realportfolioforstudentteaching.weebly.comrealportfolioforstudentteaching.weebly.com/uploads/... ·...

Contextual Factors for West Salem Middle School

SCHOOL DISTRICT

The total enrollment in the West Salem School District is 1812 students. There are three schools in this district: West Salem Elementary, West Salem Middle School, and West Salem High School. Troy Gunderson is the superintendent for the district. His offices are located next to the high school.

SCHOOL

West Salem Middle school currently has 411 students enrolled. The grades included at this school are sixth, seventh, and eighth grade. The ratio of boys versus girls is almost half and half. 49.9% of the students are girls, and 50.1% are boys. 91.2% of the students are white/Caucasian and 8.8% are of ethnic backgrounds (.5% American Indian, 2.2% Asian, 1.5% Black, 2.4% Hispanic). 25.11% of the students attending West Salem Middle School are considered economically disadvantaged, while 74.9% are not. There are many academic programs and extracurricular activities offered at West Salem Middle School. They include: Fall Sports: Cross Country 6-8, Football 7-8, Volleyball 7-8; Winter Sports: Wrestling 6-8, Boys/Girls Basketball 7-8; Spring Sports: Softball 7-8, Track7-8; Band, Jazz Band, Choir, Show Choir, Math Counts (Math Club), and the Advisee/Advisory Program. The average class size in the middle school is approximately 25 students. Dean Buchanan is the Principal, Mike Lang the Counselor, and Janel Lochen and Anita Jagodzinski are Administrative Assistants. These four are considered the leaders of the school. West Salem also offers many different kinds of specialists. They include:Heidi Horton, School Psychologist; Heather Jehn, Middle School Special Education (CD); Michael Land, MS School Counselor; Tiffany Lisk, Nurse; Jennifer Mick, Speech and Language Pathologist; Stacy Rel, MS EDB; Stacy Spors, MS LD; Tina Thompson, MS SLD/EBD; Gwen Treu, MS LMC Director; Connie Troyanek, Nurse; and Barb Thompson, School Forest Coordinator. West Salem Middle School has 3 floors. The first floor houses the offices, the gym, the band and choir rooms, health room, the locker rooms, some classrooms and some lockers. The second floor includes more classrooms, more lockers, bathrooms, the library and the computer labs. The basement is home to the school cafeteria, more lockers, bathrooms, and more classrooms. The hallways are very spacious and each student has his or her own locker, which is nice and provides them with enough space to store their gym shoes if needed. Also, in the hallway, there is student work on display. Some are class projects and some are artwork. There is also always a smiling face in the hallway. Most teachers stand outside their classroom during passing time.

CLASSROOM

Mrs. Thompson’s room is a rather large and bright room. There is one large window located right behind the teacher’s desk. There are 27 desks, all in rows. There are three rows of five desks and two rows of six desks. Located in the back of the room are two computers that the students are able to use. These computers are situated right next to Mrs. Thompson’s own school computer that she enters grades on and takes attendance on. There is no smartboard in Mrs. Thompson’s room. Instead it is an old wheel crank projector that you write all your notes on using those overhead markers. I really enjoyed using this because it is easier to write out math notes on an overhead instead of making a powerpoint (for math). In the front, around the overhead, there are two tables which hold all sorts of stuff. The shelves have Mrs. Thompsons items on it, but on the top there are pens, pencils, sticky notes, rulers, and protractors (all for the students use). There are two big

1

cupboards in 2 corners of the rooms. One has cubbies for her AA students, and the other holds other school supplies. There is a phone in the room that students are allowed to use in emergencies

Stands outside every class period, welcomes them into the room. If there is some major announcement that teachers were to give in AA, she will re-announce it to make sure each student heard it. The students really know that Mrs. Thompson cares about them. Mrs. Thompson also gives time each day for the students to work on their homework. During this time, the students are able to get one on one help from Mrs. Thompson. They really take advantage of that, asking as many questions as they have. During note taking, I welcomed questions and was happy that they asked some. Mrs. Thompson does the same thing and no student ever feels like their question isn’t worth answering. She’s friendly with the students, but expects respect and quiet. She doesn’t grade homework every night, so she does homework check on Fridays, in which she spot checks some of the homework. There is atmosphere of learning in her classroom. Students don’t walk into her classroom and think “Oh yea, it’s time to goof off!” The students talk and chit chat before class starts, but when class starts they know that it’s time for class. They sit down. Each day, Mrs. Thompson writes on the board what the homework is and whether they’ll be taking notes that way the students know what’s going on for the day.

Mrs. Thompson’s teaching techniques include a mixture of lecture and some group work. Unfortunately, Math must include a lot of lecture simply to get the point across, but Mrs. Thompson really tries to engage the students in the lecture by allowing them to working in partners, check their work with the students around them and working through the problem as a class to find the answers.

This class period is a time full of students who like to talk and ask questions. They seem to really want to learn and take excellent notes. Some students understand the math a little easier than others, but that is to be expected. Some students asked a lot of questions during the homework time, which is great because it shows that they really want to understand the concepts. There is an equal number of boys and girls, 10 and 10, so the mixture of personalities is wide. It is fun to see how they interact with each other. I noticed that this class really likes to bounce questions off each other. One student may ask a question, and another student puts his hand done because their question just got asked by another student and then answered. It was great to see. There are no special needs students in fourth period, but I know that Mrs. Thompson, along with all teachers, have the ability to have an aide in the room if the students need one. 2 of the afternoon classes each have aide. Also in this class, there was not a wide diversity range, but there was one African American boy. The rest of the class was Caucasian.

