Fractions Unit Plan · 3 Common Core CCSS.MATH.CONTENT.5.MD.B.2 Make a line plot to display a data...

$Page 1: Fractions Unit Plan · 3 Common Core CCSS.MATH.CONTENT.5.MD.B.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions$
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Fractions Unit Plan Multiplying and Dividing

Grade 5

Alexa Rahrle Spring 2014

St. John Fisher College

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Table of Contents Common Core State Standards…………………………………………………………………………………………………..3

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

Essential Questions and Enduring Understandings………………………...…………………………………………..6

Objectives Overview……………………………………………………………………………………………………………………7

Lesson Sketch Day 1 – What Is a Fraction?......................................................................................8

Lesson Sketch Day 2 – Small Particles in Science…………………………………………………………………………9

Small Particles in Science Full Lesson Plan…………………………………………………………………………………10

Small Particles in Science Graphic Organizer……………………………………..……………………………………..14

Lesson Sketch Day 3 – Expressing Division Problems as Fractions…………………………………………..…16

Lesson Sketch Day 4 – Beginning to Multiplying Fractions…………………………………………………….….17

Lesson Sketch Day 5 – Multiplying Fractions by Whole Numbers…………………………………….………..18

Lesson Sketch Day 6 – Multiplying a Fraction by a Fraction…………………………………………………….…19

Lesson Sketch Day 7 – Dividing a Fraction by a Whole Number…………………………………………………20

Lesson Sketch Day 8 – Dividing a Whole Number by a Fraction…………………………………………………21

Lesson Sketch Day 9 – Dividing Fractions Using Decimals………………………………………………………….22

Dividing Fractions Using Decimals Full Lesson Plan……………………………………………………………………23

Dividing Fractions Using Decimals Gallery Walk Problems………………………………………………………..28

Lesson Sketch Day 10 – Dividing Fraction Review………………………………………………………………..……31

Dividing Fractions Review Full Lesson Plan………………………………………………………………………………..32

Dividing Fractions Review Healthy Lifestyle Worksheet…………………………………………………………….38

Dividing Fractions Review Create Your Own Word Problem Worksheet………………………………….…39

Lesson Sketch Day 11 – Performance Task – Dividing Pizza Equally…………………………………………..40

Lesson Sketch Day 12 – Performance Task – Adapting the Recipe…………………….………………………41

Lesson Sketch Day 13 – Performance Task – Answering Customers’ Questions………………………..42

Lesson Sketch Day 14 – Performance Task – Written Report and Reflection……………………….…….43

Performance Task – Task Analysis…………………………………….……………………………………………………….44

Performance Task GRASPS………………………………………………………………………………………………………..45

Performance Task Student Work Packet…………………………………………………………………………………..46

References…………………………………………………………………….………………………………………………………….57

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Common Core

CCSS.MATH.CONTENT.5.MD.B.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. CCSS.MATH.CONTENT.5.MD.A.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems. CCSS.MATH.CONTENT.5.NF.B.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. 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.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

CCSS.MATH.CONTENT.5.NF.B.7.A Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. CCSS.MATH.CONTENT.5.NF.B.7.B Interpret division of a whole number by a unit fraction, and compute such quotients. CCSS.MATH.CONTENT.5.NF.B.7.C 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. CCSS.ELA-LITERACY.W.5.4 Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1-3 above.) CCSS.MATH.CONTENT.5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. CCSS.ELA-LITERACY.W.5.2 Write informative/explanatory texts to examine a topic and convey ideas and information clearly.

http://www.corestandards.org/Math/Content/5/MD/B/2/

http://www.corestandards.org/Math/Content/5/MD/A/1/

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

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




http://www.corestandards.org/Math/Content/5/NF/B/7/b/

http://www.corestandards.org/Math/Content/5/NF/B/7/c/

http://www.corestandards.org/ELA-Literacy/W/5/4/



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Rationale This unit plan was created to teach students how to multiply and divide fractions. Not

only are students learning how to solve these problems, they are applying the concepts to real-

world problems. By connecting the concepts to relatable situations, the context becomes more

applicable to students’ lives. Instead of solving worksheets of equations, students solve word

problems. They use reading skills to understand what the question is asking, and then use their

skills in multiplying and dividing fractions to answer the question. These types of problems help

students become true problem-solvers in their lives because they have the skills and knowledge

to apply math to real-world situations.

The unit focuses on dividing fractions, but the lessons at the beginning of the unit plan

help students to gain skills on dividing fractions by learning how to multiply them. These lessons

can be review of a previous unit in multiplying fractions. However, students need the basic

multiplication skills of fractions and they need to understand what a fraction is in order to divide

them, convert them to workable numbers if they are in decimal form, and apply the skills to

word problems.

In connection to social justice ideas, this unit aims to help students reach their highest

achievements in multiplying and dividing fractions. The unit builds the students’ understanding

of mathematical concepts to promote growth. The problem-based learning fosters an engaging

environment for students to participate in and learn multiplying and dividing fractions in a

relevant, realistic way. This helps students achieve the skills necessary for life outside of the

classroom when they can problem-solve on their own.

For the social justice idea of knowledge, students are given the skills to solve the

equations presented through the unit plan lessons. Their knowledge is constructed through

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personal and intellectual connections. These connections help the students apply what they

know in the real-world contexts of word problems.

Lastly, the unit nurtures compassion for the mathematical content that the students will

be learning. By modeling excitement for the topic, the students will come to be engaged as

well. The problem-solving components of the unit give students a chance to become detectives

and work hard to solve the problems. Since the problems are real-world situations, students

might come across similar scenarios in their own lives. From the unit plan, they will have the

compassion for solving the problems they come across from their strong foundation in word-

problem solving skills.

Students will practice procedural steps in solving fractions problems. However, the

math becomes more real to the students when a word problem is put in place of a blank

equation with no context. Word problems help students see scenarios where fractions would

be applicable to their own lives. This shows students how math is useful and necessary in their

lives outside of the classroom.

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Essential Questions

What are some things you can’t see but you know exist?

Why is it important to know about things we cannot see?

Where have you seen decimal numbers in your life outside of school?

What are some other school subjects that might require students to know how to divide fractions?

Why should we apply the idea of perspectives to math problems?

How do we use fractions to solve problems outside of school?

What sorts of problems can be solved by dividing fractions?

How can you use fractions to help make healthy food choices?

How can fractions be used during exercise?

Enduring Understandings

There are particles around us everywhere that are too small to be seen, but they still exist and can be detected.

Decimals can be represented as fractions by multiplying the fraction by 10/10, 100/100, etc. in order to convert the decimal into a fraction that can be divided.

Real-world contexts can be used to solve fraction division problems.

Fractions can be divided by multiplying by the reciprocal.

Dividing fractions can be useful in everyday life and help us make good choices in physical exercise and healthy foods.

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Objectives Overview:

Day 1 Objective: Students will be able to measure different classroom objects with rulers to the nearest ½, ¼, and 1/8 and compare the differences in lengths.

Day 2 Objective: Students will be able to explain that some particles are too small to be seen. Students will be able to use a number line to accurately measure the balloon size using measurements to the nearest 1/8.

Day 3 Objectives: Students will be able to use tape diagrams to model fractions as division problems.

Day 4 Objective: Students will be able to multiply a whole number by a fraction with the aid of a tape diagram.

Day 5 Objective: Students will be able to solve word problems by multiplying fractions by whole numbers using measurements.

Day 6 Objective: Students will be able to multiply a fraction by another fraction.

Day 7 Objective: Students will be able to divide a whole number by a unit fraction.

Day 8 Objective: Students will be able to divide unit fractions by whole numbers.

Day 9 Objective: Students will be able to practice dividing decimals by converting them to fractions and solving real-world context word problems. Students will be able to create a poster that demonstrates their interpretation and solution to a problem from the Gallery Walk activity.

Day 10 Objective: Students will be able to solve real-world word problems using their knowledge of dividing fractions.

Day 11 Objective: Students will be able to help customers divide their pizza equally in the Performance Task by dividing fractions.

Day 12 Objective: Students will be able to adapt recipes using their knowledge of fractions to create different sized pizzas.

Day 13 Objective: Students will be able to apply their knowledge of fractions to answer customers’ questions from the Performance Task.

Day 14 Objective: Students will be able to write a report and reflection that explains their understanding of the performance task items and apply their knowledge of fractions.

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Unit Calendar:

Day 1: What is a Fraction?

Standard Connection:

CCSS.MATH.CONTENT.5.MD.B.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots.

Objective: Students will measure different classroom objects with rulers to the nearest ½, ¼, and 1/8 and compare the differences in lengths.

Materials: Rulers Paper strips Various classroom objects (pencils, desks, paper, crayons, etc.)

Learning Activities: At first, students will work in groups to try and solve a word problem. You have a friend that thinks his pencil is larger than yours, but they look to be the same size. How do you determine which pencil is larger? Students will be given strips of paper to use for number lines. Students will begin by measuring the objects they have at their desk. Starting with their pencils, students will measure the pencil to the nearest ¼ inch. Students will continue to measure their objects with a ruler on their number line. Once students have measured their items, they will compare their number lines in order to compare the different sized objects. Students will answer several questions that involve comparing the object lengths.

