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EDUC 351 Unit Plan: Adding, Subtracting, and

Multiplying FractionsFifth Grade

By, Madison Dixon-Schwabl

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Table of Contents:

Common Core Standards………………………………………………….Pg. 3

Enduring Understandings and Essential Questions……………………….Pg. 3

Rationale…………………………………………………………………..Pg. 4

Objectives Overview……………………………………………………...Pg. 5

Unit Calendar……………………………………………………………..Pg. 6-25

Day 1……………………………………………………………...Pg. 6-7

Day 2……………………………………………………………...Pg. 8-9

Day 3: Untaught Lesson……………………………………..........Pg. 10-14

Day 4……………………………………………………………...Pg. 15-17

Day 5: Second Taught Lesson……………………………………Pg. 18-21

Day 6: First Taught Lesson……………………………………….Pg. 22-25

Day 7-10: Performance Task…………………………………......Pg. 26-37

Reference List…………………………………………………………….Pg. 38

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In this unit plan the following are included and will be addressed:

1. Common Core Standards for Mathematics:

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

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

CCSS MATH CONTENT 5. NF 4. Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

CCSS MATH CONTENT 5.NF.B.4.a Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.)

2. Enduring Understandings: Fractions can be used to aid in explaining real world problems. Adding and subtracting fractions with unlike denominators through word problems is an

important strategy in solving real world problems. You must find common denominators when adding fractions. Multiplying fractions by fractions is useful when finding part of a whole. Multiplying fractions by whole numbers can result in a fraction or mixed number. Multiplying fractions as well as whole numbers by fractions can be used in everyday life

situations.

3. Essential Questions: Why is addition and subtraction of fractions the best operation for certain situations? What does it mean to add and subtract fractions? Why is multiplication of whole numbers and fractions the best operation for certain

situations? What does it mean to multiply whole numbers and fractions?

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http://www.corestandards.org/Math/Content/5/NF/A/2/

Rationale:

The introduction of fractions is very important as fractions are used in everyday life. There are countless ways that we use fractions during a typical day that many do not realize. Since fractions relate to real life students are encouraged and typically more interested in learning about them. Fractional concepts are also important building blocks of elementary school mathematics curriculum. After learning about fractions students are able to use this concept and apply it to more advanced mathematics.

In this unit, students will learn about how to solve addition, subtraction, and multiplication of fractions as well as fractions and whole numbers. The lessons included in this unit plan helps to reach the diversity, compassion, knowledge, and service standards (DASKS) of the Social Justice philosophy. Regarding diversity, fractions can be seen and used around the world. This demonstrates diversity because all people will understand this concept and more than likely use it on a day to day basis. Since many of these lessons call for students to work together either as a group or in pairs to complete worksheets or other certain tasks compassion is shown through their team work. When they share information in a collaborative setting they not only benefit from understanding the concept but their group members also benefit as they might be learning something they did not know before. Knowledge will also be expanded throughout this unit plan as many of the lessons include having students solve problems in their own ways, and as many as they can come up with, first and then reviewing the problem as a class with the teacher instruction. Since students have the ability and freedom to choose what ways of solving the problems make sense to them as well as learn the correct way of how to solve each problem they will be gaining a further understanding of fractions. The service aspect of this unit is that students will be able to take their learnings and understandings of fractions into many different careers and professions. Since fractions are everywhere there are a range of jobs that require the skill of knowing and being able to work with them such as an engineer, baker, architect, etc.

All of the lessons included in this unit plan are geared towards introducing students to fractions all the way to having them complete a final performance task where they will produce an outcome. This achievement aspect of this unit plan will really give these lessons purpose and interest for the students. It will teach them the importance of adding, subtracting, and multiplying fractions and encourage them to use these skills they gain to be successful in not only this task but all other tasks that involve fractions in everyday life as well.

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Objective Overview:

Day 1: Objective:SWBAT explain the details in a fraction by naming the parts of a fraction.

Day 2: Objective: SWBAT find common denominators in fraction addition problems.

Day 3: Objective: SWBAT add and subtract fractions using common denominators.

Day 4:Objective: SWBAT review and know how to add and subtract fractions with unlike denominators.

Day 5: Objective: SWBAT multiply whole numbers and fractions and demonstrate their understanding through an assessment.

Day 6: Objective: SWBAT multiply fractions successfully and be able to demonstrate their understanding.

Day 7: Objective: SWBAT demonstrate their understanding of unit lesson objectives by multiply whole numbers by fractions.

Day 8: Objective: SWABT demonstrate their understanding of unit lesson objectives by multiplying whole numbers by fractions and adding fractions with unlike common denominators.

