Scope And Sequence - Abiva Online Resources
Scope and SequenceChapter Numberand Title and Big Ideas/Lesson Numberand Title and TopicsObjectivesCorresponding K to 12 CurriculumStandards and LearningCompetencies DevelopedPerformance Tasks(for the Chapter)/Essential Questions(for the Lesson)Chapter 1 SequencesBig Ideas: Sequences suchas arithmetic andgeometric sequencesare used to modelmany real-lifephenomena. Solutions toproblems involvingarithmeticand geometricsequences makeuse of performingoperationson algebraicexpressions andsolving equations. Define and illustratean arithmetic sequence anda geometric sequence Solve problems involvingarithmetic and geometricsequencesContent StandardsThe learner demonstrates understanding of sequences.Performance StandardsThe learner is able to generatean arithmetic sequence anda geometric sequence, find thesums of the terms in the sequence,and solve problems involvingthese sequences.Create a problembook that consistsof real-life wordproblems involvingarithmetic andgeometric sequences.ix
Chapter Numberand Title and Big Ideas/Lesson Numberand Title and TopicsObjectivesCorresponding K to 12 CurriculumStandards and LearningCompetencies DevelopedPerformance Tasks(for the Chapter)/Essential Questions(for the Lesson)Lesson 1 Definition, Graph, and Sum of Consecutive Terms of SequencesTopics: Basic Conceptson Sequences General Termsof Sequences Graphs ofSequences Sums ofConsecutive Termsof SequencesThe learner . . . Define sequence and give observes and generalizesexamples of sequencesa pattern. Differentiate a finite sequence defines and illustratesfrom an infinite sequencea sequence and some types Find the terms of a sequenceof sequences (e.g., harmonic,given its general termFibonacci). Determine the nth term ofa sequence given the rule for it Graph a given sequence Find the sum of consecutiveterms of a sequence using thesummation notation How arethe notion ofa sequence anda functionrelated? How can youapply the conceptsof sequences insolving real-lifeproblems?Lesson 2 Arithmetic SequencesTopics: Define arithmetic sequence and Basic Conceptsgive examples of arithmeticon ArithmeticsequencesSequences Find the first few terms of General Term ofan arithmetic sequence givenan Arithmeticits first term and commonSequencedifferenceThe learner . . . defines, illustrates, and graphsan arithmetic sequence. gives examples of an arithmeticsequence. finds the terms of an arithmeticsequence including the generalnth term of the sequence.How important arearithmetic sequencesin solving real-lifeproblems?
Chapter Numberand Title and Big Ideas/Lesson Numberand Title and Topics Sum of theFirst n Terms ofan ArithmeticSequence Word ProblemsInvolvingArithmeticSequencesObjectives Find the nth term ofan arithmetic sequence givenits first term and commondifference Find the common difference,the first term, or a particularterm of an arithmetic sequencegiven two terms of thesequence Insert arithmetic meansbetween two given numbers Find the sum of the firstn terms of an arithmeticsequence Solve word problems involvingarithmetic sequencesCorresponding K to 12 CurriculumStandards and LearningCompetencies DevelopedPerformance Tasks(for the Chapter)/Essential Questions(for the Lesson) finds the sum of the terms ofa given arithmetic sequence. solves problems involvingsequences and their sums.Lesson 3 Geometric SequencesxiTopics: Basic Conceptson GeometricSequences The nth Term ofa Geometric SequenceThe learner . . .In what ways are Define geometric sequence and defines, illustrates, and graphs geometric sequencesgive examples of ita geometric sequence. Write the first few terms ofuseful? gives examples of a geometrica geometric sequence given itssequence.first term and its common ratio
xiiChapter Numberand Title and Big Ideas/Lesson Numberand Title and Topics Sum of the Firstn Terms ofa GeometricSequence Word ProblemsInvolving GeometricSequences Infinite GeometricSeriesObjectives Find the nth term of a geometric sequence given its firstterm and its common ratio Find the common ratio, thefirst term, or any particularterm of a geometric sequencegiven two of its terms Insert geometric meansbetween two given numbers Find the sum of the firstn terms of a geometric sequence Solve word problems involvinggeometric sequencesCorresponding K to 12 CurriculumStandards and LearningCompetencies DevelopedPerformance Tasks(for the Chapter)/Essential Questions(for the Lesson) differentiates between a finitesequence and an infinitegeometric sequence. differentiates betweenan arithmetic sequence anda geometric sequence. finds the terms of a geometricsequence including the generalnth term of the sequence. finds the sum of the terms ofa given geometric sequence,both finite and infinite. solves problems involvingsequences and their sums.Chapter 2 Polynomial FunctionsBig Ideas: One can usepolynomial functionsto model relationshipsbetween two variablesencountered in variousfields such as naturalsciences, social sciences,and businesses. Define a polynomial function Solve problems involving theRemainder Theorem and theFactor Theorem Determine the zeros ofpolynomial functions Graph polynomial functionsContent StandardsThe learner demonstrates understanding of polynomial functions.Performance StandardsThe learner is able to explorepolynomial functions.Create a PowerPointpresentation of atleast five applications of polynomialfunctions in real-lifesituations andvarious fields ofstudy.
