Scope And Sequence - Chandler Unified School District

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SAXON MATHGrades K– 8Math K– 4 / Intermediate 3–5 / Courses 1–3Scope andSequence Math K–4 Intermediate 3–5 Courses 1–3Scope and 62-9900009 781600 325625

Courses 1– 3Scope and Sequence1.2.3.4.5.6.7.8.9.Numbers and OperationsAlgebraGeometryMeasurementData Analysis and ProbabilityProblem SolvingCommunicationMathematical ReasoningConnectionsThe locators in the Scope and Sequence identify lessons in which directinstruction of a topic is presented. Once a topic is presented, students arecontinually exposed to the topic in the daily problem sets that follow.Because of space considerations, the daily problem sets are not referencedin the Scope and Sequence. Consequently, student exposure to individualtopics is actually stronger than indicated on the following pages.Saxon Math31Saxon Math Courses 1– 3This page may not be reproduced without permission of Harcourt Achieve Inc. Harcourt Achieve Inc. All rights reserved.The Scope and Sequence for the Saxon Courses 1–3 mathematics series isintended to help educators view the progression of mathematical topicsthroughout the series. Topics are grouped into nine strands:

SCOPE AND SEQUENCEThe locators in this Scope and Sequence indicate where direct instruction on each topic can be found.Locators refer to lesson and investigation numbers.Course 1Course 2Course 3Numbers and OperationsNumerationUses digits12, 21Reads and writes whole numbers and decimals35, 46Understands place value to trillions12Understands place value to hundred trillionsUses a number line (integers, fractions)9, 14, 17, 100Uses a number line (rational and irrational numbers)1, 5, 31125125124, 8, 29, 34, 59,64, 681, 1078, 8615, 31, 36Reads and writes numbers in expanded notation32, 46, 924Uses comparison symbols ( , , )94, 331, 77, 944, 78, 9362, 77, 94Uses comparison symbols ( , , , , )Compares and orders rational numbers33, 861, 5, 10Compares and orders real numbers9, 14, 44, 7610016Reads and writes numbers in scientific notation51, 57, 69, 83, 111 28, 51, 57Basic operationsThis page may not be reproduced without permission of Harcourt Achieve Inc. Harcourt Achieve Inc. and Stephen Hake. All rights reserved.AdditionAdds integers3, 5, 10, 1001, 22, 31Adds decimal numbers1, 37124Adds fractions and mixed numbers24, 26, 59, 61913Adds algebraic terms31Adds polynomials80Adds radical expressions96Solves addition problems with regrouping122, 13, 31Subtracts integers3, 5, 1001, 22, 33Subtracts decimal numbers1, 37125Subtracts fractions and mixed numbers24, 26, 369, 2313SubtractionSubtracts algebraic terms31Subtracts polynomialsSolves subtraction problems with regrouping801, 36, 48, 632313, 31, 33Multiplies integers2, 5, 10, 1121, 22, 36Multiplies decimal numbers39, 46125, 46Multiplies fractions and mixed numbers29, 66, 709, 2622, 23MultiplicationSaxon Math33

