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# Fractions

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## Megan Peoples

on 5 May 2013

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#### Transcript of Fractions

Five Day Unit Plan- 4th grade by Megan Peoples Fraction Fun What is a Fraction? Day 2 Fractions of Groups Day 3 Combinations that Equal 1 Day 1 "Fractions are a critical foundation for students, as they are used in measurement across various professions, and they are essential
to the study of algebra and more advanced mathematics"
(Bay-Williams, Karp, Van de Walle, 2013, p. 291). Why Are Fractions important ? We will begin our day reading Fraction Fun by David A. Adler and discussing students findings of fractions at home. Teaching/Learning Procedure: Practice and Application Materials/Media/Technology Standards Student Outcomes Day 1: What is a Fraction?
a. Students will gain a basic understanding of what a fraction is, how it is written, and how to label fractional parts (numerator and denominator).
b. Students will be able to draw, label, and identify fractions such as ½, 1/3, ¼, and 1/6.
c. Students will discuss how fractions are used and seen on a daily basis.
d. Students will use technology to practice fractional skills learned. a. ACOS- Math- 12.) Explain why a fraction a/b is equivalent to a fraction nxa/nxb by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
b. b. NCTM: -develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers;
c. -use models, benchmarks, and equivalent forms to judge the size of fractions; a. Math journals
b. Pencils
c. Chart paper
d. Marker
e. You Tube Videos
f. Sticky Notes
g. Assessment Chart
h. Manipulatives: fractional parts, blocks/ dryerase board
http://www.coolmath4kids.com/fractions/fractions-01-what-are-they-01.html a). Launch of Lesson- I will begin this lesson by asking student what they know about fractions. “What is a fraction? Have you ever seen fractions? Where have you seen a fraction? What do you know about fractions? Is there anything you would like to know about fractions?” I will use something similar to a KWL chart and list the things students know about fractions and the things students want to know about fractions on the chart at the front of the classroom so that all students may see. Students will copy this chart in their math journal for future use and reference.
Next students will watch the Youtube video Wholes, Halves, and Quarters Investigation and Presentation To begin our investigation and presentation of fractions I will present students with a website lesson plan that they will review themselves using Ipads. They will read pages 1-4 and practice the problems on their own.
http://www.coolmath4kids.com/fractions/fractions-01-what-are-they-01.html

Here we will answer the question “What is a Fraction?” Students will be introduced to ½, 1/3, ¼, and 1/6 fractions. We will discuss how the fractional parts added all together make one whole. I will also draw several examples of fraction such as 2/4, 4/6, 2/3, ½ and ask to name and identify the fractions. We will discuss how to make a whole from these fractions as well. We will also discuss math vocabulary like numerator and denominator. We will discuss how to label fractions and how we can remember where each number goes when you write out a fraction numerically. Next students will work together with a partner to complete Brownie sharing activity. Students will answer questions using drawings or any manipulative they like to solve the following questions. They must explain their reasoning for their answer.

•Four friends share 8 brownies. How much can each friend have? Each friend needs the same amount.
•How can 2 people share 3 brownies?
•How can 2 people share 6 brownies?
•How can 4 people share 3 brownies?
•How can 6 people share 4 brownies?
•How can 3 people share 6 brownies? Accommodations/Modifications If students finish early with the brownie question then they may use the Ipads with a partner to review http://www.kidsolr.com/math/fractions.html. They may review with the fraction practice activity as well on the same website.
Students who need extra help and more explanation will be pulled to the back table to work with them privately in a smaller setting. I will present more practice using white boards and manipulatives to help students identify and draw fractions. Extension/Challenges: Students will practice on their own flag fraction creations on the Ipad. They can also play identifying fractions game.
http://resources.oswego.org/games/fractionflags/fractionflags.html