Assessment: PLAN: I will grade the students on their ability to meet the objectives. Each objective will be a part of the assessment rubric. Thoroughness, neatness, and accuracy will all be considered in the evaluations.

TOOL(S): Students will be graded on a rubric. Each objective will be a rubric component. Students will be given a 1, 3, or 5. An exit ticket will also be given to assess their knowledge of the content and ability to apply their knowledge to a word problem.

EVALUATION: Students will be evaluated on their ability to measure different objects to the specified lengths. They will also be evaluated on how they answered the questions to compare the length sizes using their number lines. The exit ticket will provide more insight to the students’ understanding of the overall content by completing a word problem individually.


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Day 2: Small Particles in Science


CCSS.MATH.CONTENT.5.MD.B.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. 5.PS1.1. Matter of any type can be subdivided into particles that are too small to see, but even then the matter still exists and can be detected by other means. A model showing that gases are made from matter particles that are too small to see and are moving freely around in space can explain many observations, including the inflation and shape of a balloon and the effects of air on larger particles or objects. Learning Standards for the Arts Standard 1 – Creating, Performing, and Participating in the Arts Students will develop their own ideas and images through the exploration and creation of art works based on themes, symbols, and events.

Objective: Students will explain that some particles are too small to be seen. Students will use a number line to accurately measure the balloon size using measurements to the nearest 1/8.

Materials: Ruler Pencils Chart paper Balloons Hair dryer Bucket of ice water Graphic organizer – teacher made

Learning Activities: Students begin by experimenting with a balloon, hair dryer, and ice water. They use the hair dryer on the balloon and measure the balloon size. Students then place the balloon in ice water and measure the size of the balloon. After the experiment is complete, the class holds a discussion about what caused the balloon to expand or shrink. Students complete an exit ticket to demonstrate their understanding of the lesson.

Assessment: PLAN: Students will be evaluated based on their ticket-out-the-door answers and the rubric included in the full lesson below.

TOOL(S): The rubric for evaluation is included in the lesson plan below.

EVALUATION: Students will be evaluated based on the rubric. The rubric components address each of the lesson objectives. Students will be graded based on their thoroughness and accuracy in each of the rubric components.

Full lesson plan below.


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Teacher: Alexa Rahrle Date: Spring 2014 Subject: 5th Grade Science Time Estimate: 45 minutes Enduring Understandings There are particles around us everywhere that are too small to be seen, but they still exist and can be detected. Essential Questions What are some things you can’t see but you know exist? Why is it important to know about things we cannot see? Standards 5. PS1.1. Matter of any type can be subdivided into particles that are too small to see, but even then the matter still exists and can be detected by other means. A model showing that gases are made from matter particles that are too small to see and are moving freely around in space can explain many observations, including the inflation and shape of a balloon and the effects of air on larger particles or objects. 5. MD.2 Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. Math Practice Use Appropriate Tools Strategically

Students will use paper, pencils, ice water, and a hair dryer to demonstrate the effects on a balloon.

Model with Mathematics

Students will measure the balloon sizes before the experiment, after using the hair dryer on the balloon, and after putting the balloon in cold water.

Attend to Precision

When students measure the balloon size, they will accurately measure the size on a number line to the nearest 1/8 of an inch.

Learning Standards for the Arts Standard 1 – Creating, Performing, and Participating in the Arts Students will develop their own ideas and images through the exploration and creation of art works based on themes, symbols, and events Students will be asked to draw a picture of their balloon and interpret what is inside of the balloon after blowing it up. This shows students are developing their own ideas in their artistic representation of what is happening based on the theme of particles. Misconceptions

1) Air is nothing 2) Gasses are not matter because they are invisible 3) Particles can be seen easily with an optical microscope 4) In general, misconceptions can be caused by:

a. Students trying to understand a concept before exploring it themselves

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b. Teacher demonstrations are passive and students are not fully engaged Objectives

Students will explain that some particles are too small to be seen.

Students will demonstrate other ways to detect particles that cannot be seen.

Students will use a number line to accurately measure the balloon size using measurements to the nearest 1/8.

Students will apply knowledge of small particles to a real-world connection (hot air balloon). Areas of Cognitive Development Linguistic – Students will participate in group discussions about the expansion/compression of the balloon. Social – Students will be discussing in groups of 3 or 4 to collaborate and work together. Physical – Students will be moving around the room to complete the experiment. They will be blowing up their balloon, using the hair dryer on the balloon, and putting the balloon in ice water. They will only be seated during discussion. Cognitive – Students are thinking about what causes the balloon to expand and compress. Students will think about how we know that there something inside the balloon that we cannot see but we know it’s still there. Student Motivation and Classroom Culture The desks will be arranged in groups of three or four. This allows students to collaborate, discuss, and work together while completing the experiment. Students will be motivated by an engaging, hands-on task where they explore the effects that heat/cold have on a balloon. Technology (tools) Ruler Pencils Chart paper Balloons Hair dryer Bucket of ice water Graphic organizer – teacher made Anticipatory Set The teacher walks around the classroom, pointing at her skin and saying “Can you see that?” As students begin asking questions, such as “what am I looking at?” or “your skin?” look distantly in the air; not looking at anything in particular. Keep asking the students, “Do you see that?” Have them keep asking what you are looking at, but never tell them or give hints. Discrepant Event Give each student a balloon. Have them blow it up at their table. On a piece of paper, have the students draw a balloon outline and on the inside, have the students write and draw what they think is inside. The teacher should not give hints or prompt them. Instead, walk around the room and observe what the students have drawn in their balloon. Procedures Begin by telling the students a story:

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Once upon a time, you are at a carnival. It’s a hot summer day and you get a balloon to bring home. You are very happy. You go home and leave your balloon in the car on accident. It gets very cold at night, and the balloon looks different from when you got it at the carnival! What happened to the balloon? This engages students to begin thinking about what has happened to the balloon and why. Students will be given chart paper. Students in groups of 3-4 will measure their balloon using a line plot. They will mark 1/8 inches and accurately measure the length and width of the balloon to the nearest 1/8 of an inch. Students will be given a graphic organizer to complete through the investigation. After measuring the balloon at first, they will write down the measurement of the balloon on the organizer along with observations of the balloon. Students will then be given a hairdryer (The students might need to take turns to share the hair dryer). Students will write down their prediction of what will happen when they add heat to the balloon on their graphic organizer. Each group will blow warm to hot air on the balloon for 45 seconds to a minute. After this, the students should immediately record the length and width of the balloon now, using the same number line. The students should use a different color to mark the new size of the balloon to not confuse it with the other measurements. Students then record their observations in the graphic organizer. Then, students place the balloon in a bucket of ice water. The students will write their predictions of what will happen to the balloon when it’s placed in cold water. This will be written on the graphic organizer. The students leave the balloon in the ice water for 1 to 2 minutes (Students could begin with putting their balloons in ice water if there is a limited number or hair dryers, then switch). After this, the students record the length and width of the balloon in a different color and record observations on the organizer. Resolve the Discrepancy Once the experiment is completed, the students will have a group discussion within their groups of 3 or 4 to answer these questions: What did you predict was inside the balloon before the experiment? (air, particles) If you can’t see anything, how did you know it was there? (the balloon filled up, it expanded with hot air, compressed with cold air) Reworded question - (How did the expansion and deflation of the balloon prove that there was something inside the balloon?) How did putting heat on the balloon prove there was something inside the balloon that we couldn’t see? (The balloon got bigger) Show students that there are particles in the air that we cannot see, but it doesn’t mean they do not exist. There are ways to detect these particles, such as applying heat, cold, or expanding a balloon. The balloon can’t be filled with nothing. The particles are proven to be there by the way they react with the hot and cold changes. Assessments Ticket-out-the-door: If you wanted to take a hot air balloon ride, why is it important to know about the small particles in the balloon? How do we know they are there? What would happen if it was a “cold air balloon” instead of a “hot air balloon?”

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The students’ graphic organizers and line plots will also we collected to evaluate if the objectives were met. Rubric

1 3 5

Students explain that some particles are too small to be seen.

Student does not mention that some particles are too small to be seen.

Student does not mention some particles that are too small to be seen.

The student clearly states that some particles are too small to be seen.

Students will demonstrate other ways to detect particles that cannot be seen.

Students do not address the question, “How do we know they are there?”

Student attempts to answer the question but does not connect to class activity or other ways to detect particles.

Student references the experiment or describes a new way to recognize particles that are too small to be seen.

Students will use a number line to accurately measure the balloon size using measurements to the nearest 1/8.

There is no evidence of measuring the balloon size.

The student attempted to measure the balloon, but measured it to something other than the nearest 1/8.

The student accurately measures the balloon size to the nearest 1/8, with neatness and precision.

Students will apply knowledge of small particles to a real-world connection (hot air balloon).

Student did not address the question of a hot air or cold air balloon.

