Thematic Unit Plan: Fractions · Lesson 7: Fractions (Word Problems) -----Page 19 Lesson 8:...

1

Thematic Unit Plan: Fractions

Brianna Boisture Mary VanderLaan

Molly Visel SAT 495, SEC 01

2

Table of Contents Lesson 1: Fractions Introduction------------------------------------------------------------------Page 3 Lesson 2: Baking With Fractions-----------------------------------------------------------------Page 6 Lesson 4: Classroom Fractions--------------------------------------------------------------------Page 9 Lesson 5: Fractions (Multiplying Fractions with Whole Numbers) -------------------------Page 11 Lesson 6: Fractions (Multiplying Fractions with Mixed Numbers) -------------------------Page 14 Lesson 3: Slavery in the United States through Fractions-------------------------------------Page 17 Lesson 7: Fractions (Word Problems) -----------------------------------------------------------Page 19 Lesson 8: Division with Fractions----------------------------------------------------------------2 Lesson 9: Fractions Jeopardy Game-------------------------------------------------------------Page 26 Appendix A Exit Card Worksheet on Introduction to Fractions ----------------------------Page 29 Appendix B Baking With Fractions Worksheet-----------------------------------------------Page 30 Appendix C Subtracting Worksheet ------------------------------------------------------------Page 31 Appendix D Multiplying Fractions by Whole Numbers Worksheet------------------------Page 32 Appendix E Multiplying Fractions by Mixed Numbers Worksheet-------------------------Page 33 Appendix F Slavery in the United States Worksheet-----------------------------------------Page 36 Appendix G Word Problem Worksheet---------------------------------------------------------Page 38 Appendix H Division of Graham Crackers Worksheet---------------------------------------Page 39 Appendix I Exit Card after Jeopardy Worksheet ----------------------------------------------Page 41

3

Unifying Theme: Grade Level: Submitted by:

Fractions (Introduction) 5th Grade

Brianna Boisture, Mary VanderLaan, Molly Visel

Universal Design for Learning:

How have you incorporated UDL into this lesson? This lesson is incorporating several different learning strategies. The students will have the opportunity to learn fractions through visual learning, hands on learning, and auditory learning. When the teacher reads Pizza Counting to the students they will be able to see fractions visually by pictures and auditory by the teacher reading it. The students will use the hands on learning when they participate in the pizza activity. The pizza activity is a great way for the students to understand the basics and be able to relate it to their own life. The students will have the opportunity to form fractions by breaking the pizza up.

Essential Questions: What are fractions used for? Why do we have fractions? What ways do you use fractions in everyday life? What are things to remember when adding and subtracting fractions?

Common Core Standards (Math and Language Arts, GLEs for Science and Social Studies:

CCSS.Math.Content.5.NF.A.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. CCSS.ELA-Literacy. RL.5.1- Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text. CCSS.ELA-Literacy.RL.5.4- Determine the meaning of words and phrases as they are used in a text.

Curriculum Associations:

X Math oScience o English o Social Studies X The Arts o Phys. Ed. X Reading

Achievement Objectives:

-Able to properly write a fraction. -Able to list ways we use fractions in everyday life.

The concepts (Learning intentions)

Students will learn about … (what are the big ideas of your lesson) Students will be introduced to fractions after the reading of ‘Pizza Counting’ by Christina Dobson. This book easily explains what fractions are by relating different fractions to the sizes of pizza slices. After the reading students will gain experience working with fractions by using cut out pizza slices manipulative, and learning the proper way to write fractions. Next the students will be able to make their own fraction pizza slices and really gain an understanding of how a whole object can be broken down into equal pieces. After working with their table members to create whole pizzas by using these pizza slices, they will use these fraction materials to help them in solving a worksheet. This lesson will work the student’s visual spatial skills and help them to become comfortable working with fractions. This introductory lesson is to help them understand the concept of fractions and provide them with useful fraction tools (the pizza slices) to use in future lessons of this unit.

Learning Activities (in order)

What will the students and you do and in what order? The teacher will begin the unit of fractions by reading Pizza Counting by Christina

4

Dobson, which introducing the basics of fractions in a creative and interesting way that relates something known to the students. This book and pizza in general are good tools to use to teach students about fraction. The teacher will challenge and engage the students with the pictures throughout the book and ask questions throughout. After the reading, each table of students will be provided with a bag that includes a paper cut out that represents a pizza along with a couple other paper pieces that must be cut out by the students to represent slices of pieces. The purpose of the paper cut outs is for students to create their own pizzas and to be able to visually see how fractions are broken down. Connecting a difficult topic such as fractions to pizza, a popular food for 5th graders, allows them to make the content meaningful to their lives. The students will be cutting out pre-made stencils to create a whole pizza. An example of this is two halves to make a full, and thirds of a pizza to make a full and so on. The teacher will demonstrate writing the fractions on the first cut out of pieces and the students will be encouraged to write fractions on the other cut outs on their own. After the students have worked with the table to create three whole pizzas, they will be given an addition and subtraction of fractions worksheet to complete independently using their new learning tool. Students will be encouraged to turn to their group mates for help. THE EXIT CARD: To wrap up the lesson, the teacher will pass out a half sheet of paper that includes a fraction and a blank circle representing a pizza. The students will be required to draw the correct representation of the fraction and explain how they came up with that answer. This exit card will assess the students understanding of the lesson. EXTENSION: To extend this activity the teacher will prompt students to think about other ways fractions are involved in their daily life. It is important for the teacher to encourage the students to find examples that do not relate to food and test their creativity.

Resources needed What will you need to teach this unit and what will your students need to be able to learn? -Exit Card worksheet -Pizza Counting by Christina Dobson -Plastic Bag containing paper to be cut out as ‘Pizzas’ that are ready to be cut into specific dimensions. (See link)

- 1/2, 1/3, 1/4, 1/5 printout: http://donnayoung.org/f12/math-f/fractions/2345.pdf - 1/6, 1/8, 1/10, 1/12 http://donnayoung.org/f12/math-f/fractions/681012.pdf

-Writing utensil -Scissors -Spare paper to solve problems -Addition and Subtraction fraction worksheet (See link) Adding Fraction Worksheet: http://www.math-aids.com/cgi/pdf_viewer_3.cgi?script_name=fractions_adding_simple.pl&difficult=0&probs=10&language=0&memo=&answer=1&x=60&y=29 Subtracting Fraction Worksheet: http://www.math-aids.com/cgi/pdf_viewer_3.cgi?script_name=fractions_subtracting_simple.pl&difficult=0&probs=10&language=0&memo=&answer=1&x=152&y=24

Assessment: What will you do to assess student learning? How do these relate to the essential questions? Student learning will be assessed based on the students’ ability to work with their peers to create different fractions by using their fraction materials. This will be to

5

make sure the students are engaged in their learning and working together to solve problems. Students will also be assessed on their ability to use the manipulatives to solve problems on their worksheet. These manipulatives help serve as a visual representation so the students can develop a better conceptual understanding. The student’s worksheet will be graded for completion and correctness.

Assessment Criteria What is your assessment criteria? How will you know they know it? The inference on students’ understanding will be based on the student’s ability to solve the problems on the worksheet correctly and finishing the exit card. The exit card will serve to see if the student can combine all of the knowledge they learned that day and apply it to a specific problem.


Baking with Fractions

5th Grade Brianna Boisture, Mary VanderLaan, Molly Visel

6


How have you incorporated UDL into this lesson?