http://www.sheppardsoftware.com/mathgames/earlymath/fractions_shoot.htm 3. Students will use an exit slip to move on to the next thing. I will pass out sticky notes to students and have them list something they have learned and/or something they are still confused about. Before moving on, students will place their sticky note with their name on it onto the assessment poster at the front of the classroom. The assessment poster has three categories: Got It!,Almost Got It!, and Need More Help! They will complete their own self assessment by placing their sticky note under the right category they feel they are at with Fractions. Investigation/Presentation Teaching Learning Procedure:
Launch of Lesson Practice/Application Materials/Media/Technology Standards Student Outcomes Day 2: Fractions of Groups Watch this number talk I had with some students who did not fully understand numerator and denominator. It shows the importance of discussing these words and their meanings. a. Students will discover fractions of groups of things.
b. Students will compare fractions and recognize equivalent fractions.
c. Students will compare fractions using <, >, and a number line. a.ACOS- Math- 12.) Explain why a fraction a/b is equivalent to a fraction nxa/nxb by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
b. NCTM: -develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers; use models, benchmarks, and equivalent forms to judge the size of fractions; a.Fraction Fun book by David Adler
b.Chart listing fractions at home and school
c.Skittle fun packs for each student
d.Skittle fraction worksheets
f.Brainpop Video: Fraction Action i. We will start out lesson out by reviewing student’s findings of fractions they saw at home. We will list these fractions on a chart at the front of the room. We will discuss where these fractions were and how they were used.
ii. Students will also list fractions that they see at school on a daily basis.
iii. Students will then be given ten minutes to write about either why they think fractions are important or how they can see themselves using fractions in their future. Students will turn this in and I will display this on our math wall in the classroom. i. We will start our investigation and presentation of lesson 2 by reading Fraction Fun by David Adler. We will talk about the groups of fractions presented in the book.
ii. Next we will watch the Brain Pop video: Fraction Action which explains fractions of groups of things.
iii. I will give students examples of groups of things and we will write the correct fraction.
iv. Examples:
1. How many girls out of all students in our room?
2. How many boys out of all students in our room?
3. How many fourth grade classrooms out of all the classrooms in our school?
4. How many people like chocolate ice cream out of all our students?
5. How many people are wearing pants/shorts/ skirts ?
6. How many people are wearing tennis shoes/sandals/flipflops/boots/flats? i. Students will practice finding groups of things using a packet of skittles. Each student will receive one packet of skittles. Students will open the packet and count how many skittles in all. You should ask students to group skittles according to color.
ii. Students will then fill out the chart they are given to show how many skittles they have of each color and the fraction representation for each skittle color. You will also be creating a class chart on the Elmo or document camera to show students once they have finished their own. I will be using this lesson plan format I found online as my chart and questions for students. http://faculty.nwacc.edu/EAST_original/Spring2011/Independent%20Study/Niki/Working%20with%20Fractions!.pdf

iii. Students will then answer several questions about their data from the chart.
iv. Next students will form a number line using their fractions of each color skittle d. Accommodations/Modifications:
i. Students may work with a partner or the group at their table if they need help writing the fractions.
ii. Students who need more in-depth help will be pulled back for small group to complete the chart with me.

e. Extensions/Challenge:
*Students will play Fraction War using fractions cards. Each students will draw a card. The student with the biggest fraction wins all the cards drawn. The student with the most cards at the end wins.