Course 1Course 2Course 3Numbers and Operations, continuedBasic Operations, continuedMulitplication, continuedMultiplies algebraic terms15, 21, 27, 36Multiplies radical expressions96, 120Multiplies binomialsSolves multiplication problems with regrouping9222Understands multiplication notations: a b, a · b, a(b) 212DivisionUnderstands division notations: division box, divisionsign, and division bar21Divides integers5, 1121, 2Solves division problems with remainders2, 1110, 42, 44Divides decimal numbers45125, 46Divides fractions and mixed numbers50, 54, 6825, 2622, 232, 36Divides algebraic terms27, 36Properties of numbers and operations10, 1941Identifies factors2, 19, 216, 1189Identifies multiples25Understands divisibility2169Identifies prime and composite numbers19219Finds the greatest common factor (GCF)206, 21, 249, 10Finds the least common multiple (LCM)3027, 3013Uses divisibility tests (2, 3, 5, 9, 10)216969Uses divisibility tests (4, 6, 8)Finds the prime factorization of whole numbers65, 7321, 24, 30, 103,1159, 10, 15Uses positive exponents with whole numbers,decimals, fractions73, 9220, 8315, 27, 46Uses positive exponents with integers47, 10327, 36, 46Uses negative exponents with whole numbers5751, 57Uses negative exponents with rational numbersFinds square roots51, 57, 6838Finds cube roots20, 100, 103, 10615, 36, 7410615Follows the order of operations5, 84, 922, 52, 63, 8531, 33Uses inverse operations1, 2, 4, 87, 1062, 9, 10638Rounds whole numbers, decimals, mixed numbers16, 5129, 3317, 117Estimates sums, differences, products, quotients162917Estimates squares and square roots8929, 10016, 118Determines the reasonableness of a solution2917Finds approximate irrational numbers29, 10016;Investigation 2Estimation34Scope and SequenceThis page may not be reproduced without permission of Harcourt Achieve Inc. Harcourt Achieve Inc. and Stephen Hake. All rights reserved.Identifies even and odd integers

Course 1Course 2Course 3AlgebraRatio and proportional reasoningFinds a fractional part of a whole, group, set, ornumber6, 22, 77, 1178, 14, 22, 60, 71,74Writes equivalent fractions26, 29, 55, 5615, 24, 27, 48Converts between fractions, terminating decimals,and percents33, 35, 73, 74,75, 998, 43, 48;Investigation 111, 12, 71, 11943, 4830, 63, 71, 1109, 252225, 76119Converts between fractions, repeating decimals, andpercentsFinds the reciprocals of numbers30, 50Simplifies complex fractions involving one term innumerator/denominatorSimplifies complex fractions involving two terms innumerator/denominator119Finds a percent of a whole, group, set, or number94, 105, 1198, 14, 7711, 48, 58, 63,109Works with percents greater than 100%94867, 719267, 71This page may not be reproduced without permission of Harcourt Achieve Inc. Harcourt Achieve Inc. and Stephen Hake. All rights reserved.Solves percent of change problemsSolves proportions with an unknown in one term83, 85, 10139, 8134, 35, 45, 87Finds unit rates and ratios in proportionalrelationships8836, 46, 537, 29, 34, 38, 44,49, 105Applies proportional relationships such as similarity,scaling, and rates23, 80;Investigation 1146, 54, 9826, 49, 70;Investigation 12Estimates and solves application problems involvingpercent105, 11981, 11048, 58, 67, 71;Investigation 1046, 54, 987, 35, 45,49, 64, 70;Investigation 10Estimates and solves application problems involvingproportional relationships such as similarity and rateCompares and contrasts proportional and nonproportional linear relationships (direct and inversevariation)34, 41, 47, 69, 98Patterns, relations, and functionsGenerates an alternate representation of data56, 116, 120;Investigation 969Uses, describes, and extends arithmetic sequences(with a constant rate of change)10461, 73Completes input/output tables10, 82, 9616, 5641, 47, 97, 99Analyzes a pattern to verbalize a rule10, 82, 96461, 73Analyzes a pattern to write an algebraic expression56, 8761, 97Evaluates an algebraic expression to extend a pattern4, 5661, 73, 97Compares and contrasts linear and nonlinear functions12041, 88, 98, 99;Investigations10, 11Variables, expressions, equations, and inequalitiesSolves equations using concrete and pictorial modelsFormulates a problem situation for a given equationwith one unknown variableSaxon Math114, 11687;Investigation 711, 12, 13, 14335