Chapter Numberand Title and Big Ideas/Lesson Numberand Title and TopicsObjectivesCorresponding K to 12 CurriculumStandards and LearningCompetencies DevelopedPerformance Tasks(for the Chapter)/Essential Questions(for the Lesson)Lesson 1 Polynomial Functions of Degree n Define a polynomial function ofdegree n Identify whether a givenfunction is a polynomialfunction Determine the degree and theleading coefficient of a givenpolynomial functionThe learner . . . defines and describespolynomial functions. recognizes and gives examplesof polynomial functions. recognizes that linear andquadratic functions are alsopolynomial functions.Are polynomialfunctions necessary?Why or why not?The learner . . . differentiates betweenpolynomial functions andpolynomial expressions. recalls how to performoperations on polynomialexpressions. describes, illustrates, andperforms the synthetic divisionprocess for dividing polynomialexpressions by a binomial.In what way or waysare the RemainderTheorem and FactorTheorem useful?Lesson 2 The Remainder and Factor TheoremsTopics: Addition andMultiplication ofPolynomials Division ofPolynomials The RemainderTheorem The Factor Theoremxiii Determine the quotient of twopolynomials using long division Find the quotient andremainder of the polynomialf(x) divided by x – c usingsynthetic division State and illustrate theRemainder Theorem State and illustrate the FactorTheorem
xivChapter Numberand Title and Big Ideas/Lesson Numberand Title and TopicsObjectivesCorresponding K to 12 CurriculumStandards and LearningCompetencies DevelopedPerformance Tasks(for the Chapter)/Essential Questions(for the Lesson) states the Remainder Theoremand provides a proof of thetheorem. states the Factor Theorem andprovides a proof of the theorem. factors polynomial expressionsusing synthetic division, theRemainder Theorem, and theFactor Theorem.Lesson 3 Zeros of Polynomial FunctionsTopics: The Rational ZeroTheorem Descartes’s Rule ofSigns Upper and LowerBounds of Zerosof PolynomialFunctionsThe learner . . . State and illustrate the finds the zeros of polynomialRational Zero Theoremfunctions. Use the Descartes’s Rule of solves problems involvingSigns to find the possiblefactors and zeros of polynomialnumber of positive and negativefunctions.real zeros of a given polynomialfunction Determine if the given value isan upper or a lower boundof the zeros of a polynomialfunctionIn what way or waysare the RationalZero Theorem andDescartes’s Rule ofSigns useful?
Chapter Numberand Title and Big Ideas/Lesson Numberand Title and TopicsObjectivesCorresponding K to 12 CurriculumStandards and LearningCompetencies DevelopedPerformance Tasks(for the Chapter)/Essential Questions(for the Lesson) Find the zeros of polynomialfunctions whose degrees aregreater than 2 using the FactorTheorem, factoring, syntheticdivision, and depressedequationsLesson 4 Graphs of Polynomial FunctionsTopics: Characteristics of theGraphs of PolynomialFunctions Steps in Graphinga PolynomialFunction Recognize the characteristicsof graphs of polynomialfunctions Graph polynomial functionswhose degrees are greaterthan 2The learner sketches graphs ofpolynomial functions.In what way orways are graphs ofpolynomial functionsuseful?xv
xviChapter Numberand Title and Big Ideas/Lesson Numberand Title and TopicsObjectivesCorresponding K to 12 CurriculumStandards and LearningCompetencies DevelopedPerformance Tasks(for the Chapter)/Essential Questions(for the Lesson)Chapter 3 CirclesBig Ideas: Circles,along with tangentand secant lines, haveinteresting propertiesthat make them usefulin many real-lifesituations. Define, identify, and illustratethe parts of a circle Derive the relationships amongchords, arcs, central angles,and inscribed angles State and prove the theoremsrelating chords, arcs, centralangles, and inscribed angles Define and illustrate linestangent and secant to a circle State, prove, and apply theproperties of tangent andsecant lines Determine the degree measuresof arcs and angles of a circle,and those formed by tangentand secant lines Solve problems involvingcircles, secant, and tangentlinesContent StandardsThe learner demonstratesunderstanding of the concepts ofcircles.Performance StandardsThe learner is able to find partsof a circle and solve problemsinvolving the circle and its parts.Create and design atleast five geometricconstructionsinvolving circles,tangents, secants,inscribed orcircumscribedpolygons, and otherrelated curves.Compile themin a mini bookentitled “GeometricConstructions MiniBook on Circles andCurves.” Includethe step-by-stepinstructions,importantproperties, and reallife applicationsof each geometricconstruction in themini book.