This lesson incorporates UDL by teaching to your auditory learners through the read aloud. Teaching to your hands on learners through the baking activity, and teaching to your drill and practice learners through the worksheet. This lesson helps all students gain familiarity of working with fractions and confidence working with fractions by the read aloud and the worksheet. Students will also gain a deeper understanding of adding fractions from the baking activity. Here they will be able to visually see the addition process and be able to think of the fractions in a way that is familiar to them and in a way they are comfortable working with.

Essential Questions:

-What are some real-life examples of when you use fractions besides baking? -In what ways does baking incorporate fractions? -When adding fractions, what must you find first? -Can you add fractions that have a different numerator? Can you add fractions that have a different denominator?


CCSS.Math.Content.5.NF.A.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.

CCSS.Math.Content.5.NF.A.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.

CCSS.ELA-Literacy.RI.5.7 Draw on information from multiple print or digital sources, demonstrating the ability to locate an answer to a question quickly or to solve a problem efficiently.

CCSS.ELA-Literacy.RI.5.8 Explain how an author uses reasons and evidence to support particular points in a text, identifying which reasons and evidence support which point(s).

Need some for a different subject


X Math X Science o English o Social Studies o The Arts o Phys. Ed. X Reading


By the end of the lesson the students will be... -Able to make connections from the addition of fractions to the book read aloud, Funny & Fabulous Fraction Stories. -To add fractions using real life experiences and without.


Students will learn about… (what are the big ideas of your lesson)

-The real life examples where fractions can be used. -The addition of fractions through baking/mixing of ingredients.


What will the students and you do and in what order? The teacher will begin the lesson by picking out a math tale out of the book Funny & Fabulous Fraction Stories by Dan Greenberg. This book is full of engaging fraction tales and problems to practice fraction skills. There are many tales to pick from. The teacher will pick a story that he or she feels will engage the students and best meets their interest.

After reading the story to the class the teacher will introduce and teach the concept of addition of fractions. Addition of fractions is difficult because students must understand how to find the least common denominator. The teacher will introduce each part of a fraction, the numerator and denominator. The teacher will explain that in addition problems with fractions, the denominators must be the same number in order to successfully solve them. Once the students have a clear understanding about each part of a fraction, the teacher will write an example problem on the board and solve it while they follow along. After the

Resources needed What will you need to teach this unit and what will your students need to be able to learn?

-Addition of Fractions with Baking Worksheet -Funny & Fabulous Fraction Stories By: Dan Greenberg -Recipe for No Bake Cookies -Dry erase boards and markers.

Assessment:

What will you do to assess student learning? How do these relate to the essential questions?

The teacher will assess the students with an exit card. The exit card will ask the students to write out the steps of solving addition problems with fractions using both words and

7

Assessment:


The teacher will assess the students with an exit card. The exit card will ask the students to write out the steps of solving addition problems with fractions using both words and numbers. This will allow the teacher to check for their understanding and see which students did not fully grasp the lesson taught. This is beneficial for the teacher to see which students need extra practice and where they are struggling. When students are asked to write out their understanding it is more of a challenge.

Assessment Criteria

What is your assessment criteria? How will you know they know it?

Teacher will read the student’s exits cards and see how well they explained each step in solving addition fraction problems. Due to the fact that it is the first assessment after learning about addition of fractions, the teacher will be more lenient and see where the students are struggling. The struggling areas can be readdressed in the following class period.

9


Classroom Fractions

5th Grade Brianna Boisture, Mary VanderLaan, Molly Visel


How have you incorporated UDL into this lesson? This lesson addresses kinetic learners because they are actively taking part in the lesson by using the class to represent the whole and dividing into smaller fractions seeing how the numbers break down visually. This lesson adapts to visual learners because they are able to see the class divide into smaller sections. This lesson also addresses auditory learners because they are able to hear “The class is now divided into halves, thirds, fourths, etc.” By hearing this and seeing this it will help them learn the way fractions are divided.


-What patterns did you notice when the class was divided into fractions? -What must we do when we are subtracting fractions that do not have the same denominator? -How do you reduce a fraction? -Why is it important to reduce fractions?


CCSS.ELA-Literacy.RF.5.4a: Read grade-level text with purpose and understanding

CCSS.ELA-Literacy.RF.5.4c: Use context to confirm or self-correct word recognition and understanding, rereading as necessary CCSS.ELA-Literacy.RI.5.7 Draw on information from multiple print or digital sources, demonstrating the ability to locate an answer to a question quickly or to solve a problem efficiently. CCSS.Math.Content.5.NF.A.1-Add and subtract fractions with unlike denominators by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators.


X Math o Science o English o Social Studies o The Arts X Phys. Ed. X Reading


By the end of the lesson the students will be... -Able to solve subtraction fraction problems on a handout. -Able to solve subtraction fraction problems at a fast speed against classmates. -Able to express thoughts and feels about subtraction fraction lesson with the teacher.


Students will learn about … (what are the big ideas of your lesson) -Students will learn about different ways that we use fractions in everyday life. -Students will learn how to solve subtraction fraction problems.

- Students will learn how to split groups into different fraction sizes.


What will the students and you do and in what order?

The teacher will start off the lesson by inviting the class to come together as a WHOLE and sit in the front of the room by her chair. Throughout the day, we will be splitting into fraction sizes amongst the class. The teacher will reading the book Fraction Fun written by David A. Adler and illustrated by Nancy Tobin. This book a fun way to teach students about fractions being everywhere throughout life and the different ways that we use them all of the time. When we tell time we use fractions, when we count money we use fractions, or even when we eat a slice of pizza. When students are aware of the reasons for using fractions, they are more willing to learn and engage. The teacher will engage the listeners by asking questions about the book throughout, primarily about subtraction of fractions and asking the students if they realized they were using fractions when participating in these particular tasks.

The teacher will then ask the class to split into equal HALVES, depending on the size of the class and if the two groups are equal the teacher may have to join in on the fun. The students will be given a practice worksheet to complete together. This will be beneficial for those that are struggling to learn from those who understand the material. The students will be encouraged to really grasp the material because the next activity is a Fraction Challenge. The winning team, that knows how to solve subtraction fraction problems the best, will receive a prize. The teacher will go over the answers to the problems with the class, checking for understanding and finding out the struggling areas. If needed, the teacher will



The teacher will start off the lesson by inviting the class to come together as a WHOLE and sit in the front of the room by her chair. Throughout the day, we will be splitting into fraction sizes amongst the class. The teacher will reading the book Fraction Fun written by David A. Adler and illustrated by Nancy Tobin. This book a fun way to teach students about fractions being everywhere throughout life and the different ways that we use them all of the time. When we tell time we use fractions, when we count money we use fractions, or even when we eat a slice of pizza. When students are aware of the reasons for using fractions, they are more willing to learn and engage. The teacher will engage the listeners by asking questions about the book throughout, primarily about subtraction of fractions and asking the students if they realized they were using fractions when participating in these particular tasks.

The teacher will then ask the class to split into equal HALVES, depending on the size of the class and if the two groups are equal the teacher may have to join in on the fun. The students will be given a practice worksheet to complete together. This will be beneficial for those that are struggling to learn from those who understand the material. The students will be encouraged to really grasp the material because the next activity is a Fraction Challenge. The winning team, that knows how to solve subtraction fraction problems the best, will receive a prize. The teacher will go over the answers to the problems with the class, checking for understanding and finding out the struggling areas. If needed, the teacher will practice the difficult problems together.

