1 Table of Contents Pedagogic Creed........................................................................................................................................ 3 What is Education?..........................................................................................................3 What is the school?..........................................................................................................3 What is Math Education?.................................................................................................3 The Nature of Method?....................................................................................................4 The School and Social progress?.....................................................................................4 Unit Plan:..................................................................................................................................................... 6 Objectives:.......................................................................................................................7 Big Idea/ Essential questions:..........................................................................................7 Academic Vocabulary:.....................................................................................................7 Pretest:.............................................................................................................................8 Post-test:..........................................................................................................................8 Authentic assessment:......................................................................................................9 School Demographics:......................................................................................................................... 17 Classroom Demographics:................................................................................................................. 18 Lesson plan-Day 1:................................................................................................................................ 20 Standard(s):....................................................................................................................20 Objective:.......................................................................................................................20 AIM:..............................................................................................................................20 Academic Language/Vocabulary:..................................................................................20 Do Now:.........................................................................................................................20 Mini Lesson...................................................................................................................21 Independent Learning....................................................................................................22 Lesson Plan- Day 2................................................................................................................................ 24 Standard(s):....................................................................................................................24 Objective:.......................................................................................................................24 AIM:..............................................................................................................................24 Academic Language/Vocabulary:..................................................................................24 Do Now:.........................................................................................................................24 Mini Lesson...................................................................................................................24 Independent Learning....................................................................................................25 Assessment:...................................................................................................................26 Lesson Plan-Day 3:................................................................................................................................ 27 Standard(s):....................................................................................................................27 Objective:.......................................................................................................................27 AIM:..............................................................................................................................28 Independent Learning....................................................................................................28 Assessment:...................................................................................................................29 Unit 5 Review Worksheet..............................................................................................30 Lesson Plan-Day 4:................................................................................................................................ 32 Standard(s):....................................................................................................................32 Objective:.......................................................................................................................32 AIM:..............................................................................................................................32 Mini Lesson...................................................................................................................33

2 Independent Learning....................................................................................................33 Party time group Worksheets:........................................................................................35 Group 1- Sâ€™mores Trail Mix......................................................................................35 Group 2- Name cards.................................................................................................36 Group 3- Gift Bags....................................................................................................37 Group 4-Party Punch.................................................................................................39 Lesson Plan-Day 5:................................................................................................................................ 42 Standard(s):....................................................................................................................42 Objective:.......................................................................................................................42 Independent Learning....................................................................................................42 Assessment Data and Graphs:.......................................................................................................... 43 Reflection/Re-teach:............................................................................................................................. 45 Embracing Diversity Project:............................................................................................................ 49 Women of Mathematics.................................................................................................49 Women of Mathematics Rubric.....................................................................................51

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Pedagogic Creed What is Education? Education is not achievable or attainable. Education is life. It is a constant gain of knowledge and skills that allow us to find beauty, meaning, and purpose throughout the world we live in. I believe our world is ever changing and as human beings we never reach a capacity of knowledge. Education is not confined to the walls of a classroom, it can occur anywhere at anytime. I believe education is a beautiful thing that provides us with the ability to thrive instead of merely surviving. What is the school? The purpose of the school is to instill the basic building blocks of life within each and every child. While learning content is important the school is also responsible for making sure every child knows how to learn on their own, think for themselves, and analyze beyond what they are told. I believe the most important role in the school is the teacher. The teacher encounters opportunities every day to reach a child in ways they may never experience otherwise. It is important for the teacher to nurture the children of tomorrow in a way where they feel safe, comfortable, and accepted. I believe the purpose of the school is to provide students with the tools they need to thrive and the guidance they need to find their own doorway to success. What is Math Education? I believe that math education should equip each student with problem solving skills they can use beyond the classroom. The goal of math education is to provide the understanding of different operations that will allow students to create a sustainable and

4 successful life. The mathematical experience should be personalized for each individual student and applications to their current and future lives should be used every day. As a teacher it is my job to see that this happens in the classroom. The Nature of Method? Effective math pedagogy should incorporate aspects of both a traditional and constructivist classroom. When given something new it is a childâ€™s first instinct to explore and discover everything about the object at hand. I feel the same is true for mathematics. I believe that in order to create a concrete understanding one must first participate in an individual exploration. Manipulatives and group work should be used to support the concrete learning of mathematical content. While I strongly believe in a constructivist classroom, I do feel that there are multiple occasions in math when a teacher must first tell the student how to complete a problem before letting them explore. I also feel there are time when repetition is vital to students ability to perform and understand a concept. Balance is key in a math-based classroom. The School and Social progress? Our school system is in the midst of chaos, confusion, and change. Teachers are standing up for the rights of our students all across our nation. I see more and more teachers moving away from the banking approach and moving toward approaches that encourage creativity, individualism, exploration, inquiry, and collaboration. Moving away from a standardized classroom not only allows freedom for individuals it allows us to open the minds of our society. When we can encourage students to open their minds to views, opinions, and choices that differ from their own, we are setting a stage for equality

5 in our communities. While there is still a lot to be done in our educational system teachers are making the classroom more inviting and engaging to our students. I believe this is the first step to a new chapter of education. We must first start by changing the outlook students have on education from a negative to a positive. Starting at the bottom and working our way up is the most effective thing we can do for the minds of our future.

