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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

Intermediate 3– 5This page may not be reproduced without permission of Harcourt Achieve Inc. Harcourt Achieve Inc. All rights reserved.The Scope and Sequence for the Saxon Intermediate 3–5 mathematicsseries is intended to help educators view the progression of mathematicaltopics throughout the series. Topics are grouped into nine strands:1.2.3.4.5.6.7.8.9.Numbers and OperationsMeasurementGeometryPatterns, Algebra, and FunctionsStatistics, Data 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 Math21Saxon Math Intermediate 3– 5Scope and Sequence

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.Intermediate 3Intermediate 4Intermediate 5Uses digits to write numbers11, 323, 5, 101, 4, 7Reads and writes whole numbers through 999127Reads and writes whole numbers through 999,99932Numbers and OperationsNumerationReads and writes whole numbers through 999,999,99933Reads and writes whole numbers through999,999,999,99952Identifies place value through hundreds11Identifies place value through hundred thousands32Identifies place value through hundred millions433334Identifies place value through hundred billions52Locates and names whole numbers on a number line4, 15, 17, 33Investigation 112, 27, 33Reads and writes numbers in expanded form11, 13, 1416, 333, 48Uses comparison symbols ( , , )17, 2756, 91, 1034Compares and orders whole numbers17, 27, 39, 99,1035, 7, 33, 34;Investigation 14, 7Models addition6, 9, 13, 1616, 41Adds whole numbers6, 8, 9, 10, 13,16, 18, 24, 36,92, 941, 2, 11, 13, 456, 8, 10, 24Adds decimal numbers22, 25, 92, 948, 22, 43, 50, 9113, 73, 99Reads and writes numbers in expanded notationThis page may not be reproduced without permission of Harcourt Achieve Inc. Harcourt Achieve Inc. and Stephen Hake. All rights reserved.73448, 52, 78Basic operationsAdditionAdds fractions and mixed numbers41, 43, 116Uses regrouping in addition13, 16Finds the value of a collection of coins and bills21, 22, 25, 81;Investigation 28, 22Models subtraction7, 14, 1934Subtracts whole numbers7, 8, 14, 19, 20,6, 12, 14, 16, 25,23, 28, 40, 92, 94 418, 9, 14, 16, 24Subtracts decimal numbers26, 92, 9413, 73, 99, 1026Subtraction30, 43, 50, 91Subtracts fractions and mixed numbersUses regrouping in subtractionSaxon Math9, 41, 43, 59, 6341, 43, 59, 63,11614, 19, 28309, 1623

Intermediate 3Intermediate 4Intermediate 5Models multiplication54, 55, 57, 60,61, 623517, 76, 86Understands the relationship between multiplicationand repeated addition5427;Investigation 313, 17Multiplies by one-digit whole numbers56, 59, 61, 64,70, 7629, 32, 3817Multiplies by two-digit whole numbers81, 8444, 48, 87, 9051Multiplies by three-digit whole numbers91, 9758, 11355, 56Uses regrouping in multiplication84, 91, 97Multiplies by multiples of 10 and 10067, 85, 8629, 111Multiplies by multiples of 100085111Multiplies decimal numbers67109, 110, 111Numbers and Operations, continuedBasic Operations, continuedMultiplication17, 51, 55, 56Multiplies fractions and mixed numbers76, 86, 120DivisionModels division82, 85, 101Divides whole numbers82, 83, 85, 86,89, 90, 10146, 64, 65, 68,71, 76, 80, 88,105, 110, 11819, 20, 22, 26,42, 54, 92Understands and uses division notations: division box,division sign, and division bar8247, 6520Solves division problems with remainders53, 68, 71, 76,80, 88, 105, 11822, 26, 40, 58Divides decimal numbers76117, 118, 11987, 9687, 96Divides by multiples of 10 and 100105, 11054Properties of numbers and operationsIdentifies even and odd numbers88102Identifies and uses multiples785515, 29, 112Identifies and uses factors5515, 18, 25, 80, 82Understands divisibility64, 6525, 42Uses divisibility rules64, 65, 10522, 42Identifies prime and composite numbers5580, 112Finds the greatest common factor (GCF)82, 90Finds the least common multiple (LCM)112Uses positive exponents with whole numbers627861Investigation 378Uses the correct order of operations924524Learns fact families and understands inverseoperations8, 9, 40, 86, 892, 6, 24, 46, 478, 10, 14, 19Understands the concept of square numbers andsquare roots24Scope and SequenceThis page may not be reproduced without permission of Harcourt Achieve Inc. Harcourt Achieve Inc. and Stephen Hake. All rights reserved.Divides fractions and mixed numbers