Course 1Course 2Course 3Algebra, continuedVariables, expressions, equations, and inequalities, continuedFormulates an equation with one unknown variablegiven a problem situation11, 15, 87, 10511, 12, 13, 14,1013, 4Formulates an inequality with one unknown variablegiven a problem situation62, 77Solves one-step equations with whole numbers8741;Investigation 72, 3, 14, 38Solves two-step equations with whole numbers106, 11693, 102, 108, 10919, 50, 79Solves one-step equations with fractions and decimals90;Investigation 73, 4, 14, 38Solves two-step equations with fractions and decimals93, 108, 11050, 79Solves equations with exponents93Solves systems of equations with two unknowns bygraphing56, 82, 89Graphs an inequality on a number line78, 8662, 77Graphs pairs of inequalities on a number line94Solves inequalities with one unknown9362, 77Validates an equation solution using mathematicalproperties102, 106, 10919, 90;Investigation 8GeometryBasic terms77, 11718Describes, identifies, and draws segments77, 11718Describes, identifies, and draws rays77, 11718Describes, identifies, and draws lines77, 11718, 44, 54Describes, identifies, and names angles28, 697, 11718, 54Describes planes28, 697, 11718;Investigation 1Describes, identifies, and draws parallel,perpendicular, and intersecting lines28, 71, 977, 61, 11718, 54;Investigation 1Describes, identifies, and draws horizontal, vertical,and oblique lines18;Investigation 711744;Investigation 1107, 116, 117447, 6218, 54;Investigation 3718, 54Properties and relationships of linesFinds and uses the slope of a lineProperties and relationships of anglesDescribes, identifies, and draws acute, obtuse, andright angles28;Investigation 3Describes, identifies, and draws straight anglesIdentifies complementary and supplementary angles69, 71, 974054Identifies and finds the measures of angles formed bytransversals9710254Constructs an angle bisectorInvestigation 8Investigation 10Identifies vertical angles364054Scope and SequenceThis page may not be reproduced without permission of Harcourt Achieve Inc. Harcourt Achieve Inc. and Stephen Hake. All rights reserved.Describes and names points

Course 1Course 2Course 3Geometry, continuedProperties and relationships of angles, continuedIdentifies adjacent angles405471, 97, 98101, 10220, 54, 81, 115;Investigation 3Identifies and describes regular polygons2, 601819Identifies and describes interior and exterior angles97, 9861, 89Finds and uses the sum of angle measures984020, 115Identifies and draws diagonals8966, 74Understands the effects of scaling on areaInvestigation 118, 26, 71, 91, 108;Investigation 5Understands the effects of scaling on volume98;Investigation 1135, 71, 76, 91,106, 108Calculates to find unknown angle measuresProperties and relationships of polygonsUnderstands and applies similarity and congruence68, 79, 108, 10918, 9719Classifies triangles936220, 35Classifies quadrilaterals60, 64;Investigation 675;Investigation 6Investigation 399, 11274;Investigation 2Use Pythagorean theorem to solve problemsThis page may not be reproduced without permission of Harcourt Achieve Inc. Harcourt Achieve Inc. and Stephen Hake. All rights reserved.Uses the Pythagorean theorem to solve problemsinvolving whole numbersUses the Pythagorean theorem to solve problemsinvolving radicals66, 74, 78, 96;Investigation 2Uses trigonometric ratios112, 1183-Dimensional figuresRepresents three-dimensional figures intwo-dimensional world using netsInvestigations6, 1267;Investigation 1255, 95, 100Draws three-dimensional figuresInvestigation 667Investigation 4Investigation 756;Investigation 341, 89;Investigations 1,5, 11Identifies intercepts of a line11656, 82Determines slope from the graph of line116, 11744, 56, 113;Investigation 8Coordinate geometryNames and graphs ordered pairsIdentifies reflections, translations, rotations, andsymmetry10858, 8026;Investigation 3Graphs reflections across the horizontal or verticalaxes1088026;Investigation 580Investigation 5Graphs translationsGraphs rotationsInvestigation 5Graphs dilations60, 71;Investigation 5Graphs linear equationsSaxon Math56;Investigation 941, 47, 56, 8237

