`Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:N XK X1st 2nd 3rd 4th 5th 6th X X X X X XSerial #MATHEMATICS1I. FUNDAMENTALS OF THE DECIMAL SYSTEMXXXXXXXX2I.A. Can count to 10 by unitsXXXXXXXX3I.A.1. Table top number rodsX4I.A.2. Sandpaper numeralsX5I.A.3. Association of number rods to numeralsX6I.A.4. Spindle boxesX7I.A.5. Cards and countersX8I.A.6. Short bead stairX9I.B. Can count from 11 to 19 by unitsXXXXXXXX10I.B.1. Bead bars and cardsXX11I.B.2. Teen board and beadsXX12I.C. Can count from 1 to 100 by unitsXXXXXXXX13I.C.1. Ten boards and beadsXX14I.C.2. 100 chainXX15Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:N IK X1st 2nd 3rd 4th 5th 6th XSerial #I.C.3. Hundred Board16I.D. Can count from 1 to 1,000:XXXXXXXX17I.C.1. Linear counting with bead chainsIXX18I.C.2. Linear counting with number rollsIX19I.C.3. Skip counting with bead chains and number rollsXXXXXXXX20I.C.3.a. 2's, 5's, and 10'sXX21I.C.3.b. 3's, 4's, and 6'sXX22I.C.3.c. 7's, 8's, and 9'sXX23I.D. Numerical Place ValueXXXXXXXX24I.D.1. Can recognize quantities up to 9,999XXXXXXXX25I.D.1.a. Golden Beads onlyXXX26I.D.1.b. Number cardsXXX27I.D.1.c. Golden Beads and Number CardsXXX28I.D.1.d. Exchanging GameIXX29I.D.1.e. Stamp GameXX30Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:N IK1st 2nd 3rd 4th 5th 6th XSerial #I.D.1.f. Small Bead Frame31I.D.2. Can recognize quantities up to 9,999,999XXXXXXXX32I.D.2.a. Hierarchy of Decimal System materialIX33I.D.2.b. Large Bead FrameIX34I.D.2.c. Golden MatIX35I.D.2.d. Multiplication CheckerboardIXX36I.D.2.e. Long Division Racks and TubesIXX37I.D.2.f. Flat Bead FrameXX38I.D.2.g. PegboardXX39I.D.3. Can recognize quantities up to 999,999,999IX40I.D.4. Can recognize quantities up to 999,999,999,999IX41I.D.5. Can recognize quantities up to 999,999,999,999,999 II. OPERATIONS WITH WHOLE NUMBERS X X X X XIX42XXX43II.A. THE PROCESS OF ADDITIONXXXXXXXX44II.A.1. Addition of two 4 digit addends without exchangingXXXXXXXX45Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:N XK X1st 2nd 3rd 4th 5th 6thSerial #II.A.1.a. Golden Beads46II.A.1.b. Stamp GameX47II.A.1.c. Dot BoardX48II.A.1.d. Golden MatXX49II.A.1.e. Small Bead FrameIXX50II.A.2. Addition of two 4 digit addends with exchanging II.A.2.a. Golden BeadsXXXXXXXX51IX52II.A.2.b. Stamp GameIXX53II.A.2.c. Dot BoardIX54II.A.2.d. Golden MatXX55II.A.2.e. Small Bead FrameXX56II.A.3. Addition of multiple addendsXXXXXXXX57II.A.3.a. Golden BeadsXXX58II.A.3.b. Stamp GameXXX59II.A.3.c. Dot BoardXX60Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:NK1st 2nd 3rd 4th 5th 6th X XSerial #II.A.3.d. Golden Mat61II.A.3.e. Small Bead FrameXX62II.A.4. Addition of two 7-digit addends without exchanging II.A.4.a. Large Bead FrameXXXXXXXX63IX64II.A.4.b. Long Division Racks and TubesIX65II.A.4.c. Golden MatIX66II.A.5. Addition of two 7-digit addends with exchanging II.A.5.a. Large Bead FrameXXXXXXXX67IX68II.A.5.b. Long Division Racks and TubesIX69II.A.5.c. Golden MatIX70II.A.6. Addition: Exercises leading to the memorization of addition facts II.A.6.a. Basic addition facts: Two addends between 1-10 II.A.6.a1. Addition Snake GameXXXXXXXX71XXXXXXXX72IXX73II.A.6.a2. Bead BarsIXX74II.A.6.a3. Addition Strip BoardIXX75Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:NK X1st 2nd 3rd 4th 5th 6th XSerial #II.A.6.a4. Addition Charts76II.A.6.b. Associative and Commutative Properties of