** Students may watch the Brain pop video again and complete the quiz for extra practice. They may also complete the other extension activities on Brainpop for this video.
***Students may explore the following games online using ipads
http://www.coolmath4kids.com/fractions/fractions-04-equivalent-01.html http://www.counton.org/games/map-fractions/falling/ http://www.funbrain.com/fract/index.html Closure:
Once students finish their charts, questions, and number line I will place the chart on the Elmo and ask for a student’s data to complete my own. I will also answer the questions and have students help me complete the number line correctly. We will discuss equivalent fractions and how we know when a fraction is bigger or smaller than another. We will draw the fractions from the activity and discuss which one is the biggest and the smallest. We will also talk about which color was seen the most in the bags among students and which color was the least seen. We will wrap up the lesson by having students complete an assessment worksheet where students compare each color they had in their bag. We will again review why fractions are important and how we can see them and use them on a daily basis. Assessment a. I will assess students understanding of fractions by observing their work on their fraction charts with the skittles. I will observe whether or not they can compare the fractions and recognize equivalent fractions.
b. I will assess students understanding of charts and number lines by reviewing these skills with them and reviewing their work.
c. I will assess students understanding of comparing fractions and equivalent fractions by having them complete a worksheet that has them compare fractional amounts of colors by writing equality or inequality. They will turn this in for a grade. 1/2 1/4 1/6 1/3 1/8 1/10 1/4 1/6 2/6 4/3 1/8 2/5 6/12 2/3 2/4 1/5 4/7 Investigation/Presentation: Practice/Application Materials/Media/Technology Standards Lesson 3: Combinations that Equal One Today students Today Students will learn about combinations that make one whole. This is about students recognizing 1/2 which is important to know before they learn how to make one whole. This discussion will spark our lesson for the day. Student Outcomes Students will be able to create multiple combinations using fractions to make one whole.
Students will be able to recognize one whole.
Students will begin thinking about algebraic equations involving addition and subtraction of fractions.
Students will be able to navigate an Ipad to reach a website and collect data for an E-sheet. ACOS- Technology Education 2.) Use various technology applications, including word processing and multimedia software.
• Using navigational features commonly found in technology applications
• Identifying digital file types
ACOS- ELA 18.) Integrate information from two texts on the same topic in order to write or speak about the subject knowledgeably. [RI.4.9]
ACOS-ELA 24.) Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences. [W.4.3]
ACOS- Math- 12.) Explain why a fraction a/b is equivalent to a fraction nxa/nxb by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
ACOS- Math 14.) Understand a fraction a/b with a > 1 as a sum of fractions 1/b. [4-NF3]
a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. [4-NF3a]
b. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. [4-NF3b]
Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
c. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. [4-NF3c
d. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. [4-NF3d]
NCTM: -develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers; use models, benchmarks, and equivalent forms to judge the size of fractions; 5x12 rectangle worksheets
Crayons
My Half Day Book
Math Notebooks
Capstone Interactive Website
E-sheet
Sticky Notes Teaching and Learning Procedure: Launch of Lesson: I will begin the lesson by passing out 5x12 rectangles and crayons to each student’s table. I will begin the lesson by asking students to name some fractions they know that make one whole. I will list these on the board for all students to see. Next I will ask students to come up with a few ways on their own to create one whole using the 5x12 rectangle. Students will color in each fraction part and label it below. I will also pass out color tiles to help students if they would like to use them to help make one whole. Students may work with a partner if they need extra support. Once students have had time to create their own combinations that make one whole I will ask students to share their findings. I will ask students to bring their rectangles to the Elmo so that all students may see their combinations. I will write these combinations on the board on a chart labeled: Combinations that equal 1. We will discuss how students discovered these combinations and what helped them know that they equaled one whole. Next I will show students how to write the algebraic equations that equal 1. When we add ¼ + 1/4 +1/4 +1/4 =1. I will discuss this with students and we will talk about the symbols and the meaning of those symbols, specifically the equal sign. The equal sign does not only mean the answer is needed. It also means that the two numbers on either side of the equal sign actually mean the same thing and have the same value. I will also pose some problems for students to complete together with a partner. We will review the answers together by drawing pictures to represent the problem and also writing out the problem numerically.
¾ +___=1 2/6+___=1
½+___=1 4/5+___=1
2/4+___=1 2/9+___=1 Students will get an I pad and an E-sheet. Students will follow the directions on the E-sheet to the Capstone Interactive Web page. Students will then type in the following title: Pie Graphs in the search box. Next students will read the book either on their own or with a partner. Next students will answer the questions on the E-sheet. These questions will help students practice and apply what we have previously learned about parts that make a whole. http://www.mycapstonelibrary.com/RuntimeBookList.aspx •Students can have the book read to them if they struggle with reading.
•Students may also work with a partner if they need extra support
•Students may also work at the back table in a small group with the teacher for extra support. Accommodations/Modifications Extension/Challenges: Closure: I will close our lesson by having students share their stories they have written. We will review the topic by highlighting some things we have learned. Students will again use an exit slip to help me see where they are. They will list two things they have learned and they will place their sticky note under the correct heading on the assessment poster (Got, Almost Got It, Need Help). I will tell students that we will be talking about adding fractions tomorrow which we sort of got a head start on today. I will tell them now they are prepared for the next few days of lessons on fractions. I will assess students understanding of algebraic equations that make one whole by checking their work that they complete with a partner. I will also grade their responses on the E-sheet to make sure that they have completed each question correctly and written the fraction correctly. My last assessment for this lesson will be to check the assessment poster and meet with students who need help immediately. I will work with them and give them some extra support and problems to help me know what needs to be done to help them fully understand the concept of one whole. Assessment Day 4 Adding and Subtracting Fractions with Like Denominators Investigation/Presentation Teaching/ Learning Procedure Practice/Application: Materials/Media/Technology Standards Student Outcomes Lesson 4: Adding and Subtracting Fractions with like Denominators Students will add and subtract fractions with like denominators proficiently.
Students will be able to answer and describe addition and subtraction problems.
Students will create their own fraction story using fraction problems we have discussed throughout the week. • NCTM: -develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers; use models, benchmarks, and equivalent forms to judge the size of fractions;
• ACOS- Technology Education 2.) Use various technology applications, including word processing and multimedia software.
o Using navigational features commonly found in technology applications
• ACOS-ELA 24.) Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences. [W.4.3]
• ACOS- Math 14.) Understand a fraction a/b with a > 1 as a sum of fractions 1/b. [4-NF3]
o A. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. [4-NF3a]
o B. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. [4-NF3b]
o Examples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
o C. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. [4-NF3c
o D. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. [4-NF3d] •http://www.coolmath4kids.com/fractions/fractions-10-adding-with-like-denominators-01.html.