Day 9: Objective:SWBAT demonstrate their understanding of unit lesson objectives by multiply whole numbers by fractions.

Day 10: Objective: SWBAT demonstrate their understanding of all unit lesson objectives by applying mathematical fractions to a real life situation using a detailed sketch and write up that they will present.

Day 1: Introduction of parts of fractions CCS Standards Connection: 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

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Unit Calendar:


reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

Objective: Students will be able to explain the details in a fraction by naming the parts of a fraction.

Students will be able to simplify fraction solutions.

Materials: Mini M&M packs (enough for each student)

M&M worksheets Math Journals Pencils

Learning Activities: 1. First the teacher will use a chart, whiteboard, or Smartboard and write “numerator/denominator”. 2. The teacher will explain what the numerator of a fraction is and what the denominator of a fraction is. 3. The teacher will explain that today’s activity will include the class finding numerators and denominators of fractions. 4. The teacher will hand out a packet of M&M’s and the M&M worksheet to each student. 5. The teacher will ask the students to count how many M&M’s they have in total in their package and they will write this number accordingly in the square that’s labeled “total number of M&M’s in my bag”. 6. Next, the teacher will instruct the students to fill in the number of each color M&M they have in their bags in the boxes labeled with each color. 7. After the students find the number of each color M&M they have they will turn these numbers into fractions. Hint to the students that the total number of M&M’s in their bag is the denominator and see if they can figure out the numerator. 8. After all fractions are recorded ask the students to add two of the colors together. 9. If they need assistance on adding these fractions inform them that since you are already working with a common denominator

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you only have to add the numerators. Assessment: PLAN: Students will answer a problem

involving adding fractions of like denominators as they did today in class. TOOL: “If I had 6 M&M’s total and I have 2 red and 3 blues what fraction of my M&M’s are red and/or blue?” EVALUATION: The teacher will be able to determine if the students have a conceptual understanding of adding fractions with like denominators if they get the answer of 5/6.

Day 2: Common Denominators CCS Standards connection:

Objective:

Materials:

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Learning Activities: First students will each be given a hundreds board and 2 different colored counters (5 of each color). The teacher will explain to the students that they are going to find common denominators among fractions today. The teacher will begin the lesson by showing students two fractions that are to be added together. Explain to the students that the idea is to find a multiple that the two denominators have in common so that they can be added together. Explain the directions to the students by telling them to use one color of the counters for the first denominator on the hundreds board and the other colored counter for the second denominator on the hundreds board. Tell the students to find the first 5 multiples of the first denominator and then the first 5 multiples of the second denominator. Keep the counters on the board. The first number that is covered by 2 counters is the common multiple that you are looking for. Keep a list on the board as you find common multiples. Make sure the students understand that when one denominator is a multiple of the other, then the least common multiple is the larger number.

After playing a few rounds of this game give the students the following word problem to work on independently: In Michelle’s closet 1/2 of her shirts are pink and ¼ of her shirts are blue. What fraction of Michelle’s shirts are either pink or blue?

Give the students 5-10 minutes to figure this problem out on their own and then come back together as a class to review the answers they came up with. At this time explain to the students the correct way of finding common denominators to solve this problem.

Assessment: PLAN: Using the hundreds boards students will be asked to complete a word problem involving finding common denominators. TOOL: Students will work this word problem out on their papers and show complete work: You go out for a long walk. You walk 3/4 mile and then sit down to take a rest. Then you walk 3/8 of a mile. How far did you walk altogether? EVALUATION: Students who were able to find common denominators for these fractions and add correctly will be judged to have accomplished the objective.

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Day 3: Adding and Subtracting Fractions *See untaught lesson*CCS Standards Connection: Objective: Materials: Learning Activities: Assessment:

Untaught lesson: Adding and Subtracting Fractions:

Understanding by Design Template: Lesson Planning Block III

Teacher: Madison Dixon-Schwabl Grade: 5

Subject: Untaught Lesson Math/Health Date: 2015

Desired ResultsCCSS and/or NYS Learning Standards (Rubric Line 35 and 39):

Common Core – Standards for Mathematical Practices #1Make sense of problems and persevere in solving them.

Common Core – Standards for Mathematical Content – 5.NF: Multiplication and division of fractions.

.5.NF.A.1

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Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.).5.NF.A.2Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7, by observing that 3/7 < 1/2.

NYS Learning Standards for Health, Physical Education, Family and Consumer ScienceStandard 1: Personal Health and Fitness

Personal Health and Fitness Students will have the necessary knowledge and skills to establish and maintain physical fitness, participate in physical activity, and maintain personal health

Essential Questions (Rubric Line 36):Why is addition and subtraction of fractions the best operation for certain situations?What does it mean to add and subtract fractions?

