Title: Simplifying Fractions/Equivalent Fractions
Annotation: This lesson is designed to teach students how to simplify fractions. The first part of the lesson will be a hands-on activity and then the lesson will focus on computations. The final part will be the use of a web site to allow students the opportunity to play a matching game involving equivalent fractions.
Primary Learning Outcome: After completing this lesson, students will be comfortable with seeing that when fractions are simplified they are also equivalent. After they have finished any one of the four basic operations involving fractions, they should be able to answer whether or not the fractional sums, differences, products, or quotients are in their simplest form.
Assessed QCC 6.29; Students will be able construct visual models to represent parts of a whole for fractions.
Assessed QCC 6.40; Students will be able to find the greatest common factor by using a list of factors or by using prime factorization.
Standards: NCTM; Number and Operations.
Total Duration: One hundred ninety-five (195) minutes.
Materials and Equipment: 1. Chalkboard. 2. Overhead projector. 3. Bond paper. 4. Eegg carton (one dozen) template paper. 5. Egg (one dozen) cartons. 6. Cotton pom-pom balls. 7. Computers. 8. Student textbook Middle Grades Math, Course 1, published by Prentice Hall.
Technology Connection: Web Site URL- www.quia.com....Brainchild Personal Learning System 100 (PLS). The PLS 100 is a portable computer. It is used with various cartridges. The cartridge for this lesson is entitled Math Mechanics, Fractions.
Procedures: 1. Warm up with finding the perfect number. This activity is designed to initiate the concept of factorization. The numbers to be factored are 8, 20, and 28. They will find that: the sum of 8’s factors, excluding the 8, is 7; the sum of 20’s factors, excluding 20, is 22; and that the sum of 28’s factors, excluding 28 is 28. Therefore, 8 is a deficient number, 20 is an abundant number, and 28 is a perfect number.
2. The second warm-up is a paper folding activity. Students will do the classic “hot dog fold” to identify halves, followed by the classic “hamburger fold” to identify fourths, and finally another hamburger fold to show eighths. Students will be able to see the equivalency of the fractional parts of the folded paper; that 2/4=1/2, that 4/8=1/2, and that 2/8=1/4. Additional equivalencies can be shown on these folds, or additional folds can be made to show sixteenths, thirty-seconds etc.
3. Egg carton template paper will now be used to reinforce the concept of equivalency and simplification. Students will be asked to place the number of dots in one of the blank template patterns that matches a fractional part of twelve; then on an adjacent template they will show an equivalent set of dots. Pom-pom balls and egg cartons will follow this paper and pencil exercise using the following fractions.
2/12= 2 dots; 1/6=2 dots 2/6=4 dots; 1/3= 4 dots 12/12=12 dots no equivalent
3/12= 3 dots; 1/4=3 dots 3/6=6 dots; 1/2= 6 dots
4/12= 4 dots; 1/3=4 dots 4/6=8 dots; 2/3= 8 dots
6/12= 6 dots; 1/2=6 dots 1/12=1 dot no equivalent
8/12= 8 dots; 2/3=8 dots 5/12=5 dots no equivalent
9/12= 9 dots; 3/4=9 dots 7/12=7 dots no equivalent
10/12= 10 dots; 5/6= 10 dots 11/12=11 dots no equivalent
Point out that the fractions with no equivalents are already simplified.
4. Students will now be taught how to calculate the greatest common factor (GCF) by both listing the factors and by using prime factors.
A. 27: 1, 3, 9, 27.
45: 1, 3, 5, 9, 15, 45.
Nine is the largest common factor; therefore, the GCF of 27 and 45 is 9 using the listing of factors method.
B. 27 45
X X
3 9 5 9
X X
3 3 3 3
The product of the common factors is 3x3=9. Therefore the GCF is 9 using the prime factorization method.
5. Students will work the odd numbered problems on page 190 of the student textbook, twelve problems.
6. Students will now be taught how to simplify fractions. They will be taught that whenever the GCF is the number one, then the fraction is already simplified. Examples follow: Write 20/28 in its simplest form. The GCF is 4 found by either method in paragraphs 4A or 4B above. Now divide the numerator and denominator by 4. The simplest form of 20/28 is 5/7. Write the fraction 4/9 in its simplest form. The fraction 4/9 is in its simplest form because its GCF is 1.
7. Students will now work problems 30-41 on page 199 of the student textbook, 12 problems. They will evaluate their work with the attached rubric.
8. Students will move to the computer lab and log on the website Quia. Com. as noted in the Technology Connection paragraph on page one; click on the Instructor Zone; click on mathematics; scroll down to Game #13, Equivalent Fractions; click on the matching game; play the game whose object is to challenge them to click on the squares that have equivalent fractions. Once completing this game, students may change the size of the fractions in the matching squares, and then play another game.
9. If the computers are not available for the entire class, then they will be issued the Brainchild PLS 100 portable computer with cartridge in order to play a matching game of equivalent fractions.
Assessment: Teacher observations, student rubric, quiz.
STUDENT RUBRIC
Evaluate your work by using a checkmark with the following scale:
Yes=I did the requirement, and I understood what I did.
No=I did the requirement, but I did not understand what I did.
Almost=I did the requirement, but I need more practice to fully understand what I did.
Not Applicable=I did not need to do this to solve the problem.
1. Did I use the listing of factors method correctly and list all of the factors of the numerator and the denominator to find the GCF?
Yes______No______Almost______Not Applicable______
2. Did I use the prime factor method correctly by multiplying the common prime factors to find the GCF?
Yes______No______Almost______Not Applicable______
3. Did I find the GCF?
Yes______No______Almost______Not Applicable______
4. Did I divide the numerator by the GCF?
Yes______No______Almost______Not Applicable______
5. Did I divide the denominator by the GCF?
Yes______No______Almost ______Not Applicable______
6. Did I check to see if the GCF of the new simplified fraction was the number 1?
Yes______No______Almost______Not Applicable
NAME______DATE______
QUIZ
I. Find the GCF of the following fractions.
1. 4/12 GCF______
2. 3/27 GCF______
3. 4/9 GCF______
II. Simplify the following fractions
4. 6/18=______
5. 8/24=______
6. 9/36=______
7. 12/48=______
8. 5/16=______
9. 18/21=______
III. Solve the following word problem.
10. A package of M&M’s candy contained 56 multi-colored pieces. If 16 of the pieces were brown, then the fraction that represents the color brown in16/56. Is 16/56 in its simplest form? Yes _____ No______. If your answer is no, then what is 16/56 in its simplest form? ______.