Yumiko Kishikawa
October 31st (1st Lesson)
Objectives
Students will be able to estimate sums of fractions and mixed numbers by rounding them (Knowledge, Comprehension)
Students will be able to estimate differences of mixed numbers by rounding fractions. (Knowledge, Comprehension)
Materials
Whiteboard, color pens
Pre-requisite skills
Students should be able to identify whether the numerator is very small compared to the denominator, about half of the denominator or nearly as big as the denominator.
Anticipatory sets
If we estimate sums or differences of fractions or mixed numbers in the real world instead of finding exact values, it may help us make decisions easier or faster. For example, if you have a sheet of paper with 5 5/6 by 3 1/8 inches, you may want to tell your friend the size is about 6 x 3 inches instead of exact size.
Activities & Evaluation
9:54-10:00
Have students prepare for the lesson by reading the board.
I added the above list after the lesson.
Greeting and introducing each other
Review HW (Formative)
10:00-10:20
Draw a number line between 5 and 8, and mark 6 and 7.
Divide the segment between 6 and 7 into 6 parts.
Mark 6 1/2 with a different color pen.
Have students come up to the board and have each student mark 6 1/6, 6 2/6, 6 4/6 and 6 5/6. (Formative)
Ask if they all visually agree as a class that 6 1/6 is closer to 6, 6 2/6 and 6 4/6 are closer to 6 ½, and 6 5/6 is closer to 7. (Formative)
Tell them when the numerator is very small compared with the denominator, and it is close to zero as they see, the fraction is rounded down to zero.
Tell them a fraction is rounded to a half when the numerator is about half of the denominator as they see.
Tell them a fraction is rounded up to 1 when the numerator is nearly as big as the denominator as they see.
Tell them to draw a number line if they are not sure.
Review and ask the class how they round fractions. (Formative) *Literacy
Tell them to write them down on their notebook in their words. (Formative) *Literacy
Practice #2 on pg. 43 as a class.
Ask questions as we solve together. (Formative)
10:20-10:37
Write the questions on the board from #2, 3 and 4 on pg. 43, and have them work individually.
Tell them to ask questions if they have any.
Have them check their answers with the book.
Walk around to see if they understand. (Formative)
Practice #10-12 on pg. 44 in class. (Formative)
Have them solve #1-9 on pg. 44 individually if time is left. (Formative)
10:37-10:42
Closure (Formative) *Literacy
Have them answer individually and in class.
How do we round fractions?
How do we estimate if a fraction is very small compared to the denominator?
How do we estimate if a fraction is about half of the denominator?
How do we estimate if a fraction is nearly as big as the denominator?
Modifications and adaptations
There is no TAG, IEP or ELL student. However, some studentsmayneed longer time to understand more deeply although they may grasp most of the concepts during the lessons. Iwilltutor them after school to make sure they understandcorrectly. When they get behind from the rest of the class, I also will sitdown together with them during study hall to encourage themthatthey willdo their assignments at school so that they could ask me questions if they areconfused.
Reflection
I thought learning how to estimating fractions might be very easy for many students before I started teaching because they only need to add whole numbers after rounding. However, it was a kind of confusing for them to decide whether a fraction should be round up or should be rounded down. The textbook tells to round down to zero if the numerator is very small compared to the denominator. It should be rounded up or rounded down to a half if it is close to a half. The number “1” of 1/3 is considered to be very small compared to the numerator 3 according to the author of the textbook, and it is rounded down to zero. However, if 1/3 is placed on a number line, it is closer to one half and should be rounded up to a half. According to the book, 2 1/3 should be estimated to 2. However, those who can locate 1/3 on a number line in their mind, they would estimate 2 1/3 is 2 ½.
I like to be more precise in Mathematics, and I would say 1/3 should be rounded up to one half if I taught in Japan. I would tell students that the answer in the textbook was typo and would correct it as a half. However, this is America besides estimation is not finding an exact number and is used to find the rough idea of the value. I guessed the answers of estimations could be different by individual in America. I decided that whether a fraction is rounded up or rounded down could depend on an individual choice. I told the students that the results of estimation could be slightly different when they estimate fractions or mixed numbers according to individuals and it was all right because they were estimating.
