Tab 7: Numerical Fluency: The Whole Picture Table Of Contents
Mathematics TEKS Refinement 2006 – K-5Tarleton State UniversityTab 7: Numerical Fluency: The Whole PictureTable of Contents7-iiMaster Materials ListFractions and Numerical FluencyHandout 1-Graphic Organizer7-17-14Handout 2-Brownie Problem Student WorkTransparency 1/Handout 3-Models and Meanings*Handout 4 -Models and MeaningsSample Solutions7-157-20Handout 5-Concept of Unit7-22Handout 6-Concept of Unit Solutions7-23How Big Am I?Handout 1-Fraction BarsTransparency 1-How Big Am I? DirectionsTransparency 2/Handout 2-How Big Am I? Game BoardEquality for AllHandout 1-Unmarked Fraction BarsHandout 2-Equality for All Work MatHandout 3-Equality for All Recording Sheet7-217-247-267-287-297-307-367-377-38Handout 4-How I Am the Same7-39Handout 5-Mixing It Up7-41Transparency 1-Mixing It Up Example Problem7-46Numerical Fluency Defined7-47* This document was developed as a resource for trainers, but it may be used with participants at thetrainer's discretion.Tab7: Numerical Fluency: The Whole Picture: Table of Contents7-i
Mathematics TEKS Refinement 2006 – K-5Tarleton State UniversityTab 7: Numerical Fluency: The Whole PictureMaster Materials ListCuisenaire rodsDessert plates in two contrasting colorsDouble sided countersFraction barsFraction squaresGrid paperInstrumental musicPaperPaper bagPattern blocksPencilsTimerFractions and Numerical Fluency-Handouts and TransparenciesHow Big Am I?-Handouts and TransparenciesEquality for All-Handouts and TransparencyThe following materials are not in the notebook. They can be accessed on the CDusing the links below.Slides 76-96, Numerical Fluency PowerPointTEKS Refinements-small and enlarged printable versionsResource listTab7: Numerical Fluency: The Whole Picture: Master Materials List7-ii
Mathematics TEKS Refinement 2006 – K-5Tarleton State UniversityActivity:Fractions And Numerical FluencyTEKS:(K.3) Number, operation, and quantitative reasoning. The studentrecognizes that there are quantities less than a whole.The student is expected to:(A) share a whole by separating it into two equal parts; and(B) explain why a given part is half of the whole.(1.2) Number, operation, and quantitative reasoning. The student usespairs of whole numbers to describe fractional parts of whole objects or setsof objects.The student is expected to:(A) separate a whole into two, three, or four equal parts and useappropriate language to describe the parts such as three out of fourequal parts; and(B) use appropriate language to describe part of a set such as three outof the eight crayons are red.(2.2) Number, operation, and quantitative reasoning. The studentdescribes how fractions are used to name parts of whole objects or sets ofobjects.The student is expected to:(A) use concrete models to represent and name fractional parts of awhole object (with denominators of 12 or less);(B) use concrete models to represent and name fractional parts of a setof objects (with denominators of 12 or less); and(C) use concrete models to determine if a fractional part of a whole iscloser to 0, ½, or 1.(3.2) Number, operation, and quantitative reasoning. The student usesfraction names and symbols (with denominators of 12 or less) to describefractional parts of whole objects or sets of objects.The student is expected to:(A) construct concrete models of fractions;(B) compare fractional parts of whole objects or sets of objects in aproblem situation using concrete models;(C) use fraction names and symbols to describe fractional parts of wholeobjects or sets of objects; and(D) construct concrete models of equivalent fractions for fractional partsof whole objects.(4.2) Number, operation, and quantitative reasoning. The studentdescribes and compares fractional parts of whole objects or sets of objects.The student is expected to:(A) use concrete objects and pictorial models to generate equivalentFractions and Numerical Fluency7-1