Course 1Course 2Course 3MeasurementMeasuring physical attributesUses customary units of length, area, volume, weight,capacity7, 31, 78, 82, 10216, 70, 79, 826, 31, 42Uses metric units of length, area, volume, weight,capacity7, 8, 8232, 70, 79, 82,1146, 8, 42, 104Uses temperature scales: Fahrenheit, Celsius10, 3216, 3231Uses units of time13, 324980Converts units of measure in the U.S. CustomarySystem78, 81, 11416, 49, 506, 52, 72Converts units of measure in the metric system7, 11450, 1146, 104Converts between systems7506Uses unit multipliers95, 11450, 8852, 64, 72Finds the perimeter of polygons, circles, and complexfigures8, 47, 60, 71, 10319, 658, 31, 39, 60Finds the area of triangles, rectangles, andparallelograms31, 71, 7920, 378, 20, 37, 60, 66,92, 9675758240, 101, 11410440Systems of measurementSolving measurement problemsFinds the area of trapezoidsFinds the area of circles86Finds the area of semicircles and sectorsFinds the area of complex figures1077537Finds the surface area of right prisms and cylindersInvestigation 1210543, 44, 85105111Finds the surface area of cones and pyramids100, 114Estimates area86, 1187937, 40, 43;Investigation 1Finds the volume of right prisms, cylinders, pyramids,and cones120;Investigation 1295, 113, 117, 11942, 76, 104, 117Find the volume of spheres113, 11911178117, 11942, 76, 104, 11783;Investigation 1198;Investigation 1126, 35, 87, 91Solves problems involving similar triangles9735, 115;Investigation 12Solves problems involving indirect measurement9765, 1189835, 60Estimates volumeSolving problems of similaritySolves problems involving scale factorsSolves problems involving scale drawings:two-dimensionalSolves problems involving scale drawings:three-dimensional38Investigation 1191Scope and SequenceThis page may not be reproduced without permission of Harcourt Achieve Inc. Harcourt Achieve Inc. and Stephen Hake. All rights reserved.Finds the surface area of spheres

Course 1Course 2Course 3Measurement, continuedUse appropriate measurement instrumentsUses rulers (U.S. Customary and metric)7, 178;Investigation 10Uses a compass27;Investigation 8Investigations2, 1039Uses a protractorInvestigation 317, 9618Uses a thermometer10, 10032Collects and displays dataInvestigations 1,4, 538;Investigation 553;Investigation 6Makes and interprets tables and chartsInvestigation 5110;Investigation 9Investigations8, 11Makes and interprets frequency tablesInvestigations1, 938Investigation 6Makes and interprets pictographsInvestigation 538Makes and interprets line graphs1838;Investigation 5Makes and interprets histogramsInvestigation 1Investigation 553;Investigation 6Makes and interprets bar graphsInvestigation 438;Investigation 553;Investigation 6Makes and interprets circle graphs40;Investigation 538;Investigation 5Investigation 68690;Investigation 3Data Analysis and ProbabilityThis page may not be reproduced without permission of Harcourt Achieve Inc. Harcourt Achieve Inc. and Stephen Hake. All rights reserved.Data collection and representationMakes and interprets Venn diagramsMakes and interprets scatterplots113;Investigation 8Makes and interprets line plotsInvestigations4, 556Makes and interprets stem-and-leaf plotsInvestigation 5Investigation 4Makes and interprets box-and-whisker plotsChooses an appropriate graphInvestigation 5Identifies bias in data collectionInvestigation 410338103;Investigations6, 938Investigation 6Analyzes bias in data collectionDraws and compares different representations53, 109Investigations6, 940;Investigation 538;Investigation 5I618;Investigation 528;Investigation 47, 53, 103, 10577, 79;Investigation 47, 53Data set characteristicsFinds mean, median, mode, and rangeSelects the best measure of central tendency for agiven situationSaxon Math39