When I made my lesson plan, I tried to overestimate the time so that it would finish within the time. I anticipated that six graders would take longer time than college students to do anything. I also prepared extra materials in case they went fast and had time left. My guess was right, and I was able to finish teaching what I wanted to teach within the time.
I did not have a seating chart yet because I was not sure how the atmosphere of the class was like. Today was the first day when the 6th graders were pulled out for me to teach. There were two large semi-circle tables, and the students sat wherever they felt most comfortable at. I had no idea how this seating might affect my teaching. All of them sat facing front, but some of them had to sit having the table behind them. Some students sat too close to each other but had no choice because of the arrangement of the room and tables. I thought I needed to improve the learning environment by making an effective seating chart because this formation was producing disruptive behaviors among students.
Yumiko Kishikawa
November 1st (2nd/3rd lessons)
Objectives
Students will be able to add and subtract fractions (Knowledge, Comprehension, analyzing)
Materials
Whiteboard, color pens
Pre-assessment sheet
Pizza shaped papers (1 orange color, equally divided in 10 pieces)
Scissors
Game sheets, dice, blocks
Pre-requisite skills
Students should be able to find common denominators.
Students should be able to simplify fractions.
Students should be able to write improper fractions as mixed numbers.
Anticipatory sets
Who likes pizza? What kind of pizzas do you like?
I ordered cheese paper pizzas for you today. We are going to find out how much portion of a pizza two of you will eat in total. Then we are also going to find how much portion of a pizza is left if you give a portion to your friend.
Activities & Evaluation
9:54-10:04
Have students prepare for the lesson by reading the board.
*I added after lesson
Greeting
Walk around to stamp on their check sheet if they have done HW.
Read the answers, and have them circle their answer if it is correct and mark a cross if not with a red pen.
Review HW as a class if necessary. (Formative)
10:04-10:25
Distribute Pre-Assessment paper.
Tell them that the assessment is to find out what they know and what they do not before we start the new unit.
Tell them they won’t be graded.
Tell them what time the test is over
Tell them the time 5 min before the end of the test
Collect the papers.
Ask them what they thought about the assessment, and which question they were confused with.
10:25-10:45
Assign them to make groups of two or three.
Distribute a pair of scissors and papers.
Have them cut a pizza into 10 pieces.
Tell them student A is going to eat 3/10 of a pizza, and student B is going to eat 1/10 of a pizza.
Ask them how much portion of a pizza they are going to eat in total. 4/10(Formative)
Ask them to find an equivalent fraction to 4/10 in simplest fraction. 2/5(Formative)
Have them discuss their reasoning for 4/10=2/5 in groups and share as a class. (Formative) *Literacy
Ask them if everyone agrees.
Tell them to find out how much portion of a pizza will be left after student A had 3/10 of a pizza and gave 1/10 of a pizza to student B.
Ask them how much portion of a pizza student A has now. 2/10(Formative)
Ask them to find and an equivalent fraction to 2/10 in simplest fraction. 1/5(Formative)
Have them discuss their reasoning for 4/10=2/5 in groups and share as a class. (Formative) *Literacy
Ask them if everyone agrees. (Formative)
10:45-10:50
Break
10:50-11:15
Tell them we will practice adding and subtracting fractions as a class.
Write one example of sum and difference each on the board.
¼+ ½
5/6-1/9
Tell them to write them on their notebook too.
Write four steps to show what we do besides the each work as we solve the questions.
Ask them what they want to do first. (Formative)
Write “Rewrite the fractions using LCD by the work.
Ask them what they will do next. (Formative)
Write “Add he numerators”.
Ask them what the third step is. (Formative)
Write “Write the sum over the LCD”.
Ask them what the last thing they need to do. (Formative)
Write “Simplify”
Tell them they will practice individually.
Write the problems P 48/ example 1 and 2 on the board.
Tell them to ask questions if they have any. (Formative)
Walk around to see how they are doing. (Formative)
Tell them to check their work with the textbook when they finish.
Have them start working on homework if time is left.
Closure
11:15-11:20
Collect the materials.
Ask them 4 steps to add or subtract fractions to the class. (Formative assessment)
Write them as they answer.