Intermediate 3Intermediate 4Intermediate 5Reads and writes fractions and mixed numbers5, 29, 4122, 35, 102Investigation 2Locates and names fractions and mixed numbers on anumber line4837, 10238Compares and orders fractions43, 4956, 103;Investigation 938, 39, 116;Investigations2, 3Models a fractional part of a whole5, 29, 41, 42, 43,46, 47, 492637; Investigations2, 3Names a fractional part of a whole5, 29, 41, 46, 47,4922, 6130, 60;Investigations2, 3Models a fractional part of a group or set4970, 9546Names a fractional part of a group or set44, 4970, 74, 9530, 46Finds equivalent fractions43, 46, 4723, 79, 81, 90,103, 109, 115,116; Investigation 91; Investigations2, 39Numbers and Operations, continuedThis page may not be reproduced without permission of Harcourt Achieve Inc. Harcourt Achieve Inc. and Stephen Hake. All rights reserved.Fractions, decimals, and percentsFinds the least common denominator (LCD)116116Converts between improper fractions and mixednumbers89, 10475, 113Simplifies fractions112, 114, 119, 120 81, 82, 90, 91Reads and writes decimals4, 22;Investigations4A, 4B64, 67, 68, 70,100, 106Locates and names decimals on a number line10266, 104Compares and orders decimals22, 9169; Investigations2, 3Converts between fractions, decimals, and percents84; Investigations 30, 67, 71;4A, 4B, 5Investigations2, 3Finds a percent of a wholeInvestigation 530, 43Finds a percent of a group or set107Writes reciprocals of numbers95, 96Finds rates and ratios57, 609720, 42, 54, 11733, 62102, 103101, 104, 1062062EstimationRounds whole numbers15Rounds decimals and mixed numbersRounds money amounts to the nearest dollar96Rounds money amounts to the nearest 25 centsEstimates sums, differences, and products2030, 92, 93, 94,95, 99Estimates quotientsUses compatible numbersSaxon Math48, 49, 59, 90, 9333, 51, 55, 59, 62,73, 10159, 9333, 9492, 9425

Intermediate 3Intermediate 4Intermediate 5Describes and extends an arithmetic or geometricsequence2, 4, 53, 613, 38;Investigation 11, 2;Investigation 4Recognizes patterns in multiplication54, 55, 59, 61, 64, 2876, 78Investigation 4Completes function tables25, 3494;Investigation 11Investigation 431;Investigation 4AlgebraPatterns, relations, and functionsAnalyzes a pattern or sequence to name a ruleVariables, expressions, and equationsSolves addition equations using concrete and pictorialmodels6, 9, 13, 16, 361;Investigation 1211Solves subtraction equations using concrete andpictorial models7, 14, 19, 2825, 3135Solves multiplication equations using concrete andpictorial models55, 57, 61Investigation 12Solves division equations using concrete and pictorialmodels82, 8552, 70Writes and solves equations to solve word problems6, 7, 8, 9, 18, 20, 1, 11, 25, 31, 49,30, 36, 40, 60, 73 52, 61Chooses an appropriate formula to solve a problemSolves one-step equations with whole numbers9, 36, 40, 86Solves two-step equations with whole numbers10, 11, 16, 21;Investigation 16253, 72, 103, 11431, 49, 52, 68, 7010, 21, 3561, 9449, 62, 72, 84GeometryDescribes and names points4, 1092312Describes, identifies, and draws segmentsInvestigation 423, 4531, 32, 61Describes, identifies, and names angles6523, 4531, 36Describes, identifies, and draws rays2312, 61Describes, identifies, and draws lines23, 4512, 31, 61Describes planes32Properties and relationships of linesDescribes, identifies, and draws parallel andperpendicular lines66, 71;Investigation 4Describes, identifies, and draws horizontal, vertical,intersecting, and oblique lines23, 4531, 32, 452312, 3123, 63, 78, 8131, 36, 61;Investigation 10AnglesDescribes, identifies, and draws acute, obtuse, right,and straight angles65, 66, 69Identifies and describes interior and exterior anglesInvestigation 10Calculates to find unknown angle measuresInvestigation 102-Dimensional figuresIdentifies and describes polygons by their attributes51, 66, 67, 68, 69,10421, 6332, 36, 61Classifies triangles69783626Scope and SequenceThis page may not be reproduced without permission of Harcourt Achieve Inc. Harcourt Achieve Inc. and Stephen Hake. All rights reserved.Basic terms

Intermediate 3Intermediate 4Intermediate 5Classifies quadrilaterals51, 6663, 9232, 45Understands congruence6866, 7332, 36Understands similarity6632Identifies parts of a circle215398, 99, 100839983, 89Geometry, continued2-Dimensional figures, continued3-Dimensional figuresIdentifies and describes geometric solids by theirattributes71, 75;Investigation 8Identifies congruent parts of geometric solidsCoordinate geometryNames and graphs ordered pairs109, 110;Investigation 11Investigation 8Investigation 8Identifies types of symmetryInvestigations7, 97988, 105;Investigations8, 1273, 75, 78, 82105;Investigation 8Identifies transformationsGraphs reflections88;Investigation 8MeasurementThis page may not be reproduced without permission of Harcourt Achieve Inc. Harcourt Achieve Inc. and Stephen Hake. All rights reserved.Measuring physical attributesUses customary units of length34, 35, 37, 5839;Investigation 244, 47Uses customary units of weight74, 987747, 77Uses customary units of capacity874047, 85, 103Uses metric units of length7969, 102;Investigation 244, 65, 66Uses metric units of mass80, 987777Uses metric units of capacity874085, 103Uses temperature scales: Fahrenheit, Celsius41827, 98Measures time3, 5, 85, 542819, 2728, 35, 1087765, 72, 74, 103Converts in the U.S. Customary System40, 77;Investigation 247, 74, 77, 85Converts in the metric system40, 69, 77, 102;Investigations2, 1144, 65, 74, 77, 85108;Investigation 253Measures elapsed timeChooses an appropriate unit of measurement34, 74, 79, 80, 87Systems of measurementSolving measurement problemsFinds the perimeter of polygonsEstimates perimeterSaxon Math58, 66, 67111; Investigation 101, 104327