We didn’t discuss much of parent involvement, but when I was just observing for the day, we did discuss the upcoming parent teaching conferences. Mrs. Thompson encouraged the students to have their parents to come to the conferences and each student had to prepare their grades to what they thought their parents would be happy with (and what they wanted as well). She really empowered the students to take control of their own learning.

2

Unit Overview

Unit Topic:

Fractions and Decimals

Goals:

This unit is important because it teaches the students how to compare fractions, how to switch fractions into decimals and compare, and then add and subtract fractions with alike and unlike denominators. These skills can be used in many different real life applications, like dividing up foods.

Standards:

4.NF.2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

4.NF.7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

5.NF.1. Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

5.NF.2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Unit Goals:

1. The student will recognize and compare fractions with different numerators and denominators (4.NF.2).

2. The student will use decimals notation to compare fractions (4.NF.7).3. The student will add and subtract fractions with like and unlike denominators (5.NF.1).4. The student will decipher real world problems using comparisons of fractions and decimals

and addition/subtraction of fractions. (5.NF.2)

3

Assessment:

1. Daily Homework2. Quiz3. Pizza Club Project

Materials Needed:

1. MathThematics Textbook2. Pre-Assessment/Post Assessment 3. Notes

4. Homework/Review Sheets5. Pizza Project Handout

Pre-Assessment

Lesson Intro

Lesson 1: Comparing Fractions

Content Objectives1. The student will compare at least 10 different fractions with different denominators and

numerators using number sense. 2. The student will compare at least 6 fraction using both common denominators and decimals

Possible Assessment1. Homework

Lesson 2: Addition and Subtraction of Fractions

Content Objectives1. The student will demonstrate at least 6 times how to add and subtract fractions.

Possible Assessment1. Homework

Lesson 3: Addition and Subtraction of Mixed Numbers

Content Objectives1. The student will answer at least three-fourths of questions, involving the addition and

subtraction of mixed numbers, correctly.Possible Assessment

1. Homework/Review Sheet

Lesson 4: Pizza Proportion Project

Content Objectives1. The student will get 90% of Pizza Project Packet Complete.

Possible Assessment2. Pizza Project graded with rubric

Post Assessment (Quiz)

4

Name: ___________________________________ Date: _______________ Class Period: _____________

Pre-AssessmentPlease show all work. Use back if necessary.

Use number sense to compare the fraction. Place a <,>, or = in the .

1.12

13 2.

79

315 3.

910

1920

Use a common denominator to compare the fractions. Show all work. Place a <,>, or = in the .

4.57

13 5.

29

38

Use decimals to compare. Place a <,>, or = in the .

6.4345

6673 7.

963

887

Find each sum or difference, Write each term in lowest term.

8.67+ 7

14=?

79−4

6=?

Find each sum or difference. Write each term in lowest terms.

9. 2 12+19 5

7=?

10. 12 56−5 1

12=?

5

Name: KEY Date: _______________ Class Period: _____________

Pre-AssessmentPlease show all work. Use back if necessary.


1.12> 1

3 2.79> 3

15 3.9

10< 19

20


4.57> 1

3 5.29< 3

8


6.4345

> 6673 7.

887

< 963

Find each sum or difference, Write each term in lowest term.

8.67+ 7

14=?

1214

+ 714

=1914

=1 514

9.79−4

6=?

1418

−1218

= 218

=19


10. 212+19 5

7=?

2 718

+19 1014

=21 1714

=22 314

11. 12 56−5 1

12=?

121012

−5 112

=7 912

6

Lesson 1

Contextual Factors:

In 4th period Math, there are ten boys and ten girls. There are no students with special needs, and there is only one African American boy. This class is somewhat chatty, but they are really engaged in the lecture and discussion. They are not hesitant to ask questions when they are confused. They are also always willing to answer questions. The students know what’s expected of them when they enter the classroom and look to the board for direction as to what they are doing during the class period. The back of the room is primarily empty, so the students do sit as close to the front as possible. The class does not talk while someone else is talking and they always raise their hands to ask a question!

Goals:

This unit is important because it teaches the students how to compare fractions. This skill can be used in many different real life applications, like dividing up foods.

Standards:

4.NF.2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

4.NF.7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.

Objectives:

The student will compare at least 10 different fractions with different denominators and numerators using number sense.

The student will use decimals to compare 3 different fractions.The student will compare 6 fraction using common denominators.

Time Frame

41 minutes

Resources

8

MathThematics TextbookNotesHomework Pages

Instructional Procedure

Lesson 1: Comparing Fractions

Day 1 (Monday)

Intro (3 minutes):

Define the word inequality

Inequality: A statement that uses the symbol > (greater than) or < (less than) to compare two numbers

Ask students if they’ve seen the symbols before, make sure they know the difference and then do 2 examples below.

Ex: 4 < 16 -3 > -6

Developmental Lesson (27 minutes)

Today we’re going to learn how to compare fractions by Using Number Sense.

