NCSOS:

1.11 Compare & order fractions

1.12 Use models/pictures to add & subtract fraction & mixed numbers

Big Ideas:

1. Fractions surround us and we encounter them on a daily basis.
2. The world does not always come in "wholes."
3. Students can learn about math and their world through individual activities as well as social interaction

Objectives:

1. TSW identify what fractions are and where they are used.
2. TSW use the region model to represent fractions.
3. TSW represent the same fraction in several ways (equivalent fractions).
4. TSW recognize the relative size of fractions.
5. TSW learn vocabulary of fractions such as numerators and denominators.

Multiple Intelligences:

1. interpersonal- class discussion, sharing of ideas on fractions in groups
2. visual/spatial- students representing fractions, drawn & written on board
3. mathematical/logical- actual fractions being discussed

Universal Design:

ESL/EC- fraction circles make the concept of fractions more concrete and allow students who may not understand the verbal or written explanations another way of learning the material; also the visual example of folding a piece of paper

AG/EC- allowed to work with each other on higher level thinking questions; the questions will challenge but they have support by working together

Materials: board, pre-made questions, fraction circle manipulatives, measuring cups, paper to fold

Procedure:

1. The world doesn’t always come in wholes. Usually we only eat a couple pieces of a whole pizza. (draw pizza on the board and color in 2 pieces) This is 2/8 of a pizza. When we cook, we don’t just put in a full cup of everything. You might have to put in ¼ cup of water and ½ cup of oil. (show the measuring cups and pass them around the class)
2. Where else might we find fractions in our world? What other circumstances do we use parts of a whole thing?
3. Today we’re going to start learning about fractions. I will think of a fraction and write it on the board. Once we get our fraction, we should think of it as "how much pizza we ate." So I will draw a pizza to represent the fraction on the board. You can look at the fraction circles on your table because they are also like pizzas. The bottom number (denominator) will be how many slices there are and the top number (numerator) will be the pieces I ate. I will then model drawing the picture of our first fraction. Since the bottom number is 6, that is how many slices I am drawing, and since the top number is 1, I will shade them in so we know that I ate those!
4. Repeat this procedure, but ask the students to tell me how many slices the pizza must have and how many were eaten and so on.
5. Now what if I said I ate 4/8 of a pizza, then someone else said that I ate ½ the pizza. Who is right? I would draw both pizzas on the board. I would ask students to look at their fraction circles to help them figure this out.
6. After student input, I would explain that 4/8 and ½ are equivalent (or the same). Four pieces of an eight-slice pizza is like eating ½ of the pizza. I would put the ½ fraction circle and the 4/8 fraction circle on the overhead to show that they were equivalent (can place them on top of each other to see they are equal).
7. I would ask students to look for other fraction circles that were equivalent. They can figure this out by laying the pieces on top of each other. (this is a cooperative group time). I will circulate the room to make sure everyone is on-task and understands the directions.
8. I would write all the equivalent fractions on the board like 1/3 =2/6. Once the students finish sharing equivalent fractions, I will comment on how many fractions are equal to each other. I will show students how to make equivalent fractions, you multiply the top number (numerator) and bottom number (denominator) by the same number. The 1 and the 3 were multiplied by 2 to get 2/6. I will show this process with each of the equivalent fractions.

(I also showed students that when reducing fractions they were using the "greatest common factor," which they have been learning with Ms. Bateman).

9. I would then erase the equivalent fraction and write ½, ¼, and 1/8 on the board. I would give students the example of how much of a pizza they would want to eat. (They will also have their fraction circles to refer to---I will use one at the front of the class to show the difference as well as asking them to look at the ones at their table.
10. I will address a misconception about fractions with the example of ½, ¼, and 1/8. "I know you usually think of a bigger number like eight meaning that it is the greatest. This is not true in fractions; we picked ½ was the greatest instead. Usually a larger denominator (the bottom number) actually means the fraction is smaller. Since we only had ‘1 of 8,’ we didn’t have as many as we do when we have 1 of 2. We have to think about how close the numerator (top number) is to the denominator (bottom number). Since 1 is very close to 2 in ½, this is a bigger fraction. 1 is not very close to 8. What if we had 7/8 (draw a picture form on the board)?