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Unit Plan: Measurement Conversion and Unit 5 Review Topic: Using proportions to convert measurements from one unit to another. Scope and sequence: Day 1: Setting up correct proportions to determine equivalent measurements in different units. Day 2: Setting up correct proportions to determine equivalent measurements in different units continued. Day 3: Unit 5 small group and whole class review Day 4 Party timeďƒ real world application Day 5: Unit 5 test

Standards: 6.4(B) Apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates 6.4(C) Give examples of ratios as multiplicative comparisons of two quantities describing the same attribute. 6.4(D) Give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients 6.4(E) Represent ratios and percentâ€™s with concrete models, fractions, and decimals. 6.4(H) Convert units within a measurement system, including the use of proportions and unit rates 6.5(A) Represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions.

7 Objectives: Day 1: Students perform measurement conversions between inches and feet, millimeters and centimeters, seconds and minutes, and quarts and gallons by applying their previous knowledge of proportions. Day 2: Students will construct appropriate proportions that assist them in setting up and solving conversion problems. Day 3: Students will apply their knowledge of ratios, unit rates, proportions, and measurement conversions to a series of complex problems in order to create a series of problem solving steps that can be used on the unit test. Day 4: Student will actively engage in planning a party by solving a series of ratios, unit rates, and measurement conversions to create and construct products for the party guests. Day 5: Asses students understanding of ratios, unit rates, proportions, quantitative and qualitative predictions, and measurement conversions.

Big Idea/ Essential questions: 1. How are proportions used to convert measurements from one unit to another? 2. How can I model and represent measurement conversions? 3. When are proportions and conversions used in every day life?

Academic Vocabulary: Ratio Multiplication Fractions Graphs Tables Numerator Denominator Equivalent Units Whole numbers Proportion

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Pretest: 1. Madison ran 15 feet on Thursday. How many inches did Madison run on Thursday? 2. Sarah has to buy 4 gallons of milk every week. How many quarts of milk does Sarah buy every week? 3. How many seconds is equal to a minute? a. 10 seconds b. 77 seconds c. 60 seconds d. 66 seconds Post-test: 1. Ashley ran 75 feet and Lauren ran 960 inches. Who ran the furthest? 2. Explain how you apply proportions to conversion problems. (List the steps) 3. True/False. There are 10 quarts in a gallon. Explain using numbers and words.

Authentic assessment: My authentic assessment will be my lesson for day four. Students will be required to create a product for a party that they are helping me plan. Students will work in pairs to complete this task and they will have a guide that they must complete as they are working to accomplish their specific task. There will be four different groups responsible for four different products. I have chosen this assessment because it allows students the opportunity to apply their new knowledge from unit 5 in a real world situations. Celebrations are apart of every culture, thus this allows all students the opportunity to form connections to their authentic lives at home.

Group 1- Sâ€™mores Trail Mix

9 S’mores Trail Mix Ingredients:

Ingredients Mini Marshmallows Teddy Grahams Mini Pretzels M&M’s

Amount for 5 people 1 cup 2 cups 1 cup 2 cups

1. What is the ratio of Marshmallows to mini pretzels?

2. What is the ratio of Teddy Grahams to Marshmallows?

3. What is the ratio of M&M’s to mini pretzels?

4. If there are 10 people coming to the party how many cups of M&M’s are needed? What about 20 people?

5. There are 60 people coming to Addison’s party and we need enough trail mix for everyone. How much of each ingredient do I need in order to feed all 60 guests?

10

Ingredients

Amount for 60 people

Mini Marshmallows Teddy Grahams Mini Pretzels M&Mâ€™s 6. It takes Addisonâ€™s mom 30 minutes to make enough trail mix for 60 people. How long would it take her to make trail mix for 5 people?

Group 2- Name cards Name Cards

Each guest needs a name card placed at his or her seat. The dimensions for one name card are 200mm X 200mm.

1. I only have a centimeter ruler to measure out the dimensions for each card. What are the dimensions of each card in centimeters?

2. If I have a piece of construction paper that measures 60cm X 60 cm how many cards can be made from one sheet of paper?

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3. If there are 60 guests coming to the party how many sheets of construction paper do I need in order to make all 60-name cards? 4. It took me 45 minuets to complete all 60-name cards. How many seconds did it take me to finish all 60?

5. How many seconds would it take to make: a. 45 name cards?

b. 20 name cards?

c. 1 name card?