Chapter Numberand Title and Big Ideas/Lesson Numberand Title and TopicsObjectivesCorresponding K to 12 CurriculumStandards and LearningCompetencies DevelopedPerformance Tasks(for the Chapter)/Essential Questions(for the Lesson)Lesson 1 Arcs and AnglesTopics: Basic Concepts onCircles Central Angles Arcs Formed byCentral Angles Arc Measures Inscribed Angles Identify and illustrate the keyconcepts related to circles Define, identify, and illustrateminor arcs, major arcs, andsemicircles in a circle Define, identify, and illustratecentral angles and inscribedangles Determine the degree measuresof arcs and angles of a circle Derive the relation amongchords, arcs, central angles,and inscribed angles State and prove the theoremsrelating chords, arcs, centralangles, and inscribed anglesThe learner . . . defines, identifies, andillustrates the parts of a circle:the center, radius, diameter,interior and exterior, chord,arc, central angle, andinscribed angle. derives the relation amongchords, arcs, central angles,and inscribed angles. states and proves the theoremsrelating chords, arcs, centralangles, and inscribed angles.What propertiesof circles make itsuitable to use invarious real-lifesituations?The learner . . . defines secant and tangentlines and segments, and sectorof a circle.How do you use theproperties of arcsand angles formedby tangents andsecants to a circle inreal-life situations?Lesson 2 Tangent and Secant LinesxviiTopics: Tangent Lines Angles Formed bySecant and TangentLines Define secant and tangent linesand segments Draw and illustrate tangentand secant lines to a circle
xviiiChapter Numberand Title and Big Ideas/Lesson Numberand Title and TopicsObjectives State and apply the propertiesof tangent and secant lines Determine the measures ofangles formed by tangent andsecant lines State and prove theorems onsecant and tangent lines Solve problems involving secantand tangent linesCorresponding K to 12 CurriculumStandards and LearningCompetencies DevelopedPerformance Tasks(for the Chapter)/Essential Questions(for the Lesson) states and prove theorems onsecant and tangent lines andsegments. solves problems that involveparts of circles.Chapter 4 Plane Coordinate GeometryBig Ideas: Manygeometric propertiescan be justifiedor proven usingcoordinate proofs. Derive and apply the distanceand midpoint formulas Use coordinate proofs to verifyproperties of geometric figures Solve problems involvinggeometric figures on thecoordinate plane Determine the equation ofa circle and express it indifferent forms Find the center and radius ofa circle given its equation Sketch the graph of a circle onthe coordinate planeContent StandardsThe learner demonstratesunderstanding of concepts ofcircles.Performance StandardsThe learner is able to exploregeometric figures on therectangular coordinate plane.Create a portfoliothat consists of atleast five coordinateproofs of geometricconjectures ortheorems andthe extension ofthe concepts intwo-dimensionalcoordinate system tothree-dimensionalspace.
Chapter Numberand Title and Big Ideas/Lesson Numberand Title and TopicsObjectivesCorresponding K to 12 CurriculumStandards and LearningCompetencies DevelopedPerformance Tasks(for the Chapter)/Essential Questions(for the Lesson)Lesson 1 Coordinate ProofsTopics: The DistanceFormula The MidpointFormula Coordinate Proofs ofGeometric Theorems Derive and apply the distanceformula Derive and apply the midpointformula Use coordinate proofs to verifyproperties of geometric figures Solve problems involvinggeometric figures in thecoordinate planeThe learner . . . derives the distance formulabetween two points on theplane. applies the distance formulato derive and prove somegeometric properties. solves problems involvinggeometric figures in thecoordinate plane. How do you findthe shortestdistance betweentwo locations? How do youprove geometricconcepts andproperties usingthe coordinateplane? How do you applyboth geometryand algebra insolving real-lifeproblems?Lesson 2 Circles on the Coordinate PlaneTopics: Forms of Equationsof Circles Equations of CirclesTangent to a Linexix State and derive the centerradius form of the equation ofa circle Determine the equation ofa circle given its center andradiusThe learner . . . derives and states the centerradius form of the equation ofa circle. finds the center and radius ofa circle given its equation andvice versa.How do you relatethe geometric andalgebraic propertiesof circles using thecoordinate plane,and apply themin solving real-lifesituations?
