Math 5th Grade Unit - SAUSD
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Information, Media and Technology:Critical Thinking & Problem SolvingTier III:MultiplyDivideSimplest formMixed numberDenominatorNumeratorUnit fractionImproper fractionMixed numberEquivalent fractionReciprocalHardwareCreativity & Innovation3How will pre-assessment guide instruction?Students missing two or more in any section will need interventionthrough the Preparing the Learner lessons.SoftwareCommunication & CollaborationHow are fractions related to division?How can the area of a rectangle with fractional sides be represented?How can a visual model help to show multiplication of a fraction by a whole number?How does multiplying by a fraction or by a mixed number affect the size of the product?How can multiplication of fractions and mixed numbers be used in real life situations?How can division of fractions be used in real life situations?Learning and Innovation: Multiplying and Dividing Fractions5th GradeTime Frame: 3 weeksThe properties of multiplication and division of whole numbers apply also to the multiplication and division offractions.Online ToolsEssentialTier elessMoreoverIn additionSimilarlyWhat pre-assessment will be given?Prerequisite Skills Test21st CenturySkills:Unit Title:Grade Level:Big nta Ana Unified School District Common Core Unit Planner-Mathematics
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Other Evidence:Teacher observationsS: Performance Task: Culminating TaskS: End of Unit AssessmentS: Benchmark Tests5Studentcomprehension ofunit concepts and thebig idea:The properties ofmultiplication anddivision of wholenumbers apply alsoto the multiplicationand division offractions.Ongoing evidence ofstudents’understanding of theconcepts presentedDiagnosticinformation forintervention oraccelerationF: Problem solving journalF: Visual representation of thinkingF: Performance Task : Lesson 1-4 Review TasksF: Lesson 7 Performance TaskCommon Core Mathematics Content Standards:Number and Operations–FractionsApply and extend previous understandings of multiplication anddivision to multiply and divide fractions.3. Interpret a fraction as division of the numerator by the denominator (a/b a b). Solve word problems involving division of whole numbers leading toanswers in the form of fractions, mixed numbers, e.g., by using visualfraction models or equations to represent the problem.4. Apply and extend previous understandings of multiplication to multiply afraction or whole number by a fraction.a. Interpret the product (a/b) q as a parts of a partition of q into b equalparts; equivalently, as the result of a sequence of operations a q b. Forexample, use a visual fraction model to show (2/3) 4 8/3, and create astory context for this equation. Do the same with (2/3) (4/5) 8/15.(Ingeneral, (a/b) (c/d) ac/bd.)b. Find the area of a rectangle with fractional side lengths by tiling it withunit squares of the appropriate unit fraction side lengths, and show that thearea is the same as would be found by multiplying the side lengths. Multiplyfractional side lengths to find areas of rectangles, and represent fractionproducts as rectangular areas.5. Interpret multiplication as scaling (resizing), by:a. Comparing the size of a product to the size of one factor on the basis ofthe size of the other factor, without performing the indicated multiplication.b. Explaining why multiplying a given number by a fraction greater than 1results in a product greater than the given number (recognizingmultiplication by whole numbers greater than 1 as a familiar case);explaining why multiplying a given number by a fraction less than 1 resultsin a product smaller than the given number; and relating the principle offraction equivalence a/b (n a)/(n b) to the effect of multiplying a/b by 1.6. Solve real world problems involving multiplication of fractions and mixednumbers, e.g., by using visual fraction models or equations to represent theproblem.7. Apply and extend previous understandings of division to divide unitfractions by whole numbers and whole numbers by unit fractions.a. Interpret division of a unit fraction by a non-zero whole number, andcompute such quotients. For example, create a story context for (1/3) 4,and use a visual fraction model to show the quotient. Use the relationshipAssessment of StandardsWhat assessments will be utilized for thisWhat does theunit? (F formative, S summative)assessment tell us?StandardsCommon Core Learning Standards Taught and Assessed