** I would let students express their opinions about how 7/8 compared to 1/8 and ½ then would add further explanation if necessary. I would use the picture and example of the fraction circles to help them understand how 7/8 is greater than both ½ and 1/8.

Assessment:

1. Where do we see fractions in the world around us?
2. Why do we need fractions? (Does the world always come in wholes?)
3. Can the same fraction be shown in different ways? Please share some examples.
4. What is "tricky" about fractions? Why is 1/8 less than ½?

Pre-Assessment (written on overhead)

**I explained that this was to see what they already knew and that it wouldn’t be graded. Ms. Bateman said they were used to "pre-tests," so I referred to it as that. The questions were also easier to read handwritten on the overhead

1. Use a model or paper/pencil to find each equivalent fraction.

a) ½ = ?/8

2. 6/10 = ?/5

2. Write the next two fractions in the pattern.

 

2/3 , 4/6, 8/12, 16/24, ___, ____

3. Add. Write the answer in simplest form.

1. 5/8 + 2/8 =
2. 6 3/8 + 1 7/8 =
3. 7/10 + 1/5 =

2. Subtract. Write the answer in simplest form.

1. 13/15 –8/15 =
2. 7/12 – ¼ =

I gave them about 10 minutes to complete this. When I felt a majority were close to finishing, I announced they had 1.5 minutes to complete it.

Reflection:

I was very happy about how this lesson went. I was considerably nervous about forgetting sections of the lesson and having to look at my notes too often. Once I was at the front of the class, I felt quite comfortable. The students were all very well behaved for my first lesson. I hope it was because of it being especially engaging. I really liked how the students jumped into working with the fraction circles in order to find equivalent fractions. They seemed very excited and as I moved between the groups, they were all on-task. The other part of my lesson that I felt worked very well was when I had the students compare ¼, ½, and 1/8. I told them that I wanted them to order them from least to greatest. Most of the students had actually come with the prior knowledge of ordering these fractions. The misconception of the larger denominator meaning a smaller fraction had already been addressed in a previous year. I then asked them where 7/8 would fit into the order. This question was challenging for them. I think I handled the situation well due to my reading about the CGI method. One of the students raised her hand and said she thought the order should be 1/8, 7/8, ¼, ½ (I wrote the order on the board). This was such an opportunity to explore! I asked if anyone else had a different answer and a student said 1/8, ¼, ½, 7/8 (I wrote this on the board too). I then told students to help their classmates out and decide which order it must be; I suggested the fraction circles could help them make the decision. There was immediate working with the manipulatives by the students. Then a student raised his hand and said that the order was definitely 1/8, ¼, ½, 7/8. He explained it by saying that ¼ was 2/8 and ½ was 4/8. He had been able to compare these fractions with the fraction circles and had come up with a wonderful explanation. The student that had such an insight was one of the students I performed the Wasik-Day on. He had been continuously off-task. I was very happy that he had seemed to be challenged and was paying attention.

I would have liked if students had been able to work in pairs with the manipulatives; there were some groups that only had one set of fraction circles for four students. I think my weakest area of the lesson was the assessment; I should made an activity such as a game where they would practice making equivalent fractions. The students did do a good job at answering my general assessment questions as a closure. In my pre-assessment that I gave them at the end of my lesson, the first question had been addressed in my lesson. Sixteen of the eighteen students present got it correct whereas all the other questions had much lower ratios of correctness. The two students that did not achieve my objectives this time, I think will succeed next time. I think they primarily need more practice than other students did. I will make sure that in my future lessons that my objectives of this lesson will be quickly revisited.

My cooperating teacher has difficulty with one particular student. He was not in school the day of this lesson. I was hoping he would be and would enjoy it. He has been isolated to a desk at the back of the room for a couple of weeks. Monday will be his first day sitting in a group again. I am concerned about his behavior due to missing the prior lesson. If he is confused about what is going on, he might feel it is an opportunity to misbehave. I hope to have an overview of the previous lesson so that he will feel comfortable.