xxChapter Numberand Title and Big Ideas/Lesson Numberand Title and TopicsObjectives Find the center and radius ofa circle given its equation Determine the equation ofa circle given its radius andthe point of tangency Sketch the graph of a circle onthe coordinate plane Solve problems involving circleson the coordinate planeCorresponding K to 12 CurriculumStandards and LearningCompetencies DevelopedPerformance Tasks(for the Chapter)/Essential Questions(for the Lesson) sketches the graph of a circle onthe coordinate plane. solves problems involvinggeometric figures in thecoordinate plane.Chapter 5 Measures of Position and SkewnessBig Ideas: Measures ofposition and skewnessare importantnumerical measuresin describing andanalyzing a statisticaldata set. Define and describe themeasures of position andskewness Describe a statistical data setusing the measures of positionand skewnessContent StandardsThe learner demonstratesunderstanding of measures ofposition.Performance StandardsThe learner is able to describea set of data using measuresof position.Gather data onthe scores in pastexaminations of yourclass. Analyze thedistribution of thedata by calculatingthe measuresof position andskewness. Draw theboxplot of the dataset. Include a reporton the computationsand descriptions ofthe obtained data.
Chapter Numberand Title and Big Ideas/Lesson Numberand Title and TopicsPerformance Tasks(for the Chapter)/Essential Questions(for the Lesson)ObjectivesCorresponding K to 12 CurriculumStandards and LearningCompetencies Developed Define and describe thefollowing measures of position:quartiles, deciles, andpercentiles Explain and interpret quartiles,deciles, and percentiles Calculate percentiles of a setof data Use measures of position todescribe a data set and infersome information about the data Solve problems involvingquartiles, deciles, andpercentilesThe learner . . . defines and describes the following measures of position: quartiles, deciles, and percentiles. explains and interprets quartiles,deciles, and percentiles. calculates specified percentiles(e.g., 90th percentile) of a setof data. uses measures of position todescribe a set of data and inferssome information about the data. solves problems involvingquartiles, deciles, and percentiles.Why is it importantto know the measuresof position indescribing a particular data set?The learner constructs a boxplotfrom a set of data.How can the relationship among themeasures of centraltendency, namely,mean, median, andmode affect thedistribution of a setof data?Lesson 1 Measures of PositionTopics: Percentiles Quartiles DecilesLesson 2 Measure of Skewness and BoxplotxxiTopics: Types ofDistributions Coefficient ofSkewness Boxplots Define and describe themeasure of skewness Use the measure of skewnessto describe a set of data andinfer some information aboutthe data Construct a boxplot from a setof data
xxiiChapter Numberand Title and Big Ideas/Lesson Numberand Title and TopicsObjectivesCorresponding K to 12 CurriculumStandards and LearningCompetencies DevelopedPerformance Tasks(for the Chapter)/Essential Questions(for the Lesson)Chapter 6 Counting Techniques and Probability of EventsBig Ideas: Counting techniquesare used to calculatethe number ofoutcomes ina particularexperiment. Knowing how tocount the possibleoutcomes inan experimentor a situation isessential in calculating probabilityof events. Count the number ofoccurrences of an event usingdifferent counting techniques Determine the probabilities ofevents Solve problems involving theconcepts of probabilityContent StandardsThe learner demonstratesunderstanding of basiccombinational concepts andprobability.Performance StandardsThe learner is able to . . . count occurrences of an eventand arrangements usingthe Fundamental CountingPrinciple, permutations, andcombinations. find the probability ofcompound events.Role-play orsimulate real-lifesituations thatinvolve the applications of thedifferent countingtechniques.Lesson 1 Counting TechniquesTopics: FundamentalCounting Principle Permutations Combinations Count the number of waysan event can occur usinga grid table, a tree diagram,or systematic listingThe learner . . . counts the number ofoccurrences of an event using(a) a grid table, (b) a treediagram, and (c) systematiclisting.How can youapply the differentcounting techniquesin real-lifesituations?
