NCTM FOCAL POINTS AND SINGAPORE MATH SYLLABUSNew Curriculum is more in line with International Standards
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NCTM FOCAL POINTS
SINGAPORE MATH SYLLABUS
 About Curriculum Focal Points: ..."Curriculum focal points are the most important mathematical topics for each grade level. They are the topics that should be considered as the basis for decisions about curriculum development..." souce About the Singapore Math Syllabus:Listed below are the mathematics topics for each grade level. For outcomes and remarks see the source links below for the primary and secondary school syllabus sites. Grade 1 Curriculum Focal PointsNumber and Operations and Algebra: Developing understandings of addition and subtraction and strategies for basic addition facts and related subtraction facts develop strategies for adding and subtracting whole numbers understand the connections between counting and the operations of addition and subtraction use properties of addition (commutativity and associativity) understand the sequential order of the counting numbers and their relative magnitudes and represent numbers on a number line.Number and Operations: Developing an understanding of whole number relationships, including grouping in tens and ones compare and order whole numbers (at least to 100)Geometry: Composing and decomposing geometric shapes compose and decompose plane and solid figures initial understandings of such properties as congruence and symmetry. Explanations and Connections to Focal Points Related Expectations from Principles and Standards for School Mathematics Content Standards: Grade 1 Prmary 1:Whole Numbers1) Number and Notation and Place Values2) Cardinal and Ordinal numbers3) Comparing and Ordering of Numbers4) Addition and subtraction of single and 2- digit numbers5) Multiplication (multiplication of numbers whose product is not great than 40.6) Division -- dividing numbers not greater than 20.Money and Measures1) Measurement of length and mass2) Time3) Money Statistics1) Picture GraphsGeometry1) Shapes2) Patterns Grade 2 Curriculum Focal PointsNumber and Operations: Developing an understanding of the base-ten numeration system and place-value conceptscounting in units and multiples of hundreds, tens, and ones, as well as a grasp of number relationshipsunderstand multidigit numbers in terms of place value,Number and Operations and Algebra: Developing quick recall of addition facts and related subtraction facts and fluency with multidigit addition and subtraction develop, discuss, and use efficient, accurate, and generalizable methods to add and subtract multidigit whole numbersdevelop fluency with efficient procedures, including standard algorithms, for adding and subtracting whole numbers, Measurement: Developing an understanding of linear measurement and facility in measuring lengths standard units of measure (centimeter and inch), and the inverse relationship between the size of a unit and the number of units Explanations and Connections to the Focal Points Related Expectations from Principles and Standards for School Mathematics Content Standards: Grade 2 Primary 2.Whole Numbers1 Number notation and place values2) Addition and Subtraction of two numbers up to 3 digits3) Multiplication and division within the 2,3,4,5, and 10 times table4) Word Problems (solving 1 step word problems involving the four operationsMoney and Measures1) Measurement of length, mass and volume -- estimating and measuring using metric system of measures2) Addition and subtraction of length, mass and volume3) Time -- tell and write time from the clock4) Addition and Subtraction of Money) 1-step Word Problems involving length, mass, volume and money.Statistics1) Pictures and graphs using scale representations, solve problems using information in picture graphs Grade 3 Curriculum Focal PointsNumber and Operations and Algebra: Developing understandings of multiplication and division and strategies for basic multiplication facts and related division facts use properties of addition and multiplication (e.g., commutativity, associativity, and the distributive property) to multiply whole numbers Number and Operations: Developing an understanding of fractions and fraction Equivalence solve problems that involve comparing and ordering fractions Geometry: Describing and analyzing properties of two-dimensional shapes investigate, describe, and reason about decomposing, combining, and transforming polygons to make other polygons.   Explanations and Connections to the Focal Points Related Expectations from Principles and Standards for School Mathematics Content Standards: Grade 3 Primary 3.Whole Numbers1) Number Notation and Place Values -- reading and writing numbers up to 10,0002) Addition and Subtraction of number up to 4 digits3) Multiplication tables up to 10 x 104) Multiplication and Division by a 1 digit number5) Odd and Even numbers6) Word problems using 2 steps and the four operations on whole numbersMoney and Measures1) Units of Measures -- standard numbers and measuring in compound units for length, mass, time, area and volume, conversions of units2) Addition and Subtraction of length, mass, volume and time.3) Addition and Subtraction of money and measures in compound units using decimal notation4) Word Problems using 2-steps involving money and measures5) Perimeter of a Rectilinear Figure6) Area and Perimeter of a Square and a RectangleStatistics1)Bar Graphs Fractions 1) Equivalent Fractions2) Comparing and Ordering FractionsGeometry1) Concepts of Angles Grade 4 Curriculum Focal PointsNumber and Operations and Algebra: