Human-Computer Interaction: Communication, Cooperation, and Application Design

By Hans-Jörg Bullinger; Jürgen Ziegler | Go to book overview

measures proficiency in the following NCTM standards: spatial sense, patterns, computation, statistics, and communication. Integral assessment components are designed into the multimedia project that enables teachers to quickly evaluate the students and their mathematical progress.

The mathematics involved in Wyzt's Playground are significant and have extensions in school mathematics beyond the fourth grade. The mathematical concept underlying Wyzt's Playground is a linear programming problem with constraint inequalities about space, time and money. The optimization function maximizes the number of kids who can play on the playground. Moreover, the answers must be integers. Thus, the mathematical problem, and the related assessment, can extend beyond fourth grade through high school algebra.


3 The Mathematical Model

The model is formulated in the following way: maximize z=ax + by + c where a, b, c are positive integers chosen for the number of kids using the equipment, choices represented by x, y and a required basketball court, and

dx + ey ≤ f (Space) gx + hy ≤ i (Cost) where d,e,f,g,h,i are all appropriate numbers selected on the basis of reasonableness of the solution, and x and y are the numbers of each type of equipment as above.

The solution then, is an integer choice of z representing the highest number of children on the playground constructed with pieces of x pieces of one equipment and y pieces of another, each of which will occupy space and cost money. As mentioned earlier, a third piece of equipment (a basketball court) was required for all playgrounds.

To illustrate the model and the solution, let us consider one of many playgrounds we could build. Suppose that we choose swings and slides as the type of equipment we will use along with the basketball court. An amount of $10,000 is available for the playground. We also know that swings cost $1000 each and can hold 8 kids, slides cost $500 and can hold 4 kids, and the basketball court cost $2500 and can hold 10 kids (at a time). Furthermore, the space available for the playground is 4900 square feet. The basketball court uses 1500 square feet of space, swings occupy 300 square feet of space and slides occupy 150 square feet of space. Our problem is now:

maximize z = 8x + 4y + 10 such that 300x + 150y + 1500 ≤ 4900 (Space) 1000x + 500Y + 2500 ≤ 10000 (Cost) where x, y and z must all be positive integers.

The solutions to some of our playground problems are not unique. For instance, one of several solutions to the example is x = 1, y = 13 and z = 70. Another is x = 7,y = 1 and z=70.

-678-

Notes for this page

Add a new note
If you are trying to select text to create highlights or citations, remember that you must now click or tap on the first word, and then click or tap on the last word.
One moment ...
Default project is now your active project.
Project items

Items saved from this book

This book has been saved
Highlights (0)
Some of your highlights are legacy items.

Highlights saved before July 30, 2012 will not be displayed on their respective source pages.

You can easily re-create the highlights by opening the book page or article, selecting the text, and clicking “Highlight.”

Citations (0)
Some of your citations are legacy items.

Any citation created before July 30, 2012 will labeled as a “Cited page.” New citations will be saved as cited passages, pages or articles.

We also added the ability to view new citations from your projects or the book or article where you created them.

Notes (0)
Bookmarks (0)

You have no saved items from this book

Project items include:
  • Saved book/article
  • Highlights
  • Quotes/citations
  • Notes
  • Bookmarks
Notes
Cite this page

Cited page

Style
Citations are available only to our active members.
Buy instant access to cite pages or passages in MLA, APA and Chicago citation styles.

(Einhorn, 1992, p. 25)

(Einhorn 25)

1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

Cited page

Bookmark this page
Human-Computer Interaction: Communication, Cooperation, and Application Design
Table of contents

Table of contents

Settings

Settings

Typeface
Text size Smaller Larger Reset View mode
Search within

Search within this book

Look up

Look up a word

  • Dictionary
  • Thesaurus
Please submit a word or phrase above.
Print this page

Print this page

Why can't I print more than one page at a time?

Help
Full screen
/ 1364

matching results for page

    Questia reader help

    How to highlight and cite specific passages

    1. Click or tap the first word you want to select.
    2. Click or tap the last word you want to select, and you’ll see everything in between get selected.
    3. You’ll then get a menu of options like creating a highlight or a citation from that passage of text.

    OK, got it!

    Cited passage

    Style
    Citations are available only to our active members.
    Buy instant access to cite pages or passages in MLA, APA and Chicago citation styles.

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn, 1992, p. 25).

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences." (Einhorn 25)

    "Portraying himself as an honest, ordinary person helped Lincoln identify with his audiences."1

    1. Lois J. Einhorn, Abraham Lincoln, the Orator: Penetrating the Lincoln Legend (Westport, CT: Greenwood Press, 1992), 25, http://www.questia.com/read/27419298.

    Cited passage

    Thanks for trying Questia!

    Please continue trying out our research tools, but please note, full functionality is available only to our active members.

    Your work will be lost once you leave this Web page.

    Buy instant access to save your work.

    Already a member? Log in now.

    Author Advanced search

    Oops!

    An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.