SCIENCE AND TECHNOLOGY

J. INQUIRY AND PROBLEM SOLVING
Students will apply inquiry and problem-solving approaches in science and technology
Scientific inquiry, problem solving, and the technological method provide insight into and comprehension of the world around us. A variety of tools, including emerging technologies assist, the inquiry processes. Models are used to understand the world.

MATHEMATICS

A. NUMBERS AND NUMBER SENSE
Students will understand and demonstrate a sense of what numbers mean and how they are used. Numbers are used to describe and interpret phenomena. Building a sense of number relationships is essential for developing the ability to deal with any set of numbers. Number sense involves understanding the meaning of numbers, relationships among numbers, relative number magnitudes, and the effects of operations on numbers. Skilled estimation is also an important component of number sense.

B. COMPUTATION
Students will understand and demonstrate computation skills. Understanding the fundamental operations of addition, subtraction, multiplication, and division is central to knowing mathematics. Proficiency in computational skills is essential to problem-solving and other mathematical activities. Estimating, evaluating reasonableness of answers, and obtaining accuracy in calculations are included in this proficiency. Understanding relationships in operations allows students greater facility with mental computation. Computational skill promotes efficient and confident learners.

E. GEOMETRY
Students will understand and apply concepts from geometry. Geometry is the study of the spatial world and its symmetries. The ideas of geometry are used to describe, interpret, represent, and change the spatial world in which we live. The understanding and development of spatial and visual skills strengthens problem-solving abilities.

F. MEASUREMENT
Students will understand and demonstrate measurement skills. Measurement is valuable as an integrating skill throughout the curriculum and in everyday life. The use of estimation is vital in determining the reasonableness of measurement. Measurement attributes (e.g., length, volume, minutes), units, and tools enhance the ability to describe and understand the world.

H. ALGEBRA CONCEPTS
Students will understand and apply algebraic concepts. Algebra and analytic thinking are fundamental tools for working in and thinking about mathematics. These tools provide ways to generalize and predict problem solutions when not all information is known. Taught within the context of mathematical and practical applications, the concept of functions is a unifying theme for algebraic concepts.

Procedure

This is a one-day (45 minute) module with follow-up homework, or a 2-period module with follow-up discussion. The initial presentation should take about 20 minutes, and 15 allowed for students to complete at least the initial portion of the worksheet. At this point, there can be a brief demonstration that, in fact, 2 sugar cubes can support a 150 lbs student. The students can then finish the worksheet for homework or in a second period, followed by a discussion (possible areas for discussion listed below in the detailed section of the procedure.

I. Initial presentation

1. PowerPoint presentation "An Introduction to Structures, Forces and Stress" should be introduced by saying that structural engineering involves designing structures that we are fairly sure will work. In order to do this, we need to understand loads and strengths. In order to discuss strength, we need to introduce force and stress.
2. After showing initial graph showing steel with a breaking strength of 400 lbs and plastic with a strength of 500 lbs is a good time to ask the students which is stronger based on the experimental results. In general they can be convinced that the graph shows that plastic is stronger, but that they feel that steel is stronger. Some students will ask how big each test specimen is, otherwise, the next step is to show the class first the plastic specimen then the steel specimen.
3. Finish the presentation.

II. Marshmallow testing

1. This can be introduced with, ”Now we are going to apply the concepts of force and stress to non-traditional building material.”
2. Set 10 marshmallows upright in a fairly tight pattern (about 2”x3”). Show class how testing apparatus works (i.e. that light bulb comes on when indicator comes in contact with plate.)
3. Set indicator amongst marshmallows and plate on top of them.
4. Ask for predictions of how many pennies it will take to fail the marshmallows (nothing that we have defined failure in this case to be when the plate touched the indicator).
5. Set pennies on plate, evenly distributing them, until light bulb lights. It helps to have sets of 10 pennies already Scotch taped together.
6. Due to creep, loading should occur fairly quickly.

III. Worksheet portion

1. One sheet per student.
2. Students should be allowed to spend some time before helping begins. In general this is good 1-1 time. Students may need help with units, ratios, and determining size of shapes with a certain area.

IV. Intermediate follow-up

1. Students should get to point on sheet where they determine that 1-2 square inches of sugar cube will support them. Someone will express disbelief, and this is fairly easy to promulgate.
2. Set two sugar cubes on the floor, place board on top of them and help student onto it. Great care must be taken to set the student on the board evenly and prevent wobbling.
3. Having survived, cubes should be shown to class.

V. Terminal follow-up

Discussion items for column:

1. Why is it important to specify where the experiment is going to take place when we are dealing with mass?
2. How strong would a marshmallow be on the moon (gravity = 1/6G)
3. What shape (square, circle or triangle) would be best for a column?
4. How about a tall column?
5. How do columns actually fail?
6. What is the difference between a sugar cube failing and a marshmallow failing (elastic versus brittle)?
7. How about steel (or chewing gum)?

Expected Results

Students should gain appreciation of the need for stress as a concept, and understanding of the difference between force and stress. The module should increase students’ interest in math, science and engineering. The students should also develop additional skill using unit conversion, geometry and algebra.

Troubleshooting

There were two main technical difficulties. The marshmallows need to be loaded carefully and smoothly and the wire connecting the indicator to the plate needs to be flexible enough that moving things around will not mess up the marshmallow set-up. The other issues is that is difficult to set the student smoothly on the board without having the corners of the cubes get crushed. It may help to break the cubes in half so that the board can be held up in each of its four corners.