The teacher will bring the class back together as a WHOLE in the front of the room and ask the students to split up into equal FOURTHS (or whatever works best with your class size). This will create small groups for the students to work with. The groups will become their Fraction Team for the Fraction Challenge. The students will split into their groups and find a table to work at. The game will consist of the teacher writing out problems on the board for the teams to solve. The team that solves the problem the fastest and correctly will win that round. There will be a total of 10 rounds (problems) or until at least each student answers two problems. The students can look to their teammates for a hint when struggling with a problem. The purpose of this game is for the students to practice their skills in solving subtraction fraction problems, this game will help to build their confidence in solving. The winning team will be allowed to pick a prize from the Mystery Bucket.

As an exit card, the students will share with the teacher on a provided piece of paper how they felt the day went working with subtraction fraction problems. The students will be encouraged to be honest and share their thoughts.


-Fraction Fun written by David A. Adler and illustrated by Nancy Tobin -Handout on subtraction of fractions -Markers to write on the whiteboard -Dry erase boards and markers for the students -Three by five cards for exit card activity -Mystery Bucket

Assessment:


The teacher will incorporate a variety of assessment throughout the lesson. The teacher will check for understanding by asking Fraction Fun. The questions will relate to subtraction of fractions along with how fractions are used in everyday life. The teacher will wander around the classroom while the students are completing the handout to help in assisting those who are struggling. After completion of the handout, it will be turned into the teacher. The teacher will then check the students work and answers to see if they are understanding how to solve correctly. The teacher will read over the exit cards to see the student’s thoughts about the day spent practicing subtraction of fractions, this will provide the teacher with information about how well the lesson went and how successful it was.

Assessment Criteria


The teacher will know that the students have a clear understanding of the material by

10


Fractions (Multiplying Fractions with Whole Numbers)

5th Grade Mary VanderLaan, Brianna Boisture Molly Visel



This lesson is incorporating several different learning strategies. The main ones that are being incorporated are auditory learning, hands on learning, and visual learning. The students will start off by using auditory learning by listening to the teacher. Then the students will use hands on learning when they are forming their own slices of brownies. The students will also be allowed to work in groups and with their table members if they need help solving the problems. This will help students who need to discuss the material a chance to help verbally work out their thought process. Not every student is the same; this means we might need to explain the information differently to a student who is having a harder time understanding the material.


What portion of the brownie picture represents the brownies that are not eaten? What fraction of the brownie tray has not been eaten? What must we do with the improper fraction once we solve this problem?


CCSS.Math.Content.5.NF.B.4A- Interpret the product (a/b) x q as parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q divided by b. For example use a visual fraction model to show (2/3) X 4 = 8/3 and create a story context for this equation. Do the same with (2/3) X (4/5) = 8/15. CCSSM.Math.Content.5.NF.B.4b - Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same, as it would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

CCSS.ELA-Literacy.RF.5.4a: Read grade-level text with purpose and understanding

CCSS.ELA-Literacy.RF.5.4c: Use context to confirm or self-correct word recognition and understanding, rereading as necessary.


✓ Math Science English Social Studies ✓ The Arts Phys. Ed. ✓ Reading


By the end of this lesson students will be able to: - Multiply a fraction by a whole number.

- Demonstrate pictorially or visually what is being multiplied.


Students will learn about … (what are the big ideas of your lesson)

-Students will learn that there are different ways of doing fractions -Students will learn the steps to multiply a fraction by a whole number

- Students will learn different ways of representing the problems: pictorially or visually.


What will the students and you do and in what order? The teacher will begin the lesson by asking the students what in our everyday lives can be used to represent fractions. After writing out a short list together on the board. The teacher will share a short story about how she baked brownies for her sister’s birthday and ask the students if brownies could be used to represent fractions. After listening to the student’s responses, the teacher will provide the students with materials to represent a couple trays of brownies. The teacher will demonstrate the fraction 2 x ½ in front of the class using the brownie cut outs to help solve the equation. The teacher will engage the students by asking questions along the way and having them guide her.

Example questions: -What does the two represent in this problem? Answer: The two trays of brownies. -What does the ½ represent? Answer: Half of each tray. -What does the shaded portion of the square represent? Answer: What is missing.

-What does the non-shaded portion of the square represent? Answer: The leftovers.

The teacher will write a new problem on the board for example 3 x ¾. She will ask

the students how many brownie trays they will need to represent this problem, Once the students come to the correct answer of 3, the teacher will pass out 3 pieces of paper to each group of students, that represent the 3 brownie trays. The teacher will then ask the students how they will represent ¾ on the brownie trays. After all of the students have come to an agreement on how to cut the brownie trays into ¾, they will draw it out onto the brownie trays they have been given. The students will be given the option to shade or write a letter on each fourth that represents ¾. The teacher will ask a volunteer to share the number shaded in vs. the number of non-shaded pieces. This will help students grasp an understanding of how the brownies help solve the problem. The teacher will constantly be walking around the room to check for understanding of the problem.

The teacher will write a third problem on the board for the students. She will tell the students to come up to the front of the room and grab the materials needed, number of brownie trays. The students will be given the option to work independently or with a partner. Once the class seems to be finishing up, the teacher will bring the class back together to go over the problem.

The teacher will hand out a worksheet to work on other problems that are very similar but a little more complicated to challenge them. They will be encouraged to use tools with either draw them out or use the cubes to help represent the problems. During this time the teacher will be walking around to help the students out by answering their questions.


-Medium sized construction paper to represent brownie trays. -Worksheet consisting of whole fraction multiplication problems.

Assessment:


Summative assessment will be used throughout the lesson by asking the students the

11

Assessment:


Summative assessment will be used throughout the lesson by asking the students the essential questions such as: What portion of the brownie picture represents the brownies that are not eaten? What fraction of the brownie tray has not been eaten? What must we do with the improper fraction once we solve this problem? If students are able to answer these questions correctly that shows that they have somewhat of an understanding of multiplying whole fractions. Working on problems with their group will also assess the students, the teacher will wander around the classroom to assist and check for understanding. The teacher should pay attention to how the students are using the brownie trays to help solve the problems. Lastly, a worksheet will be provided at the end of the lesson that the students will begin working on and possibly finish for homework. This worksheet will allow the teacher to see the students work and if they correctly solved the problems.

Assessment Criteria


The students will be assessed on answering the essential questions. Explaining and talking out why and how you do something is always a challenge and will test their understanding. The teacher should look at the student’s ability to use the brownie trays as a helpful tool but should not penalize students for not using it. Students learn in a variety of ways and may have other techniques for solving the problems. The worksheet will provide the teacher with evidence of how well the student understands multiplying fractions with whole numbers based on the number of correct answers, the teacher must look over the students work and should consider asking the student to explain how they found each answer.

12 Unifying Theme: Grade Level: Submitted by:

Fractions (Multiplying Fractions with Mixed Numbers) 5th Grade

Brianna Boisture, Molly Visel, Mary VanderLaan


How have you incorporated UDL into this lesson? This lesson is incorporating several different learning strategies. The main ones that are being incorporated are auditory learning, hands on learning, and visual learning. The students will start off by using auditory learning by listening to the teacher. The students will engage in hands-on learning through group activity. The group activity will allow the students to get out of their seats and work their way through some easy and difficult multiplication of mixed fraction problems. The students will also be allowed to work in groups and with their table members if they need help solving the problems. This will help students who need to discuss the material a chance to help verbally work out their thought process. Not every student is the same; this means we might need to explain the information differently to a student who is having a harder time understanding the material.