S: Design and write a recipe using fractional partswhich must be multiplied or divided to change thequantity of the recipe.4. Report on a topic or text, or present an opinion, sequencing ideas logicallyand using appropriate facts and relevant, descriptive details to support mainideas or themes; speak clearly at an understandable pace.F: Work collaboratively to solve complexproblems while treating each other with respect.F: Ask and answer questions in pairs and smallgroups during and after lessons.F: Participation in presentations of solutions forgroup work.Teacher Evaluation of student speaking andlistening:1. Engage effectively in a range of collaborative discussions (one-on-one, ingroups, and teacher-led) with diverse partners on grade 5 topics and texts,building on others’ ideas and expressing their own clearly.a. Come to discussions prepared having read or studied required material;explicitly draw on that preparation and other information known about thetopic to explore ideas under discussion.b. Follow agreed-upon rules for discussions and carry out assigned roles.c. Pose and respond to specific questions by making comments thatcontribute to the discussion and elaborate on the remarks of others.d. Review the key ideas expressed and draw conclusions in light ofinformation and knowledge gained from the discussions.Bundled Speaking and Listening Standard(s):6. Acquire and use accurately grade-appropriate general academic anddomain-specific words and phrases, including those that signal contrast,addition, and other logical relationships (e.g., however, although,nevertheless, similarly, moreover, in addition).S: Use of accurate mathematical terms andappropriate relationship language in culminatingwritten word problem and its solution.3. Use knowledge of language and its conventions when writing, speaking,reading, or listening.F: Teacher evaluation of student use ofappropriate mathematical academic languageduring partner, small group, and class discussions.Bundled Language Standard(s):between multiplication and division to explain that (1/3) 4 1/12 because(1/12) 4 1/3.b. Interpret division of a whole number by a unit fraction, and compute suchquotients. For example, create a story context for 4 (1/5), and use a visualfraction model to show the quotient. Use the relationship betweenmultiplication and division to explain that 4 (1/5) 20 because 20 (1/5) 4.c. Solve real world problems involving division of unit fractions by non-zerowhole numbers and division of whole numbers by unit fractions, e.g., byusing visual fraction models and equations to represent the problem. Forexample, how much chocolate will each person get if 3 people share 1/2 lb.of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?6Can students plan anddeliver aninformativepresentation withappropriately detailedsequencing? Do allstudents participate inthe thinking,conversation, andfinal product? Dothey follow rules andWhen talking aboutmathematics in pairsand groups, dostudents followprotocol/rules/routines forcollaborativediscussions?Do students use theappropriate academiclanguage whenspeaking in classdiscussions andpresentations andwhen writing in theirdaily math journals?
8. Students will notice that Multiplication Properties apply to themultiplication of fractions and mixed numbers.4. Students will create visual models of operations with fractions.1. Students analyze fractional parts and understand how they arerelated to multiplication and division.demonstrate these Mathematical Practices?)Opportunities for Observable Data (How will studentsMathematical Tools: tiles or counters, fraction bars, graph paper, colored water-based markers, colored pencilsMedia/Technology: ST Math Fraction Concepts; Fraction Concepts L1; Fractions Multiplication, Fraction Division; NCTMIlluminations Website http //illuminations.nctm.org (Fractions games: Drop Zone, Fraction Feud, Dig It, Equivalent Fractions,Fraction Game, Fraction Models)Supplementary Materials:(Check all that apply)1. Make sense of problems and persevere in solvingthem.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoningof others.4. Model with mathematics.5. Use appropriate tools strategically.6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeatedreasoning.7Interdisciplinary Cite several interdisciplinary or cross-content connections made in this unit of study (i.e. literature, science, socialConnections:studies, art, etc.)Art projects using tessellations of geometric figures showing fractional parts.Data analysis where statistics are related as fractions.Resources/Materials:Standards ofMathematicalPractice:guidelines forcollaboration?
DifferentiatedInstruction:Based on desired student outcomes, what instructionalvariation will be used to address the needs of EnglishLearners by language proficiency level? Use of sentence frames (appropriate for language level)to facilitate academic language and conversations. Useof visual organizers to assist processing mathematicalideas Explicitly teach key academic vocabulary. Use of manipulatives to facilitate conceptualunderstanding Flexible grouping to support language acquisition andtarget instruction Use of collaboration to promote socio-cultural learning Opportunities for verbal rehearsal of concepts8GATE Use of pre-assessment results to accelerate/compactcurriculum and instruction for students who demonstratemastery (85% ).Special Needs Use of visual organizers in organizing and evaluatingevidence. Explicitly teach key academic vocabulary. Monitor student responses for corrective teaching Use of games ST Math Opportunities for verbal rehearsal of conceptsBased on desired student outcomes, what instructionalvariation will be used to address the needs of students withspecial needs, including gifted and talented?
