<p>This lesson will build on students' prior experiences of sharing to develop fraction concepts. Students are going to: - gain knowledge about partial components of a whole. - build a fraction of a whole.</p>

<p>- What mathematical representations exist for relationships? - How does effective communication benefit from mathematics? - How do we represent, compare, quantify, and model numbers using mathematics? - What does it mean to evaluate or estimate a numerical quantity? - What qualifies a tool or strategy as suitable for a particular task?</p>

<p>- Denominator: The bottom number of a fraction. Tells the number of parts the whole is divided into. - Fraction: Part of a whole. A number written with the bottom part (the denominator) telling you how many parts the whole is divided into, and the top part (the numerator) telling how many you have. - Numerator: The top number of a fraction. Tells how many parts of the whole you have.</p>

<p>- Stuart J. Murphy. (1996). <i>Give Me Half. </i>HarperCollins. - one piece of paper for each student for Paper Fair Share Activity - plate with three brownies for Brownie Fair Share Activity - Brownie Problems worksheet (M-3-3-1_Brownies on Paper and KEY) - Fraction Practice Problems worksheet (M-3-3-1_Fraction Practice Problems and KEY) - Judith Stamper. (2003). <i>Go, Fractions! </i>Grossett & Dunlap. - Jerry Pallotta. (2002). <i>Apple Fractions.</i> Scholastic. - Jerry Pallotta and Robert C. Bolster. (1999). <i>The Hershey’s Milk Chocolate Bar Fractions Book.</i> Cartwheel Books.</p>

<p>- As the students work on the brownie task, keep an eye on them and probe them with questions to find out how much they understand. - For a more thorough assessment of students' mastery, use the think-pair-share fraction exercise.</p>

<p>Modeling, Active Participation, and Scaffolding W: By utilizing sharing, students will learn how to connect fractional models with numerical fractions. H: To generate interest in fractions, read Give Me Half by Stuart J. Murphy to students, and encourage critical thinking as you discuss the story. E: Initiate a conversation with your students about justice by using the Paper Fair Share Activity to explore the concept of receiving an equal or fair share. R: Encourage the students to come up with solutions for the Brownie Fair Share Activity. There are multiple approaches to solving this problem. Provide them with the Brownie Problems worksheet to review and practice what they have learned.E: While students are completing the Brownie Problems worksheet, observe them and ask them questions. T: Adapt the lesson to the different needs of your students by incorporating any useful ideas from the Extension section. Students who might benefit from more practice or direction are the target audience for the Small Group activities. Students who desire a more rigorous education than what is required by the standard can utilize the Expansion section. Students can use the ideas from the Routine section to reinforce fraction concepts throughout the academic year. O: The goal of this unit is to strengthen students' understanding of fractions, particularly fractions of a whole. If you start with a fraction and not necessarily a whole, the second activity expands on the first activity's explanation of the idea that shares must be equal for a situation to be fair. </p>