Developing quick recall of multiplication facts and related division facts and fluency with whole number multiplication develop fluency with efficient procedures, including the standard algorithm, for multiplying whole numbers, understand why the procedures work (on the basis of place value and properties of operations), and use them to solve problems.Number and Operations: Developing an understanding of decimals, including the connections between fractions and decimals relate their understanding of fractions to reading and writing decimals that are greater than or less than 1, identifying equivalent decimals, comparing and ordering decimals, and estimating decimal or fractional amounts in problem solving. Measurement: Developing an understanding of area and determining the areas of two-dimensional shapes select appropriate units, strategies (e.g., decomposing shapes), and tools for solving problems that involve estimating or measuring area Explanations and Connections to the Focal Points Related Expectations from Principles and Standards for School Mathematics Content Standards: Grade 4 Primary 4Whole Numbers1) Number and Notation and place value up to 100,0002) Approximation and estimation to nearest 10 and 100, estimations involving addition, subtraction and multiplication3) Factors and multiples up to 1004) Multiplication by a number up to 2 digits5) Division by a 1-digit number and by 106) Word problems using 3 steps involving whole numbersMoney and Measures1)Multiplication and division of length, mass, volume and time2) Multiplication and division of money3) Units of measure for volume4)Volume of a cube/'cuboid and liquid5) Area and Perimeter of a square, rectangle and related figures6) Word problems involving volumeStatistics1) Tables2) Bar Graphs3) Word Problems using data from bar graphsFractions1) Addition and Subtraction2) Product of a proper fraction and a whole number3) Mixed numbers and improper fractions4) Word problems - 2-step word problems involving fractionsDecimals1) Number notation and place value2) Addition and Subtraction3) Multiplication and division decimals up to 2 decimal places and 1-digit whole number4) Conversion between decimals and fractions5) Approximation and estimation 6) Word problems involving decimals Geometry1) Perpendicular and parallel lines2) Angles in degrees3) Symmetry4) Geometric Figures -- understanding different triangles and quadrilateral figures5) Properties of a square and rectangle6) 2-D representation of a 3-d solid Grade 5 Curriculum Focal PointsNumber and Operations and Algebra: Developing an understanding of and fluency with division of whole numbers develop fluency with efficient procedures, including the standard algorithm, for dividing whole numbers, understand why the procedures work (on the basis of place value and properties of operations), and use them to solve problems.Number and Operations: Developing an understanding of and fluency with addition and subtraction of fractions and decimals apply their understandings of decimal models, place value, and properties to add and subtract decimalsdevelop fluency with standard procedures for adding and subtracting fractions and decimals. make reasonable estimates of fraction and decimal sums and differences.Geometry and Measurement and Algebra: Describing three-dimensional shapes and analyzing their properties, including volume and surface area decompose three-dimensional shapes and find surface areas and volumes of prismsmeasure necessary attributes of shapes to use area formulas to solve problems Explanations and Connections to the Focal Points Related Expectations from Principles and Standards for School Mathematics Content Standards: Grade 5 Primary 5 -EM1/2Whole Numbers1) Number notation and place values up to 10 million2) Multiplication and division up to 4 digits by a 2-digit number 3) Factors and multiples4)Order of operations5) Word problems using whole numbersMensuration1)Conversion of measurements involving decimals and fractions2) Volume of a cube/cuboid -- finding the edge of a cube3) Area of a triangle Statistics1) Line graphsFractions1) Addition and subtraction2) Product of fractions 3) Concept of fraction as division4) Division of a proper fraction by a whole number5) Word problems involving fractionsDecimals1) Multiplication and division of decimals up to 3 decimal placesGeometry1) Angles2) 8-point compass3) Properties of a parallelogram, rhombus, trapezium, and a triangle4) Geometrical Constructions5) TessalationsAverage, Rate and Speed1) Calculating averages2) Calculating rate3) Word problems involving average and rateRatio and Proportion1) Ratio recognition and interpretation, word problems using ratiosPercentages1) Concept of percent - change fractions and decimals to percentages and vica versa, express a part of a whole as a percent.2) Percentage of a quantity3) Two step problems using percentage Curriculum Focal Points and Connections for Grade 6Number and Operations: Developing an understanding of and fluency with multiplication and division of fractions and decimalsuse the relationship between decimals and fractions, as well as the relationship between finite decimals and whole numbers use common procedures to multiply and divide fractions and decimals efficiently and accurately.Number and Operations: Connecting ratio and rate to multiplication and division extend whole number multiplication and division to ratios and ratessolve a wide variety of problems involving ratios and rates.Algebra: Writing, interpreting, and using mathematical expressions and equations solve simple one-step equations by