Mathematics TEKS Refinement 2006 – K-5(B)(C)(D)Tarleton State Universityfractions;model fraction quantities greater than one using concrete objects andpictorial models;compare and order fractions using concrete objects and pictorialmodels; andrelate decimals to fractions that name tenths and hundredths usingconcrete objects and pictorial models.(5.2) Number, operation, and quantitative reasoning. The student usesfractions in problem-solving situations.The student is expected to:(A) generate a fraction equivalent to a given fraction such as 1/2 and 3/6or 4/12 and 1/3;(B) generate a mixed number equivalent to a given improper fraction orgenerate an improper fraction equivalent to a given mixed number;(C) compare two fractional quantities in problem-solving situations usinga variety of methods, including common denominators; and(D) use models to relate decimals to fractions that name tenths,hundredths, and thousandths.(5.3) Number, operation, and quantitative reasoning. The studentadds, subtracts, multiplies, and divides to solve meaningful problems.The student is expected to:(E) model situations using addition and/or subtraction involving fractionswith like denominators using concrete objects, pictures, words, andnumbers.Overview: This section on Fractions and Numerical Fluency was developed to bepresented in a 1½ hour professional development session. The purpose ofthis professional development is to help teachers understand the conceptof a whole as well as the refinements that have been made to the K-5TEKS regarding fractions. As will be seen in students’ work, fractions areoften misunderstood. As professional educators, reflection of our ownlearning and understanding of fractions must occur.The K-2 educators need to be presented the material in this section fromthe beginning up until the How Big Am I? Activity. The presentation maythen skip to the closing activity. Educators in grades 3-5 need to bepresented the material in its entirety.In identifying the TEKS for all sections of this professional development,the underlying processes and mathematical tools were not listed, but it isevident with all the problem solving that occurs that they are beingaddressed. It is the writers’ intention that the underlying processes andmathematical tools are the framework of how you investigate themathematical concepts for each grade level. The intention was to focusFractions and Numerical Fluency7-2
Mathematics TEKS Refinement 2006 – K-5Tarleton State Universityspecifically on identifying the Number, Operation, and QuantitativeReasoning as well as the Patterns, Relationships, and Algebraic ThinkingTEKS that directly affects numerical fluency.Materials:Fractions and Numerical FluencySlides 76-96, Numerical Fluency PowerPointHandout 1-Graphic Organizer (page 7-14)Handout 2-Brownie Problem Student Work (pages 7-15 - 7-19)TEKS Refinements- small and enlarged printable versionsTransparency 1/Handout 3-Models and Meanings (page 7-20)Handout 4-Models and Meanings Sample Solutions (page 7-21)Handout 5-Concept of Unit (page 7-22)Pattern blocksDouble sided countersCuisenaire rodsHandout 6-Concept of Unit Solutions (page 7-23)Dessert plates in two contrasting colors, 2 different colored plates perparticipantHow Big Am I?Handout 1-Fraction Bars (pages 7-26 – 7-27)Paper bagTransparency 1-How Big Am I? Directions (page 7-28)Transparency 2/Handout 2-How Big Am I? Game Board (page 7-29)Equality for AllHandout 1-Unmarked Fraction Bars (page 7-36)Handout 2-Equality for All Work Mat (page 7-37)Handout 3-Equality for All Recording Sheet (page 7-38)Handout 4-How Am I the Same (pages 7-39 – 7-40)Fraction squaresHandout 5-Mixing It Up (pages 7-41 – 7-45)CountersFraction barsCuisenaire rodsPattern blocksGrid paperPencilsTransparency 1-Mixing It Up Example Problem (page 7-46)Numerical Fluency DefinedPaperTEKS Refinement Wall still intactInstrumental MusicTimerResources listFractions and Numerical Fluency7-3