•http://www.coolmath4kids.com/fractions/fractions-11-subtracting-with-like-denominators-01.html.
•White Boards
•Dry Erase Markers
Fraction Fiasco Game and Game Pieces. Launch of Lesson:
•http://www.coolmath4kids.com/fractions/fractions-11-subtracting-with-like-denominators-01.html Students will practice subtracting and adding fractions with like denominators using the addition and subtraction Fractions Fiasco game. http://www.learn-with-math-games.com/printable-fraction-games.html Allow them to play the game for around 30 min. 15 min using addition and 15 min using subtraction. . http://www.learn-with-math-games.com/printable-fraction-games.html Accommodations/Modifications:
•I will place students in groups according to their behavior and also place those who struggle with those who can help them succeed.
•I will play with students at the back table who need extra support.
Extension/Challenges
•Students can try rotating operations each time they roll, adding one turn and subtracting the next as a challenge when playing fraction fiasco.
•Students can create their own story word problem using addition or subtraction of fractions. Closure: I will give students 2 problems, one addition and one subtraction, to solve as an exit slip that they will turn in and I will assess later.

Next I will read My Half Day by Doris Fisher and Dani Sneed to students. We will discuss the fractions in the book, the addition and subtraction of fractions, and the ways fractions are seen in everyday life. I will ask students to write their own fractions story. They must include fractions that make one whole, addition and subtraction problems, and fractions of groups of things. Students will illustrate their books and prepare to share and turn in on Friday. Once students finish their story they should review it and complete self-assessment checklist. They should also trade with a partner and have the student check their partner’s story and checklist before turning it in. Students should correct all mistakes. They will have Friday to complete if they do not finish. Students should take this home for homework to complete if they need to before Friday. This story will be graded Friday using a rubric. Assessment • I will assess students understanding of addition and subtraction of fractions by asking them to explain their work verbally to me and also walking and around and checking their work on the dry erase board.

• I will assess students understanding by checking their exit slips to see if they can write the fraction and the problem correctly and get the correct answer.

• Students will assess themselves and others fraction story by editing others papers to check for grammatical mistakes, incomplete sentences, or incorrect math problems.
Improper Fractions and Mixed Numbers Investigation/Presentation Practice/Application Materials: Standards: Student Outcomes: Lesson 5: Improper Fractions and Mixed Numbers •Students will be able to explain, describe, and write improper fraction into a mixed number.

•Students will review fractions from the week using PowerPoint presentation.

•Students will complete fractions unit test.

•Students will turn in completed fractions story with correct problems displayed throughout the story. NCTM: -develop understanding of fractions as parts of unit wholes, as parts of a collection, as locations on number lines, and as divisions of whole numbers; use models, benchmarks, and equivalent forms to judge the size of fractions;
•ACOS- Technology Education 2.) Use various technology applications, including word processing and multimedia software.
oUsing navigational features commonly found in technology applications
•ACOS-ELA 24.) Write narratives to develop real or imagined experiences or events using effective technique, descriptive details, and clear event sequences. [W.4.3]
•ACOS- Math 14.) Understand a fraction a/b with a > 1 as a sum of fractions 1/b. [4-NF3]
oA. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. [4-NF3a]
oB. Decompose a fraction into a sum of fractions with the same denominator in more than one way, recording each decomposition by an equation. Justify decompositions, e.g., by using a visual fraction model. [4-NF3b]
oExamples: 3/8 = 1/8 + 1/8 + 1/8; 3/8 = 1/8 + 2/8; 2 1/8 = 1 + 1 + 1/8 = 8/8 + 8/8 + 1/8.
oC. Add and subtract mixed numbers with like denominators, e.g., by replacing each mixed number with an equivalent fraction, and/or by using properties of operations and the relationship between addition and subtraction. [4-NF3c
oD. Solve word problems involving addition and subtraction of fractions referring to the same whole and having like denominators, e.g., by using visual fraction models and equations to represent the problem. [4-NF3d] •Dry Erase Boards/Markers
•Paper/Crayons
•PowerPoint Presentation
•Student Clickers for Activote
•Unit Tests
•http://www.coolmath4kids.com/fractions/fractions-07-improper-01.html