Addition II.A.6.b1. Bead BarsXXXXXXXX77IXX78II.A.6.b2. Flash Card SetsXX79II.A.6.c. Missing addends c1. Bead BarsXX80II.A.6.c2. Flash Card SetsXX81II.A.7. Addition: The Passage to AbstractionXXXXXXXX82II.A.7.a. Two Addends up to 9,999XX83II.A.7.b. Multiple addends up to 9,999,999XX84II.B. THE PROCESS OF SUBTRACTIONXXXXXXXX85II.B.1. Subtraction of two 4 digit numbers without exchanging II.B.1.a. Golden BeadsXXXXXXXX86XX87II.B.1.b. Stamp GameXX88II.B.1.c. Golden MatX89II.B.1.d. Small Bead FrameXX90Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:N XK X1st 2nd 3rd 4th 5th 6th X X X X X XSerial #II.B.2. Subtraction of two 4 digit numbers with exchanging II.B.2.a. Golden Beads91IX92II.B.2.b. Stamp GameIX93II.B.2.c. Golden MatXX94II.B.2.d. Small Bead FrameXX95II.B.3. Subtraction of two 7-digit numbers without exchanging II.B.3.a. Large Bead FramesXXXXXXXX96XX97II.B.4. Subtraction of two 7-digit numbers with exchanging II.B.4.a. Large Bead FramesXXXXXXXX98XX99II.B.5. Subtraction: Activities Leading To The Memorization of Subtraction Facts II.B.5.a. Basic subtraction facts: Relationships between the numbers 1-18 II.B.5.a1. Subtraction Strip BoardXXXXXXXX100XXXXXXXX101IX102II.B.5.a2. Subtraction ChartsIX103II.B.5.a3. Flash CardsIX104II.B.5.a4. Negative Snake GameIX105Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:N XK X1st 2nd 3rd 4th 5th 6th X X X X X XSerial #II.B.5.b. Missing Factors106II.B.5.b1. Bead BarsXX107II.B.5.b2. Flash CardsXX108II.B.6. Subtraction: The Passage To AbstractionXXXXXXXX109II.B.6.a. Numbers up to 4 digitsXX110II.B.6.b. Numbers up to 7 digitsXX111II.C. MULTIPLICATIONXXXXXXXX112II.C.1. The Process of MultiplicationXXXXXXXX113II.C.1.a. Multiplication of a 4 digit number by a 1 digit multiplier II.C.1.a1. Golden BeadsXXXXXXXX114XX115II.C.1.a2. Stamp GameXXX116II.C.1.a3. Golden MatX117II.C.1.a4. Small Bead FrameX118II.C.1.b. Multiplication of a 7 digit number by a 1 digit multiplier II.C.1.b1. Golden MatXXXXXXXX119XX120Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:NK1st 2nd 3rd 4th 5th 6th X XSerial #II.C.1.b2. Large Bead Frame121II.C.1.b3. Multiplication CheckerboardIX122II.C.1.b4. Flat Bead FrameIX123II.C.1.c. Multiplication of a 7 digit number by a 2 digit multiplier II.C.1.c1. Golden MatXXXXXXXX124X125II.C.1.c2. Large Bead FrameX126II.C.1.c3. Multiplication CheckerboardXX127II.C.1.c4. Flat Bead FrameXX128II.C.1.c5. Junior Bank GameXX129II.C.2. Multiplication: Activities Leading To The Memorization of Multiplication Facts II.C.2.a. Basic multiplication facts: Tables 1-10XXXXXXXX130XXXXXXXX131II.C.2.a1. Bead ChainsIXXX132II.C.2.a2. Bead BarsIXXX133II.C.2.a3. Multiplication ChartsIXX134II.C.2.a4. Flash CardsIXX135Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:NK1st 2nd 3rd 4th 5th 6th I X XSerial #II.C.2.a5. Deconomial136II.C.2.b. Multiplication: Missing FactorsXXXXXXXX137II.C.2.b1. Bead BarsXX138II.C.2.b2. Card SetsXX139II.C.3. Multiplication: The Passage to AbstractionXXXXXXXX140II.C.3.a. Multiplying numbers up to 4 digits by 1 digitXX141II.C.3.b. Multiplying numbers up to 7 digits by 1 digitXX142II.C.3.c. Multiplying numbers up to 7 digits by 2 digitsXX143II.D. DIVISIONXXXXXXXX144II.D.1. The Process of DivisionXXXXXXXX145II.D.1.a. Division of a 4 digit number by 1 digit divisor with no remainder a1. Golden Beads II.D.1.a2. Stamp GameIX146XX147II.D.1.a3. Golden MatX148II.D.1.a4. Long