THE FRACTION TRANSACTION

Reducing Fractions for Upper Elementary Students

Written by Kimberly Wells, Fifth Grade Teacher,

Sylvan-Verona Beach Elementary School, Oneida, New York

1. Learning Content

1. Standards

MST

* Standard 2: Students will access, generate, process, and transfer information using appropriate technologies.

* Standard 3: Mathematics –Students will understand mathematics and become mathematically confident by communicating and reasoning mathematically, by applying mathematics in real world settings and by solving problems through the integrated study of number systems, geometry, algebra, data analysis, probability and trigonometry.

B. This experience is one small part of a four-five week unit on fractions. The concept of reducing fractions is often difficult for students. But through using a variety of instructional strategies, as presented in this experience, students will both "see" and understand how to reduce fractions.

1. Prior Knowledge Necessary for this Lesson

*Students need to know that fractions are a part of a whole.

*Students need to know that a fraction is made up of a numerator and denominator.

*Students need to know what a factor is.

*Students need to know how to list the factors for a specific number.

*Students need to know how to divide.

*Students need to know how to follow directions for the Internet.

Declarative Knowledge

*Students will understand that GCF stands for greatest common factor

*Students will understand the concept of putting a fraction in lowest terms

*Students will understand reasons for putting fractions in lowest terms

Procedural Knowledge

*Students will be able to find the GCF for a set of numbers

*Students will reduce fractions to lowest terms

1. Procedure

Students will be given a sheet of loose-leaf paper, 12 beans and a string. They will be asked to represent the fraction 4/8 on the paper, using the beans and the string. The teacher will check to make sure that all students have this by modeling what it should look like on the overhead. After that, the teacher will review that the numerator is the 4 and the denominator is 8, so that students are constantly exposed to the language.

The teacher will then model 4/8 on the overhead using transparent manipulatives. Students will easily be able to see that 4/8 is equal to ½. If students do not refer to this as ½, pretend the pieces are each a slice of pizza and have them explain how much of the pizza they would have.

Ask students why someone might want to change 4/8 to ½. If they do not know that it is usually easier to work with lower numbers when doing fractional computations, put the fractions 513/1026 and 432/864 on the overhead. Ask them how many of them would like to have to add those. Show students that both of those numbers represent ½.

Once students understand the reasons for reducing fractions, explain the term and the process. Explain to students that the easiest way to reduce a fraction to lowest terms is by finding the GCF of both the numerator and the denominator.

Model for students the 4/8 problem as follows, while talking aloud through your steps.

4 factors 1, 2, 4

8 factors 1, 2, 4, 8

Underline all common factors. Then circle the greatest common factor. Once this is done, show students how to divide both the numerator and denominator by that number.

4 divided by 4=1

1. divided by 4=2

Explain that the answer you get is the same fraction reduced. Show the check for this on the overhead by splitting the original beans into groups of 4. The numerator will have one group and the denominator will have 2 groups.

Guided practice-Give students 8 more beans. Have students represent 8/12 with their beans. Have them follow the same process, listing, underlining, circling, dividing, and checking. Once students have solved several problems that could be checked with their beans, give them 2-3 problems that cannot be checked with beans. Insist that they follow the same process.

Once students are capable of reducing fractions, allow them to show off their stuff by using the Internet. Give students the attached direction sheet and have them follow the directions and record the necessary information. Site: http://www.aplusmath.com/flashcards/index.html

Closure: Once all students are familiar with the process for reducing, close your lesson with a discussion on why people, not just students need to reduce. Have them generate a list of people who might use this in their jobs. Close the lesson by having students chant the process for reducing. Give students a bonus that can be done at home!

1. Instructional/Environmental Modifications

*Students use manipulative materials to help them understand/see a difficult concept.

*The teacher should review terms that have already been learned, such as numerator, denominator,

greatest common factor and factor.

*Students remember the process because of the repetition throughout the lesson.

• Materials and Supplies

*enough beans for each student to have 20

*string

*overhead projector

*loose-leaf paper

*transparent manipulatives

*Internet access

*enough direction/handout sheets for the class

• Assessment Tools and Techniques

*Students will be assessed during the lesson by teacher observation and through discussion.

*MST Standard 3 will be assessed through the handout that students will turn in upon completion of their Internet experience.

*Students will be asked to record the process for reducing as the bell ringer in the math lesson that

follows.

*Students will show the knowledge gained during the culminating performance of the fraction unit where

they will be required to double or triple recipes and prepare them for the class.

• Time Required

*Planning Time-30 minutes to explore A+Math Web Site

*Implemetation-45 minutes to 1 hour

*Assessment-ongoing throughout the lesson and the unit

• Student Work

*Students use the attached handout.

• Reflection

This is an important concept to teach. I have had classes that needed more than an hour before they all understood. I have had classes that worked better when they were able to work on chart paper on the floor instead of loose-leaf at their desk. This lessons allows for the students who "get it" to move at a faster rate by being challenged by the Internet. A definite benefit of this lesson is that by presenting the materials in 4 ways, students are able to find a way that they understand.

Name ____________________________ Date _________________________

1. Log into the computer.
2. Type in http://www.aplusmath.com/flashcards/index.html
3. Choose Reducing Fractions under Non-Java Flashcards.
4. Double click on this.
5. Once the screen opens, the timer starts.
6. Write the problem on the bottom of this sheet.
7. Then click on continue.
8. Fill in the problem on the screen and press enter. While you are waiting record the answer on this sheet.
9. The computer will let you know if you solved the problem correctly.
10. If you solved the problem right, your score is recorded. If not, it remains the same.
11. If you miss a problem, it tells you the answer. Record the answer next to your original.
12. Once you have completed 15-20 problems, record your score at the bottom of this page.
13. If you had difficulty with any problems, please give a brief description of what happened on the bake of this sheet. If not, good going, I’ll have to find something more difficult.

NUMBER CORRECT __________ NUMBER ATTEMPTED __________