Enduring Understandings(Rubric Line 36):Students will understand that…Addition and subtraction of fractions is useful in a variety of everyday situations. How to use addition and subtraction of fractions to solve word problems.

Objectives (Rubric Line 31):Students will be able to add and subtract fractions through reasoning, thinking, and understanding. Students will be able to explain how to add and subtract fractions using the diagrams.

Assessment Evidence (Rubric Line 32)Performance Tasks:For assessment I will present the following problem and ask students to explain the “mathematical way” of solving in their math journals.

Sally, Joe, and Callie are making cupcakes. Each person has a different color of frosting. Sally has pink frosting and she is decorating 2/8 of the cupcakes. Joe has blue frosting and he is decorating 3/5 of the cupcakes. Callie has purple frosting and will be decorating the cupcakes that are leftover. How many cupcakes will have purple frosting? Please show your work and use diagrams to help you.

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Scoring Rubric (to be used on the material they write in their math journal):

Low Medium High

Correctness of Answer

10 pts

Incorrect answer given Correct answer given

Accuracy of Explanation

10 pts

Explanation leads to incorrect answer if followed exactly

Explanation includes some unclear or ambiguous steps that may or may not lead to the correct answer

Explanation leads to correct answer when followed exactly

Other Evidence:

Areas of Child Development (Rubric Line 28)

Cognitive development is supported because children learn to make sense of how to add and subtract fractions with unlike common denominators what that means. Linguistic development is supported because children must explain their thinking about addition and subtraction of fractions with unlike common denominators to the teacher and to one another. Social development is supported because children must work together and must ensure that their classmates understand their ideas about addition and subtraction of fractions with unlike common denominators.

Learning PlanClassroom Arrangement:Get all the materials ready ahead of time.Prepare the opening problem on an overhead or computer screen or flip chart ahead of time. Have all students in their seats or outside in a circle (depending on weather)

Materials: Math journals Pencils White board or Smart board Playground (optional)

Learning/Instructional Activities (Rubric Lines 29, 33, 34, 39):

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Anticipatory Set (Rubric Line 38): If the weather allows and there are limited distractions I will have the lesson take place outside near the playground of the school to stimulate interest in the lesson. At this time I will also ask the students what they do to get exercise. Answers may range from sports, running around, playing on the playground, etc.

OR

If weather does not allow for the class to be outside, I will display a picture of a playground on the Smartboard to get the students attention. Also, at this time I will also ask the students what they do to get exercise. Answers may range from sports, running around, playing on the playground, etc.

Procedure Story Problem (Rubric Line 40):

A school wants to make a new playground by cleaning up an abandoned lot that is shaped like a rectangle. They give the job of planning the playground to a group of students. The students decide to use 1/4 of the playground for a basketball court and 3/8 of the playground for a soccer field. How much is left for the swings and play equipment?

Students will work to solve the problem in as many ways that makes sense to them. When they have come up with their own ideas/solutions I will let them partner up with a classmate. Together, they will share each of their understandings and how they found the answer. I will ask students to try to come up with another way to find or understand the problem/answer with their partners if they still have time.

When all groups have found at least one way, I will call on selected groups to share with the class their way of solving. I will call on two or three different groups to share.

I will then present the mathematical way of solving this type of problem: adding and subtracting fractions.

I will first write this problem on the Smartboard or white board so that all students can see it. *1/4 + 3/8

I will make the point that we first need to find common denominators because when we add fractions we have to have the same whole.

I will ask students what common denominators, if any, that they found. I will go through this step by writing out the multiples of 4 and the multiples of 8. I will

remind the students that when we find the same number for both the multiples of 4 and 8 that becomes our least common denominator and that’s what we want to use.

After we conclude that the least common denominator for these two fractions is 8 we will rewrite the fractions:

*¼ becomes 2/8 because you multiply the numerator and denominator both by 2 and 3/8 stays the same.

I will explain to the students that now that we are working with the same whole we can add

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the numerators (2 and 3) and keep the denominator the same. I will work out the problem by adding 2 and 3 so the numerator becomes 5 over the

denominator (the whole) 8. After getting the answer 5/8 I will ask if anyone knows what we do from here. The response

of subtract the whole (8/8) by 5/8 because we are looking for the amount of space there is available for a swings and other play equipment. We already know that in total 5/8 of the playground is already taken up with a basketball court and a soccer field.

8/8 - 5/8 = 3/8 The goal is that students can complete the following sentence or something like it: “There is

3/8 of the playground left for swings and other play equipment after factoring in the space that is already being used for a basketball court and soccer field”.