<p><strong>"Today, I'm going to read you a book. You will finish an assignment in your math journals at the end of math class." </strong>As an introductory exercise, you could read Stuart J. Murphy's book "Give Me Half" to your students. If this book is not available, you could consider using "Go, Fractions!" by Judith Stamper, "Apple Fractions" by Jerry Pallotta, or "The Hershey's Milk Chocolate Bar Fractions Book" by Jerry Pallotta and Robert C. Bolster as excellent substitutes. During the exercise, it would be helpful to examine the images and discuss the contents of each page with your students.<strong>"Before I give you a problem to solve, would you like me to read you a book? Let's examine the cover and try to guess what the book is about."</strong>Accept student suggestions and predictions about the book.Stuart J. Murphy's book is titled "Give Me Half." I want you to pay attention to the methods the kids in the book employ to get through their problems as we read the story. As you read, quiz the students on the book and the clusters of objects on each page. Typical inquiries might be:<strong>"What did the book teach you?"</strong><strong>"What was the issue in the story's opening?"</strong><strong>"What is the definition of sharing?"</strong><strong>"Is the amount we receive when sharing something always the same?" </strong><i>(Recall that all fractions of a whole have the same size.)</i><strong>"Give an instance of equitable sharing from the book. Explain."</strong><strong>"What transpired during the cleanup phase after the narrative?"</strong><strong>Paper Fair Share Activity</strong>Start a lesson where students will ultimately receive one piece of paper, showing that everyone has received their fair share.<strong> "I have a stack of papers here,"</strong> say to students. <strong>"Will you please pass them out so there are no extras?"</strong> asks a student. <strong>"There should be an equal amount for everyone."</strong> (Every student ought to be given one.)To each student, the student distributes one piece of paper. There aren't any additional papers for the student. <strong>"All of you raise your papers above your heads. What quantity of paper did you receive?"</strong> (Students say, "We got the same thing; we got one sheet of paper.")<strong>"You're right, everyone has an equal portion of the paper."</strong> Mention how they are certain that everyone received a fair portion.<strong> "Please put that paper in your desk's upper left corner. After the lesson, you will need it."</strong><strong>Brownie Fair Share Activity</strong><strong>"I have a problem that needs to be solved. I thought you could help me, so I brought a plate of brownies. Tonight is my book club meeting. Yesterday, after school, I made some brownies and put them on a plate. While I was out shopping, my family had some of the brownies. Now, I only have three brownies left, but there will be six people at my house tonight. What should I do?"</strong>Ideas from students include baking fresh brownies, purchasing brownies from a store, or speculating that "Maybe some of your friends won't want a brownie."<strong> "But what happens if everyone wants a brownie? I have to make enough brownies so that everyone who wants one can get a fair share of them."</strong>A student might remark, "It would be enough if you chopped one of the brownies into smaller pieces."<strong> "Would you please come to the board and show your point?"</strong> The student comes to the board and draws three brownies. Next, the student divides the first brownie into four pieces.</p><p>The student says, "You now have six brownies. Since it's larger, I would choose one of these." <strong>"You're correct. If I cut the brownies the way you illustrated them on the board, there would be six of them. However, would it make you happy if I gave you one of the first pieces?"</strong> <strong>"At your desk, talk to your partner. Draw how you would distribute the brownies so that each person gets a fair portion using the paper from the desk corner."</strong> Ask students to present their ideas to the class and to a partner. Emphasize the best approaches to taking on the problem. Ask groups to present potential fixes for the brownie dilemma.Possible Solutions:</p><p>Depending on what numbers are used, the relationship between the quantity of items to be shared and the number of people sharing can be as simple as sharing paper or as complex as sharing brownies.Let students carry on with their problem-solving after the brownie-sharing exercise.<strong>"I appreciate how well you helped me with the brownie problem. Proceed to solve additional brownie problems using the Brownie Problems worksheet (M-3-3-1_Brownies on Paper and KEY). Together, let's look over the instructions and solve the first problem."</strong>(Example: demonstrate how to resolve the issue. Two children need to share six brownies, according to the first problem. Hence, three brownies are given to each child. This is how a model might appear:</p><p>Find out if the students have any questions, and if so, make sure the instructions are clear.) <strong>"Now that you and I have finished the first problem, move on to the next one. Proceed to solve the remaining issues once you believe you have a solution. I'm going to stop by and look over your work."</strong>After students have completed the Brownie Problems worksheet, model the following problems using the think-aloud technique. This worksheet (M-3-3-1_Fraction Practice Problems and KEY) contains the following problems:5 brownies shared with 4 children2 brownies shared with 4 children4 brownies shared with 8 children3 brownies shared with 4 childrenIf students continue to divide things into four groups of five, they will eventually run out of two halves to give to each group of four. Some believe that splitting each half in half is the best course of action, meaning that "each child gets a whole and a half of a half." Somebody will cut the five things in half and then distribute the halves.<strong> "Every child gets two halves and a half of a half" is the solution to this issue. After providing modeling, assign students to work alone or in pairs to finish the Fraction Practice Problems worksheet (M-3-3-1_Fraction Practice Problems and Key).</strong>As students work through the brownie problems and engage in discussions and questions, you will have the chance to evaluate them. To help students better understand, you might need to pull them into small groups. Alternatively, you could test students' knowledge at a different time.Here are a few examples of possible questions:<strong>"Why were the brownies cut in this manner?"</strong><strong>"Explain the steps you took to solve this problem."</strong><strong>"Did you notice anything similar about solving the solution when you solved multiple problems?"</strong><strong>"What do you find challenging about this problem?"</strong>Ask students to write down the fraction and a justification for their ideas. Emphasize the equivalency of various representations when students present their answers. For students to completely comprehend the connection between <strong>fractions and real-world experiences, they will need to work through a lot of fraction problems.</strong><strong>Extension:</strong><strong>Routine: </strong>Use this fraction think-pair-share activity to practice these ideas, as a warm-up for the following day or all through the school year. Ask students to find a partner. After that, give a half-sheet of paper to each student. For example, write, "Six students want to share four licorice whips equally," on the board with a fraction problem. Allocate a specific number of licorice whips to each student. Give students 30 seconds or so to consider a solution to the problem. They might employ any tactic. Allow students to complete the task in approximately one minute and record their solution on a half sheet of paper. Students should present their responses to a partner. Students should debate why they believe their response is correct if there are differences in the answers.<strong>Small Group: </strong>To represent the brownies, give students who need more practice 2-by-4-inch pieces of paper. Students would be able to cut and stack the pieces as a result. Students can either glue their solutions to paper or illustrate their answers with drawings. For the brownies to remain the same size, some students will need to have them drawn already. For this, use the Brownie Problems worksheet (M-3-3-1_Brownies on Paper and KEY). Ask students to write down the fraction and a justification for their ideas.<strong>Extension: </strong>Assign nonrectangular shapes, such as an equilateral triangle, a circle, or an isosceles trapezoid, to students who pick up the concepts quickly and divide them equally into parts. Alternatively, assign students to divide simple fractions into equal portions, such as "Jane has half of a pizza (it could be a rectangle or a circle). She desires to split it into three equal portions. What percentage of the entire pizza will each piece contain?" Encourage students to model the problems with drawings or manipulatives.</p>