Mathematics TEKS Refinement 2006 – K-5Tarleton State UniversityGrouping:Whole group and small group instruction.Time:1 1/2 hoursLesson:Slide76Slide77ProceduresFractions and NumericalFluencyNotesIn the previous sections, we discussednumerical fluency and the revisions of theTEKS as they applied to whole numbers.Before we begin this next section reflect onhow your understanding of numerical fluencyhas changed since yesterday. On the notecard, write down your level of numericalfluency as it pertains to rational numbers andin particular fractions.Goals & Purposes Increase teacher knowledge regarding therefinements of the TEKS relating tonumerical fluency. Increase teacher knowledge of composingand decomposing numbers. Increase teacher knowledge of rationalnumbers. Develop an understanding of the use ofmetacognition in problem solving.Slide78Solve the Following Problem Think about the strategy/strategies you usedto solve the following problem. Yesterday I baked my family a 9x13 pan ofbrownies. I cut the brownies in individualservings. Russell took ½ of the brownies,Chris took 1/3 of what was left, Natalie took ¼of what was then left in the pan. An hour laterChris came back and took two more brownies,leaving one brownie for me. How manyindividual pieces did I cut the brownies into tobegin with?Problem: Yesterday I baked my family a 9X13pan of brownies. I cut the brownies in1individual servings. Russell took 2 of the1brownies, Chris took 3 of what was left, and1Natalie took 4 of what was then in the pan. Anhour later, Chris came back and took two morebrownies leaving one brownie for me. Howmany individual pieces did I cut the browniesinto to begin with?At first glance, this problem seems to be reallydifficult and can be if it is solved algebraically.But, if the participants will look at it as arectangle and split it up accordingly, theproblem becomes very simple. Participantscan use fraction squares to help them solvethe problem.Fractions and Numerical Fluency7-4
Mathematics TEKS Refinement 2006 – K-5Slide79ProceduresWrite down your thought processes as you solve the following problem.What am I supposed tofind?PictureTable/Chart/ListNumber SentenceExplain how you derived your answer(s)?Tarleton State UniversityNotesProvide participants a graphic organizer(Handout 1 page 7-14) to use when solving theproblem. Be sure to have participants try tosolve the problem in two ways.Possible solution strategy:Working backwardsfrom the drawing 1 2 1 2 6 121 1 11 2 13 2 12 3(2) (4)(3)(2) (4)(3)(2) 61 1 22 6 24 24 1213612 12 12 12 1212 1The brownies were cut into 12 pieces. Russellgot 6 of 12 pieces, I got 1 of 12 pieces, Nataliegot 1 of 12 pieces, and Christopher got 4 of 12pieces.Slide80How Did You Solve the Problem? Share your strategies with your neighbor. Share your strategies with the wholegroup.Slide81Walk around while participants are discussingsolutions and choose several strategies thatare different. Once all of the ones you havechosen have been presented, ask for othersolutions.Slides 81 – 85 show how students in the fifthgrade interpreted or misinterpreted theproblem. Copies of the student work areprovided in Handout 2-Brownie ProblemStudent Work (pages 7-15 – 7-19).The important aspect of this problem is that analgorithm is never needed in solving it. It canbe solved through drawing pictures, but aconceptual understanding of fractions must beFractions and Numerical Fluency7-5
Mathematics TEKS Refinement 2006 – K-5ProceduresSlide82Slide83Tarleton State UniversityNotesin place. The students also must be able tocomprehend what the question is asking.On slide 81, this student clearly did notunderstand the question and only multipliedthe dimensions of the pan.This student can copy what the problem isasking, but again cannot comprehend what isbeing asked. Therefore, he/she only multipliedthe dimensions of the pan.6This student was correct in picking 12 as thefirst piece. But if he/she understood that the6whole is the brownie and 12 is half of thebrownie, then he/she would know that 16 wasnot correct.Slide84This student tried to draw the picture. If he/shehad looked at what he/she designated as1Russell’s 2, he/she would have realized theanswer was wrong. What he/she colored as1Russell’s 2 is also wrong, but the firstobservation would have led the student torethink his/her actions.Slide85Fractions and Numerical FluencyIt is uncertain where this student began, buthe/she correctly solved the problem using adrawing and a number sentence. It looks likethe student did the drawing first and thenchecked his/her work with the numbersentence. Even though the student did notwrite the number sentence mathematicallycorrect, it demonstrates the student’s thoughtprocesses.7-6