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GradeLevel/Course5thGradeCommon ObjectivesDepth ofKnowledge LevelStandards forMathematicalPracticeDuration: 60 min.Date:Unit: Multiplication and Division of FractionsPreparing the Learner Lesson # APreparing a Fraction Bar Tool KitNumber and Operations–Fractions3. Interpret a fraction as division of the numerator by the denominator (a/b a b). Solve wordproblems involving division of whole numbers leading to answers in the form of fractions, mixednumbers, e.g., by using visual fraction models or equations to represent the problem.Mathematical Tools: Strips of colored construction paper, rulers, math journalsMedia/Technology to be used to deepen learning: ST Math Fraction Concepts; FractionConcepts L1; NCTM Illuminations Website http //illuminations.nctm.org (Fractions games:Drop Zone, Fraction Feud, Dig It, Equivalent Fractions, Fraction Game, Fraction Models)Content:Language:Students will understand that equivalentfractions may be divided into more or lessequal parts, but still be the same amount.Students will use language of equivalence indescribing fractional parts (is the same as, isequivalent to, is the same amount).Level 1: RecallLevel 3: Strategic ThinkingLevel 2: Skill/ConceptLevel 4: Extended Thinking1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.Focus on the StandardsCoherence within and across grade levelsRigor (Balance of conceptual understanding, procedural skill & fluency, and application of ANINGEXPLANATIONCommon CoreInstructionalShifts inMathematicsAcademic Vocabulary(Tier II & Tier entWORDSWORTHKNOWINGRepresented bySame asFoldMeasureStripsStudents should have measurement skills and basic unit fraction knowledge.Lesson DeliveryCheck method(s) used in the lesson:ModelingGuided PracticeCollaborationIndependent PracticeGuided - ‐- ‐Multiplication&DivisionofFractions12
LessonOpeningPrior Knowledge: Measurement skills, basic unit fraction knowledge.Context and Motivation:Teacher Preparation: Cut six-inch strips of the following colors of paper: red, blue, orange, yellow,green, turquoise, brown, purple, and gray. Make each strip one-inch in width. You will need one sixinch strip of each color for each student in your class. Provide an envelope or baggie for each student.Make one set of fraction bars yourself, so you will have it as a model. (Cut a few extra strips forthose who make mistakes.)“Today we are going to prepare a Fraction Bar set that we can use for the rest of this unit. I have cutstrips of paper into 6-inch lengths, so that all the fraction bars will be the same size. Each of you willneed one strip of paper of each color. We will all make each our fraction bars the same color, so wecan have a common understanding and description for each fraction bar.The colors for each bar will be: 1 whole—red, 1 half—blue, 1 third—orange, 1 fourth—yellow, 1fifth—green, 1 sixth—turquoise, 1 eighth—brown, 1 tenth—purple, and 1 twelfth—gray.”Post the colors and sizes on a chart, so students can reference them as they work. (Colors, of course,may be adjusted, if these particular colors are not available at your site.)1WholeLesson onCoreMathUnit- ‐- ‐Multiplication&DivisionofFractions13
“Mark the red bar with 1 Whole, and set it aside. Now how can we make the blue bar into halves?How many equal parts is that? What would be the best way to make sure that both parts are exactlythe same?” “We could measure it, or we could fold it very carefully. Why don’t some of you try it bymeasuring and some by folding, and we’ll compare the results?” Allow students to mark their halves,first with pencil, then with a pen or marker to show two equal pieces. “Mark each half with ½, andset the halves bar aside.”Allow students time to fold or measure their strips. Some will be easier to make by measuring, someby folding. Allow students to experiment and compare their results using various methods. Halves,fourths, and eighths can be most easily folded. Thirds, sixths, and twelfths can be measured (2 inches,1 inch, and ½ inch).Do not cut the strips into pieces. Make it very clear that each strip must equal six inches inorder to make it a valuable fraction tool. Comparisons can be made by overlaying bars, placingbars alongside, or folding strips to their fractional parts.Fifths and tenths will cause the most difficulty. Try to determine the closest possible measurementyou can for these two fraction bars. The actual measurement for a 1/5 bar would be 1 1/5 inch (whichis very close to 1 3/16 inch). The measurement for a 1/10 bar would be 3/5 inch (which is very closeto 10/16 of an inch).Activities/Tasks/ ng/Checking for UnderstandingWhen all the students have finished preparing their fraction bar sets,spend a few minutes acquainting the students with them. Lay out allthe fraction bars in sequence by fractional size.