Division Racks And TubesXX149II.D.1.b. Division of a 4 digit number by 1 digit divisor with a remainderXXXXXXXX150Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:N IK1st 2nd 3rd 4th 5th 6thSerial #II.D.1.b1. Golden Beads151II.D.1.b2. Stamp GameIXX152II.D.1.b3. Golden MatXX153II.D.1.b4. Long Division Racks And TubesXX154II.D.1.c. Division of a 7 digit number by 1 digit divisor with or without a remainder II.D.1.c1. Golden MatXXXXXXXX155XX156II.D.1.c2. Long Division Racks And TubesXX157II.D.1.d. Division of a 7 digit number by a 2-digit divisor with or without a remainder d1. Long Division II.D.1.e. Division of a 7 digit number by a 3 or 4-digit divisor with or without a remainder II.D.1.e1. Long Division Racks And Tubes X X XIXX158XXXXX159XXX160II.D.2. Division: Exercises Leading To The Memorization of Division Facts II.D.2.a. Basic division facts: Divisors 1-9XXXXXXXX161XXXXXXXX162II.D.2.a1. Units Division BoardXX163II.D.2.b. Basic division facts for divisor of 10XXX164II.D.2.c. Missing FactorsXX165Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:N XK X1st 2nd 3rd 4th 5th 6th X X X X X XSerial #II.D.3. Division: The Passage To Abstraction166II.D.3.a. Numbers up to 4 digits divided by a 1-digit divisor with no remainder II.D.3.b. Numbers up to 4 digits divided by a 1-digit divisor with a remainder II.D.3.c. Numbers up to 7 digits divided by a 1-digit divisor with or without a remainder II.D.3.d. Numbers up to 7 digits divided by a 2-digit divisor with or without a remainder II.D.3.e. Numbers up to 7 digits divided by a 3 or 4-digit divisor with or without a remainder III. FACTORS X X XIXX167IXX168IXX169IXX170IXX171XXXXX172III.A. MultiplesXXXXXXXX173III.A.1. PegboardXX174III.B. Lowest Common MultipleXXXXXXXX175III.B.1. Bead ChainsXX176III.C. Factoring numbers from 1 to 50XX177III.D. Can identify the prime numbers from 1 to 50XX178III.E. Knows the rules of divisibility for 2's, 5's, 10's, and 9's IV. FRACTIONS X X X XXXX179XXXX180Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:N XK X1st 2nd 3rd 4th 5th 6th X X X X X XSerial #IV.A. Introduction To Fractions181IV.A.1. Recognition of fractions: concrete material &amp; symbol IV.A.1.a. Fraction SkittlesXXXXXXXX182IXX183IV.A.1.b. Fraction CirclesIXXX184IV.A.2. EquivalencesXXXXXXXX185IV.A.2.a. Fraction CirclesXXX186IV.A.2.b. Fraction Circle BoxXX187IV.A.2.c. Fraction ChartsXX188IV.B. Operations With FractionsXXXXXXXX189IV.B.1. Addition of fractions that share a common denominator IV.B.1.a. Fraction CirclesXXXXXXXX190XX191IV.B.1.b. Fraction Circle BoxXXX192IV.B.1.c. Fraction ChartsXXX193IV.B.2. Subtraction of fractions that share a common denominator IV.B.2.a. Fraction CirclesXXXXXXXX194XXX195Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:NK1st 2nd 3rd 4th 5th 6th X X XSerial #IV.B.2.b. Fraction Circle Box196IV.B.2.c. Fraction ChartsXXX197IV.B.3. Multiplication of a whole number by a simple fraction IV.B.3.a. Fraction CirclesXXXXXXXX198XXX199IV.B.3.b. Fraction Circle BoxXXX200IV.B.3.c. Fraction ChartsXXX201IV.B.4. Division of a fraction by a whole numberXXXXXXXX202IV.B.4.a. Fraction CirclesIXX203IV.B.4.b. Fraction Circle BoxIXX204IV.B.4.c. Fraction ChartsIXX205IV.B.5. Addition of fractions that have different denominators IV.B.5.a. Fraction CirclesXXXXXXXX206IXX207IV.B.5.b. Fraction Circle BoxIXX208IV.B.5.c. Fraction ChartsIXX209IV.B.6. Subtraction