Mathematics TEKS Refinement 2006 – K-5ProceduresSlide86TEKS Each group will be assigned a grade level. Identify the TEKS in your grade level (K-5)that students must master in order to havesuccess in solving this 5th grade problem. Are there any refinements that need to beidentified? Add refined TEKS needed toteach this concept to the TEKSRefinement Wall.Tarleton State UniversityNotesWhat is necessary? Possible choices are:K.3 (A), (B)1.2 (A), (B)2.2 (A), (B), (C)3.2 (A), (B), (C), (D)4.2 (A), (B), (C)5.2 (C)Have the participants post the refined TEKS onthe wall under their particular grade level.(See materials list for link to TEKSRefinements.)Slide87Development of FractionsWhere and How Do We SeeFractions?Importance of the WholeDevelopment of Fractions Fractional parts are equal shares of aWHOLE. A fraction is the relationshipbetween the parts and the WHOLE. Itsays nothing about the size of the wholeor the size of the parts. Denominator tells how many equal partsin which the WHOLE is divided. Numerator tells how many of thoseequal parts are of interest to you. The more fractional parts the whole isdivided into, the smaller the parts.Where and How Do We See Fractions?Use Transparency 1/Handout 3-Models andMeanings (page 7-20) with the whole group toidentify classroom models of fractions and reallife connections to fractions. Follow thefollowing steps:1. Ask participants to identify classroommodels to teach fractions using sets ofobjects. If they are struggling with ananswer, have them look at the TEKS forexamples. Trainers should refer toHandout 4-Models and Meanings SampleSolutions (page 7-21). This handout wasdeveloped only for use by trainers and notto be distributed to participants.Trainers should not be surprised if teachersFractions and Numerical Fluency7-7
Mathematics TEKS Refinement 2006 – K-5ProceduresTarleton State UniversityNotessay pattern blocks, fraction circles, andother models that are more appropriate foreither area or measurement when they areasked for sets of objects. The set model isnot often used to teach fractions eventhough it is specifically required by theTEKS beginning in first grade. (1.2)Number, operation, and quantitativereasoning. The student uses pairs of wholenumbers to describe fractional parts ofwhole objects or sets of objects. (B) useappropriate language to describe part of aset such as three out of the eight crayonsare red.2. Ask teachers to identify real life situationsthat allow for identifying fractions using theset model.3. Repeat this process until answers havebeen given for classroom models and reallife connections for sets, area, andmeasurement interpretations.The division row of the handout will behandled when discussing improper fractionslater in the professional development.Importance of the WholeHave participants work in groups to answerquestions on Handout 5-Concept of Unit (page7-22). Participants will need pattern blocks,double sided counters, and Cuisenaire Rods.Walk around and monitor as they complete theactivity. Pay special attention to the CuisenaireRods. This part confuses participants.Handout 6 (page 7-23) give solutions for theConcept of Unit activity.Fractions and Numerical Fluency7-8