What daily real life examples can you think of that could be a fraction multiplied by a mixed number? What are the steps to solving a problem of a fraction multiplied by a mixed number?


CCSS.Math.Content.5.NF. B.5 Interpret multiplication as scaling (resizing), by: -CCSS.Math.Content.5.NF.B.5a: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

-CCSS.Math.Content.5.NF.B.5b: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 is a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number and relating the principle of fraction equivalence a/b= (n x a) / (n x b) to the effect of multiplying a/b by 1.


✓ Math Science English Social Studies ✓ The Arts Phys. Ed. Reading


By the end of this lesson students will be able to: • Covert mixed fractions into improper fractions. • Simply fractions to the lowest form. • Multiply fractions with mixed numbers.


Students will learn about … (what are the big ideas of your lesson)

• Students will learn an effective method for converting a mixed number into an improper fraction.

• Students will learn the steps to multiply mixed fractions.



The teacher will begin the lesson by reminding the students of what was taught in class on Monday, multiplying fractions with whole numbers. During that lesson the students were challenged to work with improper fractions, which will again happen in this lesson. The teacher will teach the 3 main steps of solving a multiplication of mixed fractions problem. These steps should be a review of what the students have been learning in the classroom. The teacher will write an example problem on the board and invite the students to try solving it. Once the students feel comfortable they will engage in a classroom activity.

The classroom activity will allow the students to get out of their seats and move from

each cluster of desks to complete multiplication of mixed fraction problems. Some problems will be more challenging than others. The students will be encouraged to work with their classmates at the table. Once the students finish a problem, they will move on to the next. There will be a total of four problems for the students to complete. After completing all four problems, the students will be asked to return to their seats until everyone is finished and as a class they will discuss the answers.

To end the lesson, the teacher will hand out a worksheet for the students to work on individually before the class period ends. This will challenge the students to see if they understand the proper steps to multiply mixed fractions. For those students who do not complete the worksheet in class will be asked to finish for homework.


• Four sheets of construction paper with a multiplication mixed fraction problems on

each for the class activity. • Worksheet consisting of mixed number (fraction) multiplication problems.

Assessment:


Summative assessment will be used throughout the lesson by asking the students the essential questions such as: -What daily real life examples can you think of that could be a fraction multiplied by a mixed number? -What are the steps to solving a problem of a fraction multiplied by a mixed number? If students are able to answer these questions correctly that shows that they have somewhat of an understanding of multiplying mixed fractions. Working on problems with their group will also assess the students, the teacher will wander around the classroom to assist and check for understanding. The teacher should pay attention to each step the students are taking in order to solve the problems. Lastly, a worksheet will be provided at the end of the lesson that the students will begin working on and may possibly need to finish for homework. This worksheet will allow the teacher to see the student’s progress and check if they correctly solved the problems.

Assessment Criteria


The students will be assessed on answering the essential questions. Explaining and talking out why and how you do something is always a challenge and will test their understanding. Students learn in a variety of ways and may have other techniques for

13

solving the problems. The worksheet will provide the teacher with evidence of how well the student understands multiplying fractions with mixed fractions based on the number of correct answers, the teacher must look over the students work and should consider asking the student to explain how they found each answer.

14


Slavery in the United States through Fractions 5th Grade




This lesson incorporates UDL by having three different levels of worksheets. The first worksheet helps students who might struggling with this content and decoding the information. It is more taking the numbers and plugging them in, it does not require as much critical thinking/ The second worksheet is for the advanced students because it requires higher reading abilities and has more critical thinking. The problems are not as directed. The third worksheet is for students who are in between these two phases. They are not yet advanced, but they are up to beat with the content.


-What were the slaves on your plantation daily lives like? -How large was your plantation compared to some of your classmate’s. -Where was your plantation located? Can you show this on a map?


5-U2.2.2: Describe life of enslaved Africans and free Africans in the American Colonies.

5-U2.3.4: Describe development of the emerging labor force in the colonies (e.g.: cash crop farming, slavery, indentured servants)

-CCSS.Math.Content.5.NF.B.5a: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication.

-CCSS.ELA-Literacy.RF.5.4c: Use context to confirm or self-correct word recognition and understanding, rereading as necessary.

-CCSS.ELA-Literacy.RL.5.4- Determine the meaning of words and phrases as they are used in a text.


X Math o Science o English X Social Studies o The Arts o Phys. Ed. X Reading


By the end of this lesson students will be:

-Show on a map where their plantation was located. -Understand how fractions can be taken out of informational text. -See how plantations were ran and gain a better understanding of their size and what happened on plantations. -Develop a deeper understanding of what a slave’s life was like. When fractions are related to amounts of people understand that decimals cannot exist and numbers must be rounded to the nearest whole number.


Students will learn about … (what are the big ideas of your lesson) -Daily lives of slaves -Plantations and their size, location, and purpose -Learn what information this required for each problem -The importance of rounding in certain situations.


What will the students and you do and in what order? Yesterday in Social Studies class we talked about slavery in Colonial America. Today we are going to relate what we learned to math with fraction word problems. There will be three different groups with different passages from different plantations. After reading the different passages with your group there will be questions to follow. These questions are to be done independently, but you may ask your group members questions along the way if you have questions. Hand out the worksheets (the worksheets are made for different math and reading


What will the students and you do and in what order? Yesterday in Social Studies class we talked about slavery in Colonial America. Today we are going to relate what we learned to math with fraction word problems. There will be three different groups with different passages from different plantations. After reading the different passages with your group there will be questions to follow. These questions are to be done independently, but you may ask your group members questions along the way if you have questions. Hand out the worksheets (the worksheets are made for different math and reading ability. Worksheet 1 is for students who struggle in both categories. Worksheet 2 is for students who need a challenge in both categories. Worksheet 3 is for students who are average learners. This allows everyone to finish around the same time.) Once the students are done have them come up with their group members a list of things they learned from their passage that they would want to share with their classmates. This will take about 5 to 10 minutes. Then start with Group 1 discussion because they have the least amount of information. Then have the other two groups follow. Write the information on the board so all the students can see the information.


-Slavery in Colonial America fractions word problem worksheets; Group 1, Group 2, Group 3. -Classroom Map -Pen or Pencil -Calculator (In case some students are having issues with multiplying the fractions.

Assessment:


The teacher will be grading the worksheets for an in class participation grade. You want to make sure students understand fractions by grading their work. An exit card will be used to check their understanding on what they read and what others present about their plantation. Exit card: What was one thing you found interesting about a plantation other than yours? What was one thing you found interesting about your plantation?

Assessment Criteria

What is your assessment criteria? How will you know they know it? Students will be assessed on their knowledge based on their ability to complete their assigned worksheet correctly. The main focus is their understanding of how to apply their knowledge of multiplying fractions and use it in this lesson. Even though the students will be given only a participation grade it is important that they know how to solve these problems appropriately. The exit card will be used to gain more insight on what the students learned historically from this lesson and how much it impacted them.

16


Fractions (Word Problems) 5th Grade

Molly Visel, Mary VanderLaan, Brianna Boisture



Having the students show a picture of how they solved the problem incorporates UDL. Also at the beginning of class we will run through a few word problems together, allowing any auditory learners the chance to listen in on the material and add to their understanding. Students will be engaged in the discussion allowing group work and the exchanging of ideas and information. The students will engage in a classroom worksheet in which they will be challenged to draw fractions pictorially, this will incorporate hands-on learning for the students.


