What's a Per-"cent"?
Percents are a part of every day life. When your students go out to dinner their parents use percents to figure out how much money to leave for a tip. When they go shopping they frequently see items that are a certain percent off. And, of course, sales tax is based upon a predetermined percent. Even on their tests your students usually see their scores in terms of percentages.
With your class, build upon their current knowledge of percentages by using coins as your basis. Begin exploring what your students already know about percents - make sure to review that a percent is a part of a whole expressed in hundredths.
Explain the rules of your activity, and explain the directions for the activity prior to distributing any materials. You should have the steps written and posted for all the students to read, or distribute a worksheet that includes instructions for the activity. Break your students into pairs and walk from group to group, allowing each pair to take a handful of coins (it's probably best to use plastic coin manipulatives rather than real coins) from the class bank. This bank could be something as simple as a milk jug or a shoebox that you've filled with the plastic coins. Instruct your students to place the coins on their desks where both members of the group can see the coins. Each pair will also need a worksheet, such as the one available on this site, a calculator (if you feel this is necessary for the division), and markers or crayons.
In the groups have your students sort their coins according to value. After all coins are sorted, instruct your students to calculate and create a bar graph that displays the number of each type of coin found in their assortment. Make sure to remind your students to label each axis! Have your students calculate their total number of coins, and then create fractions to see what fraction of the handful was represented by each coin (i.e. 6/22 of the coins were pennies).
At this point have all your students stop. Display a sample graph to your students about the coins you had in your hands and go over the data you collected about these coins. Also show your students a pie graph of the same information and explain that each piece of the pie graph represents a certain "percent" of the whole assortment. Walk your students through converting your fractions to percents. In their pairs, have your students calculate which percent of their coins were pennies. Have a few students tell their percentages and show on the board how they determined this. Go on and have your students determine what percent of their coins were nickels. Again, allow a few of your students to display their results and demonstrate how they came upon their answers. Continue this sequence for the rest of the coin types that were available (dimes, quarters, half dollars, golden dollars). Once all the percentages have been figured out, have the students add the percentages together...they should just about equal (this depends on how the numbers were rounded) 100.
To wrap up, have your students discuss, or write in their math journals about the relationship between fractions and percents.
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:
Numbers and Operations: Students will use their understanding of fractions as parts of unit wholes to help them recognize and generate equivalent forms of decimals, and percents. By studying percents in conjunction with fractions and decimals, students will be able to select the appropriate form to use in solving problems and expressing quantities.
Communication: By allowing the students to explain how they determined the different percentages, and by having the students write about the connections they've discovered, the teacher provides different contexts in which students can organize and consolidate their mathematical thinking, and express their understanding of proper procedures.
Connections: In this activity, the students will recognize the mathematical connections between fractions and percents.
Representation: Students will develop and study graphs to make connections between their data and what it represents.