(1) See if the numerators or the denominators are the same.

Ex: 12> 1

3→→

numeratorsare equalsmaller denominator , bigger fraction therefore

12> 1

3

711

> 713

2543

< 2530

Ex: 25< 3

5→→bigger numerator , bigger fraction

denominators are equal therefore 25< 3

5

67> 3

7 1225

< 1325

(2) See if one fraction is greater than ½ and the other is less than ½

EX: 34> 4

9 because 34is greater than 1

2because half of 4 is2∧3is bigger than 2,

9

¿49isless than 1

2becuase half of 9 is4.5∧4 is less than 4.5

613

< 815

79> 3

7 7

16< 2

3

(3) See if both fractions are one part less than a whole.

Ex: 78> 6

7→bigger denominator bigger fractions .The ONLY way this works is if BOTH

fractions are one less than a whole. 7 is one less than 8, 6 is one less than 7.

1415

>78

2728

< 2930

Now we are going to Use number sense to order fractions from LEAST to GREATEST. ALWAYS pay attention to how the directions ask you to order the numbers, that way you will for sure get them in the right order!

7475, 1225, 150, 99100

, 13

1

50(1 ) 1

31225

(2 ) 7475

(3 ) 99100

Each number in the parentheses represents the number sense I used to solve for this order sequence. Walk the students through this example. Put the next six fractions up and give the students time to work through it on their own, then ask different students to help you put them in order. Ask for the number they started with and then work from there.

53, 5

6, 35, 1

8, 3

4, 19

19

(1 ) 18

(2 ) 35

(1 ) 34

(3 ) 56

(1 ) 53

Closure (11 minutes)

Assign Homework pg 291, problems 1-15. After assigning, go through the directions of the homework. Allow 10-15 minutes for homework/question time.

Day 2: (Tuesday)

Intro (5 minutes):

10

First ask if there are questions over the homework from last night. Then review the 3 different ways to use number sense to compare fractions. (1) See if the numerators or the denominators are the same. (2) See if one fraction is greater than ½ and the other is less than ½ (3) See if both fractions are one part less than a whole.

Developmental Lesson (30 minutes):

Today we’re going to learn two different ways to compare fractions besides using number sense from yesterday. We’ll start with using a common denominator. Step 1: Solve for Common Denominator. This step is where we take the bottom two numbers and make them the same. We want to find the smallest number that the two denominators have in common, therefore we can change out step one to Step 1: Solve for ^Least Common Denominator. Now Step 2: Solve for the new numerator. We know that whatever we do to the bottom of the fraction, we must do to the top so it can be an equivalent fraction. Ask students: What does the word equivalent mean? They should respond with that it means that the two are equal. Now, Step 3: Compare fractions and enter correct inequality symbol. Go through examples below following steps.

710× 7

7=49

70> 4

7× 10

10=40

70

23× 8

8=16

24> 5

8× 3

3=15

24

4

17× 5

5=20

85<2

5× 17

17=24

85

After three examples are completed, start new section. Using Decimals to compare fractions. Step 1: Divide each numerator by denominator (can use calculator). Step 2: See which decimal is bigger. You may have to look further that just the tenth’s place, even further than maybe the hundredths place too! Step 3: Compare and enter correct inequality symbol. Go through examples below. When done with example 1, ask students: “What do we with a decimal that has repeating numbers?” They should respond with, put a bar above the repeating numbers.

35=.6> 6

11=.54

49=.44> 9

21=.428571

7

44=.159091< 8

41=.195122

Closure (6 minutes)

11

Assign homework and allow time to work on it. Pg 291, 16-30, 33-36.

Adaptations/Accommodations:

There are no students in the class that are classified as special needs. If there is a student who is not understanding a concept, or a student who needs a little extra help here is what I would do. I would work with the student one on one during the homework time. I would also provide the students with more detailed notes if that is needed, perhaps copies of my lessons that way they can always follow exactly my thinking of why I am teaching the lesson the way I do. Also, if they are having difficulties grasping the concepts in the traditional manor of teaching, I would create a new way of displaying the lesson, perhaps with more visuals and different things that I could provide for the student to use at home.

Assessment:

The student will complete the homework assignment, but it will not be collected or graded. We will go over it the next day in class to make sure every student really understands the homework problems. Instead it will be a completion grade. This will require me walking around the room to check that every problem is done. Mrs. Thompson does homework checks on Friday’s so I have no data for my assessment for the lesson I taught (Day 1). The homework check is also a completion grade. She just checks to make sure that they have all their homework done and if they do, the students get full credit.

Analysis

Because my lesson consisted of a homework check at the end of the week, there is no quantitative data for this individual data. I would collect all the homework for grading on the last day of the week. But for each individual homework assignment, I would collect completion grades for each assignment. This is very typical for math classes because homework is assigned for the students to practice their skills. The homework is reviewed the day after and students are allowed to fix their mistakes. The completion grade is taken before the review happens, that way the students cannot just simply add their answers.