Step 1: Find the common least denominators.
Step 2: Find equivalent fractions with the CLD.
Step 3: Add or subtract the numerators.
Step 4: Simplify the fraction.
11:20-11:40
Tell them they will play a game until the end of the period.
Make them groups of two or three.
Explain the rules of the game.
Have them start playing.
11:40-11:42
Have them stop playing.
Ask them how far they reached and applaud the person who reached the furthest.
Collect the materials.
Modifications and adaptations
There is no TAG, IEP or ELL student. However, some studentsmayneed longer time to understand more deeply although they may grasp most of the concepts during the lessons. Iwilltutor them after school to make sure they understandcorrectly. When they get behind from the rest of the class, I also will sitdown together with them during study hall to encourage themthatthey willdo their assignments at school so that they could ask me questions if they areconfused.
Reflection
Yesterday, five students sat at the left table and six sat at the right table. JJ, TD, MM, WT, RC, who were all males, sat along the curved area and a female student SM sat at the straight side at the left table. AL, EH and RS were all female and sat along the curved side at the right table. The two male students, SH and KW, sat along the straight side at the same table.
SM was most distracting. She raised her hand and asked if she could go to get some tissue from the office five minutes after the class started. She came back with a sheet of tissue and blew her nose. She raised her hand again and asked the same another five minutes later. I told her bring a box of tissue, and she did. Then, she asked if she could go and sharpen her pencil that she only had. I let her. At the same time, KW was totally disengaged and kept trying to get his friends’ attention. I told him he should focus on the lesson. SM raised her hands again and said KW was distracting her. I told her not to pay attention to him and ignore whatever he did. But she said she could not and kept telling me he was distracting, which resulted in distracting the whole class.
I talked to other teachers during the lunch hour about the situation. They said they were all having the same issues with SM and KW. They have been working with them for one to two years unsuccessfully. They also said TD just transferred to the school and that we had to watch him too because he was one of the students who could get easily fall into their group. I had the three most trouble makers of the school in my class at one time!
So, I made a new seating chart, and assigned a seat to each student to help them decrease disruptive behaviors. Everyone sat facing front having a table in front of them. None of two students sat too close to each other. I also considered who would sit next to each other. EH, RS, AL and MM focus on their studies well, I paired up EH and RS, and AL and MM. I decided to have KW sit between the two pairs by separating him from the rest of the boys. I brought in a small desk and placed it in front of me, and had SM sit there. She directly faced me and I already told her she needed to finish whatever she needed to do before she came to class. I told her she sat there because I wanted to help her focus on learning. I also told her she would sit in the back as soon as she became confident in focusing. Since TD also easily distracted SH, I had them sit apart. TD sat in the middle of one side of a table besides JJ who focused lessons well. This seating chart went pretty well, and the students’ attention improved greatly.
Referring to the objectives for today’s lesson, the students understood the four steps of adding and subtracting fractions. When I asked them questions about the steps they should take as a class, they fairly answered correctly. I also saw that they were able to add and subtract fractions individually as I walked around while they were solving them. However, some students forgot to simplify the fractions after they got a sum or a difference. I had to remind them to do that a couple of times. I thought I needed to emphasize that they always should check their answers if they could simplify them further. Since I will teach more about operations of fractions in the future, I will keep reminding them to make sure to check if they could simplify fractions in their answers.
Yumiko Kishikawa
November 3rd (4th lesson)
Objectives
Students will be able to organize their notebook.
Materials
Whiteboard, color pens
Notebook, textbook
Guidance paper for notetaking
Pre-requisite skills
Students should be able to organize their notebook.
Anticipatory sets
Today is a notebook checking day. Take out your homework for today although we are not reviewing today. While you are waiting for your turn, please work on the problems on the board. If you do not finish, it will be an assignment for tomorrow.
Activities & Evaluation
10:04-10:38
Have students prepare for the lesson by reading the board.
Greeting
Have them get ready for notebook check.
Tell them to work on problems on the board.
Have them put their check sheet, past homework pages and today’s homework.
Check each student’s notebook and see what they understood and what they still need to work on. (Formative)
Review the answers if there is enough time.
