Designed for two 50-minute classes
Grade Level: 6
Materials: Paper, pencils, line-up card assignment
Optional materials: Overhead of field, calculators
Objectives: The students should be able to convert fractions to decimals, and decimals to fractions. Students will also be able to solve problems for unknowns.
Math Concepts: fractions, decimals, rounding, and problem solving
NCTM Standards for grades 5-8: Standard 1- Mathematical Problem Solving, Standard 4- Mathematical Connections, Standard 5- Number and Number Relationships, and Standard 6- Number Systems and Number Theory
Procedure:
Yesterday, the children learned how to convert fractions to decimals. Today, we are going to learn how to convert decimals to fractions. To learn this concept, we are going to take a look at the Florida Marlins. Explain a bit about the current baseball season or past season (See suggested references). Ask students about their favorite players for the Marlins. Take about 5-10 minutes to explain some baseball terms such as: hit, run, error, single, double, triple, home run, at bat, strike-out, strike, ball, walk, and batting average. It may be helpful here to draw a field on the board or use a overhead.
Now, go into detail about batting average. The rest of this presentation of the lesson should take about 35 minutes. The batting average is a 3-digit decimal that represents the fraction hits/at bats. If the batting average has 3 numbers to the right of the decimal, the decimal goes to the thousandths place.
Show Example: .371 The 3 is in the tenths place, the 7 is in the hundredths place, and the 1 is in the thousandths place.
Now show simple conversion of decimal (batting average) to fraction. Use 3 examples.
Example 1: .370 = 370/1000 Example 2: .282 = 282/1000 Example 3: .476 = 476/1000
Ask students to recall how to reduce fractions. Discuss reducing fractions. Then, ask students to reduce the three examples on the board. When the students are finished, ask for three volunteers to put the answers on the board.
The answers are 1) 37/100 2) 141/500 3) 119/250
Make sure the students understand the concept of reducing fractions.
Evaluation: Give a homework assignment to convert batting average to fraction and reduce. The students should begin the homework assignment the last ten minutes of class.
The problems should be:
1).500
2).350
3).400
4).452
5).360
6).225
7).464
8).222
9).175
10).369
Day Two:
To start class, review homework problems, then continue with lesson.
Refer back to batting average. For example, Jeff Conine has 37 hits out of 100 at bats.
Now, take the batting average one step further. Give the batting average and at bats, and show how to find the number of hits.
Example: Terry Pendleton has a .300 batting average and 500 at bats. Find the number of hits.
300 = X
1000 500 (batting averages are set up as fractions)
First, Show conversion as equivalent fraction (reducing or common multiple). For instance, what number divides 1000 to get 500. The answer is 2, so 300 is divided by 2 to get the answer 150.
1) average = .500 200 at bats
answer = 100
2) average = .100 500 at bats
answer = 50
Now, explain the process of cross multiplication to solve to same problems.
Example: 500 = X
1000 200 1000X = 500 (200) or 500 (200) divide 1000 = 100
Show the second example using cross multiplication.
Now show one example given the batting average and the number of hits. Solve the problem using both methods.
Example: Chuck Carr has a .220 average and 50 hits. How many at bats?
250 = 50
1000 X X=200
Now, Review on how to convert fractions to decimals. Now convert hits and at bats to batting average.
Example: Greg Colbrunn has 60 hits in 200 at bats. Find the batting average.
60/200 = .300
Evaluation: For the last 10 minutes of class, hand out the line-up card assignment, and have them start. Go around the room and answer any questions they might have.
Player Batting Average Hits At Bats Chuck Carr .220 X 150 Quilvio Veras X 50 200 Gary Sheffield .355 70 X Jeff Conine .400 X 250 Greg Colbrunn X 40 220 Terry Pendleton .325 36 X Kurt Abbott .176 X 200 Charles Johnson X 78 320 Chris Hammond .235 10 X
Students should be instructed to solve for X.
References: Marlins Magazine (the program for the Florida Marlins at the game)
Contributors: Major: Kari A. Kupfer
Minor: Carol A. Marinas