Group 3- Gift Bags Gift Bags

Each bag contains the fallowing:

2 pencils 1 container of bubbles 3 suckers 2 packs of mini M&M’s

1. What is the ratio of suckers to pencils in one gift bag?

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2. What is the ratio of M&Mâ€™s to everything in the bag? Write it as a fraction in simplest form.

3. What is the fraction of bubbles in one bag?

4. How many of each item will be needed to fill 60 gift bags? Items

Amount needed for 60 bags

Pencils Bubbles Suckers Mini M&Mâ€™s Bags

5. The gift bags come in packages of 6. How many packages to I need to buy in order to have enough for everyone?

6. The total cost for all the packages is $22.50. How much does each package of bags coast? How much would it coast to buy two additional packages of bags? Group 4-Party Punch

13 Party Punch Punch recipe:

Ingredients:

Amount for 15 people

Lemon Lime Soda

1 liter

Pineapple Juice

16 ounces

Hawaiian Punch

2 liters

1. What is the ratio of lemon lime soda to Hawaiian punch?

2. What is the ratio of pineapple juice to Hawaiian punch?

3. There are 60 people coming to the birthday party how much of each ingredient is needed to make enough punch for everyone? Ingredients: Lemon Lime Soda

Amount for 60 people

14 Pineapple Juice Hawaiian Punch

4. It took Sarah 10 minuets to make one batch of punch that feeds 15 people. If Sarah has to make enough punch for all 60 guests how much time should she plan to make punch?

Each group will also be responsible for filling out the form below:

1. How many students are in the class today?

2. How much of each ingredient do you need in order to have enough of your product for everyone?

3. Make your grocery list below (include amounts):

Take your grocery list to the teacher and she will give you what you need if the amounts are correct. If they are not correct she will send you back to your group to rework the problem. Once you have your ingredients you will use the above information to produce the product for the class. Authentic Assessment rubric: Category

Below Expectations

Developing

Meets expectations

Exceeds expectations

15 Group Participation: ____/30

Work Shown: _____/35

Answer: ____/25

Product: ____/10

Did not talk or collaborate with other group members. Did provide input or help to solve problems. Off task and disrupting the entire time. (0 Points) There is no work shown for any of the problems. (0 points)

Provided minimal input and only collaborated when cued by the teacher. Off task and a lot of teacher redirection. (10points)

Some work is shown on few problems. There is also missing steps in the work provided. (10 points) There is not an Some answers answer are accounted provided for for but many any question. problems are (0 points) missing answers. More wrong answers than right answers. (5 points) No final product was provided. (0 points)

Total: ______/100 Notes:

School Demographics:

Provides sufficient input and collaborates well. Few disruptions and minimal teacher redirection. (25points)

Focused on the task at hand. Collaborates the whole time and provides input and help solving problems. No teacher redirection (30 points)

There is work shown for every problem but there are some missing steps. (25 points)

All work is shown and all steps are present. (35 point)

All answers are accounted for. Mix between right and wrong answers. (20 points)

All answers are accounted for and correct. (25 points)

Complete Product provided (10 points)

16 Wallace Middle School has a total of 846 students in grades 6-8. When broken down we can see that 48% of those students are of female gender and the remaining 52% of the students are male (figure 1). Wallace Middle School has a semi diverse ethnic population. Their student body consist of 68% Hispanic students, 28% White students, 3% African American students, and 1% multiracial students (figure 2). Wallace Middle School serves 126 or 11% English Language Learners (figure 3). Figure 1:

Males Vs. Females at Wallace Middle School Males Females

48%

52%

Percentage of male and females in Wallace Middle School. Figure 2:

Break down of Wallace Middle Schools Race/Ethnicity Hispanic White African American Multiracial

3% 1% 28% 68%

Percentages of different ethnicities within the student body population at Wallace Middle School. Figure 3:

17

English Language Learners 11%

ELL's Non-ELL's

89%

Wallace Middle School ELL students.

Classroom Demographics: This semester I have had the opportunity to work with two of Mrs. Longoriaâ€™s classes, 1st and 2nd periods. 1st period has a total of 26 students, 12 of those students are female and the remaining 14 students are Male. In contrast, 2nd period is made up of 29 students, 9 females and 20 males. When combined I have worked with a total of 54 students and out of those 55 students 21 are females and 34 are males (figure 4). Figure 4: Mrs. Longoria's Male Students vs. Female Students--1st and 2nd period 35 30 25

Males females

20 15 10 5 0

1st period

2nd period

total

Male and female students in Mrs. Longoriaâ€™s 1st and 2nd period.