using number sense, properties of operationsconstruct and analyze tables (e.g., to show quantities that are in equivalent ratios), and they use equations to describe simple relationships (such as 3x = y) shown in a table. Explanations and Connections to the Focal Points Related Expectations from Principles and Standards for School Mathematics Content Standards: Grade 6 Primary 6 - EM1/EM2 StreamMensuration1) Area and circumference of a circle2) Area and perimeter of a figure related to square, rectangle, triangle and circle3) Volume of a solid made up of cubes/cuboids and volume of liquidsStatistics1) Pie chartsGeometry1) Angles in geometric figures2) 2-D representation of a 3-D solid, visualize a prism and pyramid from drawings3) Nets, identify nets of cubes, prism, pyramidAverage, Rate and Speed1) Time using the 24 hour clock2) Speed, distance and time 3) Word problems using average, rate and speedRatios and Proportion1) Ratio and direct proportionPercentage1) one quantity as a percentage of anotherAlgebra1) Algebraic expression in one variable Grade 7 Curriculum Focal PointsNumber and Operations and Algebra and Geometry: Developing an understanding of and applying proportionality, including similarity use ratio and proportionality to solve a wide variety of percent problems, including problems involving discounts, interest, taxes, tips, and percent increase or decrease Students graph proportional relationships and identify the unit rate as the slope of the related line. They distinguish proportional relationships (y/x = k, or y = kx) from other relationships, including inverse proportionality (xy = k, or y = k/x).Measurement and Geometry and Algebra: Developing an understanding of and using formulas to determine surface areas and volumes of three-dimensional shapesselect appropriate two- and three dimensional shapes to model real-world situations and solve a variety of problems (including multistep problems) involving surface areas, areas and circumferences of circles, and volumes of prisms and cylinders.Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equationsextend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers.Make strategic choices of procedures to solve linear equations in one variable Explanations and Connections to the Focal Points Related Expectations from Principles and Standards for School Mathematics Content Standards: Grade 7 Secondary One Level O Numbers and Algebra1) Numbers and the four operations, negative numbers, rational numbers, using of greater, less than symbols2) Ratio, rate and proportions3) Percentage including expressing one quantity as a percentage of another, problems involving percentages4) Speed, concepts of speed, average speed, conversion of units5) Algebraic representation and formulae6) Algebraic manipulation7) Functions and graphs8) Solutions of equations and inequalitiesGeometry and MeasurementAngles, triangles and polygons including classifications and constructionsStatistics and ProbabilityData handling Grade 8 Curriculum Focal PointsAlgebra: Analyzing and representing linear functions and solving linear equations and systems of linear equations ...proportions and constant of proportionality, understanding slope of a line...linear and quadratic equations...motion problems Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle ...Use of facts about distance and angles to describe and analyze figures in 2 and 3 dimensional space...Pythagorean Theorem...Parallel lines...Cartesian coordinate systemData Analysis and Number and Operations and Algebra: Analyzing and summarizing data sets mean, median, mode Curriculum Focal Points and Connections for Grade 8 Related Expectations from Principles and Standards for School Mathematics Content Standards: Grade 8 Secondary Two Level ONumbers and Algebra1) Ratio, rate and proportion including map scales and direct/indirect proportions2) Algebraic manipulation including factorization, addition, subtraction, multiplication of fractions 3) Functions and graphs including quadratic functions4) Solutions of equations including simultaneous linear equations5) Set language and notationGeometry and Measurement1) Congruence and similarity2) Pythagorean Theorem3) Mensuration including volume and surface area of pyramid, cone and sphereStatistics and Probability1) Data analysis - mean, mode and median2) Simple probability problems Pre 1-6 Curriculum Prekindergarten Curriculum Focal PointsNumber and Operations: Developing an understanding of whole numbers, including concepts of correspondence, counting, cardinality, and comparison Geometry: Identifying shapes and describing spatial relationships Measurement: Identifying measurable attributes and comparing objects by using these Attributes Explanations and Connections to the Focal Points Related Expectations from Principles and Standards for School Mathematics Content Standards: Prekindergarten Kindergarten Curriculum Focal PointsNumber and Operations: Representing, comparing, and ordering whole numbers and joining and separating sets Geometry: Describing shapes and space Measurement: Ordering objects by measurable attributes Related Expectations from Principles and Standards for School Mathematics Content Standards: Kindergarten SOURCE: NCTM -- Curriculum Focal Points for Mathematics in Prekindergarten through Grade 8 SOURCE: See below for full explanation of topics, outcomes and remarks. Note: These are both large pdf files. They may load slowly, so be patient. It is worth your wait to view them both. SINGAPORE Secondary School Mathematics Syllabus

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