Tools 4 NC Teachers | Math Science Partnership Grant Website



If I Were a Fraction In this lesson, students are identifying fractions in their environment. It is suggested that this lesson is done at the beginning of the fraction unit. NC Mathematics Standard(s):Numbers and FractionsNC.3.NF.1 Interpret unit fractions with denominators of 2, 3, 4, 6, and 8 as quantities formed when a whole is partitioned into equal parts;Explain that a unit fraction is one of those parts.Represent and identify unit fractions using area and length models.Additional/Supporting Standards:NC.3.NF.2Interpret fractions with denominators of 2, 3, 4, 6, and 8 using area and length models.Using an area model, explain that the numerator of a fraction represents the number of equal parts of the unit fraction.Using a number line, explain that the numerator of a fraction represents the number of lengths of the unit fraction from 0.Standards for Mathematical Practice:2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of others.4. Model with mathematics. 8. Look for and express regularity in repeated reasoning.Student Outcomes: I can understand that fractions are parts of a wholeI can determine the denominator in a fraction by relating the parts to the wholeI can identify unit fractions in a fractional representationMath Language:What words or phrases do I expect students to talk about during this lesson? numerator, denominator, fraction, whole, half, thirds, fourths, eighths, unit fraction450215012763500Materials: Paper, pencilsAdvance Preparation: Book “If You Were a Fraction” by Trisha Speed Shaskan Launch:Introduce Problem (5-7 min)Read the book If you were a Fraction by Trisha Speed Shaskan. After reading the story ask the students “What are some fractions you see in your everyday routine?” You can list what the students say on the board or chart paper. Possible responses include:Eggs in a cartonJuice boxes in a packA pack of pencilsSlices of pizza Slices of pie“Wow! There are fractions all around us! When looking at each of these items, you need to find how many parts make up the whole. The number of parts that make the whole is the denominator. The number of pieces you are talking about is the numerator. For example, 1 pencil in a pack of 8 is ? of the pack. 1 juice box from a pack of 6 is ? of the pack. 1 piece of pie out of 4 pieces is ? of the whole pie.”“It is also important to understand the unit fraction. The unit fraction is the value of each piece within the whole. For example, if a pizza is cut into 8 slices, the unit fraction for each piece is ?. If a cake is cut into 4 pieces, the unit fraction for each piece is ?. “Now you will explore the fractions you see in this room. Using the activity sheet, record the fractions you see in the room.”Note: In 3rd grade, the focus needs to be fractions as parts of a whole and NOT fractions of a set (for example: eggs in a carton or juice boxes in a pack). Students may give this as a response, but future instruction on this concept is not needed.Explore:Activity Sheet (10-15 min)Allow students time to work on the activity sheet. This activity can be done independently, in pairs, or groups. While the students are working, observe their identification of fractions within the classroom. Think about these ideas while monitoring the students: Observe:Are the students seeing parts within a whole?Are they correctly identifying the denominator?Are they correctly writing the numerator/unit fraction?ObservationQuestions to AskIf students are struggling to get started.Do you see anything in the room that is split into parts?If students have an idea of an item but cannot represent it with a fractionHow many parts are in the entire item (cubby, bookshelf)?What would one part of that be? Which of those numbers would be the denominator? Numerator? Carefully select students to present to the class. Look for students who modeled the problem and kept track of their thinking. Also look for strategies that will generate discussion to help others move toward a deeper understanding of the mathematical goal.Discuss:Discussion (10-15 min)Bring the group back together and have selected students share their strategies for solving the task. When sharing strategies, make sure students identify the parts within a whole, the unit fraction, and what fraction the unit represents (halves, thirds, fourths, sixths, eighths). Sample QuestionsPossible Responses or Talk FramesWhy did you chose this item to represent fractions?The item was divided into partsThe parts put together make up the whole itemHow do you know how many parts make up this whole?I counted the parts (1,2,3)I saw groups of….How did you know which number is the denominator?The denominator is the number of parts of the wholeIt is the total number of pieces in a whole How do you know what the unit fraction is?The unit fraction is the value of one piece of the wholeIf there are ____ pieces, one of these pieces is the unit fractionEvaluation of Student UnderstandingInformal Evaluation: Observe students and ask questions as they are completing the task. Ask them questions about their work.Take note of students who are not showing an understanding of parts within a fraction.Formal Evaluation/Exit Ticket: Scott recorded observations of objects with fractions around his house. Fill in the unit fraction that Scott sees. Pizza – 1/8 Window – 1/6File Cabinet – 1/4Meeting the Needs of the Range of LearnersIntervention:Give pictures of everyday items that can be represented in fractions (pizza, pie, cubbies, bookshelf). Ask the following questions to help build understanding. “This is a picture of a ________. Is this picture a whole or a part?”“What would be the parts of the whole item?”“So if I have one part of _______ the fraction would be ________.” “Can you use that understanding to think of a fraction for this picture?”Extension: Present the students with a problem involving one of the items:If two of the cubbies were filled, what fraction of the cubbies have things in them?If I ate 4 slices of pizza for dinner, what fraction of the pizza do I have left if there were 8 slices?If 1 of the 4 shelves on the bookshelf is full, what fraction of the bookshelf has books on them?Possible Misconceptions/Suggestions:Possible MisconceptionsSuggestionsStudents do not think that a unit fraction has to have a “1” in the numerator.Remind students that a unit fraction represents just one fractional part. For example the fraction ? could be broken apart into unit fraction pieces of ?.Students choose objects around the classroom that do not have equal parts.Remind students that fractions must be broken into equal parts or same-size parts.Possible Solutions: 1523365-721995Activity Sheet Record objects around your classroom where you see fractions. Record the unit fraction and provide a drawing of your observation.ItemUnit FractionDrawingExit TicketScott recorded observations of objects with fractions around his house. Fill in the unit fraction that Scott sees. ItemUnit FractionPicturePizza slices missingBroken windows18400155357Open drawers ................
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