18 When examined further, there are multiple ethnicities that make up the student body population of 1st and 2nd periods. 1st period consist of 6 white students, 16 Hispanic students, and 13 African American students. On the other hand 2nd period contains 14 white students, 11 Hispanic students, and 4 African American students. When combined the total number of White students is 20, the total number of Hispanic students is 27, and the total number of African American students is 17 (figure 5). Figure 5: Clasoom Race/Ethnicity- Mrs. Longoria's 1st and 2nd period. 30 25

White Hispanic African American other

20 15 10 5 0

!st period 2nd period

Tottal

Diversity of ethnicities in Mrs. Longoriaâ€™s 1st and 2nd period classes. Between the two classes there were only 2 ELL students. The 2 ELL students were both female and they were in 1st period. Overall, 1st period was completely different than 2nd period in the fact that it was an inclusion class. This meant that the students who made up the classroom all had a different type of special need. Many of them had a 504 or were apart of the special education program. Since this class had a wide range of needs that needed to be met an extra teacher accompanied Mrs. Longoria in teaching 1st period every day. In contrast, Mrs. Longoria was the only teacher present in her 2nd period class and the kids were all considered to be advanced in mathematics. The differences between the two classes were very black and white.

19 Lesson plan-Day 1: Measurement Conversions

Created by: Ashley Harmon Materials: Chart Paper and markers Standard(s): 6.4(H) Convert units within a measurement system, including the use of proportions and unit rates

Objective: By the end of class, students will be able to perform measurement conversions between inches and feet, millimeters and centimeters, seconds and minutes, and quarts and gallons by applying their previous knowledge of proportions.

AIM: How can you find the equivalent measurement using a different unit?

Academic Language/Vocabulary: Equivalent, conversion, proportion

Do Now: Have students complete a ratio table to refresh their memory on how to solve problems using ratios. Students will be utilizing this skill throughout the entire lesson.

[Share Out]

20 Mini Lesson Connect: Todays Lesson will focus on conversions and finding equivalent measurements using different units. Students will work collaboratively to create a concrete understanding of conversions and the steps involved in converting measurements into different units.

Direct Instruction (if needed): The first thing that students need to understand is how to accurately set up conversion problems. The concept of dimensional analysis will be introduced. The first step for students to do is to set up an initial fraction that compares the two units. For example, if we are converting feet to inches students will need to set up a fraction comparing 1 foot

to the corresponding amount of inches,

1 foot . Once the base fraction is set up 12 inches

students can set up a proportion to solve for any value.

For example, if a student needs to know how many inches are in 3 feet they would set up

a proportion similar to

1 ft . 3 ft . = . From here students will use cross multiplication 12âˆˆ. X

to find the value of X, the total number of inches in 3 feet.

Students can set this problems up in the opposite way as well, having inches on the top and feet on the bottom of the fraction.

This process will work for converting measurements of any unit.

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Model: I will start off with a basic relationship table for students. This relationship table will compare feet and inches. I will work collaboratively with the students to complete and graph the relationship table.

You-try-it: Students will work with their shoulder partner to complete the relationship table for comparing inches to feet. They will also be required to graph the numbers within the table. Each pair will share by completing one row to the classroom table and adding one point to the classroom graph.

Independent Learning Task: Students will be working with their shoulder partner for the remainder of the lesson. They will be working together to complete three stations involving a different unit conversion. At each station students will be completing two different relationship tables for the two types of ratios and then graphing each of the tables. They will also be asked to compare and contrast each table as well as complete a few fallow-up questions using the tables.

Station 1: Minutes to seconds Station 2: Millimeters to centimeters Station 3: Quarts to gallons

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Discussion/Share Out: Two student pairs will combine making a group of four. Each group of four will be responsible for transferring their information to chart paper and then presenting the chart paper to the class. Assessment: Students will have an exit ticket that asks them to covert four different problems. One of each, centimeters to millimeters, gallons to quarts, minutes to seconds, and inches to feet.

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Lesson Plan- Day 2 Measurement Conversions Continued

Created by: Ashley Harmon Materials: Handouts Standard(s): 6.4(H) Convert units within a measurement system, including the use of proportions and unit rates

Objective: By the end of class, students will be able to construct appropriate proportions that assist them in setting up and solving conversion problems.

AIM: How do you use proportions to convert measurements into different units?

Academic Language/Vocabulary: Equivalent, conversion, proportion

Do Now: Students will complete a warm-up over ratios, proportions, and conversions.

[Share Out]

24 Mini Lesson Connect: Todays Lesson will focus on extending students knowledge on measurement conversions and the relationship they have with proportions. Students will continue to work collaboratively on developing their concrete understanding of converting measurements into different units.

Model: I will start off with a basic relationship table for students. This relationship table will compare pints to gallons. I will work collaboratively with the students to complete and graph half of the relationship table on the board.

You-try-it: Students will work with their shoulder partner to complete the remaining parts of the relationship table and graph for comparing pints to gallons. After three minutes students will share out and non-volunteers will be called on to help complete the classroom chart and graph.

