COVER UP
Cindy Boyd
Anthony Ice
Phyllis Slayton
Barb Steinbrunner
Class:
Algebra I, Pre-Algebra, or General Math
Materials:
Rulers, tape measures, scissors, newspaper/butcher paper, and various sized
textbooks.
Goal:
To develop formulas, to apply reasoning/logic skills, and to use discriminating skills.
Time
Required:
Two to four days.
Background: Linear measurement skills, book-covering concepts.
Setting:
The students have been approached by the Mean Office Supply Company to
determine the size(s) of four-fold book covers needed at the school.
Problem:
The students want to develop a formula to give the dimensions of the ideal four-fold
book cover for any given book and to decide upon a book cover size that will cover
the largest number of books. (Is it possible to cover all books with one size? Is it
possible to cover all books with two sizes? What range can a book cover
encompass?)
Evaluation: An oral group presentation and individual written reports. The oral presentation
should be a sales pitch to the Mean Office Supply Company which includes a sample
book cover(s), explanation of method, assumptions, and conclusions. The written
report should include a statement of the problem, data, process of developing the
formula, the formula, explanation of methods, assumptions, options, conclusions, and
reflections on the project.
Extensions:
1.
The students can explore the types of paper that can be used to manufacture the book covers
and the costs involved with using a certain type of paper.
2.
The students can determine if printing is needed on the book covers and what the cost of the
printing would be. Students could also develop artistic patterns for the book covers.
3.
If the students recommend different sized book covers, they can explore what is the Abest@
way to cut the different sizes out of a roll of paper.
The students can figure the selling price of a book cover and determine a profit margin.
4.
Funded in part by the National Science Foundation and Indiana University 1995
5.
The students can estimate the number of book covers needed at their school and estimate
how many of each type the bookstore should stock.
Teacher Notes:
1.
Teachers need to have a fairly large number of textbooks available in class for the students to
measure. The textbooks must be of various sizes; the greater the variance the better.
2.
Teachers also need a large supply of newspaper or butcher paper for the students to use while
testing a variety of book cover sizes. The students can be asked to bring in old newspapers
from home.
3.
To fold a four-fold book-cover.
First, make equal folds at the top and
bottom edges of the book cover, so that
the remaining length is equal to that of
the book length.
Second, make equal folds at the left and
right edges of the book cover, so that the
remaining width is equal to the binding
and twice the width of the book.
Then, the edges of the hardcover of the
text may be slipped into the left and right
pockets created by the folds.
4.
The book covers must be able to stay securely on the book (when the book is open and when
the book is closed) without the aid of tape or any other adhesives or foreign objects. The
folded flaps cannot overlap and they cannot be double folded. The book cover cannot be cut
to fit a smaller size.
5.
Example outlines of the formulas for the dimensions of the ideal book cover are:
o
Width of book cover = 2 (width of the book) + binding + 2 (width of a vertical fold).
o
Length of book cover = length of the book + 2 (width of a horizontal fold). The
thickness of the hard cover of the text may be figured into the formulas.
6.
Overlapping will occur and a book cover will not properly fit a book if either of the
following is true:
o
Length of book cover > 2(length of the book),
o
Width of book cover > 4(width of the book) + binding.
COVER UP
Funded in part by the National Science Foundation and Indiana University 1995
The Mean Office Supply Company (MOSC) is the nation=s leading producer of the four-fold book
cover. MOSC wants to be your school=s only book cover supplier and is enlisting your help in
determining the size or sizes of book covers that are needed. Your group will need to prepare an oral
presentation for the MOSC president to influence MOSC that your proposal is the best, and each
group member will need to prepare an individual written report.
Four-fold book cover specifications set by MOSC:
o
o
o
o
Parallel flaps do not overlap
Flaps are not double folded
Only folding is used in assembly (no cutting the book cover)
No tape or adhesives of any kind are used to secure the book cover.
The presentation must include:
o
o
o
o
o
o
Assumptions
Data
Explanation of methods
Sample book cover(s)
Formula for determining the size of the ideal book cover when given the book measurements
Conclusions
The written reports must include:
o
o
o
o
o
o
o
Statement of the problem
Assumptions
Data
Explanation of methods
Formula for determining the size of the ideal book cover when given the book measurements
Conclusions and options
Reflection on the strengths and weaknesses of the proposal
Funded in part by the National Science Foundation and Indiana University 1995