“Which numbers did we not use for our fraction bars? (7, 9, 11) whydo you think that is? The fraction bars we made today are the mostcommonly used fractions. If we know how to use these, we can figureout how to compare fractions using those other numbers, when wecome across them.”“Find all the strips that can be folded to equal one half. How many canyou find? What are the names of these strips?” (2/4, 4/8, 3/6, 6/12)Some children may realize that 1/6 and 1/3 equal ½ as well. They canalso combine twelfths with the other strips to equal ½.Differentiated Instruction:English Learners:Modeling halves, thirds,fourths, etc.Sentence frames:can be represented by.is equivalent to.is the same as.(Students should sketch and record findings in their math journals.)“Find all the strips that equal 1/3. (2/6, 4/12) These are calledequivalent fractions. Can you find any other equivalent fractions?”(1/4 and 2/8, 1/5 and 2/10, 1/6 and 2/12)“Let’s pose a problem for you. If you share a candy bar that is cut intosix equal pieces with just one friend, how many sixths will you eacheat? Can you show me with your fraction bars?” (3/6) What is anothername for this fraction?Special Needs:Pair up to complete thework.Same sentence frames as ELLearners.Use of hands-on materials“I will give a few problems, and I want you to use your fraction barsto show the answer to the problems. Use your fraction bars to makecandy bars that are cut into different numbers of pieces.“How many ways can you show to share 2 candy bars among 4friends? How would you write the fractions to show this?” (1/2, 2/4,3/6, 4/8, 6/12, 5/10)SAUSDFifthGradeCommonCoreMathUnit- ‐- ‐Multiplication&DivisionofFractions14
Activities/Tasks/ ng/Checking for Understanding“How can 4 friends share 3 candy bars? Is there more than one way?(3/4, 6/8, 9/12)Accelerated Learners:How can 3 friends share 4 candy bars? (1 ¼ , 1 2/8, 1 3/12)Make fraction bars forsevenths, ninths, elevenths.How can 8 friends share 3 candy bars? Is there more than one way?(With these fraction bars, only 3/8, or ¼ and 1/8)Students should record their representations in their math journals.Use calculators to divide 6inches into equal lengths anddetermine the length of eachsegment. Convert tenths tosixteenths.Can you make up a problem using your fraction bars to representcandy bars? Ask students to write a problem, then select students toshare their problems with the rest of the class.Math Meeting:Gather students together to share fractional equivalence problems theywrote using the fraction bars.Ask other students to solve the given problems and give reasons fortheir answers.Possible sentence frames:If friends share candy bars, each will get candybar, because .is equivalent to because .Lesson ReflectionTeacherReflectionEvidencedby athUnit- ‐- ‐Multiplication&DivisionofFractions15
Fraction monCoreMathUnit- ‐- ‐Multiplication&DivisionofFractions16
GradeLevel/Course5thGradeCommon ObjectivesDepth ofKnowledge LevelStandards forMathematicalPracticeDuration: 60 min.Date:Unit: Multiplication and Division of FractionsPreparing the Learner Lesson # BLaunching Mathematical Discourse5th Grade Number and Operations—Fractions 5.NF 33. Interpret a fraction as division of the numerator by the denominator (a/b a b). Solve wordproblems involving division of whole numbers leading to answers in the form of fractions, mixednumbers, e.g., by using visual fraction models or equations to represent the problem.Speaking and Listening Standard:4. Report on a topic or text, or present an opinion, sequencing ideas logically and usingappropriate facts and relevant, descriptive details to support main ideas or themes; speak clearly atan understandable pace.Mathematical Tools: Fraction barsMedia/Technology to be used to deepen learning: ST Math Fraction Concepts; FractionConcepts L1; NCTM Illuminations Website http //illuminations.nctm.org (Fractions games:Drop Zone, Fraction Feud, Dig It, Equivalent Fractions, Fraction Game, Fraction Models)Supplementary Materials: Problems about EquivalenceContent:Language:Students will solve problems aboutequivalence using fraction bars and othervisuals.Students will express their solution strategies usingcollaborative behaviors of taking turns, adding on toanother’s thinking, and disagreeing respectfully.Level 1: RecallLevel 3: Strategic ThinkingLevel 2: Skill/ConceptLevel 4: Extended Thinking1. Make sense of problems and persevere in solving them.2. Reason abstractly and quantitatively.3. Construct viable arguments and critique the reasoning of others.4. Model with mathematics.5. Use appropriate tools strategically6. Attend to precision.7. Look for and make use of structure.8. Look for and express regularity in repeated reasoning.Common CoreInstructionalShifts inMathematicsFocus on the StandardsCoherence within and across grade levelsRigor (Balance of conceptual understanding, procedural skill & fluency, and application of UREOUTTHEMEANINGAcademic Vocabulary(Tier II & Tier nsiderationsEquivalencePortionsVisual representationSharing equallyWORDSWORTHKNOWINGAdding onDisagreeing withStudents will have a set of Fraction Bars to assist their thinking in this lesson.SAUSDFifthGradeCommonCoreMathUnit- ‐- ‐Multiplication&DivisionofFractions17