How can we tell what a practice problem is asking? What are keywords to look for? Can you write out in a number sentence what the problem is? Can you visually represent what the problem is asking?


-CCSS.Math.Content.5.NF.A.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 -CCSS.Math.Content.5.NF.B.4A- Interpret the product (a/b) x q as parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q divided by b. For example use a visual fraction model to show (2/3) X 4 = 8/3 and create a story context for this equation. Do the same with (2/3) X (4/5) = 8/15.

-CCSS.Math.Content.5.NF.B.5b: Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 is a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number and relating the principle of fraction equivalence a/b= (n x a) / (n x b) to the effect of multiplying a/b by 1. -CCSS.Math.Content.5.NF.B.5a: Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. -CCSS.ELA-Literacy.RF.5.4c: Use context to confirm or self-correct word recognition and understanding, rereading as necessary.

-CCSS.ELA-Literacy.RL.5.4- Determine the meaning of words and phrases as they are used in a text.


✓ Math ✓ Science ✓ English ✓ Reading o Social Studies o The Arts o Phys. Ed.



-Able to list ways we use fractions in everyday life. -Able to decode what a word problem is saying and rewrite the problem in a number sentence. -Visually or pictorially represent what a problem is asking. -Able to write their own word problems involving fractions

17



-Able to list ways we use fractions in everyday life. -Able to decode what a word problem is saying and rewrite the problem in a number sentence. -Visually or pictorially represent what a problem is asking. -Able to write their own word problems involving fractions


Students will learn about … (what are the big ideas of your lesson) -What words in word problems tell us to multiply, subtract, add, or compare.

-Decoding what a problem is asking, and what steps you must need to complete (and show) in order to solve that problem.

-How fractions are used in our everyday lives, and how these word problems could be real

life examples of when to use these mathematical skills.


What will the students and you do and in what order? As a class we will discuss how comfortable we feel with word problems. After learning the student’s perspective I will ask the class to give me a fraction problem. After writing this on the board I will ask them if we can turn this into a word problem. If they are unable to do this I will change it to a word problem. Next, I will ask the class, “how we know what the problem is asking? What keywords give away if the problem is asking us to multiply, add, or subtract?” We will discuss keywords and their meanings to make sure students have a clear understanding of how to decode word problems. We will run through a few word problems on the board and after I feel the students are confident in solving these I will hand out the worksheet. The worksheet will contain word problems related to multiplying a fraction by a mixed number, a fraction multiplied by a fraction, a mixed number multiplied by another mixed number, and addition and subtraction fraction problems. After each word problem there will be a space provided to write what the numerical problem is asking. I plan on having these problems randomized. This will help the students learn to read the sentences carefully so they can solve the problem appropriately. I also plan on having at least one of each fraction problem ask the student to represent the problem pictorially so they can show their conceptual understanding.

Resources needed What will you need to teach this unit and what will your students need to be able to learn? -Writing Utensil -Notebook Paper -Classroom worksheet -Scrap Paper/crayons to show problems pictorially (optional)

Assessment:


Students will be assessed on their ability to solve these word problems and their understanding of keywords that tell the reader what problem they are to be solving. These keywords are essential to know so the students can solve confusing word problems on standardized tests. If the student is able to learn these keywords they will be able to decode what a word problem is asking. Students will have their worksheets checked by an adult to make sure their answer and their numerical problem they gathered from the word problem is correct. Students will also be assessed on their ability to visually represent the problem correctly; this will show their conceptual understanding.

Assessment:


Students will be assessed on their ability to solve these word problems and their understanding of keywords that tell the reader what problem they are to be solving. These keywords are essential to know so the students can solve confusing word problems on standardized tests. If the student is able to learn these keywords they will be able to decode what a word problem is asking. Students will have their worksheets checked by an adult to make sure their answer and their numerical problem they gathered from the word problem is correct. Students will also be assessed on their ability to visually represent the problem correctly; this will show their conceptual understanding.

Assessment Criteria

What is your assessment criteria? How will you know they know it? Students will be assessed on their ability to answer the essential questions. They will also be assessed on their completion, and correct answers on their worksheet. This worksheet will provide the teacher with a clear explanation of how well the students understand the material and their ability to apply their knowledge of fractions to word problems. This will also give the instructor clarity on if they might need to readdress any information from the unit before continuing.

19


Division with Fractions 5th Grade




This lesson addresses many different learning styles. It first helps hands on learners by giving them manipulatives to help them solve problems. This is done by using the Hershey bars or graham crackers to divide fractions. Auditory learners are taken into consideration by reading aloud the Hershey’s Fraction Book and also singing the fraction song about dividing fractions. Visual learners are accommodated by displaying visual representations of the problem being divided. Students who are strong social learners are given the opportunity to work with others during the group work where they must work together to write division word problems. Musically inclined students are also given the chance to learn the content in a way that relates best to them from the dividing fractions song.

Essential Questions: -What is the process of dividing a fraction? -What keywords indicate that a word problem is a dividing fractions problem? -How do you visually represent dividing fractions? -What real life examples can you relate dividing fractions to?


CCSS.Math.Content.5.NF.B.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

CCSS.Math.Content.5.NF.B.7b Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

CCSS.Math.Content.5.NF.B.7c Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

CCSS.ELA-Literacy.RL.5.7 Analyze how visual and multimedia elements contribute to the meaning, tone, or beauty of a text (e.g., graphic novel, multimedia presentation of fiction, folktale, myth, poem).

CCSS.ELA-Literacy.RL.5.1 Quote accurately from a text when explaining what the text says explicitly and when drawing inferences from the text.


X Math o Science o English o Social Studies X The Arts o Phys. Ed. X Reading


By the end of this lesson, the students will... -To divide fractions with whole numbers using the tool of graham crackers or Hershey’s Chocolate Bars. -To divide fractions with whole numbers by reversing the fraction and multiplying across. -To sing the “Division of Fractions Song” to help remember the steps involved.

The concepts (Learning Students will learn about … (what are the big ideas of your lesson)

20

intentions) -The steps for dividing fractions with whole numbers, using a “Division of Fractions Song”. -An effective tool for solving division of fraction problems with whole numbers, which is using graham crackers or Hershey’s Chocolate Bars.


What will the students and you do and in what order? The teacher will start with this quick and simple activity that will teach the students the concept of dividing whole numbers by fractions—using some children’s favorite snacks, Graham crackers (or hershey's chocolate bars). Graham crackers and Hersheys are perfect for this activity because they are easily divided into equal parts…and they are delicious to eat afterward. *Hint: if you use Hershey’s place in freezer beforehand to avoid melting). Hershey chocolate bars can be split into more pieces than graham crackers therefore students that are struggling with fractions may stick to using graham crackers while those excelling can use the Hershey's chocolate bar.

The students will work at their table with their group members, at each table there will be a pile of graham crackers in the center of the table. The teacher will solve an example division problem in front of the class. The problem is 1 divided by 1/2. The teacher will grab one whole graham cracker (or Hershey bar) and explain to the class that this one whole graham cracker (Hershey bar) represents the number 1. If I divide the graham cracker (Hershey bar) in half by bending it down the middle, I now have two pieces. Therefore, 1 divided by 1/2 is 2. The teacher must take this explanation slow to ensure that the students have a clear understanding.

