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Brittany Schenkel4th grade Math February 25, 2013Essential Questions:What is an improper fraction and how it is represented?What is a mixed number and how is it represented?What is the relationship between a mixed number and an improper fraction and how can they be converted?Vocabulary:Improper fraction – a fraction with a numerator greater than or equal to its denominatorMixed Number – the sum of a whole number and a fractionSkills:ConvertVisualize a relationshipObjectives:Students will understand that improper fractions and mixed numbers are interchangeableStudents will be able to convert an improper fraction to a mixed number Common Core Learning Standards:Math Standards:Number & Operations—Fractions 4.NF Extend understanding of fraction equivalence and ordering. 1. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) 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. 2. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers. 3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b. a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole. 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. 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.Language Arts Standards:Speaking and Listening - Grade 4Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 4 topics and texts, building on others’ ideas and expressing their own clearly. a. Come to discussions prepared, having read or studied required material; explicitly draw on that preparation and other information known about the topic to explore ideas under discussion. b. Follow agreed-upon rules for discussions and carry out assigned roles. c. Pose and respond to specific questions to clarify or follow up on information, and make comments that contribute to the discussion and link to the remarks of others. d. Review the key ideas expressed and explain their own ideas and understanding in light of the discussion.Pre-Assessment: The students have previously begun their unit on fractions. They have an understanding of what a fraction is and are able to recognize equivalent fractions and know how to write a proper fraction in simplest form. They also have been introduced to the idea of what an improper fraction looks like as well as what a mixed number looks like.Lesson Presentation:Set Induction – The students will all be called to the meeting area and told to bring a pen or pencil with them. When they come to the meeting area I will begin by giving them directions about the activity they are about to complete. There will be five stations set up around the room with fraction pizzas of various amounts of 1/2, ?, 1/3, 1/8, 1/16 fractions and the students will be walking around the room in 5 groups of 6 students completing a worksheet given to them. The worksheets will already be at the tables for them to save the time it takes to hand them out. The worksheet will require them to draw what they see, write the value of one piece of pizza and write the improper fraction of the total amount of pieces. There will also be a section for them to convert the improper fractions to a mixed number, however I will instruct them to leave that column blank because we will go over it as a class. There will be an example at the top of the chart modeling my expectations. The students will be given no more than 3 minutes at each station and I will be circulating around the room to assist with any questions. If I see the students do not need to full 3 minutes at the stations I will have them switch by clapping my hands to gain their attention and have them move to the next station. (For the students who have prior knowledge on this subject and will go through it quicker than the rest, I will tell them to come up with as many equivalent fractions as they can think of for the one fraction.)Lesson Presentation – Lesson/ Guided Practice: Once the students have finished circulating each station, I will call them back to the meeting area to discuss our findings. I will ask the students what they noticed about the fractions they wrote down (the numerator was larger than the denominator, they were improper fractions, etc.). After I give them a minute or so to share, I will begin by teaching the students how to writing an improper fraction. I will start the conversation by saying “have you ever heard someone go into a pizzeria and order 3/2 of a pizza? .... Exactly, they would order 1 1/2 pizza pies or 1 whole pies and 4 slices (if the pie has 8 slices). The reason this is because no one really uses improper fractions in their everyday discussions because they can get confusing. This is why it is important for us to know how to turn improper fractions into their equivalent Mixed Numbers.” We will start with converting the improper fraction from the ? station (5/2). The students will follow the steps provided as we figure it out as a class. Step 1: divide the numerator by the denominator (fraction means divide so when we see a larger number on top we divide {5/2 = 2 r 1}) I will also be drawing 5 circles and grouping them into two different boxes to show that the middle circle needs to be split in half and each half goes into a different box, meaning each box gets 2 1/2 circles. Also Step 2: write the remainder as a fraction (2 1/2). I will have a picture of the visual used at the ? station on a smartboard page to reference back to so that the students can visually see how 5/2 = 2 ?. We will go through these steps for each fraction on the chart, leaving one or two at the end for the students to try on their own, or with a partner, in the meeting area and we will go over it when they finished. Applying the Lesson- After I have finished the lesson, I will explain to the students that we are going to eventually be playing a game with our new knowledge of fractions, but we need to finish making our game boards. At their seats will be a Bingo game board with improper fractions listed in the boxes, however I need their help converting them into mixed numbers before we can play. They will have the opportunity the work with a partner after five minutes of trying independently, however only if I see they are trying. When I am finished giving them directions and they understand their task, I will have them go back to their seats to begin. Closure – At the end of the lesson, depending on how much time the students need to complete the Bingo boards, we will either play a game or just go over a few conversions that they needed to do on the board. Materials and Resources:SmartboardFraction Pizzas for stationsChart worksheetHomework worksheetBingo game boardsPen/ pencilBingo game pieces (if time allows)Follow- Up Assignment: For homework that night, the students will complete a worksheet that requires them to convert improper fractions to mixed numbers in order to give them extra practice with their conversions. Evaluation or Assessment: The students will be assessed on their completed class work, participation during the lesson and the homework assignment in order to determine if the students have met the objectives of the lesson. Differentiation: This lesson is applied to various learning styles due to the visuals, hands on station work and treating the independent work as a game. For the students who need more assistance during the lesson, I will be circulating for questions. The group work throughout the lesson also gives these students a chance to ask their peers for help. For the students at a higher level, I will be placing a bonus question on the homework assignment that requires them to take a mixed number and convert it into an improper fraction. The game boards are also differentiated because they will not all be the same. Since I am handing them out to the students, I will save the more difficult boards for the students who can handle the challenge. The set induction will also have more tasks for these students to complete such as forming equivalent fractions out of the improper fraction found at each station, while they wait for the rest of the class to finish at their station. Name_______________________Date__________________Directions: Using either the pictures or division method from today’s lesson, convert these Improper Fractions into Mixed Numbers. Show all your work. 46. 163 797. 237 3138. 2910 5299. 378 81910. 194 2Challenge: Try converting these Mixed Numbers into Improper Fractions3 3/4 2 5/8 ................
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