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Introduction:Multiplying unit fractions by unit fractions, Math, 60 minutesMaterials:NYS Common Core Mathematics Curriculum SmartBoard Activity Paper, pencilsPreparation:Gather materialsEnsure SmartBoard & Laptop are working properlyGrade Level:5th Enduring Understandings:Multiplication of unit fractions is used in a variety of everyday situations. Essential Questions:How can multiplying unit fractions be used in the real world?How are fractions used in problem-solving situations?What does it mean to multiply two unit fractions?Objectives:Students will learn how to multiply unit fractions first by drawing diagrams and then by simplifying and multiplying. This will be seen in their work and through what they are able to express to their partners and class. Areas of Development:Social: Students will be expressing their thoughts, work and questions to their peers as they work on each problem. Through their interactions with peers, students will develop in how to express their ideas, appreciate others contributions and work collaboratively to solve problems.Linguistic: Students will be verbalizing and writing down the steps they used to solve the problems, in small groups & as a whole class. Bloom’s Taxonomy:In this lesson plan students will be using various levels of higher order thinking. They will start by expressing their initial comprehension through the Grapple problem. They will apply and analyze their knowledge through the additional problems and they will evaluate their peers work against their own in order to solve the problems with an accurate answer and correct procedure. Common Core & Mathematical Practice Standards: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 SS.Math.Practice.MP6 Attend to precision. Mathematically proficient students try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose, including using the equal sign consistently and appropriately. They are careful about specifying units of measure, and labeling axes to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context. In the elementary grades, students give carefully formulated explanations to each other. By the time they reach high school they have learned to examine claims and make explicit use of definitions.Physical Education Learning Standards:A Safe and Healthy Environment Standard 2: work constructively with others to accomplish a variety of goals and tasksChildren’s Literature Connection:This lesson contained a lot of concept development through work problems and equations. There was no time to incorporate literature into the lesson and it would not have helped students gain a better understanding of the topic. Engage & Explore:GrappleProblem #1: Jan has 4 pans of crispy rice treats. She sends 1/2 of the pans to school with her children. How many pans does Jan send to school?Students will be presented this problem on the SmartBoard to work on. They will be given a minute to read and solve the problem. Then as a class we will discuss the answer. The teacher will then change 4 to 2 and have students do the same. Then change the 2 to 1. Then change the 1 to ?. Explain:After students have been given 3 minutes to work on the last variation of the problem they will be asked to do a Turn & Talk with their “elbow partner” to explain how they solved the problem- what diagram they drew, etc. and what answer they got. Students do this during every math lesson and are often able to work through misconceptions with their peers. The teacher will listen to pairs as they discuss and present any common errors or methods during the whole class discussion. Whole Class DiscussionAs a class students will discuss their work and answers. After students have presented their work and how they came to the answer the teacher will reveal the work included in the module to show a clear diagram and work. The teacher will address questions and misconceptions as they present themselves Learning TargetStudents will then be presented with the learning target of the lesson- “I can multiply a unit fraction by a unit fraction.”This will allow for a class discussion about what a unit fraction is- see if the students can figure out what a "unit" might mean. The teacher will have them turn and talk first, and then a few students will asked to share what they discussed. Try to bring to their minds that a unit is ONE; like one inch, one meter, one foot, one pound. So a unit fraction is one "size piece", like 1/4, 1/2, or 1/6. This idea of a unit is very important later on in the year and in 6th grade, too.Concept DevelopmentStudents will be given problems on the SmartBoard to further develop the concept introduced in the Grapple. Students will be asked what the difference is between these problems and the ones they previously worked on- multiplying and dividing fractions. After the class discusses the concept development problems students will complete the problem set.This worksheet contains problems and word problems for students to show their work, draw diagrams and explain their answers. This additional exposure allows students to work at their own pace and become more familiar with the procedures and problem types. Evaluate:At the end of the lesson students will complete an exit ticket. This will allow the teacher to evaluate their understanding of the concept. The exit ticket contains 1 problem and one word problem. Draw a model & show your work to solve: 1/3 x 1/3 =Ms. Shepard cuts ? of a piece of construction paper. She uses 1/6 of the piece to make a flower. What fraction of the sheet of paper does she use to make the flower? Assessment:Students will be assessed on the completion and accuracy of their exit tickets. This assessment will allow the teacher to determine whether this lesson needs to be continued the following day or if they are ready to transition to the next lesson- multiplying unit fractions by non-unit fractions. Differentiation: This lesson allows students to collaborate with their peers many times. This will allow students to gain a better understanding of the material from repeated exposure and explanation from their peers. Also, when this lesson is taught, there will be 3 adults in the room who can circulate and assist students as needed. When the SmartBoard is in use, students will be asked if they have clear sight of the board- students with visual impairments will be allowed to move closer to the board during instruction.Expected Misconceptions:Before being introduced to fractions, students expect multiplication problems to result in a larger number than the original two numbers. It can be expected that some students will hold this belief when multiplying two fractions. ................
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