The teacher will pass of a Division of Fractions worksheet. The students will work with a partner to complete the worksheet. First the students will predict the answer to the first problem, for example 2 divided by 1/2. They will write their prediction on the line provided. To find out if their prediction is correct the students will grab 2 graham crackers or Hershey bars because the problem is 2 divided by 1/2, therefore 2 graham crackers or Hershey bars are needed. The students must then divide the graham cracker in half by bending it down the middle, they must do this for both graham crackers or Hershey bars. The next question of the worksheet asks, how many graham cracker or Hershey bar pieces are there now? The student should write down the 4 pieces as their answer. Graham crackers or Hershey's chocolate bars are a great tool to help solve division of fraction problems.

The teacher will explain that there is a way to divide whole numbers by fractions without using graham crackers or Hershey’s chocolate bars. The teacher will introduce the method of solving whole numbers by the fraction. The teacher will put an example on the Smart Board for the whole class to see.

Problem: 1 divided by 1/2; 1 x 2/1 (2 over 1) and multiply across. The teacher will explain that the fraction must be reversed when solving division of fraction problems. Any whole number is equivalent to that number, over 1.

1 x 2/1 = 2 OR 1/1 x 2/1 = 2

The teacher will write 5 problems on the Smart Board for the students to solve on a piece of lined paper, this will help them practice what they have learned without using graham crackers or hersheys chocolate bars.

The teacher will introduce the “Dividing Fractions Song” to help students remember the steps when dividing. Incorporating songs is a great way to engage students and a fun way to remember the steps. The teacher will teach the song to the class, pass out a handout with the song lyrics on it and then the class will sing the song together a couple

21

of times together.

"Dividing fractions, as easy as pie, Flip the second fraction, then multiply."

"And don't forget to simplify, Before it's time to say goodbye"

To conclude this lesson students will work with their group members at their tables to come up with three to five dividing fractions word problems. Once these word problems are written students will raise their hands and the teacher will go around and revise the written problems. Once all groups have three to five revised and approved word problems written they will exchange their problems with another group. (All groups will have equal abilities, by dividing students up of all academic levels.) Once the groups have exchanged their word problems the students will individually solve the word problems given to them. Students will be encouraged to solve their problems correctly by demonstrating their knowledge. This will be done by writing out the number problem they are solving, and showing in at least one problem a visual representation of the problem.


-Hershey Bars (frozen) -The Hershey’s Fraction Book by Jerry Pallotta -Expo markers to write the lyrics of the dividing fractions song on the board -Dry erase board (if not available a projector or chalkboard will work) -Graham Crackers (Whole pieces that can be divided into smaller pieces. -Graham Crackers with Division of Fractions Worksheet -Smart Board to solve example problems in front of the class. -Lined paper and a pencil for the students to solve practice problems and write group word problems. -Dividing Fractions Song Handout -Writing utensil -Extra crayons or colored pencils for students who need color-coded visual representation

Assessment: What will you do to assess student learning? How do these relate to the essential questions?

To conclude this lesson students will work with their group members at their tables to come up with three to five dividing fractions word problems. Once these word problems are written students will raise their hands and the teacher will go around and revise the written problems. Once all groups have three to five revised and approved word problems written they will exchange their problems with another group. (All groups will have equal abilities, by dividing students up of all academic levels.) Once the groups have exchanged their word problems the students will individually solve the word problems given to them. This is where students will be assessed based on their ability to solve the problems correctly. Students will also be assessed on their conceptual understanding by their ability to write out what number problem they are solving, and the ability to give a visual representation of at least one problem they are solving.

Assessment Criteria What is your assessment criteria? How will you know they know it?

22

The teacher will gain inference of the students knowledge by assessing them on their completion and correctness of the material. Teachers will also see the student’s conceptual understanding by their ability to write appropriate word problems for dividing fractions, and the students visual representations to solve these problems. When the teacher is approving of the student’s word problems they will have the opportunity to correct any misunderstandings that arise in the student’s work and help them rephrase their word problems so the problems main ideas are communicated appropriately.

23


Fractions Jeopardy Game 5th Grade




UDL is incorporated into this lesson by allowing students who are hands on learners that kinesthetic movement of writing on the whiteboard, standing up to show they are done solving a problem, and the constant movement to keep their attention and concentration. Students who are musically inclined or auditory learners might like having the Jeopardy Music playing in the background and it might help keep their attention better. Students who are social learners will really enjoy the group work aspect of this lesson and could really enjoy the friendly competition.

Essential Questions: -What are the keywords in a word problem that indicate what process (adding, subtracting, multiplying or dividing) is needed to solve the problem? -How do you add fractions and mixed numbers? -How do you subtract fractions and mixed numbers? -How do you multiply fractions and mixed numbers? -How do you divide fractions and mixed numbers?


CCSS.Math.Content.5.NF.A.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. CCSS.Math.Content.5.NF.B.4A- Interpret the product (a/b) x q as parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a x q divided by b. For example use a visual fraction model to show (2/3) X 4 = 8/3 and create a story context for this equation. Do the same with (2/3) X (4/5) = 8/15. CCSS.Math.Content.5.NF.B.6 Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

CCSS.Math.Content.5.NF.B.7b Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4.

CCSS.Math.Content.5.NF.B.7c Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?


X Math o Science X English o Social Studies X The Arts o Phys. Ed. X Reading


Students will use the prior knowledge they gained in the previous lessons to solve fraction word problems. These word problems will touch on all aspects of fractions (multiplying fractions, dividing fractions, addition of fractions, and subtraction of fractions.) This lessons objective is to review all of these concepts and tests the students’ ability to to work together to efficiently solve these problems.

24


Students will learn about … (what are the big ideas of your lesson) -Fraction problems through the game of Jeopardy. The students will practice their skills to check for understanding. Students will be able to work in groups to help them solve problems more efficiently and also gain more experience solving problems in different ways.


What will the students and you do and in what order? The first part of this lesson is to prep the room. To start this the teacher will instruct the students to take out all of their fraction notes and previous homework. Next, students will push all of the tables and chairs to the perimeter of the room so that there is a lot of space for movement. The teacher will call out the students names and tell them what group they are in. These groups will be groups of 3 and will be broken up so that all abilities are represented in one group. This is to help divide the skill levels so groups are more equal. This will also make the game more competitive and help in evening out the point. Allow the groups to make up a name for themselves. After the groups are made instruct one student from each group to come to the front of the class and get a personal whiteboard and dry erase marker, and share their group’s name with the teacher.

After all the students have gone back to their groups explain the rules. The rules of Fraction Jeopardy are as follows: One member of each group will be the recorder (the one who writes the problem and answer on the whiteboard), Researcher (looks through notes or previous homework for helpful tips to solve the problem), and the Facilitator (the one who keeps the group on task and helps where he/she is needed.) Group roles are rotated after every problem. Once a group is done solving the problem they will stand up and remain standing until the teacher comes to check their work. The teacher will come to the groups based on the order of who solved the problem first, second, and so on. If the first group to solve the problem got the answer right they will receive the full amount of points for their work. After that the remaining groups who solved the problem correctly will receive half the amount of points the problem was worth. If a group does not get the answer correct they will receive no points. The first team to solve the problem correctly will also be given the privilege of picking the next question. The teacher will keep track of the points on the whiteboard.

To start the game the teacher will put on the ‘Jeopardy thinking music’ and pull up the game board. The teacher will read out the categories and start the game by choosing a 100 point question of their choice. After all of the problems have been solved the teacher will then hand out a worksheet that has four 500 point questions on it. These questions will be word problems from each category. Each student is required to complete the worksheet on their own. In this worksheet they must choose two problems to display a visual representation.