The relation to health and fitness was covered in the anticipatory set. (This is an evaluation-level question from Bloom’s Taxonomy.)

DIFFERENTIATION: Since students are encouraged to solve “in whatever way makes sense to them,” differentiation is built in to this lesson design. Students will choose their preferred method. During direct instruction, accommodations will be made for students who have hearing or vision difficulties by making appropriate technologies and/or materials available to them. Students with IEP’s will receive individual help to ensure that their goals are being met.

ASSESSMENT: Pose the assessment question, “Sally, Joe, and Callie are making cupcakes. Each person has a different color of frosting. Sally has pink frosting and she is decorating 2/8 of the cupcakes. Joe has blue frosting and he is decorating 3/5 of the cupcakes. Callie has purple frosting and will be decorating the cupcakes that are leftover. How many cupcakes will have purple frosting? Please show your work and use diagrams to help you”.

Closing Activity: I will end the lesson by playing this kids Zumba exercise video from YouTube https://www.youtube.com/watch?v=Q4PYNK9tDxM

This will encourage students to exercise in a fun and engaging way and teach them that exercise is important for staying healthy! Students will be welcomed to dance along with the video as a form of exercise and I will discuss why and tips on how to exercise with them after.

Evaluation of Teaching *done after the lesson is taught*:

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https://www.youtube.com/watch?v=Q4PYNK9tDxM

Day 4: Review Adding and Subtracting Fractions with unlike denominators CCS Standards Connection: .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. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

Objective: Students will review and be able to add and subtract fractions with unlike denominators.

Materials: Computers or laptops for each student Adding and Subtracting Fractions worksheet Pencils

Learning Activities: 1. The teacher will introduce the lesson by explaining that today will be a review of yesterday’s conceptual understandings of adding and subtracting fractions. 2. Students will be reminded to keep the idea of finding common denominators while solving the problems. 3. The teacher will have the students long onto the computers and sign into the following website: http://www.softschools.com/math/games/fractions_practice.jsp4. On this website students will have the opportunity to solve problems in an interactive way involving adding and subtracting fractions with both like and unlike common denominators. 5. After students have practiced on the computers for about 15-20 minutes (depending on how much practice the teacher thinks they need with it) they will log off.

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http://www.softschools.com/math/games/fractions_practice.jsp


6. The teacher will then hand out an adding and subtracting worksheet (attached on the next page) to all of the students which they will complete independently or with one other partner.

Assessment: PLAN: After they hand in the adding and subtracting worksheet the students will be asked to complete one more problem. Their answer to this problem will indicate to the teacher if they have the conceptual understandings necessary for this topic. TOOL: The teacher will post the following question on the board and students will be asked to complete the problem and explain every step they took to solve it and why they took those steps: “A cake recipe calls for ¼ cup of sugar and 2/5 cup of flour. Altogether, how much sugar and flour will be needed for this recipe? Please explain each step that you take to complete this question in full detail!”EVALUATION: The teacher will have an understanding of who grasps this concept of adding and subtracting fractions and who still needs more time on it by grading the explanations and answers to the above question. If students answer correctly with thorough explanations of each step they took including finding common denominators and then adding the numerators but keeping the denominator the same and why you do this then they will be marked as acceptable. If students answer incorrectly with incomplete explanations of the steps they took to solve this problem then they will be marked not acceptable and will get more practice on this topic.

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Adding and Subtracting Worksheet (to be completed independently or with one other partner):

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Day 5: Multiplying Whole Numbers by Fractions

*See second taught lesson*

CCS Standards Connection:

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Objective: Materials: Learning Activities: Assessment:

Second Taught Lesson: Multiplying Whole Numbers by Fractions:



Subject: Lesson Plan 2 - Math/Health Date: 2015







Elementary Health Education Key Idea #1: Students will understand human growth and development and recognize the relationship between behaviors and healthy development. They will understand ways to promote health and prevent disease and will demonstrate and practice positive health behaviors.

Essential Questions (Rubric Line 36):Why is multiplication of whole numbers and fractions the best operation for certain situations?What does it mean to multiply whole numbers and fractions?

Enduring Understandings(Rubric Line 36):Students will understand that…

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Multiplication of whole numbers and fractions is useful in a variety of everyday situations.

Objectives (Rubric Line 31):Students will be able to multiply whole numbers and fractions through reasoning, thinking, and understanding. Students will be able to explain how to multiply fractions using the diagrams.