Chapter Numberand Title and Big Ideas/Lesson Numberand Title and TopicsObjectivesxxiii State and explain theFundamental CountingPrinciple Use the Fundamental CountingPrinciple to determine thenumber of ways a task can becarried out Recognize groupings thatrequire order and groupingsthat do not require order Define permutation andcombination Derive the formulas forfinding the permutation andcombination of n objects takenr at a time Find the permutation ofn objects taken r at a time Find the combination ofn objects taken r at a timeas a subset Explain the relationship ofa permutation to a combinationof n objects taken r at a time Solve problems involvingpermutations and combinationsCorresponding K to 12 CurriculumStandards and LearningCompetencies Developed states and explains the Fundamental Counting Principle. uses the FundamentalCounting Principle to countthe number of arrangementsor ways that a task can becarried out. recognizes groupings thatrequire order and groupingsthat do not require order. defines a permutation ofn objects taken r at a time. derives and uses the formulafor finding the permutation ofn objects taken r at a time. defines a combination of n objectstaken r at a time as a subset. derives and uses the formulafor finding the number ofcombinations of n objects takenr at a time. explains the relationship ofa permutation to a combinationof n objects taken r at a time. solves problems involvingpermutations andcombinations.Performance Tasks(for the Chapter)/Essential Questions(for the Lesson)
xxivChapter Numberand Title and Big Ideas/Lesson Numberand Title and TopicsObjectivesCorresponding K to 12 CurriculumStandards and LearningCompetencies DevelopedPerformance Tasks(for the Chapter)/Essential Questions(for the Lesson)Lesson 2 Probability of EventsTopics: Sample Spacesand Events Complementof an Event Operationson Events TheoreticalProbability Probability Rules Recognize events, union ofevents, and intersection ofevents Define the probability of theunion of two events Find the probability ofP(A B) and P(A B) Define events that areindependent Solve problems on probabilityinvolving union andintersection of eventsThe learner . . . recognizes events, union ofevents, and intersection ofevents. finds the cardinality of a unionof two sets A and B. defines the probability ofa union of two events using thedefinition of the probability ofan event E. finds the probability P(A B). defines events that areindependent. finds the probability P(A B). solves problems involvingprobabilities of union andintersection of events.How can recognizingthe union andintersection ofevents be used insolving problemsinvolving probabilityof compound events?
an arithmetic sequence given its first term and common difference The learner . . . defines, illustrates, and graphs an arithmetic sequence. gives examples of an arithmetic sequence. finds the terms of an arithmetic sequence including the general nth term of the sequence. How important are sequenc
Introduction to PYP social studies scope and sequence 2 Social studies scope and sequence Developing a school's social studies scope and sequence Unless a school has adopted the PYP sample programme of inquiry, the social studies content in its own scope and sequence will be different from the sample provided here. Some schools may need to .
Chapter 5 Project Scope Management Chapter 5 Project Scope Management 5.1 Plan Scope Management 5.1 Colect Requirements 5.2 Collect Requirements 5.2 Define Scope 5.3 Define Scope 5.3 Create WBS 5.4 Create WBS 5.4 Verify Scope 5.5 Validate Scope 5.5 Control Scope 5.6 Control Scope PMBOK 5th Edition
AFWA Scope and Sequence Page 4 of 105 AFWA K-12 Conservation Education Scope and Sequence Overview The AFWA K-12 Conservation Education Scope and Sequence is a detailed list of what all students are expected to know and be able to do at each level of our educational system in the areas of science, social science, and health and fitness.
Notes for the Teacher - Tips on Teaching the Scope and Sequence This Scope and Sequence is very ACTIVITY focused. The activities are used to make learning fun, but are also intended to help children learn the skill, attitude and information in ways that enhance learning. The Scope and Sequence is organised into units and lessons.
Master Syllabi for Grade 6 Courses 1 Grade 6 Math: TX Fundamentals of Geometry and Algebra Scope & Sequence: Scope & Sequence documents describe what is covered in a course (the scope) and also the order in which topics are covered (the sequence). These documents list instructional objectives and skills to be mastered. K¹² Scope & Sequence
Scripture Press scope and sequence - May 2019.indd 2 6/11/19 11:38 AM. SCRIPTURE PRESS SCOPE & SEQUENCE Primary Two-year scope and sequence for children in grades 1 and 2. Fall Winter Spring Summer Year 1 Unit 1: Knowing God Cares for Us Exodus Unit 1: Knowing Jesus Matthew, Luke
An example of the type of information needed prior to developing a Scope & Sequence for a school focused on the media & design industry is included in the following table: 3. What is the process for developing the first draft of the Scope & Sequence? In constructing the first draft of the scope and sequence, begin by gathering the following .
Korean and Chinese belong to different language families. In terms of their linguistic structures, they are extremely dissimilar. Beginning Korean: A Grammar Guide 2 Autumn 2004 Finally, hangeul is uniquely associated with the language, literature, and people of the Korean peninsula. No other community uses the hangeul system for graphically representing the sounds of their language. Given the .