of fractions that have different denominatorsXXXXXXXX210Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:NK1st 2nd 3rd 4th 5th 6th I X XSerial #IV.B.6.a. Fraction Circles211IV.B.6.b. Fraction Circle BoxIXX212IV.B.6.c. Fraction ChartsIXX213IV.B.7. Multiplication of a fraction by a fractionXXXXXXXX214IV.B.7.a. Fraction CirclesIXX215IV.B.7.b. Fraction Circle BoxIXX216IV.B.7.c. Fraction ChartsIXX217IV.B.8. Division of fractions by fractionsXXXXXXXX218IV.B.8.a. Fraction CirclesIXX219IV.B.8.b. Fraction Circle BoxIXX220IV.B.8.c. Fraction ChartsIXX221IV.C. Improper Fractions: Mixed NumbersXXXXXXXX222IV.C.1. Simplification of improper fractions.as whole numbers: 12/6 = 2 IV.C.1.a. Fraction Circle BoxXXXXXXXX223IXX224IV.C.2. Simplification of improper fractions as mixed numbers: 15/6 = 2 1/2XXXXXXXX225Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:NK1st 2nd 3rd 4th 5th 6th I X XSerial #IV.C.2.a. Fraction Circle Box226IV.C.3. Addition of mixed numbersXXXXXXXX227IV.C.3.a. Fraction Circle BoxIXX228IV.C.4. Subtraction of mixed numbersXXXXXXXX229IV.C.4.a. Fraction Circle BoxIXX230IV.C.5. Multiplication of mixed numbersXXXXXXXX231IV.C.5.a. Fraction Circle BoxIXX232IV.C.6. Division of mixed numbersXXXXXXXX233IV.C.6.a. Fraction Circle BoxIXX234IV.C.7. In long division, can express the remainder as a fraction IV.D. Can count by fractions to 100 by: 1/2's 1/3's 1/4's 1/5's 1/6's 1/7's 1/8's 1/9's 1/10ths IV.D.1. Number lines X X X X XIXX235XXX236IX237V. DECIMAL FRACTIONSXXXXXXXX238V.A. Introduction to Decimal FractionsXXXXXXXX239V.A.1. Nomenclature and Recognition of Decimal Fractions to .9999XXXXXXXX240Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:NK1st 2nd 3rd 4th 5th 6th I X XSerial #V.A.1.a. Decimal Fraction Board241V.A.2. Equivalences to regular fractions: 1/2 to 1/10XXXXXXXX242V.A.2.a. Fraction CirclesIXX243V.A.2.b. Decimal Fraction BoardIXX244V.A.2.3. Equivalences to any other regular fractionsIXX245V.B. Operations With Decimal FractionsXXXXXXXX246V.B.1. Addition of Decimal FractionsXXXXXXXX247V.B.1.a. Decimal Fraction BoardIXX248V.B.2. Subtraction of Decimal FractionsXXXXXXXX249V.B.2.a. Decimal Fraction BoardIXX250V.B.3. Multiplication of Decimal FractionsXXXXXXXX251V.B.3.a. Decimal Fraction BoardXX252V.B.4. Division of Decimal FractionsXXXXXXXX253V.B.4.a. Decimal Fraction BoardXX254V.B.5. Nomenclature and Recognition of Decimal Fractions to .999999IXX255Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:NK1st 2nd 3rd 4th 5th 6th X XSerial #V.C. Conversion of fractions (less than 1) to percent equivalents V.D. Conversion of percents (less than 1) to fraction equivalents X X X X X X256XX257XX258VI. ROUNDING OFF NUMBERSXXXXXXXX259VI.A. Can round whole numbers off to the nearest unit of tens, hundreds, or thousands VI.B. Can round mixed numbers off to the nearest whole number VI.C. Can round mixed numbers off to the nearest unit of tenths, hundredths, or thousandths VI.D. Can accurately estimate sums or differences, using sums up to 3 digits VI.E. Can estimate sums, differences, products, or quotients, using very large sums or very small VII. PRACTICAL APPLICATIONS OF MATHEMATICS VII.A. Solving Word Problems X X XIXX260IX261X262XXX263X264XXXXX265XXXXXXXX266VII.A.1. AdditionXXXX267VII.A.2. SubtractionXXXX268VII.A.3. MultiplicationXXXX269VII.A.4. DivisionXXXX270Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:NK1st 