Reflection (Day 1)

I think this lesson went very well. I had modified it slightly from the previous classes, but only to help the students. I added a few more examples, took more time going through the examples, and then when we started the homework, I read the directions to them. I would, however, change how I read the directions. I would make sure each student had their books out so that way they can follow along with the directions as I read them. I would also go through a few of the homework problems, maybe just one or two examples. I really enjoyed teaching this class because the students were very interactive. They really participated in the discussion and seemed to really understand and grasp the concepts. I think that each of the lesson’s that are in my lesson plans would be lengthened based off how this lesson went. I feel the repetition of the practice would be beneficial for the students in each of the classes. My cooperating teacher was very supportive while I was teaching. She gave me very constructive comments and between

12

each class would discuss with me what I could modify the lesson. I was impressed by the student’s level of participation, as was Mrs. Thompson. Like I said before, I was very pleased with how this lesson ended up. I wasn’t even nervous before I taught this day. Mrs. Thompson said I was “cool as a cucumber”. I felt very calm and relaxed. I knew going into it that I was going to learn a lot from each class and modify my lessons from there, but I also knew that no matter what, the students would learn the information accurately. I really felt like I learned about my teaching style this day and I loved teaching the students. I just tried to enjoy myself and show my enthusiasm to the class. They seemed to notice it and really keyed into the fact that I was having fun, and so they could have fun too. I tried to show my personality in my teaching style and give each student the ability to “show me what their made of” in a way. It was so much fun and solidified the fact that I want to teach middle school someday.

13

Notes for Board

Inequality: A statement that uses the symbol > (greater than) or < (less than) to compare two numbers

Ex: 4 < 16 -3 > -6Using Number Sense.

(1) See if the numerators or the denominators are the same.

Ex: 12> 1

3→→

numeratorsare equalsmaller denominator , bigger fraction therefore

12> 1

3

711

> 713

2543

< 2530

Ex: 25< 3

5→→bigger numerator , bigger fraction

denominators are equal therefore 25< 3

5

67> 3

7 1225

< 1325

(2) See if one fraction is greater than ½ and the other is less than ½

34> 4

9 6

13< 8

15 79> 3

7 716

< 23

(3) See if both fractions are one part less than a whole.

Ex: 78> 6

7→bigger denominator bigger fractions .

1415

>78

2728

< 2930

Use number sense to order fractions from LEAST to GREATEST.

7475, 1225, 150, 99100

, 13

1

50(1 ) 1

31225

(2 ) 7475

(3 ) 99100

53, 5

6, 35, 1

8, 3

4, 19

19

(1 ) 18

(2 ) 35

(1 ) 34

(3 ) 56

(1 ) 53

14

Day 2

Using a Common Denominator to Compare Fractions

(1) Solve for ^Least Common Denominator(2) Solve for the new numerator(3) Compare the fractions and enter correct inequality symbol

710× 7

7=49

70> 4

7× 10

10=40

70

23× 8

8=16

24> 5

8× 3

3=15

24

417× 5

5=20

85<2

5× 17

17=24

85

Using Decimals to Compare Fractions.

(1) Divide each numerator by the denominator (Can use Calculator)(2) See which decimal is bigger(3) Enter correct inequality symbol

35=.6> 6

11=.54

49=.4 4> 9

21=.428571

744

=.159091< 841

=.195122

15

Lesson 2

Contextual Factors:


Goals:

This unit is important because it teaches the students how to add and subtract fractions with alike and unlike denominators. These skills can be used in many different real life applications, like dividing up foods.

Standards:


Objectives:

The student will demonstrate at least 6 times how to add and subtract fractions.

Time Frame

41 minutes

Resources

MathThematics TextbookNotes Homework Sheets


Lesson 2: Addition and Subtraction of Fractions (Wednesday)

20

Intro (3 minutes):

Ask if there are questions over the previous night’s homework. Then introduce next lesson by stating what they’ll be learning about: Addition and subtraction of fractions.

Developmental Lesson (32 minutes)

Write out and go through the steps to add fractions: Adding Fractions.

First we want to make sure the fractions have the same or common denominator. While saying this, write (1) Write the fractions with a common denominator. When we change the denominators, we have to make sure we multiply the numerator by the same number to make each fraction equal or equivalent, like we learned yesterday. Then (2) Add the numerators. Then (3) Write the sum of the numerators over the common denominator. Go through examples below:

37+ 1

3=?

CD=21 , so the fractionsturn into

921

∧7

21.

921

+ 721

=9+721

=1621

411

+ 37=?

CD=77

2877

+ 3377

=28+3377

=6177

19+ 3

5=?

CD=45

5

45+ 27

45=5+27

45=32

45

Make sure to go through each step with each example. First write out the addition problem with the ? in it. Then, have the students find the common denominator. From there, solve

21

for the numerators. Write the new fractions below the original equation. Then solve for final answer by adding the numerators.

Subtracting Fractions

Subtracting fractions is VERY similar to addition, just instead of adding the numerators we subtract them. So we will just write out the same steps, except with subtraction instead of addition. (1) Write the fractions with a common denominator. (2) Subtract the numerators. (3) Write the difference of the numerators over the common denominator. Go through examples below:

23−1

2=?

CD=6

Equations turnsinto : 46−3

6=4−3

6=1

6

67−3

9=?

CM=63

5463

−2163

=3363

12−1

5=?

CM=10

5

10− 2

10= 3

10

Make sure to go through each step with each example. First write out the subtraction problem with the ? in it. Then, have the students find the common denominator. From there, solve for the numerators. Write the new fractions below the original equation. Then solve for final answer by subtracting the numerators.