10: 38-10:42
Tell them to write page numbers and question numbers.
Tell them to leave a space between questions.
Tell them to write letters and numbers in appropriately sizes.
Tell them to write so that other persons can read.
Modifications and adaptations
There is no TAG, IEP or ELL student. However, some studentsmayneed longer time to understand more deeply although they may grasp most of the concepts during the lessons. Iwilltutor them after school to make sure they understandcorrectly. When they get behind from the rest of the class, I also will sitdown together with them during study hall to encourage themthatthey willdo their assignments at school so that they could ask me questions if they areconfused.
Reflection
I was told that all the teachers should check students’ notebooks today to make sure that they were well-written and well-organized. Students graded their homework and kept records about how they did on their homework on their check sheet for themselves at the beginning of each lesson. I only needed put a mark on the check sheet if I see that they recorded on them other days. Every Thursday, I was supposed to check how they actually did their assignments and also check if their grading was appropriate. I was also told to check how well their notebooks were organized and had to grade the organizations.
Since I teach the third period, I was relaxed at the beginning of the first period and was about to start thinking how I should do checking. Then a student came up to me and said that they were waiting for me in the class. I did not know what they were talking about because Mr. R did not mention my class was the first period when we talked about today’s schedule yesterday afternoon. I found my supervising teacher and asked her if I would be teaching the first period today. She said she did not think so. The student was still waiting for me to come, and I went to seek for Mr. R. When I talked to him, he said he forgot to tell me yesterday. I just ran toward the class.
I intended to plan how I would precede the note-checking during the first two periods. I make my lesson plans a couple of days before at least and keep modifying to adjust proceeding lessons. Since I did not teach content, the lesson should have been easy today. It turned out to be a chaos for multiple of reasons. I went in the class late because I did not know I had the class. I did not have my system for that because I was planning to make it during the first and the second period. I had not seen other teachers evaluate students’ notebook and did not know how to do it because it was a new system the school started.
However, I thought the biggest mistake was checking the notebooks for the previous week. Students forgot where the pages were and each student took time to locate them. It took me three to five minutes to check, evaluate and record each individual notebook. It was not easy to go through all old assignments how well they did each day and how well each page was well-written. I expected that I would finish within twenty minutes and might do some lesson, but it took a whole hour.
I asked other teachers how they did, and they said they did not teach regular lessons on Thursday because it usually took whole an hour. I thought it was a waste of time to check their notebook a couple of days to a week later they did. Rather, I want to check them every day and have a regular class from next week. Then I will be able to gather data more timely on what they still need to learn.
Yumiko Kishikawa
November 4th (5th lesson)
Objectives
Students will be able to add and subtract mixed numbers by writing them as improper fractions. (Knowledge, Comprehension)
Materials
Whiteboard, color pens
Pre-requisite skills
Students should be able to add and subtract fractions.
Students should be able to write mixed numbers as fractions.
Students should be able to simplify fractions.
Anticipatory sets
We already know how we can add and subtract fractions on Tuesday. Can anyone share how we did?
We are going to investigate how we can find the sum of 2 1/4 and 1 5/6 today.
Activities & Evaluation
9:54-10:04
Have students prepare for the lesson by reading the board.
Greeting
Review HW (Formative)
10:04-10:30
Have students discuss how many ¼ are in 2 ¼ in groups of two. *Literacy
Have them share their thoughts as a class by drawing. (Formative) *Literacy
Ask them how we can write 2 ¼ as improper fraction. (Formative)
Ask the class if they agree. (Formative)
Have them discuss why we can write 1 5/6 as 11/6 in groups. *Literacy
Have them share their thoughts as a class by drawing. (Formative)
Ask them if they agree. (Formative)
Have them solve 9/4 + 11/6 individually.
Ask them how they find the answer. (Formative)
Ask the class if they agree. (Formative)
Review how we can add 2 ¼ and 1 5/6 as a class by asking questions. (Formative)
Solve P53 #10, 12, 22 and 24 as a class by asking questions. (Formative)
10:30-10:37
Have them individually work on even number questions on pg. 53.
