Day 5: Mixing Juice --- Adding Fractions

NSCOS:

1.12 Add fractions—like denominators

Big Ideas:

1. Fractions surround us and we encounter them on a daily basis.
2. Students can learn about math and their world through individual activities as well as social interaction
3. Students can learn according to their level with differentiated, enriching activities that are learner-centered

Objectives:

1. TSW use manipulatives to help solve the word problem
2. TSW work cooperatively with other students to solve the words problem
3. TSW explain his/her method of solving the problem to the class

Multiple Intelligences:

1. Interpersonal Skills through cooperative groups
2. Visual/Spatial through use of manipulatives and process each group uses is posted clearly on chart paper
3. Logical/Mathematical through working the actual word problem

Materials:

1. chart paper
2. crayons/markers to write on chart paper and figure out the problem
3. overhead/overhead projector to post the problem and the job each student has in their group

Grouping:

Students are already well set up in groupings of high diversity and mixed ability level. I will ask them to remain in their group for this activity to make it seem more usual and to keep them comfortable with who they are working with.

Universal Design:

EC- the students will have stronger students in their group to find the solution and all students will gain a great deal from sharing how they solved the problem; the multiple explanations will reinforce the information for these students

EC/AIG- the assessment index cards will be specifically made for the ability level of the student

ESL- the original problem from the book had difficult English words and I have removed these and replaced them with much simpler words

Procedure:

1. I will write 1/3 and 3/8 on the board. As a review, I will ask them questions about why these fractions can’t be compared just by looking at them.
2. After discussion of how we compare fractions, I will write the addition problem 2/8 + 3/8 on the board. I would introduce that today we are going to be adding fractions rather than just comparing them. I would ask a student to solve this equation for me. The students will have to prove the answer by using their fraction circles. I will address the misconception that the denominators are added by drawing a picture on the board. I will show that when the denominators are added and the numerators are added, the new fraction does not make sense.
3. I will then write on the board 7/23 + 8/23 and ask students to solve this problem.
4. I will explain that today we are going to figure out how to add fractions with different denominators. Students can use all the information they’ve already learned about fractions when comparing them. They can also use the fraction circles.

 

CGI Word Problems: found on p. 391 of their textbook (problem 22)

Cindy likes to make a blend of juices to sell. At the end of the day, Cindy has ¼ can of orange juice in one can and 5/6 can of grape juice in another can. If the cans are the same size, how much concentrate does she have left?

5. Students will explain their method of solving the problem. If no student solves the problem by drawing a picture, I will show that as an example at the end. I will also show the example of using LCM if that is not shown by the students.

Assessment:

1. Why did we add 3/12 + 10/12 when the original problem was ¼ + 5/6? Did we do the right thing? Why can we write ¼ as 3/12 instead?
2. Why can’t we add fractions with different denominators the same way we add fractions with the same denominators? (apples and oranges)
3. How is adding fractions with unlike denominators similar to comparing fractions with unlike denominators?
4. Where do you think we would need to add fractions with unlike denominators in the real world?

Reflection:

I think the introduction of the lesson went very well. I’m glad that I was able to address a misconception about adding fractions. Most of the students were familiar with how to add fractions, but I don’t think many of them understood why just the numerators were added. Also, the pre-test I gave them helped me realize I needed to address this misconception for some of the students. I was worried about how the CGI method would go over with the students. I was taking a leap in faith by having them learn to add fractions in this manner. I was very pleased that all the groups made the connection that they needed to find common denominators like they had learned for comparing fractions. After going through the discovery process, the students seemed relieved. They even were asking if that was the only problem because they felt it had been easy. I think the fact that they discovered how to add the fractions will allow more residue for remembering and understanding than if I had done this lesson as direct instruction. Even though I was apprehensive about using this process, I now feel like it was probably the best way adding fractions could have been introduced.

The grouping of the students worked out well. Each group had an AIG student involved and 3 of the 4 groups had a student who had already correctly answered a question on adding fractions with unlike denominators on the pre-test. As I walked around the room, I could tell that the AIG students were not telling everyone what needed to be done. Most of the students were realizing they needed to find common denominators and also realized they knew how to find them. The one regret I have in this lesson was how I designated certain jobs in each group. I gave the job of the reporter to students I felt were "middle of the road." Students in the class were obviously not accustomed to explaining how to solve a math problem and coming up to the front of the room. As I walked around the room between groups, I told the students to make sure that the reporter could explain everything on the paper. Most of the groups did a good job coaching the reporter before they presented to the class. What I had not taken into account was general shyness of students and their inexperience with having to explain how to solve math problems. I think for this lesson, a stronger student should have been designated as the reporter or I could have pointed to a group and asked them to share an explanation (then it would be more of a choice of the student to speak). After I realized the difficulty the students were having, I made the reporting job easier by asking specific questions for them to answer and I guided them through explaining their solution.

Also, when I asked my first assessment question to see if they truly made a connection about how they were solving these problems, I got a bunch of blank stares. I asked why all the groups had eventually added 3/12 and 10/12 instead of ¼ and 5/6. No one knew! So I wrote on the board, ¼ = 3/12 and 5/6 =10/12. Then I asked, if it was okay to use 3/12 instead of ¼ when in the problem if they were equal to each other. I unfortunately got more blank stares. I’m not sure how I could have re-worded these questions. I don’t know if what I was saying wasn’t clear, if they were too focused on lunch coming soon, or if they had not understood the process of finding equivalent fractions to put in the equation. I’m glad I addressed it though and I plan on re-addressing it in my next lesson.

***Yesterday, when I went in to make a computer program using fractions, I was able to make a document for students to match equivalent fractions as well as a document for students to practice adding fractions. Mr. Cain, the technology specialist, was impressed by the programs we developed together. He is going to save the programs on Ms. Bateman’s computers and allow students to log-in and be able to pull up both programs. The computers will be one of my centers during the last days I teach. Mr. Cain also felt that the programs were good enough to share with a class he is teaching for teachers. He said they were all impressed by the programs we had created together. I’m excited to use them with the students!