# Fun with Fractions

## Overview

After visiting the American Revolution in the Time Machine, students will play a math game to gain a better understanding of fractions.

## Activity

In the American Revolution section of the Time Machine, the American soldiers try to purchase pies from a local farmer.  The farmer refuses the copper coins that the soldiers offer, and instead he requests silver, such as that contained in Spanish Silver Dollars.  After exploring this era, your students should understand that Spanish Dollars were often broken into eight pieces for easier spending.  These pieces were often called pieces of eight as they represented 1/8 of the whole Spanish Dollar.  This topic lends itself perfectly to a math connection!  Build upon this Time Machine topic by introducing your class to a study of fractions.

Give each of your students a copy of the Fraction File, a circle that is meant to represent a Spanish Silver Dollar.  Direct your students to cut out the circle and fold it along the center line.  Discuss with your class that a fraction is a part of a whole, and that they have divided the coin into 2 equal parts (stress that when dealing with halves that the parts are equal - one half cannot be larger than another).  Instruct your students write on one of the 2 halves the fraction 1/2 and color that half (lightly) entirely in blue.

Have your students fold the paper in half a second time and ask your students how many even parts the coin has been broken into now (4).  Explain that each of those four parts is ¼ of the whole coin (one of four even pieces of the coin).  In one of the uncolored quarters of the coin, instruct your students to write ¼ and color that area red (lightly).  Repeat this process again to create eighths.  Either independently or in small groups, allow the students to explore the number of smaller fractions make up the larger fractions.

After you have explored halves, quarters and eighths with your students, play a fraction game with your students.  Make an overhead version of the Fraction File.  Display this overhead for the whole class to see.  Tell your students that they are going to pretend that they use Spanish Silver Dollars as their currency.  As a class they're going to pretend to go to the store with the one Spanish Silver Dollar that their mother gave them.  Invite two students to come to the overhead projector and give them an erasable projector pen.  Give the pair a situation such as, "Your mother sends you to the store to buy milk.  There's a container that costs ¼ of a silver dollar and one that costs 1/8 of a silver dollar.  Which container is less expensive?"  Have the students discuss and fill in the fraction for the appropriate response.  Ask the students to defend their responses.  Call up a second pair of students and describe a different, but similar, situation.  Continue playing this game for as long as necessary.

## Extension

Prepare a worksheet with written scenarios, and small versions of the fraction circles.  Allow the students to work independently to respond to these scenarios.

Extend this activity by suggesting scenarios where students compare equivalent fractions.

Discuss the relation of fractions to our country's currently circulating coinage (quarters are ¼ of a dollar, dimes are 1/10 of a dollar, etc.)

For older students, introduce common denominators and have the students add fractions to see if they have enough money to pay for multiple items at the store.

Learn more about Spanish Silver Dollars in the Coin of the Month section of the United States Mint H.I.P. Pocket Change Web site.

## Standards

The project described above reflects some of the national standards of learning as defined by the National Council for the Social Studies (NCSS), the National Council for Teachers of English (NCTE), and the International Society for Technology in Education.  These standards are listed below:

### Mathematics Standards

Problem Solving:  Students will explore fractions through their responses to the fraction scenarios.

Communication:  Students will demonstrate their understanding of fractions by visually communicating their responses to the scenarios.

Representation:  Students will create visual representations to demonstrate their understanding of the concept of fractions.