# Ancient Egyptian Cookies

## Unit fractions are used in this fraction game. Students build complete cookies with unit fraction parts.

# INSTRUCTIONS

This Make Cookies for Grampy game is much like the Cookies for Grampy game, but this time you will use unit fractions.

To use unit fractions you go by these rules:

(1) All unit fractions have a numerator of one.

(2) Each cookie can have only one of each fraction. For example, you cannot use 1/8 + 1/8.

As you can see, it's bit more difficult to put together a whole cookie using unit fractions. At times you will have to approximate a whole cookie.

Your job is to make as many cookies as you can with the pieces given on the screen and with the pieces you input. Try to make complete cookies or close to complete cookies. An amount less than a complete cookie will deplete the spare cookie that is pictured in the upper left of the screen. For example, if you drag the 1/2 piece and 1/4 piece and then entered 8 for 1/8 you would have built 7/8 cookie. Since the cookie is missing 1/8 the spare cookie will decrease 12 percent (12/100) to 88 percent(88/100) because 1/8 rounds down to 12 percent of the cookie.The computer will keep track of and will picture the remaining amount in the spare cookie.

Your score is the number of cookies you can make. That score is given on the bucket that Grampy is holding.

After you build a whole cookie or enter a denominator, Grampy will take the cookie. It does not have to be a complete cookie. Grampy will take what he can get so try to build as complete a cookie as you can.

An Ancient Egyptian Pharaoh might be upset if he thinks you are making too many incomplete cookies for his workers.

Try to achieve a score of 10 cookies or more.

Qualify as an EGYPTIAN COOKIE MAKER by achieving a score of 12 cookies or more.

Qualify as a CHIEF EGYPTIAN COOKIE MAKER by achieving a score of 20 cookies or more.

There are combinations of unit fractions that will complete a whole cookie. For example, you could use 1/2 + 1/6 + 1/3. After you drag one cookie piece onto Grampy's cookie you will have the option of dragging another piece or of entering a denominator of your choosing.

Some other examples of complete cookies besides 1/2 + 1/6 + 1/3 are:

Drag 1/3 + 1/4 + 1/5 + 1/9 + 1/10 + enter 1/180

Drag 1/2 + 1/4 + 1/8 + 1/9 + enter 1/72

Drag 1/2 + 1/5 + 1/6 + 1/10 + enter 1/30

The computer will display the sum of the parts as you build the cookie. You will also be shown the remaining amount.

Try to use up the smaller pieces soon. If you are left with (2) 1/10 pieces you could drag one of the pieces and enter 2 for 1/2. That would give you 3/5 cookie, leaving you with 2/5 left over. That 2/5 is 40 percent of a cookie so the spare amount will decrease 40 points. The same would happen with the other 1/10.

After the cookie pieces are gone and the final cookie is complete, you may press the <New Pieces> button for more pieces. The game is finished when the spare cookie is too small for any spare amount needed.

You may press the <Start> button to reset the score back to to 0 and get a new spare cookie and new pieces.

Press the <Report> button to make a report card. This button will open a dialog that asks you to submit your name. You may prefer to submit a code for your name. The <Send> key on the dialog box will open a new browser window with your printable report card

Have fun. Grampy loves cookies.

An article in the New York State Mathematics Teachers' Journal;2010, references the use of fraction circle pieces using the unit fractions rules (above) to build a complete circle. Suggestions and advice from George W. Dombi, author of the article, were helpful as I wrote this game.

## WHAT WILL I LEARN?

- The relative sizes of 1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/8, 1/9, and 1/10.
- How to build or approximate a whole number with different fraction sizes using unit fractions.
- More practice with addition and subtraction of fractions.