Mathematics TEKS Refinement 2006 – K-5Slide88ProceduresReferents Reference points of 0, ½, and 1– Fraction Estimators.– How Big Am I?Tarleton State UniversityNotesFraction EstimatorsGive each participant 2 small dessert platesthat are different colors. Have them cut eachplate to the center. Be sure not to cut theplates all the way through. (See examplebelow.) Slide the cut edges together and turnso that the plates intersect. Turn the plates sothat the contrasting colors will show reference1points close to 0, 2, and 1. This inexpensivetool can be used as a form of assessment inunderstanding children’s grasp of fractions lessthan 1.How Big Am I?Have participants play the How Big Am I?game. Follow the procedures given How BigAm I? activity (page 7-24).Slide89Solve the Following Problem Think about the strategy/strategies youused to solve the following problem 2/4, 3/6, 4/8, and 5/10 are all equivalent to1/2. What is the relationship between thenumerator and denominator in eachfraction? Explain why they are equivalentto 1/2.Slide90Write down your thought processes as you solve the following problem.What am I supposed tofind?PictureTable/Chart/ListNumber SentenceParticipants can use the graphic organizerwhen solving this problem.Possible solutions:FractionMultiply by 1Explain how you derived your answer(s)?Fractions and Numerical FluencyFraction12222412333612444812555107-9
Mathematics TEKS Refinement 2006 – K-5ProceduresTarleton State UniversityNotesBecause I am multiplying by one each time, Iam not increasing the value of the fraction.As demonstrated in this picture, the wholeremains the same. The whole is divided intosmaller, equivalent parts. Thus, the numerator1and denominator maintain the same ratio of 2.Slide91This student has identified the pattern thatexists between the fractions: numeratorincreasing by one and denominator increasingby two. It seems that the student either hasbeen taught the algorithm incorrectly or hasmade a generalization of the rule on his/herown. There does not seem to be anyconceptual understanding of equivalentfractions. To remediate, this student needs towork with concrete and pictorial models todevelop an understanding of fractions and alsoto develop an understanding of 1 and thevarious forms in which it can be written.Slide92As in the previous example, this student doesnot demonstrate a conceptual understanding ofequivalent fractions. The student has eitherbeen taught the algorithm incorrectly or hasmade his/her own generalizations regardingthe algorithm. To remediate, this studentneeds to work with concrete and pictorialmodels to develop an understanding offractions and to develop an understanding ofand the various forms in which it can bewritten. The student also needs to learn howto correctly write a mathematical sentence.Fractions and Numerical Fluency7-10
Mathematics TEKS Refinement 2006 – K-5Slide93Slide94ProceduresTEKS Each group will be assigned a grade level. Identify the TEKS in your grade level (K-5)that students must master in order to havesuccess in solving this 5th grade problem. Are there any refinements that need to beidentified? Add refined TEKS needed toteach this concept to the TEKSRefinement Wall.Slide95Equivalent Fractions How Do I Compare? Let Me Count theWays. Equality for All Mixing It UpSlide96Building Foundations forMathematicsTarleton State UniversityNotesOn the other hand, this student demonstrates abasic conceptual understanding of equivalentfractions with his drawing but is unable todescribe what is actually happening. Thisstudent needs more practice communicatingwhat he is making with concrete and pictorialmodels. His teacher needs to work with himon bridging from the concrete to the abstract.Ask participants to look at TEKS again and seeif there are any refinements that need to beadded to the TEKS Refinement Wall.Use the Equality for All activity (page 7-30).Begin with Equivalent Fractions Activity page.Follow this for the remainder of this slide.Go back to the TEKS Wall and ask theparticipants to identify any refined TEKS wehaven’t covered.Use Numerical Fluency Defined! Activity (page7-47) to complete the Numerical Fluencytraining. This involves slides 96-99.Numerical Fluency Defined!Resources:Ashlock, R. B. (2006). Error patterns in computation (9th ed.) Saddlle River NJ:Pearson: Merrill Prentice Hall.Fractions and Numerical Fluency7-11
