## The 3 R's of Common Denominators (Math)

#### Description

Students are shown an alternative method of determining the lowest common denominator of two or more unequal denominators.

#### Objectives

The student understands that numbers can be represented in a variety of equivalent forms, including integers, fractions, decimals, percents, scientific notation, exponents, radicals, and absolute value.

#### Materials

-Chalk/eraser board
-Markers
-Paper and pencil for students
-Work sheet

#### Preparations

1. Prior to beginning Math Part 2, write the 18 words on the board, discussed in the Beacon lesson: The 3 R's of Common Denominators - Part I (See Weblinks)
2. Review examples on the board of the different types of problems demonstrated by these vocabulary words.
3. Duplicate worksheet for students.

#### Procedures

(Students have previously completed the lesson, -The 3 R's of Common Denominators - Part I-. Remind students that this is a continuation and then quickly review what they covered. This lesson can also be completed without parts 1 and 2 if students have the prior knowledge concerning fractions needed to begin this lesson.)

1. List on the board several fractions having a common denominator.
2. List on the board several fractions having unequal denominators
3. Demonstrate the method of finding a common denominator by listing the common factors that will divide into these denominators. Example: 1/6, 3/8
Common factors for 6= 6,12,18, 24; 8= 8,16,24.
4. Another method of finding the common denominator would be to multiply the two denominators together.
5. Ask, -Is there an easier method of finding a common denominator?- Explain to students that there is an alternative method.
6. Explain the following steps:
- take the denominators of both fractions (5/16, 7/32) and make a fraction. 16/32
- reduce the fraction 16/32 to 2/4
- now cross multiply the two numbers finding the common denominator.
32 X 2 or 16 X 4 = 64
The common denominator for the two fractions 5/16 and 7/32 would be 64.
7. Repeat this process several times demonstrating to students the simplicity of this method.
Illustrations: 5/8, 7/12: 5/6,2/9: 5/12, 2/3.
8. The next question would be, how does this method work with three improper fractions?
- Example 5/16, 2/3, 4/9
- Take the two numbers that will reduce an even number of times. (3,9).
- Make a fraction of these two numbers and reduce the numbers (3/9:1/3).
- Cross multiply the 1 and 9 which will be 9.
-Take the number 9 and put it over the remaining denominator 16, making the fraction 9/16. Because these numbers will not reduce, multiply the denominator times the numerator (9X16) which equals 144. The common denominator will be 144.
10. Repeat this process several times demonstrating to students the simplicity of this method.
examples: 3/13and 3/4,and5/6: 7/8and 3/7and 1/2: 6/7and3/5and 7/10.
11. After students have finished these three problems, divide the students into two groups. Put five problems on the board. Allow the students to compete against each other to assess their understanding of their progress.
12. Give the sheet to the students that is found in the Associated File.

#### Assessments

1. As students are completing the three problems in their groups, the teacher formatively assesses them concerning the process and the correct answers. If necessary, additional problems should be given to assure that individual students understand and can do the process to arrive at the correct answer.

2. When the teacher feels confident that students understand the process of finding a common denominator using the demonstrated method, assign the worksheet found in the Associated File. Students should be able to complete the sheet using the demonstrated method with 80% accuracy in order to demonstrate mastery of the benchmark. Students who do not achieve mastery should have the opportunity to relearn the process and retest.

#### Extensions

This lesson also extends to Adult Education Standards:
3.1, 3.2, 10.3, 23.5, 23.6, 23.9, and 23.12