The student explained either the hot air balloon or the cold air balloon, but not both. For the hot air balloon, the student explains that particles react to the heat. For the cold air balloon, the student recognizes that the balloon would shrink (based on the experiment).

The student accurately described that particles in the hot air balloon cause it to rise because of the heat. Without the particles, we wouldn’t know how to work a hot air balloon. For the cold air balloon, the student recognizes from the experiment that it would shrink and most likely not fly.

Differentiation This lesson can be modified based on the needs of the classroom. Students with visual impairments will have preferential seating. Those with writing struggles or physical impairments could have a scribe assist them during the graphic organizers. Students who need movement are stimulated by a hands-on experience. Children’s Literature and Extension How Do Hot Air Balloons Work? by Buffy Silverman is a paperback book on how hot air balloons fly and how people can control where they go. This book can be read at the end of the lesson as a literacy extension and also to encompass the curiosity of the hot air balloon from the ticket-out-the-door question.

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Name

______________________________________________________________

Balloon measurement #1 (Before heat or cold)

Length ____________________________

Width ____________________________

Observations

Predictions: What do you think will happen when we apply heat to

the balloon with the blow dryer? Write your predictions in the

box below.

Balloon measurement #2 (After heat)

Length ____________________________

Width ____________________________

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Write your observations of the balloon after heat was added in

the box below.

Predictions: What do you think will happen when we put the

balloon in ice water? Write your predictions in the box below.

Balloon measurement #3 (After ice water)

Length ____________________________

Width ____________________________

Write your observations of the balloon after it was placed in ice

water in the box below.

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Day 3: Expressing Division Problems As Fractions


CCSS.MATH.CONTENT.5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. CCSS.MATH.CONTENT.5.NF.B.7.A Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. CCSS.MATH.CONTENT.5.NF.B.7.B Interpret division of a whole number by a unit fraction, and compute such quotients.

Objective: Students will use tape diagrams to model fractions as division problems.

Materials: Personal White Boards Paper Pencils SMARTBoard

Learning Activities: Students will begin by solving a word problem in any way that makes sense to them. They will solve, “If 5 tons of gravel are to be put equally into 4 dump trucks, how much gravel will be in each truck?” The teacher will ask the students to show on their whiteboards what 5 divided by 4 would look like in a fraction. The teacher will model a tape diagram on the SMARTBoard to show students how to use a picture to solve the problem. The teacher will then model the same problem using the standard algorithm. The teacher will continue to use this procedure using different word problems to demonstrate how tape diagrams can be used to express fractions and division problems. The teacher will give students a worksheet with word problems. Students will work in pairs to complete the problems using a tape diagram model and division to solve the problems.

Assessment: PLAN: The teacher can assess student learning by evaluating their answers on personal whiteboards. The word problems will be collected for evaluation.

TOOL(S): A teacher-created rubric will be used to assess student understandings. Informal assessments will also be used when students hold up their answers on their whiteboards. Teachers can gather insight about what students might need extra guidance and which students are grasping the concepts.

EVALUATION: Students will be evaluated on their worksheet of word problems. Students must solve each problem using a tape diagram and also the standard algorithm. Students are expected to answer each question in a complete sentence. The students that are able to answer the worksheet word problems will prove they have reached the objectives.



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Day 4: Beginning to Multiplying Fractions


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

Objective: Students will be able to multiply a whole number by a fraction with the aid of a tape diagram.

Materials: Counters SMARTBoard Paper Pencils Worksheet – teacher created

Learning Activities: The teacher will begin by presenting the students with counters. The teacher will say, “Show me 6. What is ½ of 6?” Students will show that ½ of 6 is three. The teacher will give several more examples as students use the counters to show parts of a whole. The teacher will present another problem to the students (show me 8. What is ¼ of 8?). As this is being said, the teacher will write the multiplication form on the word to show that ¼ of 8 looks like ¼ x 8. The teacher will demonstrate a tape diagram of this problem. The teacher will draw a long rectangle and divide it into 4 parts. The teacher will ask the students how much each unit (box) is worth if the entire rectangle is 8? (2 units). Using the tape diagram model, the teacher will show that ¼ = 2 units. Therefore, ¼ of 8 = 2. The teacher will present several more examples to the students using tape diagrams to solve the problems. The students will complete a set of word problems in groups. Students will solve the problems using a tape diagram.

Assessment: PLAN: The worksheet will be collected for evaluation and understanding of using a tape diagram to solve word problems.

TOOL(S): A teacher-created rubric will be used to evaluate the worksheet completion. An exit ticket will also be given to assess individual understanding of the material. The exit ticket will include a word problem similar to ones completed in class but students will be required to work independently.

EVALUATION: The students will be assessed on their ability to solve the problem using a tape diagram. The diagram must be accurately drawn with the correct units represented for each box. A final answer must also be provided. The exit ticket will be used as an informal assessment. The teacher will use the exit ticket to see which students can (independently) solve the word problems and this information can be used to guide students in future lessons.


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Day 5: Multiplying Fractions by Whole Numbers


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

Objective: Using measurements, students will solve word problems by multiplying fractions by whole numbers.

Materials: Paper Pencils Measuring cups SMARTBoard

Learning Activities: To begin, students will write down a list of measurements and try to think of as many measurements as possible. For example, students could write 1 cup = 8 ounces. Then, students will be given a glass measuring cup and a 1 ounce container. They will be told to solve “what is ¼ of 1 cup in ounces?” Students will use the measuring cups and water to try and solve the problem. They will also have paper and pencil to write their answer out as well. The teacher will show how to solve the problem using the measuring cups, a tape diagram, and the standard algorithm (1/4 x 8 ounces = 2 ounces). The teacher will pose a word problem to the students. Using any method, students will solve the multiplication problem. The students will share their findings on the SMARTBoard in front of the class to compare and contrast the different methods of solving it. Students will be given three word problems to solve with a partner that involve multiplying a fraction by a whole number. Students will use two out of the three methods to show their work.

Assessment: PLAN: Students will be evaluated with an exit ticket. On the exit ticket, students will completed two fraction multiplication problems independently. They will also write down two places outside of school where they might need to multiply fractions and explain why.

TOOL(S): The exit ticket will have a teacher-created rubric to assess the answers.

EVALUATION: Students will be evaluated on their exit ticket answers. Students will need to correctly answer the two problems independently and use two different solution methods in order to receive full credit. The student must also provide two examples on where to use multiplication of fractions outside of school. Students that can complete the exit ticket accurately will demonstrate a full understanding of the lesson and that the objective was met.


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Day 6: Multiplying a Fraction by a Fraction


CCSS.MATH.CONTENT.5.NF.B.4 Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. CCSS.MATH.CONTENT.5.MD.A.1 Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multi-step, real world problems.

Objective: Students will be able to multiply a fraction by another fraction.

Materials: Paper Pencils

Learning Activities: Students will be given a word problem to solve (If I have ½ of a tray of brownies left. I want to eat ¼ of the brownies left. How much of the entire pan of brownies will I eat?) Students will be told to solve this problem in any way that makes sense to them. After students have a chance to explore the problem, the teacher will demonstrate how to show this problem by folding a piece of paper. The paper will first be folded in half to show the pan of brownies left. Then, that half a pan of brownies will be folded into fourths, since I want ¼ of the leftover brownies. Students will then unfold their papers and see how much of the entire pan of brownies I will eat (1/2 x ¼ = 1/8 of a pan). Students will practice solving similar word problems using their folded papers. The teacher will then model the standard algorithm on the SMARTBoard by using a problem that the students practiced with folding their papers. For example, ¼ of a ½ pan of brownies = ¼ x ½ = 1/8 of a pan. Students will practice word problems that involve multiplying fractions by fractions. These word problems will be real-world scenarios. Students will solve the problems using a diagram and the standard algorithm.

Assessment: PLAN: Students will complete a mini-quiz that includes problems with multiplying fractions by whole numbers and multiplying fractions by other fractions. Students will be evaluated on their accuracy and pictures they draw to aid their solutions.

TOOL(S): A teacher-created rubric will be used to grade the mini-quizzes. This information can be used to help the teacher create new lessons for the future and review the material that students still seem to struggle with.

EVALUATION: The students will be evaluated on their ability to accurately answer the fraction multiplication questions. Students will be required to draw a diagram and use the standard algorithm. They must provide an answer in a complete sentence and write legibly for full credit. Partial credit will be given when some work is shown but not all, or a picture/algorithm is missing. Partial credit will also be given if the work is shown correctly but the student did not provide an answer.


http://www.corestandards.org/Math/Content/5/MD/A/1/

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Day 7: Dividing a Whole Number by a Fraction


CCSS.MATH.CONTENT.5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. CCSS.MATH.CONTENT.5.NF.B.7.A Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. CCSS.MATH.CONTENT.5.NF.B.7.B Interpret division of a whole number by a unit fraction, and compute such quotients. CCSS.MATH.CONTENT.5.NF.B.7.C 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.

Objective: Students will be able to divide a whole number by a unit fraction.