Independent Learning Task: Students will be working independently on the remaining problems of the Measurement Conversion worksheet. They will be required to complete a second table and graph that compares gallons to pints. After graphs and tables are complete students will answer five

25 fallow-up questions. They will be writing the answer to these questions in multiple formats.

Discussion/Share Out: Students will have five minutes at the end to collaborate with their shoulder partner. Each partner pair will be assigned one problem from the worksheet to complete and share with the class on the whiteboard. This allows students to â€œteachâ€? students and it encourages peer interaction.

Assessment: Students will be required to finish and turn in their Proportion Evaluation worksheet for a quiz grade.

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Lesson Plan-Day 3: Unit 5 Review

Created by: Ashley Harmon Materials: Manipulative, colored pencils, markers, chart paper Standard(s): 6.4(B) Apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates 6.4(C) Give examples of ratios as multiplicative comparisons of two quantities describing the same attribute. 6.4(D) Give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients 6.4(E) Represent ratios and percentâ€™s with concrete models, fractions, and decimals. 6.4(H) Convert units within a measurement system, including the use of proportions and unit rates 6.5(A) Represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions.

Objective: By the end of class, students will apply their knowledge of ratios, unit rates, proportions, and measurement conversions to a series of complex problems in order to create a series of problem solving steps that can be used on the unit test.

27 AIM: How are ratios, unit rates, proportions, quantitative and qualitative reasoning, and measurement conversions used to solve a variety of problems?

Do Now: Complete the warm-up problem for the day.

[Share Out] Connect: Todayâ€™s class will be focused on reviewing the topics covered in unit 5. These topics include ratios, unit rates, measurement conversions, quantitative and qualitative predictions, and multiple representations. Students will work collaboratively to recall the information and practice using a variety of different types of problems.

Independent Learning Task: Students will be given a review packet during class but will not be responsible for completing the entire thing during the class period. Each student will work with a pair to complete a specific set of problems. Each pair will have one problem from each section of the review to complete. Each group will have a completely different set of problems and will be responsible for teaching their set to the class.

Students will be required to use manipulatives, drawings, and any other tools they find helpful when solving their problems. They will record their process for all 5 problems on

28 chart paper, drawing or writing anything and everything they do, and then sharing their strategies with the class. Each pair will be responsible for responding to other studentsâ€™ questions about their problems and they must work together to enhance each otherâ€™s understanding. The teacher will only intervene when absolutely necessary.

Discussion/Share Out: Student pairs will share their answers and processes for arriving at those answers with the entire class. They will be required to use manipulatives and other tools when solving their problem sets.

Assessment: Students will complete their review packet at home and use it to study for the test on Friday.

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Unit 5 Review 1. Kelly paid $36.50 for 10 bracelets last week. This week, she needs 18 more bracelets. If the price is the same, how much will she pay for the 18 bracelets?

2. Jake’s backyard is 20 feet long by 14 feet wide. What is the ratio of the width of his yard to the perimeter of the yard?

3. Martha earns $10 per hour babysitting. Her brother earns 5 more per hour than Martha. What is the ratio of the money Martha earns in an hour to the money her brother earns in an hour?

4. Five pounds of pineapples cost $15.35 at the market. What is the unit price of the pineapples in dollars per pound?

5. Marcus travels 480 miles with 16 gallons of gas in his truck’s gas tank. What is the unit rate?

6. For an Art project, Belle is recording how much paint she uses every day. On Monday, she used 0.32 gallons of paint. What fraction of a gallon of paint did she use for the painting on Monday?

7. Determine which pair of ratios are NOT equivalent ratios. Justify your solution. 2 15 24 ∧22 ∧3 ∧8 6 a. b. 12 c. 27 66 4 9 8. If 5 dozen eggs cost $23.75, how much would 4 dozen eggs cost?

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9. A plane travels 1124 miles in 2 hours. At this rate, how many hours will it take the plane to travel 2810 miles?

10. William drinks 2 gallons of water every soccer game. How many cups of water does William drink at each soccer game? 11. Jace bought 5.75 yards of wood at the lumberyard. How many feet did Jace buy at the lumberyard?

12. Of 50 cupcakes at the bakery, 36% have purple icing. What is the total number of cupcakes with purple icing at the bakery?

13. Erika plays softball and gets a base hit 46% of the time she is at bat. What fraction represents the base hits Erika hits when she is at bat?

14. Monique spends 45% of her 24 our day at work. How many hours does Monique spend working? Use the percent part to show your work.

15. Lexi shaded in the number of units in her room that she will use as her office. What decimal and percent of her room will not be used as part of her office?