Assessment Evidence (Rubric Line 32)Performance Tasks:For assessment I will present the following problem and ask students to explain the “mathematical way” of solving in their math journals.A factory puts 1/2 of a gallon of milk into each batch of ice cream. How many gallons of milk will be used in 6 batches?Scoring Rubric (to be used on the material they write in their math journal):

Low Medium High


10 pts Incorrect answer given Correct answer given


10 pts Explanation leads to incorrect answer if followed exactly



Other Evidence:Exit ticket: Have students create their own word problem using multiplying whole numbers by fractions with a complete sentence explaining their understanding of the concept.

Areas of Child Development (Rubric Line 28)Cognitive development is supported because children learn to make sense of how to multiply whole numbers by fractions and what that means. Linguistic development is supported because children must explain their thinking about multiplication of whole numbers and fractions to the teacher and to one another. Social development is supported because children must work together and must ensure that their classmates understand their ideas about multiplication of whole numbers and fractions.

Learning PlanClassroom Arrangement:Get all the materials ready ahead of time.Prepare the opening problem on an overhead or computer screen or flip chart ahead of time. Have all students in their seats.

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Materials: Math journals Pencils White board or Smart board Ice cream ingredients (optional) Empty ice cream cartons (alternative to above option)

Learning/Instructional Activities (Rubric Lines 29, 33, 34, 39):Anticipatory Set (Rubric Line 38): Make homemade ice cream quickly in front of the class! It takes only about 5 minutes. Have frozen fruit of your choice (bananas, strawberries, etc.), milk, and honey (optional). Begin to blend the ingredients together which will grab the attention of the class. Hand out small cups or bowls of the ice cream and explain that ice cream will be today’s topic! *Make a point that making homemade ice cream with the ingredients listed is a healthier alternative for a refreshing snack or dessert then regular ice cream with added sugars and other unhealthy ingredients*

If making ice cream is not an option, you could place different cartons of empty ice cream in front of the class and ask them how much milk they think is used for each different sized carton. *In this case you can still explain to your students that making your own ice cream from scratch and with healthy ingredients is a better alternative for a snack or dessert compared to buying processed ice creams with added unhealthy ingredients. Procedure Story Problem (Rubric Line 40): A factory is trying to figure out how much milk they will need for a certain amount of batches of ice cream. If the factory uses 1/2 of a gallon of milk for each batch of ice cream then how many gallons of milk will be used in 6 batches? Please work this problem out on your own first and then we will discuss it as a group. Please use any background knowledge you have for this problem and show all work. (This is an application-level question from Bloom’s Taxonomy). Students will work to solve the problem in a way that makes sense to them. When they have come up with at least one way on their own I will let them partner up with a classmate. Together, they will share each of their understandings and how they found the answer. I will ask students to try to come up with another way to find or understand the problem/answer with their partners if they still have time. When all groups have found at least one way, I will call on selected groups to share with the class their way of solving. I will call on two or three different groups to share. I will then present the mathematical way of solving this type of problem: multiplying whole numbers by fractions.

I will first ask the students what type of problem this is and what kind of math I should use. They should respond that this is a multiplication problem using a whole number and fraction.

I will then write out the problem on the SmartBoard or whiteboard so that everyone can see: ½ x 6 = ?

I will next explain that in order to multiply a whole number by a fraction we have to make the whole number into an improper fraction. I will demonstrate this simple step to the students and write 6 over 1. I will explain that it still represents 6 because any number divided by 1 is that number.

I will ask then step up the new problem: ½ x 6/1 = ?

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I will then ask the students to follow along with me as I multiply the numerators and denominators. I will explain that we are trying to find one half of 6.

This will answer to: 6/2 = 3.

I will ask the students to answer the question that they were prompted with in the beginning of the lesson in a complete sentence (if they got the answer wrong on their own) knowing that the factory needs 3 gallons of milk for 6 batches of ice cream.

I will ask students to come up with their own question using multiplying whole numbers by fractions and a one sentence explanation as an exit ticket to show their understanding of this concept.


ASSESSMENT: I will prompt an exit ticket asking students to create their own word problem using multiplying whole numbers by fractions with a complete sentence explaining their understanding of the concept.

Closing Activity: I will end the lesson by asking the students to think-pair-share on this question. “If there were three gallons of milk needed for 6 batches of ice cream then how many gallons would it take to make 10 batches of ice cream”


Day 6: Multiplying Fractions by Fractions *See first taught lesson*CCS Standards Connection: Objective: Materials:

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Learning Activities: Assessment:



Subject: Math/Health Date:







Elementary Health Education Key Idea #1: Students will understand human growth and development and recognize the relationship between behaviors and healthy development. They will understand ways to promote health and prevent disease and will demonstrate and practice positive health behaviors.