Materials: Chocolate bar Paper Pencils Worksheet – Teacher created

Learning Activities: Students will be given a chocolate bar. The teacher will begin by asking students to show with their chocolate: How many fourths are in 1 bar? How many eighths? How many halves? Students will be given another bar to work with. How many fourths are in 2 bars? How many eighths? How many halves? Students will then write down possible equations that show how they reached these answers. Students will complete an interactive SMARTBoard activity where they come up to the board and move pieces around to solve different division word problems. For example, you buy 2 pounds of pecans but only need 1/3 for a recipe. How many recipes can you make? Students will draw tape diagrams to show how many each unit would be worth. Students will have a worksheet in front of them with problems. As students come up to the board to demonstrate their solutions, students can work on the problem at their desk and try to solve it a different way (such as using the standard algorithm). The teacher will lastly review the standard algorithm and explain how to multiply the number by the fraction’s reciprocal. Therefore, 2 divided by 1/3 becomes 2 x 3/1 = 6.

Assessment: PLAN: The student worksheets will be collected and evaluated for accuracy. The worksheets will contain word problems that help students solve real-world context problems and make connections between math and life outside of the classroom.

TOOL(S): Informal assessment will be used for this day. The teacher will keep a checklist as the students come up to the board to take note on who is participating. The teacher can use this information to provide extra guidance for those who need more assistance. The teacher will also collect the worksheets for an informal assessment. The teacher will use the information to see which students are understanding the concepts. With this information, the teacher can adjust future instruction based on students’ abilities.

EVALUATION: Students will be evaluated on their participation and willingness to come to the SMARTBoard and demonstrate how they solved the problem using a tape diagram. The worksheet will also be collected to assess those that do not have a chance to come up to the board. The teacher will evaluate the students that are able to show their work by using a tape diagram and the standard algorithm. Those that cannot present both solutions will demonstrate their need for more practice.




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Day 8: Dividing Fractions by Whole Numbers


CCSS.MATH.CONTENT.5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. CCSS.MATH.CONTENT.5.NF.B.7.A Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. CCSS.MATH.CONTENT.5.NF.B.7.B Interpret division of a whole number by a unit fraction, and compute such quotients. CCSS.MATH.CONTENT.5.NF.B.7.C 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.

Objective: Students will be able to divide unit fractions by whole numbers.

Materials: Individual White Boards and markers SMARTBoard

Learning Activities: The teacher will present a word problem to the students. “If Mr. Smith has ¼ of a pan of lasagna left over and he want to be able to eat it for the next 3 days, how much of the pan of lasagna will he be able to eat each night?” Students will solve this problem any way they can. Then, students will engage in a discussion about how this word problem was different from the ones we completed yesterday. The teacher will present several word problems to the students on the SMARTBoard and students will solve the problem on their whiteboards. They will use a tape diagram for certain questions and the standard algorithm for others, depending on what the teacher asks. For some, the students will be required to show their work in both ways. Students will hold up their answers to each problem on the whiteboard and the teacher will invite students to the SMARTBoard to demonstrate their solution to the word problem.

Assessment: PLAN: When students show their whiteboards to the teacher, the teacher will be able to use that as an informal assessment to evaluate student learning and understanding. An exit ticket with two word problems will be given for students to solve independently.

TOOL(S): The white board will be used to evaluate student understandings. The exit ticket will be collected for evaluation based on a teacher-made rubric.

EVALUATION: Students will be assessed on their accuracy in solving the problems on the whiteboards. The teacher will use the whiteboards as an informal assessment to assess student learning. The teacher will use a rubric to evaluate the answers on the exit ticket. The students will need to show their work using a tape diagram or the standard algorithm. Students will also need to provide an answer in a complete sentence.




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Day 9: Dividing Fractions Using Decimals

Standard Connection: CCSS.MATH.CONTENT.5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. CCSS.MATH.CONTENT.5.NF.B.7.A Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. CCSS.MATH.CONTENT.5.NF.B.7.B Interpret division of a whole number by a unit fraction, and compute such quotients. CCSS.MATH.CONTENT.5.NF.B.7.C 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.

Objective: Students will practice dividing decimals by converting them to fractions and solving real-world context word problems. Students will create a poster that demonstrates their interpretation and solution to a problem from the Gallery Walk activity.

Materials: SMARTBoard Pencils Word problem worksheet for Gallery Walk – teacher created Notebooks Anticipatory set picture

Learning Activities: Students will view a picture that shows a horse from one angle and a frog from another angle. Students will participate in a discussion about perspectives and if someone has a different perspective, is that person right or wrong? Students will then solve a word problem in any way that makes sense to them. Students will work in small groups to collaborate. The teacher will post 2/0.2 on the board. The teacher will ask students to discuss what they notice is different about this problem. Then ask: How could we change this to a fraction with whole numbers? Students will solve problems at their desks. The teacher will review with the students how to multiply a decimal number by a fraction that equals one to convert the decimal. Students will then resolve their opening word problem and self-check their answers. Students will complete a gallery walk around the classroom to complete word problems. After the walk, students will choose one problem from their Gallery Walk questions and express the problem on a poster. The students will draw out a scene that is represented by the real-world problem (for example, if the problem asks about making a recipe, the students will draw a scene where someone is baking). On this poster, the students will also express their solution to the problem in the way that they solved it.

Assessment: PLAN: Students will complete an exit ticket with a question that asks how they can connect dividing fractions to other school subjects and life outside of school and why. The gallery walk worksheet of problems will also be collected for analysis and grading.

TOOL(S): Students will be graded using the rubric in the lesson plan below.

EVALUATION: Students will be graded on their participation during the opening group discussion. They will be observed by the teacher for full participation and engagement. They will also be graded on their gallery walk packet completion and ability to work well with group members. The exit ticket will be graded on whether both questions were answered thoughtfully and thoroughly. Lastly, students will be evaluated on the poster they create as the final product for the lesson.




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Teacher: Alexa Rahrle Date: Spring 2014 Subject: 5th Grade Math Time Estimate: 45 minutes Enduring Understandings Decimals can be represented as fractions by multiplying the fraction by 10/10, 100/100, etc. in order to convert the decimal into a fraction that can be divided. Essential Questions Where have you seen decimal numbers in your life outside of school? What are some other school subjects that might require students to know how to divide fractions? Why should we apply the idea of perspectives to math problems? Standards 5.NF.7 7. Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. b. 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. c. 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?

Learning Standards for the Arts Standard 3 – Responding to and Analyzing Works of Art Develop connections between the ways ideas, themes, and concepts are expressed through the visual arts and other disciplines in everyday life. Standard 1 – Creating, Performing, and Participating in the Arts Develop their own ideas and images through the exploration and creation of art works based on themes, symbols, and events. Bloom’s Taxonomy Application – Students will solve the word-problems for the Gallery Walk by using their knowledge and skills learned from working in groups and from having class discussions on dividing fractions. Evaluation – Students will complete an exit ticket that uses the essential question, “Why should we apply the idea of perspectives to math problems?” to demonstrate their level of understanding of the day’s lesson. Students should be able to make judgment based on the lesson, group discussion, and anticipatory set and use higher level thinking. They are not simply required to recall information to provide insight to this EQ. Math Practices

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Model with Mathematics Students will model with mathematics by applying skills to solve problems in everyday life (as demonstrated by the word problems). They will also reflect on results and improve if it doesn’t make sense when they go back and look at the opening word problem they completed and make changes when necessary.

Misconceptions

1) Students invert the wrong fraction when dividing fractions. This results from rote memorization and a mindless series of steps.

2) Students tend to overgeneralize properties of operations. 3) Some think it’s impossible to compute division problems where the dividend is smaller than the

divisor. Objectives

Students will practice dividing decimals by converting them to fractions and solving real-world context word problems.

Students will create a poster that demonstrates their interpretation and solution to a problem from the Gallery Walk activity.

Areas of Cognitive Development Physical - Students are able to move around the room to complete their Gallery Walk activity. Social – Social needs are being met because students are able to work together and collaborate with one another to solve word problems. Cognitive – Students apply problem-solving strategies to complete the opening word problem activity. Students will rely on each other to think through each problem and use a strategy to solve it that works best for them, such as a picture, diagram, or standard algorithm. Emotional – Students are working together in groups. This enhances their emotional needs because they can rely on one another to work through difficult problems that are unfamiliar to them. Student Motivation and Classroom Culture Students will be working in groups of 2-3 to complete their word problems. Students will go around the room in a Gallery Walk, where different problems from their packet are posted around the room. They will take turns at each problem in the gallery and work together to solve the word problems. They will have 4 minutes at each problem and they are to complete a total of 8 problems. This motivates students because they are able to work together in groups. They are also able to get up and move around the room instead of sitting quietly and completing practice problems. Lastly, the word problems provide real-world connections for students so they can see how dividing factions are useful and applicable to their own lives. Technology (tools) SMARTBoard Pencils Word problem worksheet for Gallery Walk – teacher created Notebooks Anticipatory set picture Anticipatory Set

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The students will be split into two groups. Group A will be show a picture while Group B turns the other way or closes their eyes. Then, Group B will be shown the picture while Group A closes their eyes or turns away.