InstructionalMethodsLessonOpeningLesson DeliveryCheck method(s) used in the lesson:ModelingGuided PracticeCollaborationIndependent PracticeGuided InquiryReflectionPrior Knowledge: Students will have a set of Fraction Bars to assist their thinking in this lesson.Context and Motivation:Today we are going to practice having a productive classroom discussion through “math talk”. Mathtalk is like telling someone else how you made something and why. Who can tell me the steps tomaking a peanut butter sandwich? (Ask for volunteers. According to responses, act really dense, anddo only what they say, with no thought of your own.) “Put the peanut butter on the bread.” (Place thejar of peanut butter on top of the loaf of bread. Children will laugh.) “Open the jar first.” Then what?(Open the jar, then place the open jar on top of the loaf of bread.) “Use the knife,” etc.If I didn’t know anything about how to make a peanut butter sandwich, could I make one with thesedirections? Math talk has to be the same way. You have to tell exactly what you did to solve aproblem, not leaving out any of the steps.Today, we’ll practice telling each other what we did to solve a problem.Activities/Tasks/ ng/Checking for UnderstandingLesson ContinuumThe purpose of this lesson is to launch quality discourse in themathematics classroom.Preparation for the lesson:Run copies of the Problems about Equivalence for each group.Post and Discuss Group Norms:1) Listen respectfully.2) Only one person can talk at a time.3) Everyone must get a turn to speak.4) Show a visual representation of your solution.Guided Practice--Fishbowl:Select one group of three or four students to demonstrate theirthinking process, while everyone else watches. Place this group in thecenter, with everyone else seated in a circle around them.Differentiated Instruction:English Learners:Use sentence frames.Special Needs:Work in small groups.Use fraction barsUse sentence frames.Adjust numbers in problemsused.Accelerated Learners:Adjust numbers used inequivalence problems.Students can write their ownequivalence problems to solve.Give them this problem to solve: “A group of 3 children are sharing 2burritos. At another table, 6 children are sharing burritos. How manyburritos should the second group receive so that each child gets thesame portion as the first group?”“Share your thinking one at a time. If you have something to add toanother person’s thinking, say it with respect. You can say, I agreewith what is saying, but in addition, I would like to say that.If you wish to disagree with someone you can say, Althoughsaid , I am thinking about this differently. I think that.SAUSDFifthGradeCommonCoreMathUnit- ‐- ‐Multiplication&DivisionofFractions18
Make sure everyone has a turn to speak. When you have solved theproblem, make a visual representation of the solution to share with therest of the class.”Teacher charts discussion/visuals shared on chart paper or whitebo
Tableof!Contents!5th!Grade!Math!! . Solve word problems involving division of whole numbers leading to answers in the form of fractions, mixed numbers, e.g., by using visual fraction models or equations to represent the problem. . 5th!Grade
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skip grade 4 math and take grade 5 math while still in grade 4 Student A, now in grade 4, qualifies for SSA and enrolls in the accelerated course, which is grade 5 math Student A, after completing grade 5 math while in grade 4, takes the grade 4 End‐of‐Grade test Grade‐Level Grade 3 Grade 4 Grade 4
c. Curriculum Map: The Curriculum Map is presented by trimester.Each trimester includes: Unit Title: These are either the title of the Open Court Unit itself, or when applicable, the SAUSD Common Core Unit of Study Date range and number of weeks: Includes the approximate dates when the unit will be taught and the estimated number of weeks classrooms will spend on the unit.
Grade 4 NJSLA-ELA were used to create the Grade 5 ELA Start Strong Assessment. Table 1 illustrates these alignments. Table 1: Grade and Content Alignment . Content Area Grade/Course in School Year 2021 – 2022 Content of the Assessment ELA Grade 4 Grade 5 Grade 6 Grade 7 Grade 8 Grade 9 Grade 10 Grade 3 Grade 4 Grade 5 Grade 6 Grade 7 Grade 8
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