Mathematics TEKS Refinement 2006 – K-5Tarleton State UniversityBender, W. N. (2002). Differentiating instruction for students with learning disabilities.Thousand Oaks, CA: Corwin Press, Inc. p. 21-22.Billstein. R., Libeskind, S. & Lott, J. (2007). A problem solving approach to mathematicsfor elementary school teachers. Boston, MA: Pearson/Addison Wesley.Burk, D., Snyder, A., & Symonds, P. (1999). Box it or bag it mathematics. Salem, OR.Burns, M. (1996) 50 problem-solving lessons: Grades 1-6. Sausalito, CA: MathSolutions Publications.Chapin, S. H. & A. Johnson. (2000). Math Matters: Understanding the Math You Teach,Grades K-6. Sausalito, CA: Math Solutions Publications.Clements, D. (1999). Subitizing, what is it and why teach it. Teaching ChildrenMathematics, 5(7), 400-405.Coolmath.com (2006, May 20). Fractions: Improper fractions. Online lFennema, E., & Franke, M. L. (1992). Teachers' knowledge and its impact. In D. A.Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp.147-164). New York: Macmillan Publishing Co.Fosnot, C. & M. Dolk. (2001a). Young mathematicians at work: Constructingmultiplication and division. Portsmouth, NH: Heinemann.Fosnot, C. & M. Dolk. (2001b). Young mathematicians at work: Constructing numbersense, addition, and subtraction. Portsmouth, NH: Heinemann.Fosnot, C. & Dolk, M. (2002). Young mathematicians at work: Constructing fractions,decimals, and percents. Portsmouth, NH: Heinemann.Hope, J., Leutinger, L., Reys, B., & Reys, R. (1988). Mental math in the primary grades.Parsippany, MJ: Pearson Learning Group.Howden, H. (1989). Teaching number sense. Arithmetic Teacher, 36(6), 6-11.Hudson, P. & Millier, S. P. (2006). Designing and implementing Mathematics instructionfor students with diverse learning needs. Boston, MA: Allyn & Bacon.Institute for Literacy. (2006, March). Put reading first - k-3 (fluency) online ations/reading first1fluency.htmlKamii, C. (1985). Young children reinvent arithmetic. New York: Teachers CollegePress.Kamii, C., and Dominick, A. (1988). The harmful effects of algorithms in grades 1-4. InThe Teaching and Learning of Algorithms in School Mathematics, eds, L. Morrowand M. Kenney. Reston, VA: National Council of Teachers of Mathematics.Learning and Performance Support Laboratory. Intermath. Athens, GA: University ofGeorgia. Online at http://intermath.coe.uga.edu.Levine, H. M. (1996). Accelerated schools: The background. In C. Finnan, E., P. St.John, J. McCarthy, & S. P. Slovacek (Eds.), Accelerated schools in action:Lessons from the field (pp. 3-23). Thousand Oaks, CA: Corwin Press.Lexico Publishing Group. (2006). Dictionary.com. Online iljedahl, P. (Summer 2004). Repeating pattern or number pattern: the distinction isblurred. Focus on Learning Problems in Mathematics. Online athttp://www.findarticles.com/p/articles/mi m0NVC/is 3 26/ai n9505504/pg 1Ma, L. (1999). Knowing and teaching elementary mathematics. Mahwah, NJ: LawrenceErlbaum Associates, Publishers.Fractions and Numerical Fluency7-12
Mathematics TEKS Refinement 2006 – K-5Tarleton State UniversityMcIntosh, A., Reys, B., Reys, R., and Hope, J. (1997). Number sense, Grades 4-6. PaloAlto, CA: Dale Seymour Publications.National Council of Teachers of Mathematics. (2000). Principles and standards ofschool mathematics. Reston, VA: NCTM.National Council of Teachers of Mathematics. (2000-2006). Illuminations PowerfulPatterns. Online at: http://illuminations.nctm.org/LessonDetail.aspx?ID U69Reston VA: NCTM.National Council of Teachers of Mathematics (2004). Nativigating through number andoperations. Reston, VA: NCTM,Nugent, G. (1995). Hands-on math: Manipulative actvities for the 2-3 classroom.Cypress, CA: Creative Teaching Press, Inc.Oster, C. (2005). Growing Patterns. Online at:http://www.mathperspectives.com/pdf docs/lesson 3.pdf. Bellingham, WA:MathPerspectives, Teacher Development Service.Richardson, K. (1997). Too easy for kindergarten and just right for first grade.Teaching Children Mathematics 3(8), 432-437.Rightsel, P. S., & Thorton, C. A. (1985). 72 addition facts can be mastered by midgrade 1. Arithmetic Teacher, 33(3), 8-10.Russell, S. J., & Rubin, A. (1998). Investigations in number, data, and space; landmarksin the hundreds. Menlo Park, CA: Dale Seymour Publications.Scharton, S. (2004). “I did it my way”: Providing opportunity for students to create,explore, and analyze computation procedures. Teaching Children Mathematics,10(5).Smith, L (1995). Early Childhood Mathematics Methods, Georgia State University.