In today's lesson, the students learn to add fractions with like denominators. They use a fraction strip handout to shade the fractions being added or subtracted. 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 adding and subtracting fractions with like denominators. "When I say like denominators, what do I mean?" I give the students a few minutes to think about the question. I call on a student and she knows that like denominators mean the "same" denominator. Before we get into the lesson, I want to review with the students. I review with my students quite often because the more I put something before them, the better they do at it. I call on various students to tell me what they have learned about fractions. Student comments: Fractions are parts of a whole, the numerator is how much they are asking us about, the denominator is how many pieces you have in all. I continue questioning the students because questioning helps me understand what the students actually know. "When might you need to add or subtract fractions with like denominators?" Student response: When you eat the pieces of a cake.
The Add and Subtract Fractions with Like Denominators.pptx power point is on the Smart board. I read the first scenario to the class. Jerry ate 1/5 of the cake. Peter ate 2/5 of the cake. How much cake did they eat in all? "What clue words in this question let us know which operation?" Student response: in all. What operation are we going to use for in all? Student response: addition. "We will add the fractions." I explain to the students that in order to add fractions with like denominators, all we have to do is add the numerator, which is the top number. If you are subtracting fractions with like denominators, you just subtract the top numbers. I remind students that the fractions we add must come from the same size whole. You can't add fractions from a small cake and a large cake together. It must refer to the same size whole. In this scenario, the cake has been cut into 5 pieces. If I take 1/5 and add 2/5, I will get 3/5. You do not change the denominators because the cake was cut into fifths. (The students can see this modeled with fraction strips in the power point.) The cake is not in tenths, so you do not add the denominators. The cake is cut in fifths, when you finish sharing the cake, it will still be in fifths. Therefore, the denominator stays the same.
Next, I discuss the subtraction scenario with the students. Jane has 5/6 of a cake left. She gives 3/6 to her brother. How much cake does Jane have now? "How much cake does Jane have now?" 2/6. She started out with how many sixths? 5. She gave away how many sixths? 3. Therefore, 5/6 -3/6 = 2/6. When you add and subtract fractions, you must write your answer in the simplest form. Simplest form means that the only factor that is common in both the numerator and denominator is 1. (I explained to the students that we do not use the number divided by itself equals that same number.) In 2/6, both numbers are even. "What number can go in all even numbers?" 2. We need to simplify 2/6.
To simplify fractions, we use division to find an equivalent fraction. We list the factors of 2 and 6. The factors of 2 are 1 and 2. The factors of 6 are 1, 2, 3, and 6. They both have a factor of 2. Therefore, we can divide 2/6 by 2/2. The answer is 1/3. (A visual model is in the power point to show that 1/3 and 2/6 are equivalent fractions.) I share with the students that when they simplify, if there is more than one factor in common with both numbers to use the largest number. If the largest number is not used, then they will have to divide the fraction more than one time in order to get to the simplest form.
For this activity, I let the students work independently. (Although, I allow them to discuss the activity with their neighbors in order to help learn the concept.) I give each student an Add and Subtract Fractions with Like Denominators.docx activity sheet, crayons, and a sheet of Fraction Strips.pdf (Mp5). The students must add or subtract the fractions with like denominators, then write the answers in simplest form.
The fraction strips are used to give the students a visual in order to gain conceptual understanding. Each student should take 2 crayons and a fraction strip handout. Add the fractions using the fraction strips. Shade the 1st fraction in one color and the 2nd fraction in another color. Add all of the shaped parts. To subtract the fractions, the students shade the 1st fraction in one color, then mark an “X” through the shaded fraction pieces that represent the second number. To find the answer, the students count all of the fraction pieces that are not marked with an “X.” They must write their answers in simplest form.
As they work, I monitor and assess their progression of understanding through questioning.
1. What operation are you using?
2. What is the first fraction? What is the second fraction?
3. What factors are common in both numbers?
4. Is your answer in simplest form?
As I walk around the classroom, I am questioning the students and looking for common misconceptions among the students. Any misconceptions are addressed at the 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.softschools.com/math/games/fractions_practice.jsp
As I walked around listening in and questioning students, I found that some of the students wanted to add the denominator. I reminded the students that they should not add the denominators because the denominator represents the number of pieces the whole was cut into. If the whole is cut into thirds, then your answer should be in thirds. I pointed this out on their fraction strips. From their shading of the fractions, they could see that 1/5 + 1/5 = 2/5.
To close the lesson, we review the answers to the problems. 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) (Student Work), as well as work that may have incorrect information.
I collect all papers from the students. All struggling students identified as I monitored during their independent activity will receive further instruction in small group.