Walk around to see how they are doing. (Formative)
10:37-10:42
Closure
Have them tell their next person how they add and subtract mixed numbers.
Have one or two pairs share as a class. (Formative)
Step 1/ Write mixed numbers as improper fractions.
Step 2/ Find the Least Common denominators and write equivalent fractions.
Step 3/ Add them together and simplify it.
Modifications and adaptations
There is no TAG, IEP or ELL student. However, some studentsmayneed longer time to understand more deeply although they may grasp most of the concepts during the lessons. Iwilltutor them after school to make sure they understandcorrectly. When they get behind from the rest of the class, I also will sitdown together with them during study hall to encourage themthatthey willdo their assignments at school so that they could ask me questions if they areconfused.
Reflection
Students were able to write mixed numbers as improper fractions. They seemed to have understood how mixed numbers can be added and subtracted by changing them into improper fractions when we solved problems as a class. After we practiced a couple of questions, I had them to work individually and told them to use the method. I walked around to see how they were doing and found many students were adding two whole numbers first and fractions secondly. Then, they added the new whole number and the new fraction. They said that they did not change mixed numbers into improper fractions because adding or subtracting the whole numbers was easier. They added that they did not like the work to change mixed numbers to improper fractions because the numerator becomes big.
I told them to use the method of changing improper fractions because they would come across in the case where the fraction in the second mixed number was greater than the first and could not subtract from the first. I also added that changing to improper fraction would become more useful later in higher math and I wanted them to understand alternatives.
I talked to other math teachers after the class. One teacher said that I should encourage them and almost force them to use the method of improper fractions because the method becomes more important and necessary in high school math and physics. She said, “I don’t know why elementary teachers teach the whole number method. They shouldn’t teach the method in the first place. And improper fractions in answers should be left without changing back to mixed numbers”. I said, “When we have large numbers in the denominators and the whole numbers, the tasks of changing improper fractions become tedious. Adding or subtracting the whole numbers may be sometimes a lot easier”. She said, “By the time they come across such cases, they are allowed to use calculators in America, and there will be no problem”.
The other teacher said it is up to me to decide whether I teach the both methods or decide which method I should encourage. He also said he would encourage the method of improper fractions because changing improper fraction becomes more powerful when subtraction is involved and the second number is greater than the first one. Basically, the both teachers favored for the improper method.
Japanese teachers teach everything in textbooks. It was interesting to know that American teachers do not have to teach the both methods and it was totally up to them to decide what to teach as far as they cover the Standard. I personally use the both methods depending on the features of mixed numbers and situations to be used. However, I favor to use the method of handling the whole numbers first. I will keep teaching the both methods and tell them they can choose whichever they feel more comfortable later.
Yumiko Kishikawa
November 8th (7th/8th lessons)
Objectives
Students will be able to add or subtract mixed numbers by borrowing 1 from the whole number (Knowledge, Comprehension)
Materials
Whiteboard, color pens
Worksheets
Pre-requisite skills
Students should be able to find the least common denominators.
Students should be able to write equivalent fractions to 1 using the LCD.
Anticipatory sets
We have learned to add and subtract mixed numbers by changing mixed numbers into improper fractions. Today, we will learn to do that by borrowing 1 from the whole number. Later, you will share your house plans in the class. I am looking forward to seeing your creative work.
Activities & Evaluation
9:54-10:04
Have students prepare for the lesson by reading the board.
Greeting
Reviewing HW (formative)
Tell them about genten
10:04-10:22
Tell them to write what I write on the board as we discuss.
Tell them we will add and subtract mixed numbers by adding or subtracting fractions first, the whole numbers second, and the fraction and the whole number last.
Tell them the whole number should be written by the fraction bar and not by the numerator.
Do the examples as a class by asking questions. (Formative)
3 5/6 + 2 3/10
3 1/12 – 1 7/8
10:22-10:40
Distribute the worksheets
Have them work individually.
Walk around and observe how they do and have them ask questions if they have any. (Formative)
Share their answers as a class
10:40-10:45
Break
10:45-11:13
Have them work on problems even numbers on p58 and 59.
Walk around and observe how they do and have them ask questions if they have any. (Formative)
11:13-11:28
Share their house plans in class. *Literacy
Have each student come up to the front and talk about what their unique points are.