Resources needed What will you need to teach this unit and what will your students need to be able to learn? -Jeopardy Music http://www.youtube.com/watch?v=rTyN-vvFIkE -Dry erase boards and markers at least one for each group -Exit card worksheet -Game: jeopardylabs.com/play/fractions1067

25

Assessment: What will you do to assess student learning? How do these relate to the essential questions? The game of Jeopardy is a great way to assess students over a large topic such as fractions. It is a fun, engaging game that will help students practice their skills with fractions and work on teamwork with their classmates. Aside from the game of Jeopardy to assess students understanding of fractions, the teacher will provide the students with a writing activity to complete. This writing activity will ask the students three different questions, the first question will be “Explain what you have learned about fractions?” The second question will be “What have you found most interesting about fractions?” The third question will be “Is there anything regarding fractions that you are or have struggled with, if so, what? Please explain.” These questions will help the teacher gauge the students understanding, what they really took away from the unit and what they may have struggled or are struggling with.

Assessment Criteria What is your assessment criteria? How will you know they know it?

Based on the students’ scores the teacher will be able to see if teams were able to efficiently solve problems, this will indicate their confidence in the material. Also, by having the teacher check the student’s work after each question she is able to see if there are any misunderstandings or recurring problems that any groups might have. The writing activity will be based on completion and be used as a way to judge how effective the teacher’s instruction has been and what areas they might need to go over before the exam for the student’s benefit and understanding.

26

Appendix A Name: _______________________________ Date_______________________

Exit Card: Draw a picture to show the problem and answer 3/5 + 1/5 =

5/6- 2/6 =

27

Appendix B Name: ____________________________ Date_______________

Baking With Fractions

No Bake Cookies Recipe: Makes 3 Dozen 1 3/4 Cups white sugar 1/2 Cup Milk 1/2 Cup Butter 4 Tablespoons unsweetened cocoa Powder 1/2 Cup Crunchy Peanut Butter 3 Cups Quick-cooking oats 1 teaspoon vanilla extract Directions In a medium saucepan, combine sugar, milk, butter, and cocoa. Bring to a boil, and cook for 1 1/2 minutes. Remove from heat, and stir in peanut butter, oats, and vanilla. Drop by teaspoonfuls onto wax paper. Let cool until hardened.

Today boys and girls we are going to try and help Julie make some no bake cookies. Along the way we are going to make sure she added the right amount of each ingredient so she ends up with delicious cookies. 1. The first thing she did was add 1/2 cups of milk to 1/2 cup of butter. How many cups of ingredients should she have after adding those together? She ended up with 1 cup. Is this right or wrong? why (Explain with showing your work) Is she right? (Circle one) YES or NO Your Work:

2. The next thing she did was add the 1 3/4 cups of white sugar to the 1/2 cups of milk and 1/2 cups of butter. How many cups of ingredients should she have after adding those together? She ended with 3 3/4 Cups. Is this right or wrong? Why (Explain with showing your work) Is she right? (Circle one) YES or NO Your Work:

3. The Final step she wants to check is when she added 1/2 cup of crunchy peanut butter and the 3 cups of Quick-cooking oats. How many cups of ingredients should she have after adding everything together minus the unsweetened cocoa Powder and vanilla extract? She ended with 6 1/4 Cups. Is this right or wrong? Why (Explain with showing your work) Is she right? (Circle one) YES or NO Your Work:

28

Appendix C Name:____________________________ Date:_________________________

Subtracting Fractions

1.) 5 1 2.) 2 1 3.)8 1 10 5 4 2 10 3 4.) 9 1 5.) 3 1 6). 2 2 10 2 5 10 3 4 7.) 3 1 8.) 6 2 9.) 3 1 5 10 10 5 5 2

29

Appendix D Name: ___________________________ Date:_______________________

Multiplying Fractions by Whole Numbers

1. I have 5 brownies of 1/3 (Hint I gave you enough boxes) Answer:__________________

2. I have 2 brownies of 5/8 Answer:_______________________





7. Bonus: I have 8 brownies of 11/16 Answer:_______________________

30

Appendix E Name: _______________________ Date:______________________ Group One

Oaks Plantation in Colbert County, Alabama

At the Oaks Plantation in Colbert County, Alabama held approximately 300 slaves. These slaves worked anywhere from 14-18 hours a day and 6 days a week. The slaves, mainly from Africa, were brought to America to harvest tobacco, sugar, and cotton to feed the consumer needs in the growing Western World. In mid August the slaves started to pick the cotton on the plantations. The life of the slaves is definitely not an easy task. Approximately seven-eighths of the slaves will get up before the sun has risen to be on the fields to start picking the crops when the sun comes up. An ordinary day's work is two hundred pounds. When it is pitch black out the slaves are allowed to leave the fields. They do not get to rest quite yet though because they have chores still to do. Approximately three fifths of the slaves feed the animals and pick up after them. Another one fifth of the slaves cut wood. The rest of the slaves do odds and ends around the plantation. After the chores are all finish the slaves are worn out and go to bed to rest for the next day. 1. Approximately how many slaves are on the fields picking cotton? (number not fraction) Answer:______________________ 2. Approximately how many slaves are not on the fields picking cotton? (number not fraction) Answer:_______________________ 3. Approximately how many slaves are feeding the animals? (number not fraction) Answer:______________________ 4. Approximately how many slaves are cutting wood? (number not fraction) Answer: ______________________ 5. How many slaves are not cutting wood or feeding the animals? (Fraction) Answer: ______________________ 6. If the Slaves are not picking cotton what might they be doing all day long? Answer:___________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 7. What might happen if the slaves do not meet their quota for the day on how much they need to pick. (One Word) Answer ____________________ Answer Key: 1. 262.5 So except 262 or 263 Slaves 2. 37.5 So except 37 or 38 Slaves 3. 180 Slaves 4. 60 Slaves 5. ⅕ of slaves are not feeding the animals or cutting the wood. 6. Answer may vary. They might be working in the house, be a driver, or etc. 7. Punished

31

Name:_________________________ Date:____________________ Group Two

McLeod Plantation in Charleston County, South Carolina

At the Mcleod Plantation in Charleston County, South Carolina held approximately 74 slaves in 26 dwellings. These slaves worked anywhere from 14-18 hours a day and 6 days a week. They would have Sundays off unless it was during harvest times. The slaves, mainly from Gambia River region of Africa, were brought to America to help with the primary crops of beef, indigo, rice and long-staple sea cotton. The process of making blur die from indigo plants made slaves sick and many died of cancer. During the growing season the slaves on the rice plantations moved through the fields in a line, hoeing rhythmically and singing work songs to keep in unison. There was approximately five-sevenths of the slaves in the fields working. At harvest time the women processed the rice by pounding it in large wooden mortars and pestles, virtually identical to those used in West Africa, and then "fanning" the rice in large round winnowing baskets to separate the grain and chaff. After the sun was down they still had work to do on the farms. One-third of the workers feed the animals and picked up after them. Another one fifth cut wood. The rest of the workers did other jobs around the plantation. There were a few workers who were lucky and were able to work in the house. Most house slaves were living under better conditions than field workers. Approximately one-tenth of the slaves on the plantation were house slaves. However, house slaves did not get Sunday off and usually attended church with the master and mistress. House slaves cleaned, cooked, served meals, and took care of the children. Some house slaves lived in attics, closets, or corners in the big house even if their families lived in the quarters. Out of the 8 slaves living in the house one-fourth of slaves lived in the closest and the other three-fourths lived in the attic . 1. Approximately how many slaves are on the fields picking cotton? Answer:_____________________ 2. Approximately how many slaves are not on the fields picking cotton? Answer:_____________________ 3. Approximately how many slaves are feeding the animals? (Hint: 8 of the slaves were house workers, so they did not take part in this) Answer:_____________________ 4. Approximately how many slaves are cutting wood? (Hint: 8 of the slaves were house workers, so they did not take part in this) Answer:_____________________ 5. How many slaves are not cutting wood or feeding the animals? (Hint: 8 of the slaves are house workers, so they did not take part in this.) Answer:______________________ 6. How many slaves on the plantations were house slaves? Answer:______________________ 7. How many of the house slaves lived in the attic? Answer:______________________ Answer Key: 1.) 52.85 so except 53 slaves 2.) 21.14 so except 21 or 22 slaves 3.) 24.66 so except 24 or 25 slaves 4.)13.2 Except 13 or 14 slaves 5.) 22 slaves 6.) 8 slaves 7.) 6 slaves