First, Group A will share out what they saw (a frog) Then, Group B will share out what they saw (a horse) The teacher will say: You’ll never believe me, but I showed you the exact same picture! The teacher will then rotate the picture to Group A and show them the horse perspective. Then, the picture will be rotated for Group B to see the frog perspective. The teacher will engage students in a short discussion: Was either group wrong because they saw the picture in a different way? Since it was the same picture, was there really only one way of seeing the picture? How can we connect this to solving math problems? The students will use the ideas of different perspectives to begin the discrepant event. They will be given an unfamiliar word problem and asked to solve it in any way they can. Thinking back to the pictures, they will realize that their way of solving a problem might be different than someone else’s. Discrepant Event You have a bag of sugar that has 2.4 grams of sugar in it. You are making several different recipes. If you need .2 grams of sugar for each recipe, how many different recipes can you make? (2.4/.2 = 12) 2.4/.2 x (10/10) = 24/2 = 12 You will be able to make 12 different recipes. Students will be given this problem to solve in their small groups. They will be encouraged to solve this in any way they can and in any way that works best for them (standard algorithm, picture, chart, etc.) Procedures The teacher will write 20/1, 40/2, 60/3 and 100/5 on the board and ask the students to solve each of the problems. Then ask them: What did you notice about the answers? How can we connect this back to the horse and frog picture we saw earlier? The teacher will prompt students in a discussion that they are equivalent fractions but they can be represented in different ways. The teacher will post 2/0.2 on the board. The teacher will ask students to discuss what they notice is different about this problem. Then ask: How could we change this to a fraction with whole numbers? Students will apply their knowledge of multiplying by a fraction that equals 1 to a decimal number in order to convert it.

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The teacher will ask students to write this problem down and try to come up with a way to multiply this fraction by another fraction that equals 1. Then, students will compare the way they did it to a neighbor. This will show the students the various ways in which their peers solved. Someone might have multiplied by 10/10 to get 20/2 = 10. Or, someone might have multiplied by 100/100 to get 200/20 = 10. Students will go back to their opening word problem and self-check to see if they multiplied the decimal by a fraction that equals 1 in order to solve. Students will self-correct their work. The teacher will then put this problem up on the board. Rather than explain it right away, the students will work in their groups to try and solve the problem on their own: 1.6/0.04. Then, the teacher will invite a group up to the board to write out their way of solving it. One by one, the teacher will invite each group up to explain how they solved the problem. After all groups have explained their reasoning, the teacher will give a brief explanation that the decimals should be multiplied by 100/100 because .04 must be multiplied by 100 to become a whole number in the fraction. Students will then break into small groups to complete a Gallery Walk. 8 different word problems will be posted around the room and groups of 2-3 will be rotating around to each problem. The students will work together to collaborate and come to a final answer for each problem. These problems will be real-world application questions and some involve multiple steps for challenge. Resolve the Discrepancy Students will participate in a small group discussion. These groups will be randomly selected so they are different from the ones they were in to solve their word problems. This will give students a different perspective from their new group members. After you have worked in groups and seen other ways to solve problems, how do they compare to the way you have solved the problem? If there were different ways of solving problems, did you arrive at the same answer? After the discussion, students will choose one problem from their Gallery Walk work questions and express the problem on a poster. The students will draw out a scene that is represented by the real-world problem (for example, if the problem asks about making a recipe, the students will draw a scene where someone is baking). On this poster, the students will also express their solution to the problem in the way that they solved it. Assessments Students will complete an Exit Ticket where they will be asked to answer these questions:

1) In what other school subjects AND in your life outside of school might you need to know how to divide fractions? Why?

The word problem packet and the opening word problem question will be collected for evaluation. The teacher will also conduct an informal assessment by prompting discussion through the lesson and listening to the students. This will give the teacher a sense of who understands the concepts, who is contributing, and who might need extra guidance in future lessons. Rubric

1 3 5

Group discussions throughout the lesson

Student did not contribute to any

Student contributed occasionally but seemed

Student was fully engaged in discussion

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discussions throughout the lesson.

to misunderstand key concepts and ideas.

and willing to share thoughtful and meaningful ideas related to the prompts given by the teacher.

Exit Ticket Student did not complete the Exit Ticket/did not attempt the Exit Ticket.

Student answered only one of the two questions on the Exit Ticket.

Student answered both questions on the Exit Ticket thoroughly.

Gallery Walk packet Student did not work with his or her small group to complete the packet. Less than 50% of the packet was complete. Student was unfocused and word problems are incomplete.

The student completed most of the Gallery Walk packet. Student became off-task at times and struggled with some concepts and ideas.

Student completed the Gallery Walk packet and was on-task during the activity. Student was able to grasp concepts and worked well with group members.

Poster Poster was incomplete or illegible. Drawings or math concepts are not evident.

Poster is neat but lacking the picture or the mathematical solution.

Poster is neat, organized, and includes both the drawing and the mathematical solution and concepts.

Differentiation Students will be grouped to promote collaborative thinking and access different levels of cognitive development. Students will be encouraged to use visuals and will be given additional visuals/pictures when needed. Those with hearing and visual impairments will be seated near the front of the room. Those who need more guidance and prompting in lessons will be grouped with those that are stronger in math but also willing to provide assistance. Children’s Literature and Extension The Hershey’s Milk Chocolate Bar Fractions Book by Jerry Pallotta and Rob Bolster is a fun way for students to practice fractions with a chocolate bar. This could be used as a Fun Friday activity or a review before a quiz or test. It engages students by using a chocolate bar to explore fractions and dividing a whole chocolate bar into pieces. The teacher could adapt this book to be used for decimals as well and adjusted for difficulty levels, depending on the class. It’s a great idea to explore fractions and provides the teacher with a base idea for a fun and engaging lesson on fractions.

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Name ______________________________________

Problem 1 Janet is making coffee for her friends. She has 3.5 ounces of coffee. If each of her coffee cups can hold .5 ounces of coffee, how many coffee cups can she fill?

Problem 2 Treyvon is measuring chemicals for a science experiment. He needs to put

0.9 grams of water in each flask. If he has 10.8 grams of water, how many

beakers can he fill?

Problem 3 Alice is baking pies. If it takes .6 pounds of apples to bake one pie,

how many pies can she make with 4.8 pounds of apples?

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Problem 4 Two wires, one 17.4 meters long and one 7.5 meters long, were cut into pieces 0.3 meters

long. How many such pieces can be made from both wires?

Problem 5 At a perfume company, they have 0.45 ounces left of Ocean Breeze Body Spray. If

the perfume bottles each hold 0.15 ounces, how many bottles of Ocean Breeze

Body Spray perfume can be made?

Problem 6 Mr. Smith has 15.6 pounds of oranges to pack for shipment. He can ship 2.4 lb of oranges in a large box and 1.2 lb in a small box. If he ships 5 large boxes, what is the minimum number of small boxes required to ship the rest of the oranges?

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Problem 7 Denise is making bean bags. She has 6.4 pounds of beans.

a. If she makes each bean bag 0.8 pounds, how many bean bags will she be able

to make?

b. If she decides instead to make mini bean bags that are half as heavy, how many

can she make?

Problem 8 A restaurant’s small salt shakers contain 0.6 ounces of salt. Its large shakers hold twice as much. The shakers are filled from a container

that has 18.6 ounces of salt. If 8 large shakers are filled, how many

small shakers can be filled with the remaining salt?

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Day 10: Dividing Fractions – Review Lesson

Standard Connection: CCSS.MATH.CONTENT.5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. CCSS.MATH.CONTENT.5.NF.B.7.A Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. CCSS.MATH.CONTENT.5.NF.B.7.B Interpret division of a whole number by a unit fraction, and compute such quotients. CCSS.MATH.CONTENT.5.NF.B.7.C 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.

Objective: Students will solve real-world word problems using their knowledge of dividing fractions.

Materials: Healthy Lifestyle worksheet – teacher created Pencils Chart paper Markers or crayons Chocolate bar (anticipatory set) “Create Your Own Word Problem” worksheet – teacher created SMARTBoard chocolate bar – there will be a chocolate bar on the SMARTBoard that will be brought up once the students finish their problem-solving in the anticipatory set. This will allow students to come up to the board and interact with the technology to move pieces of chocolate and demonstrate how they solved the problem.

Learning Activities: Students will begin with an anticipatory set word problem. Students will work together at their seats to try and solve the problem. Then, students will complete a SMARTBoard activity to demonstrate how they solved the problem. Students will then complete a “Healthy Lifestyle” worksheet which contains real-world word problems connected to healthy living habits. Throughout the worksheet, students will be prompted with discussion questions to apply fractions to healthy lifestyle habits. After the worksheet is completed, students will get into partners and choose one problem from the sheet. They will become the “experts” and write their solutions on chart paper. Students will then present their findings to the whole class. Students will then create their own word problems that use a healthy lifestyle context.