2nd 3rd 4th 5th 6th X X X XSerial #VII.A.5. Two operations in the same problem: addition and subtraction VII.A.6. Two operations in the same problem: addition, subtraction, multiplication, or division VII.B. Money X X X271XXX272XXXXX273VII.B.1. Can identify units of currencyXXXXXXXX274VII.B.1.a. CoinsIXXX275VII.B.1.b. BillsIXX276VII.B.2. Can count moneyXX277VII.B.3. Can make changeXX278VII.B.4. Can calculate simple interest on a loan or earned on savings VII.B.5. Can convert American money into a given foreign currency, and vice versa VII.C. Measurement of the physical properties of matter X X X X X XIX279IX280XX281VII.C.1. LengthXXXXXXXX282VII.C.1.a. NomenclatureXXXXXXXX283VII.C.1.a2. MetricXX284VII.C.1.b. MeasurementXXXXXXXX285Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:N IK1st 2nd 3rd 4th 5th 6th X XSerial #VII.C.1.b1. Using a ruler286VII.C.1.b2. Using a yardstick/meterstickIXX287VII.C.1.b3. Using a trundle wheelXX288VII.C.1.c. Can solve word problems involving the measurement of length VII.C.1.d. Can use a conversion table to determine English/Metric equivalent lengths VII.C.2. Weight X X X XIX289XX290XXXX291VII.C.2.a. NomenclatureXXXXXXXX292VII.C.2.a1. EnglishXX293VII.C.2.b. MeasurementXXXXXXXX294VII.C.2.b1. Using a balance scaleIXXXX295VII.C.2.b2. Using a bathroom scaleIXXX296VII.C.2.c. Can solve word problems involving the measurement of weight VII.C.2.d. Can use a conversion table to determine English/Metric equivalent weights VII.C.3. Volume X X X XIX297XX298XXXX299VII.C.3.a. NomenclatureXXXXXXXX300Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:NK1st 2nd 3rd 4th 5th 6th X X XSerial #VII.C.3.a1. English301VII.C.3.a2. MetricXXX302VII.C.3.b. MeasurementXXXXXXXX303VII.C.3.b1. Appropriate containersXXX304VII.C.3.c. Can solve word problems involving the measurement of volume VII.C.3.d. Practical Applications: Cooking, science, etc. VII.C.3.e. Can use a conversion table to determine English/Metric volume equivalents VII.C.4. Temperature X X X X X X I X XIX305XX306X307XX308VII.C.4.a. NomenclatureXXXXXXXX309VII.C.4.a1. FahrenheitIXXXX310VII.C.4.a2. CentigradeIXXX311VII.C.4.b. MeasurementXXXXXXXX312VII.C.4.b1. ThermometersIXXXX313VII.C.4.c. Can solve word problems involving the measurement of temperature VII.C.4.d. Can use a conversion table to determine Fahrenheit/centigrade equivalent temperatureIX314X315Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:NK1st 2nd 3rd 4th 5th 6th I X X X XSerial #VII.C.4.e. Practical Applications:316VII.D. GraphsXXXXXXXX317VII.E.1. Can read graphs and make inferences from the information graphically displayed VII.E.1.a. Picture graphsXXXXXXXX318IXXX319VII.E.1.b. Circle graphsIXXXXX320VII.E.1.c. Bar graphsIXXXXXX321VII.E.1.d. Line graphsIXXXX322VII.E.1.e. Scatter distributionsIXX323VII.E.2. Can prepare graphs from gathered data:XXXXXXXX324VII.E.2.a. Picture graphsIXX325VII.E.2.b. Circle graphs using fractionsIXXXX326VII.E.2.c. Bar graphsIXXXXX327VII.E.2.d. Line graphsIXXXX328VII.E.2.e. Scatter distributionsIXX329VII.E.2.f. Graphs for two variablesIXX330Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:NK1st 2nd 3rd 4th 5th 6th I X XSerial #VII.E.2.g. Circle graphs using percents331VII.E.2.h. Redraw a graph, using a different scaleIXX332VII.E.3. Tabulates data into a tableIXX333VII.E.4. Coordinate graphsXXXXXXXX334VII.E.4.a. Can show location on a 2-axis