In today's lesson, the students learn to subtract fractions with unlike denominators. They use a multiplication chart to help them find the least common denominator. This relates to 4.NF.B3a because the students understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
I begin by letting the students know that our lesson for today is subracting fractions with unlike denominators. I remind them that we added fractions with unlike denominators on the previous day. We will use what we learned yesterday for today's lesson. Before beginning the lesson, I review with the students to see how much information was retained from the previous day. "What are unlike denominators?" I give the students a few minutes to think about the question. I always tell my students to think before they speak. Student response: Denominators that are different. I tell them that when you have denominators that are different, you cannot subtract or add right away. You must first find a common denominator. To find a common denominator, we must list the multiples. What are some multiples for 5? The students begin calling out the multiples: 5, 10, 15, 20, 25, 30. That's exactly right." I go on to tell them that after we list the multiples and find the common denominator, we change our fractions to equivalent fractions using the common denominator. At this point, we can subtract the numerators. "Are we finished with the problem then?" The students yell out no, because they remember that they should write their answers in simplest form.
I instruct the students to take out a sheet of paper so that we can practice the skill together. On the Smart board, I write 6/10 - 2/5. The students copy the problem onto their paper. "You can use the multiplication chart to help you with this lesson." (Some of the students are still learning their multiplication facts. The multiplication chart will make it easier for the students to find their factors and multiples. I find that when students are behind, they tend to get frustrated easily. I do not want the fact that they do not know all of their multiplication facts to hinder their learning of this skill.") "What are the denominators in this problem?" 10 and 5. I write 10 and 5 on the Smart board. Together we list the multiples of 10 and 5. "What is the least common multiple for these two numbers?" The students know that 10 is smallest multiple common for both numbers. Therefore, we find equivalent fractions using 10 as the common denominator. We find that 6/10 will remain the same because 10 is already the denominator. In the fraction 2/5, the equivalent fraction is 4/10.
I tell the students that now since we have found the equivalent fractions, we can subtract the problem. 6/10 - 4/10 = 2/10. I ask, "Are we finished?" They yell, "No, we need to see if we can simplify." We list the factors on the board. The factors of 2 are 1 and 2. The factors for 10 are 1, 2, 5, and 10. The students see that the fraction can be simplified by dividing by 2. The answer, 2/10 = 1/5.
To make the activity more interesting, I design it were the students can each get a prize. Because this is a difficult skill, sometimes students get discouraged quickly. I have found that if I make the activity fun, they tend to get more involved with it.
For this activity, I let the students work independently. I give each student a Subtracting Fractions with Unlike Denominators.docx activity sheet, along with a Multiplication Chart.pdf (MP5). The students must subtract fractions with unlike denominators, then write the answers in simplest form. This applies to MP6 because the students calculate accurately and efficiently, and express numerical answers with a degree of precision appropriate for the problem context.
Each student should write the subtraction problems, then find a common denominator by using the multiplication chart to find the first number common in both denominators. After finding the least common denominator (LCD), the students change the fractions to equivalent fractions using the LCD. At that point, the students can subtract the fractions. They must write their answers in simplest form by finding a factor that is common in both the numerator and denominator, then dividing to find the answer.
As they work, I monitor and assess their progression of understanding through questioning.
1. What is the first multiple that is common in your two denominators?
2. How can you change them to equivalent fractions?
3. Is your answer in simplest form?
4. What factors are common in both numbers?
As I walk around the classroom, I am questioning the students and looking for common misconceptions among the students. Any misconceptions are addressed at that point, as well as whole class at the end of the activity.
Any groups that finish the assignment early, can go to the computer to practice the skill at the following site until we are ready for the whole group sharing: http://www.mathsisfun.com/fractions_subtraction.html
In today's lesson, the students did much better at finding common denominators. There were less frustrated looks on their faces today. By having an opportunity to get a prize, it really made them put more effort into accomplishing the skill. There are still a few who are getting confused about the difference between finding a common denominator and simplifying fractions. We will continue to work on this concept in small group and for board work to keep the students familiar with the skill.
To close the lesson, I check the students work individually to tally their points. Each student who earned 6 points received a prize. Then, we review the answers to the problems as a whole class. This gives those students who still do not understand another opportunity to learn it. I like to use my document camera to show the students' work during this time. Some students do not understand what is being said, but understand clearly when the work is put up for them to see.
I feel that by closing each of my lessons by having students share their work is very important to the success of the lesson. Students need to see good work samples (Student Work - Subtracting Fractions.jpg) (Student Work 2), as well as work that may have incorrect information. More than one student may have had the same misconception. During the closing of the lesson, all misconceptions that were spotted during the activity will be addressed whole class.