Closure (6 minutes):

Go through the steps of both subtraction and addition (little review). Have the students give you the steps without looking at their notes. Then assign homework. Page 313,

22

numbers 1-15. Go through the directions and explain how to do some of the problems. Do the first one together (as a class).


There are no students in the class that are classified as special needs. If there is a student who is not understanding a concept, or a student who needs a little extra help here is what I would do. I would work with the student one on one during the homework time. I would also provide the students with more detailed notes if that is needed, perhaps copies of my lessons that way they can always follow exactly my thinking of why I am teaching the lesson the way I do. Also, if they are having difficulties grasping the concepts in the traditional manor of teaching, I would create a new way of displaying the lesson, perhaps with more visuals and different things that I could provide for the student to use at home. For this lesson, if a student needs more visual aids, I could show them how to draw a picture of each fraction and then do the addition or subtraction from there. This can really help if the student is having trouble grasping the process. Since it will be simple addition and subtraction, most students should be able to see the process quickly, but for those who struggle, visuals would be able to strength those skills.

Assessment:

For this lesson, it will also be a completion grade/homework check. Completion grades are done frequently in Mathematics because the practice of the problems is necessary, but grading every problem can be stressful on students to get everything perfect. This way the students have a chance to ask questions and focus on the concepts and really learning the concepts well.

Analysis and Reflection:

There is no analysis and reflection for this lesson.

23

Notes for Board

Adding Fractions

(1)Write the fractions with a common denominator. (2)Add the numerators. (3)Write the sum of the numerators over the common denominator.

37+ 1

3=?

CD=21 , so the fractionsturn into

921

∧7

21.

921

+ 721

=9+721

=1621

411

+ 37=?

CD=77

2877

+ 3377

=28+3377

=6177

19+ 3

5=?

CD=45

5

45+ 27

45=5+27

45=32

45

Subtracting Fractions

(1)Write the fractions with a common denominator. (2)Subtract the numerators. (3)Write the difference of the numerators over the common denominator.

23−1

2=?

24

CD=6

Equations turnsinto : 46−3

6=4−3

6=1

6

67−3

9=?

CM=63

5463

−2163

=3363

12−1

5=?

CM=10

5

10− 2

10= 3

10

25

Lesson 3

Contextual Factors:


Goals:

This unit is important because it teaches the students how to add and subtract fractions with alike and unlike denominators. These skills can be used in many different real life applications, like dividing up foods.

Standards:


Objectives:

The student will answer at least three-fourths of questions, involving the addition and subtraction of mixed numbers, correctly.

Time Frame

41 minutes

Resources

MathThematics TextbookNotesReview Sheet


28

Lesson 3: Addition and Subtraction of Mixed Numbers (Thrusday)

Intro (3 minutes)

Ask how homework from previous night went and answer any questions. Introduce today’s lesson: Adding and Subtracting Mixed Fractions.


Start with writing notes: Adding Mixed Numbers

Estimating: round to the nearest whole number.

Ex :2 12+3 2

3≈3+4=7

514+6 6

9≈5+7=12

Using paper and pencil: Add the whole numbers and fractions separately. In the example below, the fractions have denominators that don’t match, therefore we must go back to previous days lesson to change fractions into fractions with the same denominator.

212=2 3

6

+3 23=+3 4

6

576=6 1

6

We want to make sure that when we have a improper fraction, we change it into a mixed fraction.

514=5 9

36

+6 69=+6 24

36

11 3336

=11 1112

29

Subtracting Mixed Numbers

Using Paper and Pencil: first subtract the fractions, then the whole number.*You may have to regroup as a whole

413=4 2

6=3 8

6→Regroupas whole !

−1 56=−1 5

6=−1 5

6

236=2 1

2

Go over regrouping as a whole: Explain that when they see the equation4 26−1 5

6 , the

fraction on “top” is smaller than the one on the bottom so they have to regroup and take one away from the whole number and put it into the fraction. That way the top fraction is bigger than the bottom one.

634=6 9

12

−4 23=−4 8

12

21

12

Using Mental Math: when subtracting, think of a related addition sentence

Ex: 8−3 56, think3 5

6+?=8

?=4 16

If you add 16 , you get 4. And from there you’d need 4 to make 8. So you need to add 4

16 to

get 8. Therefore that is the answer to the subtraction problem.

9−2 911

=?

30

29

11+?=9

?=6 211

Ask the class what number they need to add to get 3. The answer should be 211 . Then from

3, then need to add 6. Therefore ? = 6211

Closure (6 minutes):

Pass out review sheet. Tell the kids that this sheet is review for the quiz that will be tomorrow. The review sheet has more problems than the quiz will have, but it’s all to help them practice. It will be turned in and graded as well, since all the homework from the week was completion grade. Tell students that they should be able to complete this whole worksheet with their notes and it will be collected 2 days from now. That means they have 2 nights to work on it. They should really be focusing on knowing the concepts and really understanding them.