grid as blocks over or up from one axis VII.E.4.b. Can identify the location of a given ordered pair on a grid VII.E.4.c. Given a location on a grid, can identify the ordered pair VII.E.4.d. Can locate points for given coordinates and name the coordinates of a given point in any of the four VII.E.4.e. Given a sum, can graph on a grid all of the possible ordered pairs of addends VII.E.5. Introduction to statistics X X X X XIX335X336X337IX338X339XXX340VII.E.5.a. Can determine the `average' for given dataXX341VII.E.5.b. Can determine the `mean' for given data, and identify it on a graph VII.E.5.c. Can determine the `median' for given data, and identify it on a distribution table VII.E.5.d. Can construct a frequency tableXX342XX343IX344VIII. INEQUALITIESXXXXXXXX345Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:N XK X1st 2nd 3rd 4th 5th 6th X X X X X XSerial #VIII.A. Is familiar with the relationships between simple quantities and sets and their symbols VIII.A.1. &quot;Greater Than ...&quot; (&gt;)346IXX347VIII.A.2. &quot;Less Than ...&quot;IXX348VIII.A.3. &quot;Equal To..&quot;IXXX349VIII.B. Is familiar with the relationships between quantities involving multiple operations (3 x 4 &gt; 2 + 3) VIII.B.1. &quot;Greater Than ...&quot; (&gt;)XXXXXXXX350IXX351VIII.B.2. &quot;Less Than ...&quot;IXX352VIII.B.3. &quot;Equal To..&quot;IXX353IX. Ratios and percentsXXXXXXXX354IX.A. Can write the ratio of two quantities as a fracti onIXX355IX.B. Can solve for a missing term in a proportionIXX356IX.C. Can write a ratio with a denominator of 100 as a percent (%) and a percent as a ratio with a denominator IX.D. Can write a decimal (less than 1) as a percent and a percent (less than 100%) as a decimal IX.E. Can write a percent as a fraction in simplest form and a common fraction as a percent IX.F. Can find a percent (greater than 1% but less than 100%) of a given numberIXX357IXX358IXX359IXX360Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:NK1st 2nd 3rd 4th 5th 6th I X XSerial #IX.G. Can find a percent (less than 1% or greater than 100%) of a given number IX.H. Can write a decimal (greater than 1) as a percent and a percent (greater than 100%) as a decimal IX.I. Can use a proportion to determine the percent one number is greater than another number IX.J. Can use a proportion to determine the number of which a given number is a percent X. Negative numbers X X X X X361IXX362IXX363IXX364XXX365X.A. Can count from -20 to +20IXX366X.B. Can order positive and negative numbersIXX367X.C. Can name additive inverses for positive and negative numbers X.D. Can name equivalent forms for positive and negative numbers X.E. Can add and subtract positive and negative numbers X.F. Can multiply positive and negative numbersIXX368IXX369IXX370IXX371X.G. Can name reciprocals for positive and negative numbers X.H. Can divide positive and negative numbersIXX372IXX373X.I. Can simplify expressions using two or more operations and positive and negative numbers XI. ADDITIONAL TOPICS X X X X XIXX374XXX375Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:NK1st 2nd 3rd 4th 5th 6th I XSerial #XI.A. Can recognize irrational numbers such as 2 and  XI.B. Can count accurately in Base 2, Base 3, Base 4, Base 5, Base 6, Base 7 XI.C. Can identify the prime numbers from 1 to 50376IX377IX378XII. PRE-ALGEBRAXXXXXXXX379XII.A. EquationsXXXXXXXX380XII.A.1. Can Solve