Find and talk for them if they are not sure what they are.
Have them clap their hands at the end of each presentation.
11:28-11:33
Closure
Ask them what they want to be careful about when they add or subtract mixed numbers. (Formative)
Modifications and adaptations
There is no TAG, IEP or ELL student. However, some studentsmayneed longer time to understand more deeply although they may grasp most of the concepts during the lessons. Iwilltutor them after school to make sure they understandcorrectly. When they get behind from the rest of the class, I also will sitdown together with them during study hall to encourage themthatthey willdo their assignments at school so that they could ask me questions if they areconfused.
Reflection
Students have been struggling with adding and subtracting mixed numbers. When I graded their homework yesterday, I found different students have been making different mistakes. The first type of mistakes was simple mistakes such as writing 7 after adding 2 and 4. The second type was made by over confidence in mental math. If they showed their work, some mistakes could have been avoided. The third type was made by adding denominators. Instead of finding the least common denominator, they simply added denominators. The fourth type was made by forgetting simplifying the answers. The fifth was made by subtracting the second fraction from the first one when the second fraction was greater than the first one. The sixth was made by forgetting to add the whole numbers and only added fractions.
We solved a couple of fraction questions together in the last class and also told them that they should look at the examples on the page 52 about how they were supposed to show their work. When I looked at their homework, each student wrote differently and some of their writing was also disorganized. The disorganization seemed to have attributed to their mistakes. I talked to my supervising teacher about it. She suggested me to make a flow chart that they should follow when they solve problems. She did in her class, and it was successful to many students. She added she had to have them repeatedly practice before the success. She also mentioned that some young students might be very rigid and might not want to change their ways to a new system.
After receiving her advice, I spent a quite a long time to make a flow chart for today’s lesson. I expected that it would work, but it did not at all. The students started saying it was confusing because the ways they did were different from what they did. Since each student wrote their work differently, the ways they got confused with the chart were also different from each other. If they were confused in one way, I could have modified my chart in that way. I finally made decisions not to use it, and decided to divide the class in two groups. I let five students who understood most parts of the content sit together and had them work on problems on their own. I also told them to help each other when they had questions.
I started helping the most confused group of students. I gave advice to each student who needed help from me step by step. I said, “Write your letters bigger so that you won’t misread your own letters”: “Remember to simplify your fraction”: “Remember to change your improper fraction to a mixed number”: “Leave more space between your numbers so that you won’t misread them”: “Find the least common denominator first”: “You cannot subtract the first fraction from the second fraction”: “Remember to add the whole numbers too”: “You don’t want to add the denominators”: “You wrote a wrong question”: “Four plus five is not equal to eight”, etc. JJ and SH especially listened to the pieces of advice I gave and followed my instructions and caught up very well.
|
Fraction game answers/ Questions are written notecards by handwriting. |
||||
|
Factors |
1 |
6 11/30 |
36 |
5 1/3 |
|
16(1,2,4,8,16) |
2 |
2 1/30 |
37 |
1 2/3 |
|
18(1,2,3,6,9,18) |
3 |
2/3 |
38 |
1/6 |
|
24(1,2,3,4,6,12,24) |
4 |
6 1/6 |
39 |
5 ¼ |
|
27(1,3,9,27) |
5 |
1 11/15 |
40 |
2 1/6 |
|
28(1,2,4,7,14,28) |
6 |
3 13/15 |
41 |
3 1/8 |
|
30(1,2,3,5,6,10,15,30) |
7 |
7 2/3 |
42 |
1/8 |
