Oakland Schools
Collaboration / Math 4* (CC) / Grade 4 (Common Core)
Wednesday, June 26, 2013, 3:35PM
Unit: 5 - Using Fractions(Week 23, 7 Weeks)
Common Core Initiative
Overarching Questions and Enduring Understandings
In what ways areoperations with fractionssimilar to and different fromoperations withwhole numbers?
Graphic Organizer
Unit Abstract
This unit builds on fraction conceptsintroducedin thirdgrade unit7,Understand,Represent and Compare Fractions andfourth gradeunit 3,Making Sense of Decimal Fractions.
A primary understanding of thisunit is forstudents to model, recognize, andgenerate equivalent fractions.Students continue toengage withthe concept of afraction as apart of the whole and utilizeunit fractions.Theybuild fractions from unit fractions by applying and extending previous understanding of operations with whole numbers.Of primaryimportance is theconceptual understanding thatyou can name a fraction in manyways.Studentsunderstand andusevisual modelsto representequivalent fractionsand usethese models toreason aboutthe number andsize ofthe parts of two equivalent fractions.From these representations and the idea of equipartitioning,they generalizea procedureforgenerating equivalentfractions(i.e., a/b = a × n/b × n). In third grade studentscompared fractionswith common numeratorsor common denominators by reasoning about their size andevaluatingtheir position on the number line. In fourthgrade, students also usetheir new knowledgeofequipartitioningto create commonnumerators or denominatorsin addition to benchmark fractions such as0,1/4, 1/2, and1 to compare.
Operations withfractions is extended but not completed. More attention to operations with fractionsoccur infifth grade.Theyuse bothdecomposition into and compositionfrom unit fractionswithproperties ofoperations toadd and subtractfractionswith likedenominators includingmixed numbers.They usetheir procedure for generating equivalent fractions tobegin adding and subtractingfractionswith unlike denominators where one denominator is afactor of the other(e.g., 4/10 and35/100 or2/3 and1/6). In addition, studentsuse the meaning offractionsand the meaning of multiplication to multiply a fraction by a whole number by thinking about multiplegroups ofany fraction a/b.(In fifth grade,multiplication of a fraction bya whole number is expanded toinclude fraction of awhole which is not included in thisunit.)Students useestimation todetermine the reasonableness of their answers.
Unit overview 6/26/13 (word)
Unit overview 6/26/13 (pdf)
Content Expectations/Standards
CCSS: Mathematics, CCSS: Grade 4, Number & Operations—Fractions
4.NF.A. Extend understanding of fraction equivalence and ordering.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.
§ 4.NF.A.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.
§ 4.NF.A.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
4.NF.B. Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
§ 4.NF.B.3. Understand a fraction a/b with a > 1 as a sum of fractions 1/b.
§ 4.NF.B.3a. Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.
§ 4.NF.B.3b. 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.
§ 4.NF.B.3c. 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.NF.B.3d. 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.NF.B.4. Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.
§ 4.NF.B.4a. Understand a fraction a/b as a multiple of 1/b.
For example, use a visual fraction model to represent 5/4 as the product 5 × (1/4), recording the conclusion by the equation 5/4 = 5 × (1/4).
§ 4.NF.B.4b. Understand a multiple of a/b as a multiple of 1/b, and use this understanding to multiply a fraction by a whole number.
For example, use a visual fraction model to express 3 × (2/5) as 6 × (1/5), recognizing this product as 6/5. (In general, n × (a/b) = (n × a)/b.)
§ 4.NF.B.4c. Solve word problems involving multiplication of a fraction by a whole number, e.g., by using visual fraction models and equations to represent the problem.
For example, if each person at a party will eat 3/8 of a pound of roast beef, and there will be 5 people at the party, how many pounds of roast beef will be needed? Between what two whole numbers does your answer lie?
CCSS: Mathematics, CCSS: Grade 4, Measurement & Data
4.MD.A. Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
§ 4.MD.A.2. Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.
4.MD.B. Represent and interpret data.
§ 4.MD.B.4. Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Solve problems involving addition and subtraction of fractions by using information presented in line plots.
For example, from a line plot find and interpret the difference in length between the longest and shortest specimens in an insect collection. / Unit Level Standards
Studentsworkedwith decimal fractions in unit 3 of fourth grade attending to the following standards.While these are not the focus of the unit, theymayprovide nice connections.
4.NF Understand decimal notation for fractions, and compare decimal fractions.
4.NF.5. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.
For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.
4.NF.6. Use decimal notation for fractions with denominators 10 or 100
For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
4.NF.7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
Essential/Focus Questions
1. How arefractionsused in everyday life?
2. How can understandingunit fractions help us make sense of,build,anduse otherfractions?
3. How and whenareequivalentfractions helpful in solvingproblems?
4. Howis estimatinguseful whenperforming operations withfractions?
5. What models helpvisualize,reason about, and generalizeoperations withfractions? / Key Concepts
addition of fractions (joining)
benchmark fractions
compare
compose/decompose
denominator
equipartitioning
equivalency
estimation
improper fraction
like/common denominator
mixed numbers
multiplication of fractions
numerator
proper fraction
subtraction of fractions (separating)
unit fractions
Assessment Tasks
Assessment Overview 6/26/13
Student Handout 6/26/13
Professional Learning Task / Intellectual Processes
(Standards for Mathematical Practice)
Students will have opportunities to:
§ look for and express regularity in repeated reasoning when comparing and ordering fractions,
§ make sense of adding and subtracting fraction problems and persevere in solving them, and
§ model with mathematics (using visual fraction models) to show fraction equivalencies.