equations and inequalities containing positive and negative numbers and one XII.A.2. Can solve equations and inequalities containing positive and negative XII.A.numbers and one variable by multiplication X X X X XIXX381XXX382IXX383XII.A.3. Can solve equations and inequalities containing positive and negative numbers and one XII.A.4. Apply the fundamental operations to solve open sentences and word problems using real numbers XII.B. POWERS OF NUMBERS X X X X XIXX384IXX385XXX386XII.B.1. Can name the squares of the numbers 1-10XXXXXXXX387XII.B.1.a. Bead BarsIXXXX388XII.B.1.b. Bead CabinetIXXXX389XII.B.2. Can name the cubes of the numbers 1-10XXXXXXXX390Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:NK1st 2nd 3rd 4th 5th 6th I X X X XSerial #XII.B.2.a. Bead Bars391XII.B.2.b. Bead CabinetIXXXX392XII.B.3. Can calculate the square of a binomialIXXX393XII.B.4. Can calculate the square of a trinomialIXXX394XII.B.5. Can calculate the cube of a binomialIXX395XII.B.6. Can calculate the cube of a trinomialIXX396XII.B.7. Can calculate square rootsIXXX397XII.B.8. Can calculate the square roots of binomialsIXXX398XII.B.9. Can calculate the square roots of trinomialsIXX399XII.B.10. Can calculate cube rootsIX400XII.B.11. Can calculate the cube roots of binomialsIX401XII.B.12. Can calculate the cube roots of trinomialsIX402XII.B.13. Understands and can calculate exponentsXXXXXXXX403XII.B.13.a. Exponential notation 101 through 106IXX404XII.B.13.b. Exponential notation 10-1 through 10-6IXX405Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:NK1st 2nd 3rd 4th 5th 6th I X XSerial #XII.B.13.c. Exponential notation 100 through 106406XII.B.13.d. Exponential notation 107 through 1012IXX407XII.B.13.e. Exponential notation 10-1 through 10-6IXX408XII.C. Scientific notationXXXXXXXX409XII.C.1. Can convert large whole numbers to scientific notation XII.C.2. Can convert very small decimal fractions to scientific notation XIII.Geometry X X X X XIXX410IXX411XXX412XIII.A. Recognition and nomenclature of geometric figures XIII.1. Can identify basic geometric shapesXXXXXXXX413IX414XIII.A.2. Can identify types of triangle by their sidesIXX415XIII.A.3. Can identify types of triangle by their angles: right, scalene, obtuse, equilateral XIII.A.4. Can identify regular polygons through the decagon XIII.A.5. Can identify irregular polygons through the decagon XIII.A.6. Can identify all of the quadrilaterals I IIXXXX416XXXXX417IXXXX418XXXXX419XIII.A.7. Can differentiate between a circle, ellipse, and ovalIXX420Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:N IK X1st 2nd 3rd 4th 5th 6th XSerial #XIII.A.8. Can identify a cube, sphere, cylinder, pyramid, and cone XIII.A.9. Can identify a rectangular prism, triangular prism, ovoid, and ellipsoid XIII.A.10. Can identify the faces, edges, and surfaces of solid geometric objects XIII.A.11. Can identify congruent shapes by matching421IXX422IXXXX423IXXXXX424XIII.A.12. Can identify the parts of a circle: radius, diameter, circumference XIII.A.13. Can identify the parts of a triangleIXXX425IXXX426XIII.A.14. Can identify the parts of a squareIXXX427XIII.B. Angles, similarities and congruenceXXXXXXXX428XIII.B.1. Can measure angles with a protractorIXX429XIII.B.2. Can add angles and compute arcsIXX430XIII.B.3. Can recognize congruent figuresIXXX431XIII.B.4. Can recognize similar figuresIXXX432XIII.B.5. Can