There are no students in the class that are classified as special needs. If there is a student who is not understanding a concept, or a student who needs a little extra help here is what I would do. I would work with the student one on one during the homework time. I would also provide the students with more detailed notes if that is needed, perhaps copies of my lessons that way they can always follow exactly my thinking of why I am teaching the lesson the way I do. Also, if they are having difficulties grasping the concepts in the traditional manor of teaching, I would create a new way of displaying the lesson, perhaps with more visuals and different things that I could provide for the student to use at home. For this lesson, drawing pictures and charts would be helpful as well. Again, at the core of these problems are basic addition and subtraction, but the fractions can be confusing. So if a student is struggling, drawing pictures and charts could be very helpful and could strengthen those necessary skills.

Assessment:

The assessment for this lesson is a review sheet. This review sheet will be collected and graded. The students will be told this. And they have 2 nights to work on it. It is kind of a longer assignment and I want the students to really focus on this because it will be very similar to their quiz that they will have after the Pizza Party Project.

Analysis and Reflection: N/A

31

Notes for Board

Adding Mixed Numbers

Estimating: round to the nearest whole number.

Ex :2 12+3 2

3≈3+4=7

514+6 6

9≈5+7=12

Using paper and pencil: Add the whole numbers and fractions separately.

212=2 3

6

+3 23=+3 4

6

576=6 1

6

514=5 9

36

+6 69=+6 24

36

11 3336

=11 1112

Subtracting Mixed Numbers

Using Paper and Pencil: first subtract the fractions, then the whole number.*You may have to regroup as a whole

413=4 2

6=3 8

6→Regroupas whole !

−1 56=−1 5

6=−1 5

6

236=2 1

2

634=6 9

12

−4 23=−4 8

12

21

12

Using Mental Math: when subtracting, think of a related addition sentence

33

8−3 56=? 9−2 9

11=?

3 56+?=8 2

911

+?=9

?=4 16 ?=6 2

11

34


Review Sheet. Please show all work. Use back if necessary.


1.12

17

2.34

910

3.911

25

4.78

1213

5.45

27


6.25

910 7.

67

915 8.

69

78


9.3

222

11 10.855

799 11.

753

810

Find each sum. Write each term in lowest terms.

12.12+ 8

9=? 13.

34+ 13

12=? 14.

911

+ 12=?

Find each difference. Write each term in lowest terms.

15.78−3

5=? 16.

910

−37=? 17.

99100

− 225

=?

35


18. 3 45+4 2

4=? 19. 2 1

9+2 2

3=? 20. 7 3

8+1 4

7=?


21. 9 910

−6 34=? 22. 8 7

8−4 1

4=? 23. 5 9

11−2 1

9=?

Write the fractions in order from least to greatest.

24.12, 4

6, 911, 778, 95 25.

67, 45, 1

4, 3

4, 810

36

Name: KEY Date: _______________ Class Period: ____________

Review Sheet.

Please show all work. Use back if necessary.


1.12> 1

7

2.34< 9

10

3.911

> 25

4.78< 12

13

5.45> 2

7


6.25< 9

10 7.67> 9

15 8.69< 7

8

410

910

90105

64105 48

726372


9.3

22< 2

11 10.8

55> 7

99 11.753

< 810

.1363 .1818 .14545 .0707 .1321 .8


12.12+ 8

9=? 13.

34+ 13

12=?

311

+ 12=?

9

18+ 16

18=25

18=1 7

18 9

12+ 13

12=22

12=1 10

12=1 5

6 622

+ 1122

=1722

37


14.78−3

5=? 15.

910

−37=? 16.

99100

− 225

=?

3540

−2440

= 1140

6370

−3070

=3370

99100

− 8100

= 91100


17. 3 45+4 2

4=? 18. 2 1

9+2 2

3=? 19. 7 3

8+1 4

7=?

3 1620

+4 1020

=7 2620

=8 620 2 1

9+2 6

9=4 7

9 7 2156

+1 3256

=8 5356


20. 9 910

−6 34=? 21. 8 7

8−4 1

4=? 22. 5 9

11−2 1

9=?

9 1820

−6 1520

=3 320 8 7

8−5 2

8=3 3

8 5 8199

−2 1199

=3 7099

Write the fractions in order from least to greatest.

23.12, 4

6, 911, 778, 95 24.

67, 35, 14, 3

4, 810

778, 12, 46, 911, 95

14, 35, 3

4, 810, 6

7

38

Lesson 4

Contextual Factors:


Goals:

This lesson is important because it incorporates all the previous lessons into a real life simulation.

Standards:

5.NF.2. Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Objectives:

The student will get 90% of Pizza Project Packet correct, graded by rubric/checklist. Time Frame

41 minutes

Resources

MathThematics TextbookPizza Party Project Worksheets


Lesson 4: Pizza Proportion Project (Friday)

39

Intro (5 minutes)

Collect worksheet. Ask students how they think the past 4 days lessons could help them in their real life. Hopefully a student answers with the pizza theory, that they may need to know how to divide up and add pizza proportions correctly.


Tell the students that today we will be doing a project that involves using pizza to compare and add and subtract fractions and mixed numbers. Students will work in pairs, and each pair will get 2 packets (which includes directions and questions).

Students will work through the packet to compare different proportions of how much a person ate for pizza, they will tell me the different between what each person ate, they will demonstrate how much pizza they will need to get for a birthday party with 16 people and then they will tell me how much the pizza will cost for the birthday party from 3 different pizza places. There will be lots of steps involved, but the directions will be clear enough that students should be able to work through it on their own.