31

32

Lesson Plan-Day 4: Party Time Created by: Ashley Harmon Materials: Kool aid mix, water, construction paper, markers, Popcorn, M&Mâ€™s Standard(s): 6.4(B) Apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates 6.4(C) Give examples of ratios as multiplicative comparisons of two quantities describing the same attribute. 6.4(D) Give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients 6.4(E) Represent ratios and percentâ€™s with concrete models, fractions, and decimals. 6.4(H) Convert units within a measurement system, including the use of proportions and unit rates 6.5(A) Represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions. Objective: By the end of class students will be able to apply ratios and unit rates in real life situations. AIM: If I am planning a birthday party how will I be able to make enough of each item for all of my guests?

Do Now:

33 Write about a time when you used ratios to help you complete a task.

[Share Out] Mini Lesson Connect: Today I need help throwing a surprise birthday party for my niece. How many people have ever had to throw a party for someone, or even themselves, and felt really overwhelmed? Well thatâ€™sh677 exactly how I am feeling today! I have broken the tasks up and am going to assign everyone a task to complete. There will be 4 people working collaboratively on each task.

Model: We will start to work through one problem together on the boardâ€”this should be a review.

You-try-it: Have them complete the problem on their own.

Independent Learning Task:

34 The class will be broken down into groups of 5-6. Each group will have their own specific task to complete for the birthday party. They will work together to solve the task and to make the final product. Group 1- Party Punch Group 2- Sâ€™mores Chex mix Group 3- Name cards Group 4- Gift bags

Discussion/Share Out: Once the class is done making their products each team will have a chance to share what they did.

Assessment: Students will be assessed on their calculations they made in order to complete the given task.

35

Group 1- S’mores Trail Mix S’mores Trail Mix Ingredients:

Ingredients Mini Marshmallows Teddy Grahams Mini Pretzels M&M’s

Amount for 5 people 1 cup 2 cups 1 cup 2 cups

6. What is the ratio of Marshmallows to mini pretzels?

7. What is the ratio of Teddy Grahams to Marshmallows?

8. What is the ratio of M&M’s to mini pretzels?

9. If there are 10 people coming to the party how many cups of M&M’s are needed? What about 20 people?

36 10. There are 60 people coming to Addison’s party and we need enough trail mix for everyone. How much of each ingredient do I need in order to feed all 60 guests? Ingredients

Amount for 60 people

Mini Marshmallows Teddy Grahams Mini Pretzels M&M’s 7. It takes Addison’s mom 30 minutes to make enough trail mix for 60 people. How long would it take her to make trail mix for 5 people?

Group 2- Name cards Name Cards

Each guest needs a name card placed at his or her seat. The dimensions for one name card are 200mm X 200mm.

6. I only have a centimeter ruler to measure out the dimensions for each card. What are the dimensions of each card in centimeters?

37 7. If I have a piece of construction paper that measures 60cm X 60 cm how many cards can be made from one sheet of paper?

8. If there are 60 guests coming to the party how many sheets of construction paper do I need in order to make all 60-name cards? 9. It took me 45 minuets to complete all 60-name cards. How many seconds did it take me to finish all 60?

10. How many seconds would it take to make: a. 45 name cards?

b. 20 name cards?

c. 1 name card?

Group 3- Gift Bags Gift Bags

Each bag contains the fallowing:

2 pencils 1 container of bubbles 3 suckers

38

2 packs of mini M&M’s

5. What is the ratio of suckers to pencils in one gift bag?

6. What is the ratio of M&M’s to everything in the bag? Write it as a fraction in simplest form.

7. What is the fraction of bubbles in one bag?

8. How many of each item will be needed to fill 60 gift bags? Items

Amount needed for 60 bags

Pencils Bubbles Suckers Mini M&M’s Bags

7. The gift bags come in packages of 6. How many packages to I need to buy in order to have enough for everyone?

39 8. The total cost for all the packages is $22.50. How much does each package of bags coast? How much would it coast to buy two additional packages of bags? Group 4-Party Punch Party Punch Punch recipe:

Ingredients:

Amount for 15 people

Lemon Lime Soda

1 liter

Pineapple Juice

16 ounces

Hawaiian Punch

2 liters

4. What is the ratio of lemon lime soda to Hawaiian punch?

5. What is the ratio of pineapple juice to Hawaiian punch?

40 6. There are 60 people coming to the birthday party how much of each ingredient is needed to make enough punch for everyone? Ingredients:

Amount for 60 people

Lemon Lime Soda Pineapple Juice Hawaiian Punch

5. It took Sarah 10 minuets to make one batch of punch that feeds 15 people. If Sarah has to make enough punch for all 60 guests how much time should she plan to make punch?

Each group will also be responsible for filling out the form below:

4. How many students are in the class today?

5. How much of each ingredient do you need in order to have enough of your product for everyone?

6. Make your grocery list below (include amounts):

Take your grocery list to the teacher and she will give you what you need if the amounts are correct. If they are not correct she will send you back to your group to rework the

41 problem. Once you have your ingredients you will use the above information to produce the product for the class.