[unpublished work].Steele, M.M. (2002). Strategies for helping students who have learning disabilities inmathematics. Mathematics Teaching in the Middle School 8(3), 141-143.Threlfall, J. (1999). Repeating patterns in the early primary years. In A. Orton (Ed.),Patterns in the teaching and learning of mathematics (pp. 18-30). London: Cassell.Tucker, B. F., Singleton, A. H., & Weaver, T. L. (2006). Teaching mathematics to allchildren: Designing and adapting instruction to meet the needs of diverse learners(2nd ed.). Upper Saddle River, NJ: Pearson Merrill Prentice Hall.Van de Walle, J. A. (2004). Elementary and middle school Mathematics: Teachingdevelopmentally (5th ed.) Boston, MA: Allyn and Bacon.Van de Walle, J. A. (2007). Elementary and middle school mathematics: Teachingdevelopmentally (6th ed.) Boston, MA: Allyn and Bacon.Van de Walle; J. A. & Lovin, L. H. (2006). Teaching student-centered mathematics:Grades k-3. Boston, MA: Pearson Education Corp.Van de Walle; J. A. & Lovin, L. H. (2006). Teaching student-centered mathematics:Grades 3-5. Boston, MA: Pearson Education Corp.Fractions and Numerical Fluency7-13
Mathematics TEKS Refinement 2006 – K-5Tarleton State UniversityGraphic OrganizerWrite down your thought processes as you solve theproblem.What am I supposed tofind?PictureTable/Chart/ListNumber SentenceExplain how you derived your answer(s).Fractions and Numerical FluencyHandout 17-14
Fractions and Numerical FluencyMathematics TEKS Refinement 2006 – K-5Handout 2-17-15Tarleton State University
Fractions and Numerical FluencyMathematics TEKS Refinement 2006 – K-5Handout 2-27-16Tarleton State University
Fractions and Numerical FluencyMathematics TEKS Refinement 2006 – K-5Handout 2-37-17Tarleton State University
Fractions and Numerical FluencyMathematics TEKS Refinement 2006 – K-5Handout 2-47-18Tarleton State University
Fractions and Numerical FluencyMathematics TEKS Refinement 2006 – K-5Handout 2-57-19Tarleton State University
Mathematics TEKS Refinement 2006 – K-5FRACTIONSInterpretationSets of ObjectsTarleton State UniversityModels and MeaningsClassroomModelsReal Life ConnectionRegion or AreaMeasurementDivisionFractions and Numerical FluencyTransparency 1/Handout 37-20
Mathematics TEKS Refinement 2006 – K-5Tarleton State UniversityFRACTIONSModels and MeaningsInterpretationSets of ObjectsClassroomModelstwo-sided counterscolored counterscrayonsReal Life Connectioncolored candyegg cartonsRegion or Areapattern blockspaper foldingfraction circlesfraction squaresgeoboardscentimeter grid paperpizzapiesquare tiles on floorceiling tilesMeasurementCuisenaire RodsFraction stripsFolded paper stripsrulermeasuring cupsDivisionAny of the above modelscan be used to modeldivision. When teachingdivision, meaningfulproblems should be used.*See below.* The real life connection examples depend on the meaningful problems being used. Inthis professional development, it is discussed using (5.2) Number, operation, andquantitative reasoning. The student uses fractions in problem-solving situations. Thestudent is expected to: (B) generate a mixed number equivalent to a given improperfraction or generate an improper fraction equivalent to a given mixed number;Fractions and Numerical FluencyHandout 47-21
Mathematics TEKS Refinement 2006 – K-5Tarleton State UniversityCONCEPT OF UNITA.Use Pattern Blocks to solve these problems:The Yellow Hexagon is 1. What is the value of each of these pieces?1 red trapezoid1 green triangle2 blue parallelogramsChange the Unit: Now the RED TRAPEZOID is 1. What is the value of each ofthese pieces?1 green triangleB.1 blue parallelogram1 yellow hexagonUse Counters to solve these problems:Eight counters equal 1. What is the value of each of these sets of counters?1 counter2 counters4 counters6 countersChange the Unit: Now FOUR counters is 1. What is the value of the sets ofcounters listed below?1 counterC.2 counters4 counters6 countersUse Cuisenaire Rods to solve these problems:The LIME GREEN Rod equals 1. What is the value of each of these rods?RedBlackWhiteDark GreenChange the Unit: The DARK GREEN Rod equals 1. Now what is the value ofeach of the rods listed below?RedBlackWhiteLime Green(Smith, L., 1995)Fractions and Numerical FluencyHandout 57-22