Assessment: PLAN: The worksheet and “Create Your Own Word Problem” sheet will be collected for evaluation. Students must complete the “Healthy Lifestyle” worksheet, create their own word problem with a partner, and solve the word problem created by another partnership.

TOOL(S): A rubric is used to evaluate the students. The rubric is attached in the lesson plan below. The rubric evaluated the different components to the lesson.

EVALUATION: Students are evaluated based on their “Healthy Lifestyle” worksheet. Students must answer all questions and include several potential ways to solve the problem. More than 75% of the questions must be complete for full credit. Students will also be evaluated on their word problems that they create. The word problem must be solvable and relate to a healthy lifestyle habit. Students will also be evaluated on their solution to another partnership’s word problem. They will be evaluated on the accuracy of the solution.




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Teacher: Alexa Rahrle Date: Spring 2014 Subject: 5th Grade Math Review Time Estimate: 45 minutes Enduring Understandings Dividing fractions can be useful in everyday life and help us make good choices in physical exercise and healthy foods. Essential Questions How can you use fractions to help make healthy food choices? How can fractions be used during exercise? Standards 5.NF.7 Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.

a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. b. Interpret division of a whole number by a unit fraction, and compute such quotients. c. 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.

Learning Standards for Health, Physical Education, and Family Consumer Science Standard 1 – Personal Health and Fitness

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.

a. understand how behaviors such as food selection, exercise, and rest affect growth and development

b. practice and support others in making healthy choices Bloom’s Taxonomy Synthesis – Students will be providing alternative solutions to word problems when students become the “experts” on their problem and demonstrate it to the class. Other students will be able to use their own ways of solving the problem to add to the one being presented. Application – Students will use their knowledge of dividing fractions to complete real-world context problems in the Healthy lifestyle packet. This is also evident when students use the division of fractions in order to create their own word problem. They take their knowledge and apply it to a real-world context. Math Practices

1) Make sense of problems and preserve in solving them Students will be exploring real-world problems in their packets to complete. They will need to think of how to solve the problem before jumping in. Students will also be thinking of other ways to solve problems when their peers present their problem and the students notice another way to solve it. Students can understand the approaches of others and make correspondences between the way they solved it and the way their peers solved it.

Misconceptions

4) Students invert the wrong fraction when dividing fractions. This results from rote memorization and a mindless series of steps.

5) Students tend to overgeneralize properties of operations.

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6) Some think it’s impossible to compute division problems where the dividend is smaller than the divisor.

Objectives

Students will complete the Healthy Lifestyle worksheet in order to demonstrate their understanding of the division of fractions.

Students will create their own word problems to connect dividing fractions to a real-world problem.

Areas of Cognitive Development Cognitive – Students will be using critical thinking skills to answer discussion questions that connect their word problems to real-world scenarios of healthy living. They will be solving real-world context problems and use their knowledge to create their very own word problem. Social – Students will be working in groups to promote a collaborative setting and talk among one another to come up with an answer. Emotional – Students will rely on one another to help them create their own word problem but also to have their peers solve it. The students need one another to complete this portion of the lesson. Physical – Students are actively moving around the room, and an extension would be to have students physically run around outside or in the gym and calculate their distance and time. They will use these numbers to complete a math problem similar to the very first one in the packet. Student Motivation and Classroom Culture Students will be in groups in order to promote collaboration and cooperation. Students will be solving word problems and teaching one another how they found a solution to the problem. This demonstrates a welcoming classroom culture because the students that are listening to the students presenting must show active listening, engagement, and respect. Students will also be creating their own real-life word problems and sharing them with other partnerships. Students will be more motivated to solve problems that their peers have created, rather than solve problem sets with no connection to real-world scenarios. Technology (tools) Healthy Lifestyle worksheet – teacher created Pencils Chart paper Markers or crayons Chocolate bar (anticipatory set) “Create Your Own Word Problem” worksheet – teacher created SMARTBoard chocolate bar – there will be a chocolate bar on the SMARTBoard that will be brought up once the students finish their problem-solving in the anticipatory set. This will allow students to come up to the board and interact with the technology to move pieces of chocolate and demonstrate how they solved the problem. Anticipatory Set The teacher will bring in a chocolate bar, but only 4/5 of the bar. The teacher will make a scene in the classroom, saying: I brought in a special treat today! I have a chocolate bar, but I already ate 1/5 of it! Now there is only 4/5 of the chocolate bar left! I want to share the rest of the bar with you, but I don’t know how we should divide it equally. Discrepant Event

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Students will work at their desks and try to solve this problem in any ways that make sense them and find out how much of an entire chocolate bar each student in the group will have (students will be in two groups of 8). 4/5 divided by 8 = 4/5 x 1/8 = 1/10 After students have tried to solve the problem, they will be given a chocolate bar for hands-on practice for dividing the chocolate bar equally. Students will then come up to the SMARTBoard and demonstrate the ways they divided the chocolate bar. The chocolate bar on the SMARTBoard will be pre-cut into small pieces. It will be the job of the students to arrange the pieces into equal groups to show the division of the chocolate bar. Other groups will show the different ways they solved the problem. Procedures Students will have a Healthy Lifestyle worksheet which contains the different word problems we will be solving and a question relating each to a healthy lifestyle choice. Below is an example of a running word problem and an application to a healthy lifestyle.

1) The teacher will say, “Now that we have divided this chocolate, let’s go outside and run around! You are an Olympic athlete and you’re training for a running event. A track is ¼ of a mile long. If you run 3 miles, how many times have you run around the track?”

2) Some students prepare 3 different snacks. They make pound bags of nut mix, pound bags of

cherries, and pound bags of dried fruit. If they buy 3 pounds of nut mix, 5 pounds of cherries,

and 4 pounds of dried fruit, how many of each type of snack bag will they be able to make? Students will continue through the packet (see attached). Students will be use their knowledge of dividing fractions and the discussion questions will help them make connections to healthy lifestyle choices. As the students continue through the worksheet, the teacher will prompt them with “discussion breaks:”

Why do we need to exercise?

Do you think the snack bags of nut mix, cherries, and dried fruit is the healthier option, or ice cream? Which one would give you more nutrition?

What did you notice about all of the word problems in the packet? Students will work in the groups to solve the word problems. After students have completed the worksheet, they will find a partner and chose one problem from the sheet. On chart paper, the partnership will become the “experts” on their specific problem. On the chart paper, students will include:

a. The word problem number b. The mathematical solution c. A picture (the picture could be a tape diagram that represents how the problem was solved, or

an artistic representation of the word problem – a picture of a man running around a track).

Students will present their findings to their group members and teach them how to solve it. As students present their problem, the other students will come up and show how they solved the problem if they did it a different way. This will show everyone in the class a variety of solutions and that one way of solving the problem doesn’t mean it’s the only way. Resolve the Discrepancy

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The teacher will explain how we started the lesson with a word problem about a chocolate bar. As we went through the lesson, we solved problems that helped us see healthy choices in our lives, such as running, exercising, and eating a nutritious diet. Since we learned some healthier options, we are going to create a new problem using a different, healthier choice of food or a problem about physical activity. Students will create their own word problems using a healthy lifestyle choice. The students will be in partners still. They will be provided with the numbers to use for the problem (each partnership will have different numbers). This will help them focus more on creating and solving the problem rather than trying to come up with numbers that would be computable. After students create their problems, they will switch word problems with another partnership and then the students must solve the new word problem that their peers have created. Assessments The worksheets will be collected for the teacher to check for completion and understanding. Students should be able to complete most of the problems without difficulty since this is a review lesson of dividing fractions. The teacher will also do informal assessments on student participation during the group work to see who is actively engaged and who is disengaged. The “Create Your Own Word Problem” worksheets will be collected. This will show the teacher what partnership created the question and which partnership solved it. It will provide information about who created an applicable, real-world problem and who was able to solve them. Rubric

1 3 5

Healthy Lifestyle Packet 50% or less is completed with only one way of solving the problem.

75% or less is completed with only one method of solving the problem.

Student completed more than 75% of the packet and several problems include multiple solutions.

Create Your Own Word Problem

Student did not attempt to create a word problem.

Student attempted to create a word problem but it didn’t connect to health or it was not a division problem.

Student created a word problem that was health related and a solvable division problem.

Completing the Create Your Own Word Problem

Student did not complete the word problem given to them by another group.

Student attempted to complete the word problem given by another group.

Student accurately solved the word problem given to them by another student (or solved it accurately even if the word problem itself was incorrect).

Differentiation Students with visual and hearing impairments will have preferential seating. Students that struggle with the material will be purposefully partnered with another student that might be stronger and willing to assist the struggling student. Partnerships and group work help students work together to collaborate and solve problems that might be difficult. Students that show misunderstandings may be seated near the teacher for more direct guidance. Lastly, students may be purposefully paired and grouped (rather than choosing their own) for students to work with those that will be most beneficial for their learning needs. Extension

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Students can go to the gym or outside on a track (if available) and run as fast as they can. The teacher will clock their time and the distance they run. These numbers will be applied to a new division word problem (similar to the one first in the worksheet) and students will solve their “custom-made” word problem. This helps the students see a real-world problem applied to their personal selves and thus makes it more meaningful. Children’s Literature Good Enough to Eat by Lizzy Rockwell would be an excellent book to introduce a new lesson about nutrition. The teacher could adapt the book by including division problems with the healthy guide to eating that the book explains. Alternatively, the teacher could use the book as a closing to the lesson and open a discussion about what new information the book taught us about eating healthy food. The students could connect this back to the word problems they completed and compare/contrast which problems contained healthy choices and which did not.