Course 1Course 2Course 3Data Analysis and Probability, continuedData set characteristics, continuedDetermines trends from data3853, 98, 113Makes predictions from graphsInvestigation 598, 113Recognizes misuses of graphical or numericalinformation38;Investigation 553Evaluates predictions and conclusions based on dataanalysis3853ProbabilityCalculates experimental probabilityInvestigations9, 10Investigation 832, 59Makes predictions based on experimentsInvestigations9, 10Investigation 832, 59Evaluates accuracy of predictions in experimentsInvestigation 9Investigation 859Calculates theoretical probabilityInvestigation 9Investigation 832, 59, 110Identifies sample spaces583632, 68, 83Calculates simple probability58, 77;Investigation 91432, 59Calculates the probability of compound eventsInvestigation 10Investigation 832, 68Calculates the probability of the complement of anevent77;Investigation 101432Calculates the probability of independent eventsInvestigations9, 1094;Investigation 832, 839483Calculates the probability of dependent events59Problem SolvingProblem-solving strategiesActs it out or make a model10, 30, 3434, 50, 541, 6, 11Draws a picture or diagram1, 14, 1714, 17, 201, 9, 23Finds a pattern1, 4, 111, 2, 45, 10, 16Guesses and checks5, 6, 255, 18, 198, 12, 35Makes an organized list2, 26, 328, 26, 2710, 62, 64Makes it simpler4, 12, 312, 4, 64, 7, 13Makes or uses a table, chart, or graph11, 14, 5918, 21, 3817, 18, 21Uses logical reasoning3, 5, 63, 5, 712, 15, 17Works backwards15, 55, 566, 15, 352, 14, 30Writes a number sentence or equation3, 17, 223, 7, 93, 31, 32Questions and responds2, 3, 42, 4, 612, 13, 14Works with partners or in groupsInvestigations 2,4, 9Investigations 1,3, 8Investigations 1,4, 9Communicates mathematical ideas through objects,words, pictures, numbers, technology, and symbols1, 2;Investigation 25, 7, 85, 6, 8Writes about math4, 6;Investigation 111, 12;Investigation 13, 4, 5Communication40Scope and SequenceThis page may not be reproduced without permission of Harcourt Achieve Inc. Harcourt Achieve Inc. and Stephen Hake. All rights reserved.Selects and uses different models to simulate an event

Course 1Course 2Course 3Uses algebraic reasoning10, 11, 82, 87, 964, 11, 16, 41, 56,873, 41, 61, 62, 73,97Uses spatial reasoning28, 60, 64, 71,97, 108, 109;Investigations6, 127, 18, 40, 67, 75,80, 99, 102, 117;Investigation 1118, 19, 26, 44,54, 55, 60, 71,74, 91, 108, 112;Investigations 2,3, 4, 5Classifies and sorts60, 64, 93;Investigation 67, 18, 62, 67;Investigation 619, 20;Investigations3, 4Explains an answer1, 2, 32, 4, 52, 9, 10Makes generalizations1, 2, 93, 4, 52, 3, 7Justifies conclusions13, 19;Investigation 11, 2, 32, 4, 5Connects math to architecture61, 98107, 109;Investigation 1135, 42;Investigation 3Connects math to art63, 67, 11230, 56, 9431, 33;Investigation 3Connects math to geography14, 16;Investigation 113, 18, 206, 17, 28Connects math to history10, 13, 1312, 13, 143, 7, 14Connects math to science7, 10, 119, 14, 1916, 18, 2828, 29, 62537, 11, 183, 4, 6Mathematical ReasoningConnectionsConnects math to social studies4, 7, 8This page may not be reproduced without permission of Harcourt Achieve Inc. Harcourt Achieve Inc. and Stephen Hake. All rights reserved.Connects math to sportsSaxon Math41

Saxon Math 31 Courses 1– 3 Saxon Math Courses 1– 3 Scope and Sequence The Scope and Sequence for the Saxon Courses 1–3 mathematics series is intended to help educators view the progression of mathematical topics throughout the series. Topics are grouped into nine strands: 1. Numbers and Operations

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