recognize equivalent figuresIXXX433XIII.B.6. Can identify angles as being acute, right, obtuse, and straight XIII.B.7. Can identify the relations between two straight lines: parallel &amp; perpendicularIXXX434IXXX435Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:NK1st 2nd 3rd 4th 5th 6th X X XSerial #XIII.B.8. Can name angles formed by two straight lines cut by a transversal XIII.B.9. Can name the relationships between two angles XIII.B.10. The Pythagorean Theorem X X X436XXX437XXXXX438XIII.B.10.a. Recognizes the 3-4-5 case of the Pythagorean Theorem XIII.B.10.b.. Recognizes the isosceles right triangle case of the Pythagorean Theorem XIII.B.10.c.. Understands the generalized proof of the Pythagorean Theorem XIII.B.11. Can identify the sum of the interior angles of a triangle or regular polygon X X X X X I XI439I440I441X442XXX443XIII.C.. Construction of geometric figuresXXXXXXXX444XIII.C.1. Can demonstrate line symmetry in a given shape by folding along its center line XIII.C.2. Can construct an angle of a given measure with a protractor and straightedge XIII.C.3. Can bisect an angle with a compass and straightedge XIII.C.4. Can bisect a line segment with a compass and straightedge XIII.C.5. Can draw a line perpendicular to another line with a straightedge, compass, and protractor XIII.C.6. Can draw a line parallel to another line with a straightedge, compass, and protractorIXXXXXXX445IX446IXXXX447IXXXX448IXXXX449IXXXX450Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:NK1st 2nd 3rd 4th 5th 6th I X X X XSerial #XIII.C.7. Can construct a square with a protractor and straightedge XIII.C.8. Can construct a circle with a compass451IXXX452XIII.C.9. Can construct an ellipseIXXX453XIII.C.10. Can measure the radius and diameter of a circle XIII.C.11. Can measure the circumference of a circle IIX454XXX455XIII.C.12. Can construct a scale model or drawing of an object given a scale to follow XIII.C.13. Can construct a tetrahedronIX456IXX457XIII.C.14. Can construct a cubeIXX458XIII.C.15. Construct an octagon, dodecahedra, icosahedra XIII.D. CALCULATION OF AREA X X X X XIXX459XXX460XIII.D.1. Can calculate the area of a squareIXX461XIII.D.2. Can calculate the area of a rectangleIXX462XIII.D.3. Can calculate the area of a triangleIXX463XIII.D.4. Can calculate the area of a parallelogramIXX464XIII.D.5. Can calculate the area of a trapezoidIXX465Mathematics Scope and SequenceCurriculum Element -- Commonly, by the grade level(s) given below, the student will be able to:NK1st 2nd 3rd 4th 5th 6th I X XSerial #XIII.D.6. Can calculate the area of a regular pentagon466XIII.D.7. Can calculate the area of a regular hexagonIXX467XIII.D.8. Can calculate the area of a regular octagonIXX468XIII.D.9. Can calculate the area of a decagonIXX469XIII.D.10. Can calculate the area of any regular polygon XIII.D.11. Can calculate the area of any irregular polygon XIII.D.12. Can calculate the area of a circleIXX470IXX471IXX472XIII.E. Calculation of volumeXXXXXXXX473XIII.E.1. Can calculate the volume of a cubeIX474XIII.E.2. Can calculate the volume of a rectangular prism XIII.E.3. Can calculate the volume of a pyramidIX475IX476XIII.E.4. Can calculate the volume of a cylinderIX477XIII.E.5. Can calculate the volume of a coneIX478XIII.E.6. Calculate the volume of a sphereIX479MATHEMATICSXXXXXXXX481`

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