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Name ______________________________________________________

Living a Healthy Lifestyle

1) The teacher will say, “Now that we have divided this

chocolate, let’s go outside and run around! You are an

Olympic athlete and you’re training for a running event.

A track is ¼ of a mile long. If you run 3 miles, how

many times have you run around the track?”

2) Some students prepare 3 different snacks. They make

pound bags of nut mix, pound bags of cherries, and

pound bags of dried fruit. If they buy 3 pounds of nut

mix, 5 pounds of cherries, and 4 pounds of dried fruit,

how many of each type of snack bag will they be able to

make?

3) A serving of ice cream is ¾ cup. Jana wants twice as much

as one serving. Then, she decides that she wants to

share her ice cream with three of her friends. How much

ice cream would each friend get?

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4) You have pan of vegetable lasagna left in the refrigerator.

You want to cut the lasagna into equal slices so you can

have it for dinner for 3 nights. How much lasagna will

you eat each night? Draw a picture to support your

response.

5) You are running on a nature trail that is 3.75 miles long. The trail is divided into sections and each section is 0.25

miles long. How many sections are there altogether on the trail?

6) A container is filled with blueberries. of the blueberries

are poured equally into two bowls.

a. What fraction of the blueberries is in each bowl?

b. If each bowl has 6 ounces of blueberries in it, how many

ounces of blueberries were in the full container?

c. If of the remaining blueberries are used to make muffins,

how many pounds of blueberries are left in the container?

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Create Your Own Word Problem!

Created by ______________________________

You must use 1/5 and 4 in your word problem.

Solved by_________________________________

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Day 11: Performance Task – Dividing Pizza Equally

Standard Connection: CCSS.MATH.CONTENT.5.NF.B.7.A Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. CCSS.MATH.CONTENT.5.NF.B.7.B Interpret division of a whole number by a unit fraction, and compute such quotients. CCSS.MATH.CONTENT.5.NF.B.7.C 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.

Objective: Students will be able to help customer’s divide their pizza equally in the Performance Task by dividing fractions.

Materials: Pencils Paper Performance Task Packet

Learning Activities: Students are trying to get a job at the pizza shop. They begin a training session where they must help customers divide their pizza equally when there aren’t enough slices for everyone. Students will complete several real-world problems that involve dividing fractions to create equal pizza amount for each person. Students will solve the problems using equations and pictures. Students will answer all questions in the Performance Task packet in complete sentences.

Assessment: PLAN: Students will turn in their Performance Task packet to be evaluated on completeness and accuracy.

TOOL(S): The grading rubric is included in the Performance Task below. The Performance Task includes a student checklist for the student to use to help them answer all parts to the questions

EVALUATION: Students will be evaluated on their ability to help the customers to divide their pizza equally. A picture and/or equation is provided when the question called for it, and the answer was given in a complete sentence.




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Day 12: Performance Task – Adapting the Recipe to Make Different Sized Pizzas


Objective: Students will be able to adapt recipes using their knowledge of fractions to create different sized pizzas.

Materials: Pencils Paper Performance Task Packet

Learning Activities: In the Performance Task packet, students are given a recipe that makes a large pizza. They are told that doubling the recipe will make a sheet pizza, half of the recipe makes a medium pizza, and a quarter of the recipe makes a small pizza. Students use this information to adapt the recipes and make different sized pizzas. They are told that they must use their multiplying or dividing skills to solve the problems. They must show their work and also fill in a blank recipe. Using the original recipe, students must write how many pizzas of the different sizes can be made with the original recipe. They will answer these questions in complete sentences.

Assessment: PLAN: The Performance Task packet will be evaluated for completeness and accuracy in answering the questions.

TOOL(S): The grading rubric is included in the Performance Task below. The Performance Task includes a student checklist for the student to use to help them answer all parts to the questions.

EVALUATION: Students will be evaluated on three different criteria. All work must be shown for each questions. Second, the blank recipe must be completed. Third, the answer must be provided in a complete sentence. Students will be evaluated using the Performance Task rubric below.




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Day 13: Performance Task – Answering Customers’ Questions


Objective: Students will apply their knowledge of fractions to explain to customers how to divide their pizza equally.

Materials: Pencil Paper Performance Task Packet

Learning Activities: During this section of the Performance Task, students are required to answer questions that customers might have about their pizza. In the Performance Task packet, real-world scenarios are given to the students to solve by using an equation and a picture. Students must prove that they can answer the customers’ questions in order to be hired at the pizza shop. The Performance Task packet is included below.

Assessment: PLAN: Students will complete this section in the Performance Task packet and answer all parts. They must answer the question with a picture and/or equation, depending on what the question is looking for.

TOOL(S): The grading rubric is included in the Performance Task below. A student checklist is also included to help students know what they will need to write in their packets.

EVALUATION: Students will be evaluated on their ability to thoroughly answer the question, include a picture and/or equation when asked, and the answer is given in a complete sentence. The rubric for grading is found in the Performance Task below.




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Day 14: Performance Task Written Report and Reflection

Standard Connection: CCSS.ELA-LITERACY.W.5.2 Write informative/explanatory texts to examine a topic and convey ideas and information clearly. CCSS.ELA-LITERACY.W.5.4 Produce clear and coherent writing in which the development and organization are appropriate to task, purpose, and audience. (Grade-specific expectations for writing types are defined in standards 1-3 above.)

Objective: Students will write a report and reflection that explains their understanding of the performance task items and applies their knowledge of fractions.

Materials: Paper Pencil Performance Task Packet

Learning Activities: From the Performance task packet below, students will complete the fourth task. The checklist gives the students the specific guidelines to follow when completing the reflection. Students will respond to a set of questions that summarizes how they met each objective. They will describe how they used fractions to help divide pizza for the customers, how they adapted a recipe to make different sized pizzas, and how they answered customers’ questions. The reflection questions have students connect their experience in working at the pizza shop to how they can use their fractions skills in the future position. Students will thoroughly explain each question in the Performance Task packet to help them achieve their goal of being hired to work at the pizza shop.

Assessment: PLAN: Students will turn their report and reflection in to the teacher for evaluation. This is part of the Performance Task found below.

TOOL(S): The rubric is part of the Performance Task found below.

EVALUATION: Students will be evaluated on the report and reflection based on their ability to answer each part listed in the Performance Task packet below. The students must provide several examples from the Performance Task questions completed previously and use proper grammar, spelling and punctuation when completing this written portion.



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Performance Task for 5th Grade Task Analysis

Common Core State Standards

CCSS.MATH.CONTENT.5.NF.B.7.A Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. CCSS.MATH.CONTENT.5.NF.B.7.B Interpret division of a whole number by a unit fraction, and compute such quotients. CCSS.MATH.CONTENT.5.NF.B.7.C 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. Standards for Mathematical Practice 1) Model with mathematics 2) Make sense of problems and persevere in solving them

Enduring Understandings Real-world contexts can be used to solve fraction division problems. Fractions can be divided by multiplying by the reciprocal.

Essential Questions How do we use fractions to solve problems outside of school? What sorts of problems can be solved by dividing fractions?

Learning Outcomes Students will be able to solve word problems in a story-context using fractions. Students will demonstrate their knowledge of dividing fractions and describe those skills in a written report.

Materials Performance Task packet Pencils Student checklist Rubric




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GRASPS

Goal You are trying to get hired at the local pizza shop to earn some money for your trip to Disney World. The store owner is having you complete a variety of tasks to see if you are suitable for the job. You must use fractions to complete the tasks and then write a report to the store owner about your experience.

Role You are training at a pizza shop in order to prove to the store owner that you should be hired.

Audience You need to show the store owner the ways in which you can help customers in the pizza shop.

Situation You have applied to work at a pizza shop. The store owner has decided to let you complete a series of trainings to see if you are the right person to be hired. The owner has trusted you with a variety of jobs to do in the shop. First, you are required to take orders and help customers divide up their pizza into equal pieces. The next job is to use a generic recipe to make different sized pizzas. Lastly, he wants you to answer questions that the customers might have about pizza size, slices, and the amount they will need to feed their parties. You need to show your boss that you are capable of these different tasks in order to be hired for the job!

Product, Performance, Purpose You will be writing a report to your potential boss that explains each of the jobs you were assigned. You need to describe in detail the steps you needed to complete in order to solve the pizza problems. You will need to explain how you were able to help the first group of customers to divide their pizza. Then, you will need to describe how you converted the recipe given to accommodate for different pizza sizes. Lastly, you need to write about how you were able to help customers answer their questions about their pizza orders. Be sure to include your mathematical procedures and solutions when you used fractions! You will also be writing a reflection paragraph where you reflect on your experiences in the pizza shop. The requirements for the report and reflection will be included in the rubric.