Essential Questions (Rubric Line 36):Why is multiplication of fractions the best operation for certain situations?What does it mean to multiply fractions?

Enduring Understandings(Rubric Line 36):Students will understand that…Multiplication of fractions is useful in a variety of everyday situations. Using reasoning, critical thinking, and understanding they will learn what fractions represent and how to find part of a fraction. Objectives (Rubric Line 31):Students will be able to multiply fractions through reasoning, thinking, and understanding.

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Students will be able to explain how to multiply fractions using the diagrams. Assessment Evidence (Rubric Line 32)

Performance Tasks:For assessment I will present the following problem and ask students to explain the “mathematical way” of solving in their math journals.

Last week, Annie's Fruit Stand sold 1/2 of a box of oranges. Down the road, Serena’s Fruit Stand sold 2/3 as many boxes of oranges as Annie's did. How many boxes of oranges did Serena's Fruit Stand sell?

Scoring Rubric (to be used on the material they write in their math journal):

Low Medium High


10 pts Incorrect answer given Correct answer given


10 pts Explanation leads to incorrect answer if followed exactly



Other Evidence:Areas of Child Development (Rubric Line 28)

Cognitive development is supported because children learn to make sense of how to multiply fractions and what that means. Linguistic development is supported because children must explain their thinking about multiplication of fractions to the teacher and to one another. Social development is supported because children must work together and must ensure that their classmates understand their ideas about multiplication of fractions.

Learning PlanClassroom Arrangement:Get all the materials ready ahead of time.Prepare the opening problem on an overhead or computer screen or flip chart ahead of time. Have all students in their seats. Materials:

Math journals Pencils White board or Smart board Colored pencils, crayons, markers Brownies (optional)

Learning/Instructional Activities (Rubric Lines 29, 33, 34, 39):Anticipatory Set (Rubric Line 38):

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Have a pan of brownies and begin cutting them in front of the room. This will grasp the student’s attention and while they work they can have a snack related to the question to motivate them.

If you cannot have brownies then the teacher can say “Everyone we are going to start our math lesson for today. Please take out your math journals. By a show of hands who likes brownies?”

Procedure Story Problem (Rubric Line 40): For valentine’s day your mom is going to make brownies. They were so good when they came out of the oven that as a family you ate ¼ of them. The next day when you got home from school you were hungry for another brownie! Since ¼ of the pan was eaten the night before there was ¾ left. You decided you wanted to eat 1/3 of that ¾. How much of the whole pan of brownies did you eat? Please work independently and use any way that makes sense to you to find the answer for a few minutes and then I will give you time to work with a partner. (This is an application-level question from Bloom’s Taxonomy).

Students will work to solve the problem in a way that makes sense to them. When they have come up with at least one way on their own I will let them partner up with a classmate. Together, they will share each of their understandings and how they found the answer. I will ask students to try to come up with another way to find or understand the problem/answer with their partners if they still have time.

When all groups have found at least one way, I will call on selected groups to share with the class their way of solving. I will call on two or three different groups to share.

I will then present the mathematical way of solving this type of problem: multiplying fractions. I will first draw a rectangle and label it 1 pan of brownies. I will then ask the class how many parts I should divide the rectangle into based on the first

part of the question. They should answer 4 and I will draw a graph on the board with 4 equal sections.

I will ask the students what each section represents and make sure that they have an understanding that each section is ¼ before moving on.

I will then tell the students to look at the fractions in the word problem and tell me what sections I should label as ¾.

They will agree that 3 out of the 4 parts should be shaded and I will label this as ¾. I will ask students if this is an addition, division, adding or subtracting problem. If they are

having difficulty I will hint to them to think of the “of” part of the problem 1/3 of ¾. The goal is to have students say that this is a multiplication of fractions word problem and I

will ask them to set up what that looks like. Responses should be: 1/3 X ¾ = ?

I will break each of the 4 parts into 3, because we are now working with 1/3, making a total of 12 boxes within the one “pan”.

The ¾ will still be shaded and I will ask them to focus on this part as it is what we are working with right now.

I will ask students to tell me what part I need to shade in to represent 1/3 of the 3/4. We will agree on the answer of 3 boxes needs to be shaded and I will do so in a different color

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to show the differences. I will then ask how many boxes are shaded for the 1/3 section out of the WHOLE “pan” or

rectangle. They will answer 3/12 and I will ask if this number can be reduced. (1/4). I will explain that 1/3 of ¾ is ¼ because it is part of the whole that we are working with.

In the process of discussing the mathematical way of solving the problem, I will ask students to consider whether or not brownies are a nutritional snack. We can talk about how treats are ok sometimes but make sure you put a limit on them. We can also discuss healthier snack options. (This is an evaluation-level question from Bloom’s Taxonomy.)