Read over criteria checklist which is attached to each packet.

Closure (1 minute):

Remind students that this is due on Monday, no exceptions. On Monday, give students approx. 20 minutes to compare answers with their partners. If they have questions, they can ask them then. Make sure the students know they will have a brief amount of time to compare and check answers with their partners, but make sure they think it will only be like 2 minutes that way they complete the work on their own.


For this lesson, if a student is struggling with the concepts, what I could do is modify some of the questions or change the directions to make it more specific, like “Draw a picture to show how you would complete this problem”. There are many students would not need these directions, but if a student would benefit, I could instruct them to do so to help their learning of the concepts.

Assessment:

The assessment for this lesson is the grading of the Pizza Party Project Packet. It will be graded using a checklist/rubric. Rubrics are difficult to create for math, but for this project the rubric will have 3 different categories and the students will see the criteria when they get started on the packet. We will have reviewed it together. The packet will be collected the next day, along with the review sheet. Both will be graded.

40

Analysis and Reflection: N/A

41

Name: ___________________________________________ Date: _____________ Class Period: _________________

Pizza Party Project Please Show All Work

Stanley and Tori are completing a class project. They are trying to find who in their group eats the most amount of pizza in one sitting. They surveyed 6 different students besides themselves. Use the paragraph below to determine how much pizza each student ate and then put the students in order from least to greatest. If there are students with the same amount of pizza eaten, they should go alphabetically. Use the back of the paper to show work if you need more room.

Hadley can eat 1/6 of a pizza. Brian eats ¼ more pizza than Hadley. Frank eats 1/6 less pizza than Brian. Stanley, Tori and Grace can split a pizza and finish the whole thing. The pizza is divided into 12 slices. Stanley always eats one more piece than Tori and one less piece than Grace. Grace eats the same amount of pizza Brian eats. Hank eats 1/6 more pizza than Brian. Lynn eats the 1/12 less pizza than Hadley. Enter each student’s amount in the chart below.

Hadley

Brian

Frank

Stanley

Tori

Grace

Hank

Lynn

43

Order from Least to Greatest:

How much pizza do all 8 students eat together?

Now Tori and Stanley want to plan a party for their class of 16. They already know how much pizza the first group of 8 ate. Another group of 8 students eats 4 3/5 pizzas.

What is the total amount of pizza the class will eat?

How many pizzas should Tori and Stanley order to be sure there is enough?

Tori and Stanley have 3 different restaurants to order pizza from. Use the segments from each restaurant’s menu to determine which restaurant will give Tori and Stanley the best deal!

Pizza Palace:1 pizza - $14 a pieceAll pizza’s Buy One Get One Half Off.

Happy’s Pizza:1 Pizza- $15Order 5 or more, get each pizza for $10

Robinson’s Pizza Place:All Pizza Buy One Get One FreePizza- $19.50

Tori and Stanley will order their pizza from ______________________________________________________.

44

When Tori and Stanley order their pizzas, they ordered more than they needed because the class ate exactly the amount Tori and Stanley had determined they would eat. How much pizza will Tori and Stanley have left over?

Write a paragraph explaining why knowing this would be beneficial in your life or a family member’s life.

45

Pizza Party Project Criteria Checklist

Minimal (1) Basic (2) Proficient (3) ScoreStructure Paragraph includes less than 2

sentences and 1 incomplete sentence.

Paragraph includes between 2-3 sentences and no incomplete

sentences.

Paragraph has 4 or more sentences and no incomplete

sentences.Relevant Information

Explanation provided in the paragraph do not relate to the

project in any way.

Explanation provided in paper relates to the topic of the project with most of the

sentences being relevant.

Paragraph is very relevant to project topic. Each sentence

relates back to topic.

Grammar Multiple spelling and grammatical errors in paragraph

Some spelling and grammatical errors in

paragraph

No spelling or grammatical errors in paragraph

(1) (2) (3) (4) (5) (6) ScoreCorrectness Less than 60% of

mathematical problems are

answered correctly

60% -69% of mathematical problems are

answered correctly


answered correctly


answered correctly


answered correctly

96% - 100% of mathematical problems are

answered correctly.

Work Student shows work for less that 65% of

problems

Student shows work for 65% of problems




Student shows work for 100%

of problems

Total Points (out of 21)

46

Name: KEY Date: _____________ Class Period: _________________

Pizza Project Packet

Stanley and Tori are completing a class project. They are trying to find who in their group eats the most amount of pizza in one sitting. They surveyed 6 different students besides themselves. Use the paragraph below to determine how much pizza each student ate and then put the students in order from least to greatest. If there are students with the same amount of pizza eaten, they should go alphabetically. Use the back of the paper to show work if you need more room.

Hadley can eat 1/6 of a pizza. Brian eats ¼ more pizza than Hadley. Frank eats 1/6 less pizza than Brian. Stanley, Tori and Grace can split a pizza and finish the whole thing. The pizza is divided into 12 slices. Stanley always eats one more piece than Tori and one less piece than Grace. Grace eats the same amount of pizza Brian eats. Hank eats 1/6 more pizza than Brian. Lynn eats the 1/12 less pizza than Hadley. Enter each student’s amount in the chart below.