Standards and Criteria for Success Your boss will rate your abilities to work in the pizza shop based on the following demonstrations:

o The ability to show customers that pizza slices can be divided equally, even if the pizza does not come with enough slices for everyone to have one piece.

o The skill to convert a recipe that accommodates for different pizza sizes to help fulfill a variety of pizza orders.

o The capability to communicate with customers and answer their questions about making enough pizzas to be divided among many people.

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The Pizza Shop

Performance Task

Name __________________________________________________________

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Overview

You are going to Disney World with your family but your parents said

you need to make your own money to buy souvenirs. You really want to buy

something cool that will help you remember your trip. In order to do this, you

need a job. You notice that the pizza shop down the street is hiring. You go

down there to talk to the store owner about the position. He decides to let

you do a training session at the pizza shop to see if you are qualified for the

position. You must use your expert math skills to show customers how to

divide their pizza orders equally when there aren’t enough slices for

everyone. You will also need to use the pizza recipe provided and adjust it

to make different sized pizzas. Lastly, you must answer questions that the

customers might have about pizza size and how many people they would be

able to feed. These are all necessary skills that the store owner is looking

for to work in the shop. After you have mastered these skills, you will write

a report to the owner explaining what you learned. Be sure to follow the

steps carefully so you can be hired. You really need this job!

Let’s Get Started!

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Help the customers share their pizza equally

It’s your first time at the training. 8 people come into the shop first. They want to order a large pizza. If each person were to get one slice of pizza, how much of the pizza would each person get? Assume each slice is the same size. Draw a picture to show your work. Unfortunately, the 8 people realize that there are only 5 slices in a pizza! The customers come to you for help. You need to show the customers how to divide the 5 pieces equally. How much of a slice will everyone get? Draw a picture to help show the customers show they should divide the pizza. Then, two people decide they don’t want to eat pizza anymore. If two people don’t eat their share of pizza, how many pieces are left? Solve with an equation below. This large party of people leave and they are very happy that you helped them divide the pizza! You are about to leave for your break and you don’t want their pizza to go to waste! You decide to bring it to your friends.

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Of the pizza that is left, you decide to share it with your two best friends (and yourself). If you are going to split this leftover pizza into three equal sizes, how will each person get? Draw a picture and write an equation to solve it. The store owner has been watching your progress through the day as the customers divided the pizza. However, he didn’t see how you divided the leftover slices between yourself and your friends. You want to show him everything you know in order to get the job. Write a short summary below about how you were able to equally split up the leftover pizza. Be sure to write in complete sentences!

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Adapt the recipes to make different sized pizzas Instead of selling the pizzas today, you will be making them! You want to show the store owner that you are able to double the recipes as well as divide them to make different sized pizzas. Look at the recipe below for pizza dough.

1 ½ cups of warm water 1 package of active, dry yeast

3 ½ cups of flour 2 ¼ tablespoons of olive oil

2 ½ teaspoons salt 1 ¾ teaspoon sugar

You have a tight order to fill today. This recipe makes a large pizza. Doubling the recipe makes a sheet pizza. Half of the recipe makes a medium pizza, and ¼ of the recipe makes a small pizza. Using your multiplication skills, how many of each ingredient will you need to make a sheet pizza? Solve below, then fill in the blank recipe. Solve here:

___ cups of warm water ___ package of active, dry yeast

___ cups of flour ___ tablespoons of olive oil

___ teaspoons salt ___ teaspoon sugar

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Using your division skills, how much of each ingredient will you need to make a medium pizza? Solve below, then fill in the blank recipe. Solve here: How many medium pizzas could you make with the original recipe? Explain in complete sentences below. Using your division skills, how much of each ingredient will you need to make a small pizza? Solve below, then fill in the blank recipe. Solve here: How many small pizzas can you make with the original recipe? Explain in complete sentences below.







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Answering customers’ questions You are back in the store for your final training activity. The store owner wants to see how you can answer questions that the customers might have. You start with a crazy order. A woman asked if she can order 18 pizzas to feed 38 people. She wants each person to have ½ of a pizza. Will there be enough pizza to feed 38 people? Solve below. Another customer comes in with a similar question. A couple is throwing a birthday party for their 5 year-old son. There are 7 children total that will be at the party. They plan on each child eating ¼ of a pizza. If they order 3 pizzas, will there be enough for each child? Draw a picture below to show if there will be enough pizza. Will there be any pizza left over? If there is, write how much below.

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If there is any pizza left over, show how you can divide it equally among the children. How much of a slice will each child get? Solve below with an equation and a picture. The couple was very grateful for all of your help! You have one more customer’s question to answer before your training session is over. A man says that he wants to order a pizza. He wants to use only 4/5 of the pizza to share among his 8 friends (he is saving the other 1/5 for himself). How much of the whole pizza will each of his friends get? Draw a picture and solve with an equation below. The store owner is very pleased with your progress! Now, you must write a report to summarize what you have learned while training at the pizza shop. You will also write a personal reflection on your experience.

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The report In your report to the store owner, include:

Explain how you helped customers to divide their pizza equally. Describe what math procedures and equations you used to solve them.

Describe how you converted the recipe to make different sized pizzas. Discuss how used multiplication and division to show how you adjusted the recipe.

Tell how you answered the customers’ questions to help them order the correct number of pizzas. Explain your division skills that you used.

The reflection In your reflection to the store owner, include:

Why do you think you should be hired for the position? How will you use fractions if you were hired? What did you learn while working in the pizza shop?

In your report and your reflection, be sure to write in complete sentences. Use lots of details and specific examples from your experiences when answering the prompts!

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Student Checklist Help the customers share their pizza equally Answer the questions with a complete sentence Provide a diagram or picture when asked in the question Divide the leftover pizza into three equal sizes by showing a picture

and an equation

Adapt the recipes to make different sized pizzas Read the description carefully so you know how much of the recipe

makes a different sized pizza Solve for the sheet pizza by using multiplication Solve for the other pizzas using division Fill in the blank recipes for each pizza size Answer the questions using complete sentences

Answering customers’ questions Answer each question in a complete sentence Use a picture when asked by the customer Use a division equation to help you solve each question

Report/Reflection Answer each bullet point in the description Write in complete sentences using proper grammar, punctuation and

spelling Write the reflection as a separate paragraph Use specific examples from your experiences in the pizza shop Refer to the rubric

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Parts of the Project

Exemplary – 3 Proficient – 3 Developing – 1

Help customers share their pizza equally

Each question was answered thoroughly. A picture was provided when required and all work was shown. The question was answered in a complete sentence.

Some parts to the questions were missing, such as the answer or a picture. Some work is shown.

Little to no work is shown. An answer is not provided or it is not provided in a complete sentence. Pictures are missing and the work is difficult to read.

Adapt the recipe to make different sized pizzas

All work was shown for each recipe. The questions that required writing were done in complete sentences. The blank recipes were filled in. Multiplication was used correctly when required and division was used correctly when required.

Some parts to each question were missing. The blank recipes are missing a few numbers. The questions that required writing had several grammatical errors. Small errors were made in multiplication and division problems. Some work is shown.

Little to no work is shown. The blank recipes are mostly incomplete. The questions required writing were not done in complete sentences and lacked proper grammatical structure.

Answer the customers’ questions

Each question was answered thoroughly. A picture was provided when required and each part of each question was answered. The question was answered in a complete sentence and all work is shown.

A few parts to each question are missing. The answer is provided but not in a complete sentence. Some work is shown.

Little to no work is shown. An answer is not provided or it is not given in a complete sentence. Pictures are missing and the work is difficult to read.

Report/Reflection Each bullet point was answered. The report contains several specific examples from the experience at the pizza shop. The report and reflection are grammatically correct with proper spelling and punctuation. Only one or two minor errors are shown.

Some bullet points are not addressed. The report contains one or two specific examples from the experience at the pizza shop. The report and reflection have several minor grammatical errors.

Several bullet points are not addressed. The report contains no specific examples from the experience at the pizza shop. The report and reflection have many major grammatical errors and it is difficult to read.

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References

Missouri Department of Elementary and Secondary Education (2013, May 20). Alert to student

difficulties and misconceptions in science. Retrieved from

http://dese.mo.gov/divimprove/curriculum/science/SciMisconc11.05.pdf

Tirosh, D. (2000). Enhancing prospective teachers' knowledge of children's conceptions: The

case of division of fractions. Journal for Research in Mathematics Education, 33(1), 5-25.

doi: 10.2307/749817

Common Core State Standards

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

Grade 5 Mathematics Module 4

http://www.engageny.org/resource/grade-5-mathematics-module-4

Next Generation Science Standards

http://www.nextgenscience.org/next-generation-science-standards

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

http://www.engageny.org/resource/grade-5-mathematics-module-4

http://www.nextgenscience.org/next-generation-science-standards

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