams.  In S/M/T activities, newtons are described and used in more precise ways. Newtons are defined as "the unit of force which produces an acceleration of one meter per second squared in a mass of one kilogram."

1 newton =  1 Kg • m/s/s = 1 Kg • m/s2

This means that the longer a force acts on a body, the faster the body will travel.

The statement above reads that one newton (as a unit of force) will cause one kilogram to change its momentum (accelerate) by a meter per second, for each second the force acts on the mass.

Introductory/Intermediate Level

To determine the velocity of a body you can use the formulas that follow:

(1) final velocity = initial velocity + (constant velocity • time taken)
v = u + (f x t)

(2) final velocity 2 = initial velocity 2 + (2 x acceleration • distance traveled)
v2 = u2 + 2(f x s)

in both formulae

u = initial velocity (measured in meters/second)
v = final velocity (measured in meters/second)
f = constant acceleration (measured in meters/(second) 2)
t = time taken (measured in seconds)
s = distance traveled (measured in meters)

If an object (an apple etc.) falls for 1 second. It's velocity is:

v = u + ft (Note:  acceleration due to gravity is 10m/sec2)
v = 0 + (10m/sec2 x 1 second)
v = 10m/sec2

If an object (an apple etc.) falls for 2 second. It's velocity is:
v = 0 + (10m/sec2 x 2 second)
v = 20m/sec2

What would the velocity be after 3 seconds, after 4?

The force exerted by the object after 1 second is
Force = Mass  •  Acceleration.
P = ma
For a 1 kg mass the force would be
P = 1 Kg  •  10m/s2
P = 10 newtons

(Note: 1N = 1 kg  •  1 m/s2)
If you wish to be more accurate you may can use gravity force as 9.8 rather than 10 in which case
P = 9.8 N

Advanced Level

We can use another approach to determine the change in momentum during any time interval. We will use Newton’s Second Law to describe motion with a constant force.  NOTE: In the problems that follow, we will be considering "units of change" of momentum and time. A unit of change is designated by the symbol "D" which is referred to as "delta".

DP = F • Dt 
where
DP = change in momentum
F  =  Force
Dt = change in time

Apple not moving (no momentum)

If an apple weights 1/5 of a pound = 1 Newton    

Dt = 1 second

DP = F • Dt
DP = 1 Newton • 1 second
DP = 1 Newton sec
DP = 1 Kg • m/s
(Repeat for time change or time intervals)

Assuming that the gravitational force on the apple is 1 Newton, the calculated mass of the apple will be calculated as approximately 1/10 of a kilogram (100 grams). Velocity at given time intervals may be calculated.

In summary, the apple’s velocity will change over time by increasing to 10 m/s (10 meters per second) after 1 second, 20 m/s after 2 seconds, 30 m/s after 3 seconds, etc.

PROBLEM SOLVING PROCESS:

These steps may be helpful to students in approaching their activity:

• Form cooperative groups (2 to 3 people)
• Brainstorm for ideas
• Sketch possible solutions
• Decide how to construct, maneuver, operate, etc. the project
• Decide on and gather materials
• Construct your design
• Test your design
• Present your design

RESOURCES:

The intended challenges were designed to be open-ended and flexible to accommodate various learning levels. Please feel free to incorporate additional material(s) to enhance each lesson. The categories of Exploratory, Intermediate, and Advanced provide a context in which students can understand the social and personal meaning of each challenge.

Additional materials may be found at the following locations:

• Surfing the Net with Kids - www.surfnetkids.com
• "Designing for Humans: The Human Factor in Engineering," Burgess, J. Petrocelli Books
• Assorted Science Texts

PROPOSED CURRICULUM STANDARDS CONNECTIONS:

The following Curriculum/Standards Connections for grades 5-8 are intended to aid in the use and assessment of the design challenge projects.  NOTE: These connections have been extracted from the National Standards.  You should check their correlation with your own State Curriculum Standards to ensure consistency with your curriculum goals.

Note on Assessment:  We strongly recommend using the Student Reflection Sheet and the Rubric provided in the Appendix to enhance the learning process, by encouraging student awareness and participation in the assessment of their work.  These tools can help students to understand the context, meaning, and value of undertaking these challenges.