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Lesson Plan-Day 5: Unit 5 Test Created by: Ashley Harmon Materials: Test Standard(s): 6.4(B) Apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates 6.4(C) Give examples of ratios as multiplicative comparisons of two quantities describing the same attribute. 6.4(D) Give examples of rates as the comparison by division of two quantities having different attributes, including rates as quotients 6.4(E) Represent ratios and percentâ€™s with concrete models, fractions, and decimals. 6.4(H) Convert units within a measurement system, including the use of proportions and unit rates 6.5(A) Represent mathematical and real-world problems involving ratios and rates using scale factors, tables, graphs, and proportions.

Objective: By the end of class students will demonstrate their understanding of ratios, unit rates, quantitative and qualitative observations, proportions, and measurement conversions.

Independent Learning Task: Students will have the entire class period to complete their unit 5 test. The test will assess students over all the topics discussed in the last three weeks of class.

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Assessment Data and Graphs: I was only able to obtain data from my first day teaching, Tuesday November 17th. On this day students were working on furthering their understanding of measurement conversions and proportions. I had students complete and turn in a proportion evaluation. This evaluation assessed studentsâ€™ ability to set up and solve correct proportions in order to convert measurements from one unit to another unit. The differences between grades in 1st and 2nd period were drastic. In 1st period, the majority of students earned an F on this assignment. In total, 19 out of the 25 students in 1st period scored at or below 60 (F) on this assessment. Out of the remaining 6 students 2 scored between a 60 and 69 (D), 3 scored between a 70 and 79 (C), and 2 scored between an 80 and 89 (B). There were not any students in 1st period to reach and A, 90 or above on the proportion evaluation. In contrast, 2nd period had 7 students score between a 90 and 100 (A), 8 students score between a 80 and 89 (B), 12 students score between a 70 and 79 (C), 2 students score between a 60 and 69 (D), and only one student scored below a 60 (F). Between the two classes, a total of 55 students, 7 students earned an A, 10 students earned a B, 15 students earned a C, 4 students earned a D, and 20 students earned an F (figure 6).

44 Figure 6: Proportion Evaluation Grades 20

A B C D F

15 10 5 0

1st period

2nd period

Total

When the data is broken into males and female we can see that there are a full range of grades for both males and females. Overall, there are fewer females than males therefore there werenâ€™t as many scores to consider for the females. The majority of females scored either a C or a D while the majority of males scored a D. The rest of the data for males and females were very similar in numbers without any drastic changes between the two (figure 7). Figure 7: Total Male Vs. Female Proportion Evaluation 14 12 10 8 6 4 2 0

A B C D F

Male

Female

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Reflection/Re-teach: Tuesday: On Tuesday my students were extending their knowledge on measurement conversions and proportions. They had previously learned, on Monday, how to set up conversion problems and how to cross multiply using proportions, so Tuesday was meant for a review and to practice implementing the procedures with multiple types of problems. I did not have the freedom to plan this day using my own creativity; instead I simply had to implement the plans that Mrs. Longoria had already constructed. I could not deviate from her plans because the district was also enforcing that particular teaching method. During the 1st period class I did not get to teach at all. I simply observed Mrs. Longoria while she took over the entire class. It felt like another normal day in my CTâ€™s class. By the time 2nd period rolled around I was really discouraged and quite concerned about if I would actually be able to teach at all that day. However, to my surprise, Mrs. Longoria allowed me to teach the entire 2nd period. Despite the fact that I had to do exactly what Mrs. Longoria did in 1st period I was extremely excited and ready to take on the task. I opened the class up with going over a worksheet they had started the day before. Instead of simply giving them the answers I decided to make it an interactive activity where multiple students came to the board and showed their work for a particular problem. I think this allowed students to be engaged in what was going on and not simply listening to me deposit information into their brains. I noticed that there were many students volunteering to come to the board and share, even students who are typically very quite and shut off from the rest of the classroom. I also noticed that the more the students would verbalize their explanations and reasoningâ€™s the more they would catch

46 their own mistakes and correct themselves. This process of self-evaluation allowed the students to create a concrete understanding of conversions and proportions. From here we moved on to a second worksheet. This worksheet was redundant with what they had done the previous day and even on the previous worksheet. I gave the students eight minutes to complete the worksheet alone. Mrs. Longoria told me not to go over the problems that they were simply doing it to complete it and to get extra practice. With that being said, after the eight minutes were over I gave the students yet another worksheet. Before allowing them to begin this worksheet I went over the expectations for the remainder of the class period. The students received a proportion evaluation that would be taken for a quiz grade at the end of class. They were expected to work independently without any talking or communicating to one another. I had a student read the CHAMPS for a quiz/test environment and then I fallowed up by reiterating there was to be no talking or getting out of their seats. Overall, I feel like I had pretty good control over the students and they were receptive to the expectations. Students worked diligently and completed the evaluation worksheet before class was over. This was the last thing planned for the students so once they finished they could read a book or sit quietly until the bell rang. Overall I think I did well given the circumstances. If I had it to do over again with all the same stipulations, the guidelines from Mrs. Longoria, the only thing I would do differently is implement a discussion after completing the measurement conversion worksheet. I would have students share their responses to the questions and discuss the methods used with the class. If I could do it without the stipulations implemented by my CT I would change everything about the lesson. I would have developed a more