Lesson Sequence
Lesson Overview
Student Handout
Professional Learning Task Using Accessibility Strategies to Enhance Student Understanding / Resources
Instructional Resources
http://illuminations.nctm.org/LessonDetail.aspx?
ID=L541Inthis collection oflessons,students createvisualmodels of fractionstodevelop theconcept of fractions.Theyuse the visual models of fractions to compare.
http://www.sheppardsoftware.com/mathgames/fractions/Balloons_fractions1.htm
Students must identify the smaller of the two fractions and “pop” the balloons.
http://www.mathsisfun.com/numbers/ordering-game.php
Students order unit fractions/fractions from least to greatest.
http://www.beaconlearningcenter.com/WebLessons/FloweringFractions/page1.htm
Students shade in fractional parts after an introduction to fractions.
http://www.fractionmonkeys.co.uk/activity/
Students match equivalent fractions.
http://www.funbrain.com/fractop/index.html
generic review of all operations including fractions and decimals
http://fractionbars.com/BarsAndCardsGame/
This siteprovides practice withidentifying equivalent fractions.
The videositesbelow areCyberchaseepisodes.
http://www.youtube.com/watch?v=8dYiwJZGGpU “Zeus on the Loose”
http://www.youtube.com/watch?v=BR7iU0MFymA“Harriet Hippo”
http://www.youtube.com/watch?v=DtDwB0VVpHE “Piece of the Action”
http://www.youtube.com/watch?v=LkqlXNuNUqQ “Shari Spotter”
http://www.youtube.com/watch?v=YZny5bhzTfM “Fractions of a Chance”
http://www.youtube.com/watch?v=UgiOqybvAig “Peace, Love, and Hacker”
Literature Connections
Adler,DavidA.FractionFun.HolidayHouse.ISBN0823412598.1996.
Leedy, Loreen. Fraction Action. Holiday House. ISBN 13:978-0823412440. 1996.
McMillan, Bruce. Eating Fractions. Scholastic. ISBN 0590437704. 1991.
Ellington, A., Whitehead, J. Fractions and the Funky Cookie. NCTM.(2010, May). 16. Issue 9 (532).
Burns, Marilyn. Math for Smarty Pants. Little, Brown, & Co.. ISBN 978-0316117395. 1982.
Van Cleve, J. Math For Every Kid. John Wily & Sons, Inc.. ISBN 0471542652.1991.
Professional Resources
Son,J.(2011). A global look atmathinstruction.TeachingChildrenMathematics.17(6),360.
JaneJaneLo,McCoryR..(2010).Teachingteachersthroughjustifyingartifacts.
Lamberg,T.,Andreous,C.(2011).IntegratingLiterature and Math.TeachingChildrenMathematics.17(6),372-376.
Van de Walle, John A. Elementary and Middle School Mathematics. Pearson Inc. ISBN- 13: 978-0-205-57352-3. 2010.
England,L. (2010). Raise the Bar on ProblemSolving.TeachingChildrenMathematics.17(3),156.
Merritt,E.G.,RimmKaufman,E.,BerryR.,Walkowiak,T., McCracken, E.(2010).A ReflectionFramework for TeachingMath.TeachingChildrenMathematics.17(4),238.
Fosnot, Catherine and Maarten Dolk. YoungMathematicians at Work:Constructing Fractions, Decimals, and Percents. Heineman. ISBN0-325-00355-6.2002.
Shaughnessy,M. (2011).IdentifyFractions andDecimals On a NumberLine.
TeachingChildrenMathematics.17(7),428.
Kenzer,C., Verag, L.,Morales, S.(2011). A Reflective Protocal for MathematicsLearning Environment.TeachingChildrenMathematics.17(8),480.
Gould, H.(2011). Building Understandingof Fractions withLegoBricks. TeachingChildrenMathematics.17(8),498.
Parker, R.,Brey-Fogle, M.(2011).Learning toWrite AboutMathematics.TeachingChildrenMathematics.18(2),90.
Redford,C.(2011).CelebrateMathematical Curiousity. TeachingChildrenMathematics.18(3),144.
Rathouz, M.(2011).3 WaysThat PromoteStudentReasoning. TeachingChildrenMathematics.18(3),182.
Shaughnessy, Megan M.( 2011, March). Identify fractions and decimals on a number line. Teaching Children Mathematics, 17, Issue 7, (428-434).
Bray, W., Sanchez,L. Using Number Sense toCompare Fractions: Reflect and Discuss. (2010, Sept.). 17 (2). 90.
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