Mathematics TEKS Refinement 2006 – K-5Tarleton State UniversityCONCEPT OF UNIT SOLUTIONSA.Use Pattern Blocks to solve these problems:The Yellow Hexagon is 1. What is the value of each of these pieces?1 red trapezoid1 green triangle2 blue parallelograms121623Change the Unit: Now the RED TRAPEZOID is 1. What is the value of each ofthese pieces?B.1 green triangle1 blue parallelogram1 yellow hexagon13232Use Counters to solve these problems:Eight counters equal 1. What is the value of each of these sets of counters?1 counter2 counters4 counters6 counters182 1 8 44 1 8 26 3 8 4Change the Unit: Now FOUR counters is 1. What is the value of the sets ofcounters listed below?C.1 counter2 counters4 counters6 counters142 1 4 24 14621 1 1442Use Cuisenaire Rods to solve these problems:The
Fractions and Numerical Fluency 7-3 specifically on identifying the Number, Operation, and Quantitative Reasoning as well as the Patterns, Relationships, and Algebraic Thinking TEKS that directly affects numerical fluency. Materials: Fractions and Numerical Fluency Slides 76-96, Numerical Fluency PowerPoint Handout 1-Graphic Organizer (page 7-14)
May 02, 2018 · D. Program Evaluation ͟The organization has provided a description of the framework for how each program will be evaluated. The framework should include all the elements below: ͟The evaluation methods are cost-effective for the organization ͟Quantitative and qualitative data is being collected (at Basics tier, data collection must have begun)
Silat is a combative art of self-defense and survival rooted from Matay archipelago. It was traced at thé early of Langkasuka Kingdom (2nd century CE) till thé reign of Melaka (Malaysia) Sultanate era (13th century). Silat has now evolved to become part of social culture and tradition with thé appearance of a fine physical and spiritual .
On an exceptional basis, Member States may request UNESCO to provide thé candidates with access to thé platform so they can complète thé form by themselves. Thèse requests must be addressed to esd rize unesco. or by 15 A ril 2021 UNESCO will provide thé nomineewith accessto thé platform via their émail address.
̶The leading indicator of employee engagement is based on the quality of the relationship between employee and supervisor Empower your managers! ̶Help them understand the impact on the organization ̶Share important changes, plan options, tasks, and deadlines ̶Provide key messages and talking points ̶Prepare them to answer employee questions
Dr. Sunita Bharatwal** Dr. Pawan Garga*** Abstract Customer satisfaction is derived from thè functionalities and values, a product or Service can provide. The current study aims to segregate thè dimensions of ordine Service quality and gather insights on its impact on web shopping. The trends of purchases have
Miscellaneous Netdev Tree window Room View Tabs (Extended) Front Desk tab, Service tab, Marina tab, VRV tab, VAV tab, ComTrac tab Room View Tabs (General) AC tab, Version tab, Alarm tab, Device tab, Trend tab, State tab Setup Tab Add New User Utilities Central Electronic Lock Control System (CELS) Functions window, Security Monitor window .
Jan 23, 2018 · amlodipine tab 5mg 8 atorvastatin tab 10mg 4 benzonatate cap 100mg 6 carbamazepin tab 200mg 6 carb/levo er tab 25-100mg 9 carvedilol tab 3.125mg 8 citalopram tab 20mg 4 clonidine tab 0.1mg 6 clopidogrel tab 75mg 4 cyclobenzapr tab 5mg 3 digoxin tab 0.125mg 3 divalproex cap 125mg 8 divalproex tab
TARGET CONSOLIDATION CONTACT GROUP (TCCG) 4 June 2019 - 10:00 to 15:00 held at the premises of the European Central Bank, Sonnemannstraße 20, meeting room MB C2.04, on 2nd floor 1. Introductory Remarks The Chairperson of the Contact Group will welcome the participants and open the meeting introducing the Agenda. Outcome: The Chairperson welcomed the participants and briefly introduced the .
