**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** Two to four days.

**Required:**

**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.

4. The students can figure the selling price of a book cover and determine a profit margin.

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**

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 Parallel flaps do not overlap

o Flaps are not double folded

o Only folding is used in assembly (no cutting the book cover)

o No tape or adhesives of any kind are used to secure the book cover.

**The presentation must include:**

o Assumptions

o Data

o Explanation of methods

o Sample book cover(s)

o Formula for determining the size of the ideal book cover when given the book measurements

o Conclusions

**The written reports must include:**

o Statement of the problem

o Assumptions

o Data

o Explanation of methods

o Formula for determining the size of the ideal book cover when given the book measurements

o Conclusions and options

o Reflection on the strengths and weaknesses of the proposal

*Funded in part by the National Science Foundation and Indiana University 1995*