47 interactive lesson that allowed students to think and create on their own, giving them freedom in education. I would not have used worksheets, instead they would have had an exploration guide that went along with the daily activity and an exit ticket would have been their assessment for the day. I feel like too much time was spent on worksheets and not enough time was spent of learning and understanding. After reviewing the grades on the assessment I feel that the teaching style chosen by Mrs. Longoria did not meet the needs of her students. The scores were very low in both morning periods and it is extremely concerning to me. Based on the data I would assume that the students that make up 1st and 2nd periods are more hands on, active learners. With that being said I think that worksheets are not the way to go with these students. They need space and freedom to explore the concepts. They are not absorbing what is being told to them and they cannot regurgitate the information forced inside their brains. This lesson was missing what I believe are very key components. It was missing a concrete and a pictorial element. Like I said, I would have liked to have opened the lesson with some type of hands on experiment. Something that took away all the vocabulary and numbers and simply portrayed the concept. From there I would have used some type of pictorial to go even further into the concept. This could have been in the form of a video, image, diagram, etc. After these two components were implemented within the classroom, I would have introduced the vocabulary, equations, and numbers. The worksheets would have come last if I had had the opportunity plan this lesson using my own creativity. Thursday: I was scheduled to implement my authentic assessment, which also served as a review for the unit 5 test, on Thursday. However, I received a message from

48 Mrs. Longoria on Wednesday evening saying they needed more time for the review that was handed out in class on Wednesday so I would not be able to teach what I had planned. I was still under the impression that I would be allowed to lead the review session in class the next day. However, I did not get to do that either. My role on Thursday was like every other observation day. I circulated the classroom and helped students when needed. Unfortunately, I did not get to obtain any data from the Thursday class and there is not anything to reflect on due to the fact that I did not get to teach.

49 Women of Mathematics When you think about the history of mathematics, which is the first person that comes to mind? Many people are quick to throw out names such as Euclid, Isaac Newton, or even Albert Einstein. While these men were all very influential in the development of mathematics, we are missing a huge group of mathematicians that contributed just as much, female mathematicians. Women of math do not get recognized often and it is a common misconception that only males impacted mathematical history. Female mathematicians hold an important part in the development of mathematics. Starting October 6, 2015 every student in Mrs. Longoriaâ€™s 6th grade math classes will be responsible for researching a historical, female mathematician. The purpose of this research project is designed to enlighten students on the achievement of women and uncover the diversity within mathematics. For this project, students will work in pairs to complete the fallowing: 1. Students will pick a female mathematician to research. 2. Once they have made a selection you will obtain the following information about your chosen mathematician: a. When and where was she born and raised. b. How she came to be involved in mathematics. c. When, where, and how long did she attend school. d. Important milestones involving the advancement in her mathematical career. e. What made her influential in mathematics (inventions, discoveries, etc).

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3. After students have obtained the information above they will be responsible for presenting it in a creative and unique way. Some examples of this would include a poem, song, blog, website, etc. I ask that students stay away from the traditional forms such as PowerPointâ€™s or essays. Students will need at least two sources from which they obtain their information. This could include websites, books, magazine articles, etc. They must be cited and turned in on a sheet of paper with the project. This project will be due on Tuesday, October 13, 2015

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Women of Mathematics Rubric Category Information ____/5

Resources _______/2

Creativity ________/3

Total ____/10 Notes:

Below Expectations None of the appropriate information is provided. Student did not create a presentation. (0 points) Student did not use/provide any resources for the project. (0 points) Student did not create a presentation. (0 points)

Developing Student created a presentation of the information containing 2 facts about the mathematician. (1 point)

Student created an unorganized presentation that did not have any uniqueness or creativity. (0.5 points)

Meets Expectations Student created a presentation of the information containing 3-4 facts about the mathematician. (3 points) Student used/provided one resource for the project. (1 point) Student created a presentation that was more traditional but had some creative and unique touches (color, pictures, etc.). (2 points)

Exceeds Expectations Student created a presentation that contained all 5 of the mandatory fact about the mathematician. (5 points) Students provided both resources required for the project. (2 points) Student created a presentation that was original and expressed a lot of uniqueness and creativity. (3 points)

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Pedagodic creed

Published on Mar 12, 2018

Educational beliefs with unit plans and individual lesson plans

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