|
32(1,2,4,8,16,32) |
8 |
3 5/6 |
43 |
1 ¾ |
|
34(1,2,17,34) |
9 |
3 ½ |
44 |
1 4/5 |
|
36(1,2,3,4,9,12,18,36) |
10 |
4 |
45 |
6 8/9 |
|
38(1,2,19,38) |
11 |
5/6 |
46 |
1 5/9 |
|
54(1,2,3,9,27,54) |
12 |
9 ½ |
47 |
3 ½ |
|
63(1,3,6,9,21,63) |
13 |
4 1/6 |
48 |
5 5/6 |
|
72(1,2,3,4,6,8,9,12,18,24,36,72) |
14 |
1 1/3 |
49 |
4 11/12 |
|
81(1,3,7,9,27,81) |
15 |
9 2/11 |
50 |
9 1/30 |
|
|
16 |
5 1/9 |
51 |
2 2/3 |
|
|
17 |
4 1/7 |
52 |
3 1/6 |
|
GCF |
18 |
3 4/9 |
53 |
1/6 |
|
6,8(2) |
19 |
2 5/8 |
54 |
5 1/3 |
|
6,15(3) |
20 |
2 5/7 |
55 |
8 1/3 |
|
8,12(4) |
21 |
1 ¾ |
56 |
5 9/14 |
|
12,36(12) |
22 |
2 1/12 |
57 |
3 3/14 |
|
24,36(12) |
23 |
½ |
58 |
5 11/12 |
|
|
24 |
1 7/12 |
59 |
5/12 |
|
|
25 |
5 ¾ |
60 |
5 13/15 |
|
LCM |
26 |
¾ |
61 |
3 7/15 |
|
6,8(24) |
27 |
10 1/20 |
62 |
5 7/10 |
|
6,9(18) |
28 |
3 1/5 |
63 |
1 1/10 |
|
6,10(30) |
29 |
½ |
64 |
9 |
|
6,15(30) |
30 |
10 1/6 |
65 |
2 |
|
8,10(40) |
31 |
1 ½ |
66 |
14 1/6 |
|
8,12(24) |
32 |
9 5/8 |
67 |
1 ¼ |
|
12,36(36) |
33 |
4 7/12 |
68 |
3 3/4 |
|
|
34 |
4 2/5 |
|
|
|
|
35 |
0 |
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Yumiko Kishikawa
November 17th (10th Lesson)
Objectives
Students will take a post-assessment test. (Knowledge, Comprehension)
Materials
Whiteboard, color pens
Quiz sheets
Pre-requisite skills
Students should be able to add and subtract fractions.
Students should be able to add and subtract mixed numbers.
Students should be able to find the least common multiples.
Students should be able to find the least common denominators.
Students should be able to measure a length using a ruler.
Students should be able to find the perimeters.
Anticipatory sets
What have we learned a lot of things about fractions. I would like to give you a quiz to find out how much knowledge and skills you have gained.
Activities & Evaluation
8:05-8:53
Have students prepare for the test by reading the board.
Greeting
Collect HW and stamp on their check sheet.
Tell students they have time till 8:51.
Tell them to raise their hands if they have any question.
Tell them to go over if they have time left and no book reading.
Walk around to see how they are doing. (Formative)
Closure
Collect the quiz.
Modifications and adaptations
There is no TAG, IEP or ELL student. However, some studentsmayneed longer time to understand more deeply although they may grasp most of the concepts during the lessons. Iwilltutor them after school to make sure they understandcorrectly. When they get behind from the rest of the class, I also will sitdown together with them during study hall to encourage themthatthey willdo their assignments at school so that they could ask me questions if they areconfused.
Reflection
As I walked around the class while they were taking the Post-Assessment test, I noticed that some students were struggling with measuring the length of a pencil drawn on a quiz sheet. They drew a house plan for the future in a previous class and should have learned how to measure items using a customary ruler. I understand why they do not want to measure using a ruler. American measurement is so complicated for students to use them. A length may be measured to the nearest half of an inch, a quarter of an inch, an eighth of an inch and a sixteenth of an inch. They were supposed to be able to read the measurement in four different ways at least depending on how accurately it needs to be read.
I wish students could use only centimeters. Japanese students can measure things correctly using a ruler by the time they are in the second grade. It is easy to use it because the metric system goes by ten. It astonished me that I saw the sixth graders were still struggling with measuring using a ruler after multiple times of practice because the unit system is too complicated. I thought I should come back to the study of measuring after they master fractions and mixed numbers more. I will tell them to count the number of gaps of a sixteenth, express it in fraction in the form of “the number/ sixteenth” and to simplify it if possible. It kept confusing them when they counted the number of gaps of a eighth or a fourth.
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