Hadley16= 2

12

Brian512

Frank312

Stanley4

12

Tori312

Grace512

Hank712

Lynn1

12

16+ 1

4= 2

12+ 3

12= 5

12 BRIAN

512

−16= 5

12− 2

12= 3

12=1

4 FRANK

STANLEY (4 5 6 7 ) TORI (1 2 3 ) GRACE (8 9 10 11 12 )

512

+ 16= 5

12+ 2

12= 7

12 HANK

47

16− 1

12= 2

12− 1

12= 1

12 LYNN

Order from Least to Greatest:

Lynn, Hadley, Frank, Tori, Stanley, Brian, Grace, Hank

How much pizza do all 8 students eat together? 212

212

+ 512

+ 312

+ 412

+ 312

+ 512

+ 712

+ 112

=3012

=2 612

=2 12

Now Tori and Stanley want to plan a party for their class of 16. They already know how much pizza the first group of 8 ate. Another group of 8 students eats 4 3/5 pizzas.

What is the total amount of pizza the class will eat? 71

10

2 12+4 3

5=2 5

10+4 6

10=6 11

10=7 1

10

How many pizzas should Tori and Stanley order to be sure there is enough?

≈8 pizzas

Tori and Stanley have 3 different restaurants to order pizza from. Use the segments from each restaurant’s menu to determine which restaurant will give Tori and Stanley the best deal!

Pizza Palace:1 pizza - $14 a pieceAll pizza’s Buy One Get One Half Off.

4($14) +4($7) =56 +28 =$84

Happy’s Pizza:1 Pizza- $15Order 5 or more, get each pizza for $10

8($10) =$80

Robinson’s Pizza Place:All Pizza Buy One Get One FreePizza- $19.50

4($19.50) =$78

48

Tori and Stanley will order their pizza from Robinson’s Pizza Place .

When Tori and Stanley order their pizzas, they ordered more than they needed because the class ate exactly the amount Tori and Stanley had determined they would eat.

How much pizza will Tori and Stanley have left over?9

10

8−7 110

=7 1010

−7 110

= 910

Write why knowing this would be beneficial in your life or a family member’s life.

Paragraph should include something about how they may need to know how much pizza to get for a party of their own. It could also talk about how they may need to know about this so that way they know how much pizza they can get for their money. Answers will vary. When grading, look for complete sentences, 5 sentences, and relevant information. Students will have the rubric to look at and therefore will know exactly what to put in the paragraph.

49

Pizza Party Project Criteria Checklist

Minimal (1) Basic (2) Proficient (3) ScoreStructure Paragraph includes less than 2

sentences and 1 incomplete sentence.

Paragraph includes between 2-3 sentences and no incomplete

sentences.

Paragraph has 4 or more sentences and no incomplete

sentences.Relevant Information

Explanation provided in the paragraph do not relate to the

project in any way.

Explanation provided in paper relate to the topic of the

project mostly, with most of the sentences being relevant.

Paragraph is very relevant to project topic. Each sentence

relates back to topic.

Grammar Multiple spelling and grammatical errors in paragraph

Some spelling and grammatical errors in

paragraph

No spelling or grammatical errors in paragraph

(1) (2) (3) (4) (5) (6) ScoreCorrectness Less than 60% of

mathematical problems are

answered correctly


answered correctly


answered correctly


answered correctly


answered correctly

96% - 100% of mathematical problems are

answered correctly.

Work Student shows work for less that 65% of

problems





Student shows work for 100%

of problems

Total Points (out of 21)

50


Quiz



1.12+ 3

14=?

2.45+ 14

15=?

3.1114

− 212

=?

4.9

12−3

5=?


5. 5 36+6 2

4=?

6. 3 57+2 26

28=?

7. 3 110

−1 12=?

8. 4 69−1 2

3=?

Write the fractions in order from least to greatest. (#9 use any method you prefer, #10 use number sense)

51

9. 8384, 652, 77

78, 170, 4367

10. 13, 78, 56, 47, 911

Name: KEY Date: _______________ Class Period: _____________

Quiz



1.12+ 3

14=? 1

14+ 3

14=10

14=5

7

2.45+ 14

15=? 12

15+ 14

15=26

15=1 11

15

3.1114

− 212

=? 132168

− 28168

=104168

=5284

=2642

=1321

4.9

12−3

5=? 45

60−36

60= 9

60= 3

20


5. 5 36+6 2

4=? 5 1

2+ 6

2=11 2

2=12

6. 3 57+2 26

28=? 3 20

28+2 26

28=5 46

28=6 18

28

7. 3 110

−1 12=? 3 1

10−1 5

10=2 11

10−1 5

10=1 6

10=1 3

5

8. 4 69−1 2

3=? 4 6

9−1 6

9=3

Write the fractions in order from least to greatest. (#9 use any method you prefer, #10 use number sense)

52

9.8384, 652, 77

78, 170, 4367

170, 652, 4367, 7778, 8384

10.13, 78, 56, 47, 910

13

(2 ) 47

(2 ) 56

(3 ) 78(3) 9

10

Numbers in ( ) not necessary

53

realportfolioforstudentteaching.weebly.comrealportfolioforstudentteaching.weebly.com/uploads/... ·...

Documents