ASSESSMENT: Pose the assessment question “If there was only 1/3 of a pan of brownies left and you ate ¾ of what was left how much of a whole pan of brownies did you eat?” as a take-home problem that will be collected and examined tomorrow.

Closing Activity: I will end the lesson by reading “Apple Fractions” by Jerry Pallotta.


Day 7: *See Performance Task*CCS Standards Connection: Objective: Materials: Learning Activities: Assessment:

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Can you bake? We need a wedding cake!

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A Performance Task For students in grade 5

HELP WANTED – WEDDING CAKE BAKER

A couple getting married in a few short months is looking for a baker to bake their wedding cake. This wedding cake is very specific because they are trying to create enough options so that all guests can enjoy a piece of cake that they like. They are looking for two flavors of cake, two types of frosting, and a few different types of decorations to make the cake look great! They are

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accepting ideas from many people and are willing to pay more than a normal wedding cake so the pressure is high for this opportunity! Strap on your apron and get ready to bake!

To prepare for this exciting position, work through the following problems. Each one will help you understand a part of what you need to know in order to create the perfect cake for this couples interests.

After you complete the explorations, you need to make a detailed image of the cake with labels explaining what portion of the cake has what type of flavor, frosting, and decoration. You will also need to include a detailed explanation of why you think this is the best option to create this specific cake and how you plan on completing this task.

Your presentation must meet the following criteria in order for you to receive final consideration for the job:

The correct calculation of how many people can have more than one piece of cake in the case of two different scenarios and how you found your answer.

The correct calculation of how many people like each flavor type of cake with an explanation of how you found your answer as well as how you will apply this while making the cake.

The correct calculation of what portions of the cake has different decorations on it. The correct calculation of how long it will take to make the cake. A write up that gives the couple details about how you plan to go about making their wedding

cake to fit all of the wants they have given you. Remember these are your customers, their satisfaction is your goal! Be persuasive and creative!

Good luck!

Problem 1: How many pieces?

There are 200 people invited to the wedding. The couple wants to estimate the number of people who could have more than one piece of cake in the case that not all of the guests attend. If the cake is divided evenly into 200 pieces but only ¾ of the people show up to the wedding how

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many people can have 2 pieces of cake? What if 4/5 of the people invited show up? Please show work below:

¾ of guests attend: ___________number of people can have more than one piece of cake.

4/5 of guests attend: ___________ number of people can have more than one piece of cake.

Explain your answers and how you found them:

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Problem 2: What flavor of cake should we make?

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If the couple expects ¼ of the 200 guests to want chocolate cake, 3/5 of the guests to want vanilla cake, and 3/20 to want marble cake how many guests want each type of cake? Please show work below:

Chocolate: _________

Vanilla: ___________

Marble: __________

Explain your answers, how you found them, and why this information is important to you as the baker and how you will use it while baking the cake:

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Problem 3: Decorations galore!

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The bride and groom cannot decide on the same decorations to have on the cake so they are going to do both! The bride wants beautiful detailed swirls as decoration on the cake and the groom wants chocolate flakes as the cakes decoration. They do agree that they both want edible pearls on part of the cake as well. As a compromise they decide to incorporate all three ideas! If 2/8 of the cake is going to be decorated with swirls and 3/5 is going to be decorated with chocolate flakes, how much how of the cake will be decorated with just the pearls? Please show your work:

Answer: ______________

Explain how you found you’re answer and how this information will help you while baking the cake:

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

____________________________________________________________________________

Problem 4: Be wise with time!

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To give the couple all of the details appropriate for ordering a cake they should be reassured that you are aware of how you’re using your time and that you will have their cake ready for their big day! You know that it takes you ¼ of an hour to mix the cake, ¾ of an hour to bake it, and 3/5 of an hour to decorate it. How much time does it take you to make the whole cake?

Answer: _____________

Explain how you found your answer and how you will make sure your client knows that you will have enough time to make the cake:

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Final write up and picture: In this section put all of your findings together with a write up and detailed picture. Write a complete, detailed explanation of how you plan to go about making the

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wedding cake for the couple. Make sure to include all of the information from each exploration above that you have completed including how many guests can have more than one piece if certain fractions of the guests attend, how much of the cake will be each flavor, what portions of the cake will be decorated in each desired decoration, and how much time you plan on taking to make their cake as perfect as it can be! After you finish your write up create a detailed picture of the cake you intend to create. Add in any details or suggestions that you have as well that might make you stand out as a contestant in their search to finding the best baker for their wedding and remember, be persuasive and creative!