32

Name: ______________________ Date:__________________ Group 3

Lake Jackson Plantation in Brazoria County, Texas At the Lake Jackson Plantation in Brazoria County, Texas held approximately 285 slaves. These slaves worked anywhere from 14-18 hours a day and 6 days a week. The slaves, mainly from Africa, were brought to America to harvest tobacco, sugar, and cotton to feed the consumer need in the growing Western World. Slaves also cleared and prepared farmland and communities. In the urban areas, life was a little better, as they worked more as domestic than in the fields, but they were still considered the property of their owners. In mid August the slaves started to pick the cotton on the plantations. The life of the slaves is definitely not an easy task. Approximately seven-eighths of the slaves will get up before the sun has risen to be on the fields to start picking the crops when the sun comes up. An ordinary day's work is two hundred pounds. When it is pitch black out the slaves are allowed to leave the fields. They do not get to rest quite yet though because they have chores still to do. Approximately one-fifths of the slaves feed the animals and pick up after them. Another three-fifth of the slaves cut wood. The rest of the slaves do odds and ends around the plantation. After the chores are all finish the slaves are worn out and go to bed to rest for the next day. Not all the slaves work on plantations. Some slaves work in mariners. They worked on the ships and the docks. 1. Approximately how many slaves are on the fields picking cotton? (Number not fraction) Answer:______________________ 2. Approximately how many slaves are not on the fields picking cotton? (Number not fraction) Answer:_______________________ 3. Approximately how many slaves are feeding the animals? Answer:______________________ 4. Approximately how many slaves are cutting wood? Answer: ______________________ 5. How many slaves are not cutting wood or feeding the animals? (Fraction) Answer: ______________________ 6. What is one thing you learned today after reading this passage? Answer:___________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 7. What task would you like to do if you were a slave? and why? Answer:___________________________________________________________________________________________________________________________________________________________________________________________________________________________________ Answers: 1. 249.375 so except 249 or 250 slaves 2. 35.625 so except 35 or 36 slaves 3. 57 slaves 4. 171 slaves 5.1/5 of slaves are not feeding the animals or cutting wood 6. Answers will vary 7. Answers will vary

33

Appendix F Name:____________________________ Date:__________________

Fraction Word Problems

Note: In 2 of these problems you must show a picture of how the problem could be solved.

1. Terry and Jane are collecting cans for a can drive. Jane collected 1/2 as many cans as Terry did. If Terry collected 1/2 of a bag of cans, how many bags of cans did Jane collect? Numerical Problem: _______________________

2. On Wednesday the farmers at the Johnson’s Farm picked 3/5 of a barrel of potatoes. Thursday, the farmers picked 4/5 as many potatoes as on Wednesday. How many barrels of potatoes did the farmers pick on Thursday? Numerical Problem: ____________________

3) The cattle at the Mack’s Farm are fed 5/8 of a bale of hay each day. The horses are fed 1/2 as much hay as the cattle. How many bales of hay are the horses fed each day? Numerical Problem: ___________________________

4) Isabela rode her bike for 2 1/2 miles on Thursday. On Friday, she biked 4 1/3 times as far as on Thursday. How many miles did Isabela bike on Friday? Numerical Problem: _____________________

5) The seals at the John Ball Zoo are fed 2 1/5 buckets of fish each day. The sea otters are fed 3/5 as much fish as the seals. How many buckets of fish are the sea otters fed each day? Numerical Problem: ________________________

6) Last week, Greg’s Chocolate Shop sold 3 1/2 ounces of white chocolate. It sold 3 1/2 times as much milk chocolate as white chocolate. How many ounces of milk chocolate did Greg’s Chocolate Shop sell? Numerical Problem: ________________________

34

7) Larry's chocolate chip cookie recipe calls for 2 4/5 cups of sugar. How much sugar would Larry use to make 2 1/2 batches of cookies? Numerical Problem: _____________________ 8) Jamar and Ellen each made a bowl of punch. Ellen used 3 1/3 times as much lemonade as Jamar did. If Jamar used 3 2/3 cups of lemonade, how many cups of lemonade did Ellen use? Numerical Problem:_______________________________

35

Appendix G Name: Date:

Multiplying Fractions with Mixed Numbers

1. 1 ⅜ x ½=

2. 3 ½ x ⅔=

3. 1 ½ x ⅘=

4. 3 ¼ x ⅓=

5. 2 ⅕ x 1 ⅖=

6. 4 ½ x 3 ⅔=

36

Appendix H Name: ____________________ Date: ___________

Division of Fractions with Graham Crackers

1. 1 ÷ ½ = Prediction of Answer: ___________ Grab the appropriate amount of graham cracker(s) from the middle of the table and break it into the necessary amount of pieces. How many graham cracker pieces are there now? _________ Final Answer: __________ 2. 2 ÷ ½ = Prediction of Answer: ___________ Grab the appropriate amount of graham cracker(s) or Hershey bar(s) from the middle of the table and break it into the necessary amount of pieces. How many graham cracker or Hershey bar pieces are there now? _________ Final Answer: __________ 3. 1 ÷ ¼ = Prediction of Answer: ___________ Grab the appropriate amount of graham cracker(s) from the middle of the table and break it into the necessary amount of pieces. How many graham cracker pieces are there now? _________ Final Answer: __________ 4. 3 ÷ ¼ = Prediction of Answer: ___________ Grab the appropriate amount of graham cracker(s) from the middle of the table and break it into the necessary amount of pieces. How many graham cracker pieces are there now? _________ Final Answer: __________ 5. 4 ÷ ½ = Prediction of Answer: ___________ Grab the appropriate amount of graham cracker(s) from the middle of the table and break it into the necessary amount of pieces. How many graham cracker pieces are there now? _________ Final Answer: _________

37

Dividing Fractions Song

"Dividing fractions, as easy as pie,

Flip the second fraction, then multiply." "And don't forget to simplify,

Before it's time to say goodbye"

38

Appendix I Exit Card Worksheet: Name:_______________________ Date:_____________________ 1. 5 3/8 + 2 8/9 2. 6 3/7 - 4 1/8 3. 3 2/5 X 5 3/7 4. 8 1/7 5 2/3

Thematic Unit Plan: Fractions · Lesson 7: Fractions (Word Problems) -----Page 19 Lesson 8:...

Documents

Transcript of Thematic Unit Plan: Fractions · Lesson 7: Fractions (Word Problems) -----Page 19 Lesson 8:...