http://www.coolmath4kids.com/fractions/fractions-07-improper-01.html

http://www.coolmath4kids.com/fractions/fractions-02-mixed-numbers-01.html I will give students a few extra problems to practice before we move on. They will work on these for 10 min and then have a partner check them. Next students will use their Activote clickers to review the fractions we have covered this week using a fractions PowerPoint I created as a study guide. We will review for the test and students will vote using their clickers for the correct answer for each question. I will use the activate software to show the poll results of each question.
Next students will take a Unit Test and turn it in. Once they finish the test they will complete their fraction story. Students may trade with a partner and have them edit their story so they may correct mistakes before turning in. Students will have their own checklist they will check and turn in with their story. Accommodations/Modifications:
• I will read the questions to students who struggle and work with them at the back table during test.
• I will meet with students who need help writing their story.
Extension/Challenges:
• Students can write in their math journal about the things they have learned this week and the things they enjoyed the most.
• Students may review the weeks work by playing any of the fraction games they have played throughout the week. Closure: Students may share their fraction stories with the class and will be given extra points if they do so. Also, we will discuss things they learned throughout the week. We will review our chart we created on Day one and two and add to it the things we learned and enjoyed learning. Assessment •I will assess students understanding of mixed fractions and improper fractions by checking the problems they complete once they turn it in.

• I will also assess students understanding by observing and checking students answers using the activote pole to see the percentage of students who answer correctly or incorrectly.

•I will also be assessing students understanding by grading their tests and fraction stories.

•Students will be graded using a rubric for the story. Students will also have their own self-assessment checklist they will turn in when they finish their story. Fraction Story Rubric Teacher Rubric for Fraction Story Student Self Assessment •Students will create more of their own addition and story problem to show fractions adding up to equal one whole. They will draw and illustrate their story problem as well.
•Students will play Tony’s Pizza game where they will create a pizza using the correct fractional proportions to make one whole.
•http://mrnussbaum.com/pizza_game/
•This game helps students add fractions to make one whole. It is basically fraction matching. It is called Fractone http://www.coolmath-games.com/0-fractone/index.html + + _ _ 2/3 4/8 1/2 Number Talk 2: Fractions of Groups More discussion on Numerator and Denominator Day 5: Lesson 5
Student Math Survey This student math survey was one that was already prepared. I asked a students to complete this survey for me to see how they felt about math before I worked with them. It was a great chance to get to know my student and their beliefs about their math education in the classroom. This survey showed me the student loved math and would be very engaged in math lessons. I learned I could help the student by listening and understanding this students ideas and thinking when solving their work. Writing Plans:
Day 1:
Students will write in their journal what they know about fractions using a KWL chart. We will use this chart every day through the week. Students will also write about how they see fractions in their world. They will also make a list of fractions they see at home on a daily basis. They will go home and find some of these examples to share with the class Tuesday.

Day 2:
Students will share their journal writing about the fractions they found at home. We will add to their KWL chart things they have learned or questions they have about fractions. Students will then be given ten minutes to write about either why they think fractions are important or how they can see themselves using fractions in their future. Students will turn this in and I will display this on our math wall in the classroom.

Day 3:
Students will write in their journal and add anything they have learned to the KWL chart or any questions they still have. Students will also create their own story problems.

Day 4:
Students will write in their journal and add anything they have learned to the KWL chart or any questions they still have. Students will be writing a fraction story similar to the book My Half Day using specific criteria.

Day 5:
Students will complete their KWL chart. Students will also write about their favorite thing they have learned this week about fractions and how they see themselves using this later in life. Students will also be completing their fraction story.
Resources: Walle, V. D., Karp, K. S., & Bay-Williams, J. (2013). Elementary and middle school mathematics: Teaching developmentally (8 ed.). Upper Saddle River, New Jersey: Pearson
www.coolmath4kids.com
http://chalkvilleel.jefcoed.com/MC/Pages/default.aspx

http://faculty.nwacc.edu/EAST_original/Spring2011/Independent%20Study/Niki/Working%20with%20Fractions!.pdf

http://www.learn-with-math-games.com/printable-fraction-games.html
Student Work Samples This student wanted to add the denominator instead of keep it the same. She did later correct herself but she still wasn't sure this was correct. She also had problems dividing the rectangle into equal parts. She thought that she had to section of the number of squares in the denominator and then color in the numerator when really she needed to make equal pieces from the rectanlge. Student Work Sample
I drew the fraction in the boxes an asked the student to identify the fraction in numerical form. This student had problems with the last two because he said it was confusing. When I asked him why he told me because of the three different rectangles. He got the right answer but he struggled with adding the fractions.
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