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

______________________________________________________________________________

Sketch or picture of cake with labels:

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Teachers’ Edition:

Common Core Standards:

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

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

CCSS.MATH.CONTENT.5.NF.B.4Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.

Enduring Understandings:

1. Fractions can be used to aid in explaining real world problems.

2. Adding and subtracting fractions with unlike denominators through word problems is an important strategy in solving real world problems.

Essential Questions:

1. How do we add fractions that do not have the same denominator?

2. How do we multiply a whole number by a fraction?

Learning Outcomes:

Students will be able to add fractions without common denominators using complex word problems.

Students will be able to multiply whole numbers by fractions. Students will be able to apply mathematical fractions to a real life situation.

Materials:

Class set of Performance Task packets Pencils

GRASPS:

Goal: To find the best solution to what kind of cake to make for a specific wedding party. The wedding couple will look at all suggestions and ideas and choose the one they find to be the best

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http://www.corestandards.org/Math/Content/5/NF/B/4/

fit. If they choose you, you will be hired to create their wedding cake!

Role: You are an applicant to be the baker for a wedding party.

Audience: The couple getting married and their wedding planner.

Situation: A couple getting married is looking for a very specific wedding cake. There are several factors that need consideration while thinking of a plan of the best way to create this cake. Flavors, decorations, amount of cake, and time needed to bake it are all important aspects that need detailed attention. The couple is in need for a baker who is willing to be flexible with all of their needs and also be creative! If you are able to produce an idea of how to bake this special cake you may be very well hired by the bride and groom!

Product, Performance, or Purpose: You will need to create a very detailed drawing with a detailed explanation of how you would go about making this cake. The couple wants as much description as they can get because they want to make sure the cake will be suitable for their wedding party!

Standards/Criteria for Success: Your drawing and explanation must meet the following criteria in order for you to receive final consideration for the job:

You must explain how you plan to go about creating the best cake for them and why you would be the best person for this task.

You must demonstrate that because you have completed all of your calculations correctly you understand how to make the cake with the appropriate portions of cake according to what their guests prefer.

You must explain that you are aware of how long it will take you to make the cake and that you are responsible and able to use your time wisely in order to get their order done on time.

Resources:

http://www.corestandards.org/Math/Content/5/NF/

Criteria for success:

Interviewers (couple getting married) will circle yes or no to the following criteria.

Paperwork/problems:

1. All questions are completed and answered with detail and work is shown to demonstrate how the contestant got the answers.

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Yes or No

2. Correct calculation of how many people can get two pieces of cake in two different types of scenarios of the number of guests attending.

Yes or No

3. Correct calculation of the portions of cake of each flavor.

Yes or No

4. Correct calculation of the portions of the cake that will have the certain decorations.

Yes or No

5. Correct calculation of the amount of time it will take to make the cake.

Yes or No

3. All questions have a clear explanation of how the contestant got to their answers and why these points will help them in making the wedding cake.

Yes or No

Write up:

1. Writing is organized and in an orderly manner.

Yes or No

2. Proper grammar, spelling, word choice, etc.

Yes or No

3. Persuasive, and creative attracting the interviewer’s interest and convincing that this contestant is the best choice.

Yes or No

Drawing/picture:

1. Detailed with labels showing every aspect of the cake including various flavor and decoration portions.

Yes or No

2. Creative design.

Yes or No

References:

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5th Grade Math Word Problems Worksheets. (2014, January 1). Retrieved April 16, 2015, from

http://www.k5learning.com/free-math-worksheets/fifth-grade-5/word-problems

Funky Fractions For Fifth Grade. (2013, January 1). Retrieved April 17, 2015, from

https://funkyfractionsforfifthgrade.wordpress.com/

Grade 5 » Number & Operations—Fractions. (2015, January 1). Retrieved April 16, 2015, from


IXL math practice - Multiply fractions by whole numbers: Word problems (Fifth grade). (2015,

January 1). Retrieved April 10, 2015, from http://www.ixl.com/math/grade-5/multiply-

fractions-by-whole-numbers-word-problems

Pallotta, J., & Bolster, R. (2002). Apple fractions. New York: Scholastic.

Schwartz, J. (2008). The Changing Landscape of Elementary Mathematics Teaching and

Learning. In Elementary mathematics pedagogical content knowledge: Powerful ideas

for teachers (pp. 8-10). Boston: Pearson/Allyn and Bacon.

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http://www.ixl.com/math/grade-5/multiply-


https://funkyfractionsforfifthgrade.wordpress.com/

http://www.k5learning.com/free-math-worksheets/fifth-grade-5/word-problems

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