
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 Points Number
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
Numbers 1)
Number and Notation and Place Values 2) Cardinal and Ordinal numbers 3)
Comparing and Ordering of Numbers 4) Addition and subtraction of single and
2 digit numbers 5) Multiplication (multiplication of numbers whose product
is not great than 40. 6) Division  dividing numbers not greater than 20. Money
and Measures 1)
Measurement of length and mass 2) Time 3) Money Statistics 1)
Picture Graphs
Geometry 1)
Shapes 2) Patterns  Grade
2 Curriculum Focal Points Number
and Operations: Developing an understanding of the baseten numeration system
and placevalue concepts counting
in units and multiples of hundreds, tens, and ones, as well as a grasp of number
relationships understand
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 numbers develop
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
Numbers 1
Number notation and place values 2) Addition and Subtraction of two numbers
up to 3 digits 3) Multiplication and division within the 2,3,4,5, and 10 times
table 4) Word Problems (solving 1 step word problems involving the four operations Money
and Measures 1)
Measurement of length, mass and volume  estimating and measuring using metric
system of measures 2) Addition and subtraction of length, mass and volume 3)
Time  tell and write time from the clock 4) Addition and Subtraction of Money)
1step Word Problems involving length, mass, volume and money. Statistics 1)
Pictures and graphs using scale representations, solve problems using information
in picture graphs  Grade
3 Curriculum Focal Points Number
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 twodimensional 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 Numbers 1)
Number Notation and Place Values  reading and writing numbers up to 10,000 2)
Addition and Subtraction of number up to 4 digits 3) Multiplication tables
up to 10 x 10 4) Multiplication and Division by a 1 digit number 5) Odd
and Even numbers 6) Word problems using 2 steps and the four operations on
whole numbers Money
and Measures 1)
Units of Measures  standard numbers and measuring in compound units for length,
mass, time, area and volume, conversions of units 2) Addition and Subtraction
of length, mass, volume and time. 3) Addition and Subtraction of money and
measures in compound units using decimal notation 4) Word Problems using 2steps
involving money and measures 5) Perimeter of a Rectilinear Figure 6) Area
and Perimeter of a Square and a Rectangle
Statistics 1)Bar
Graphs Fractions
1) Equivalent
Fractions 2) Comparing and Ordering Fractions Geometry 1)
Concepts of Angles  Grade
4 Curriculum Focal Points Number
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 twodimensional
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
4 Whole Numbers 1)
Number and Notation and place value up to 100,000 2) Approximation and estimation
to nearest 10 and 100, estimations involving addition, subtraction and multiplication 3)
Factors and multiples up to 100 4) Multiplication by a number up to 2 digits 5)
Division by a 1digit number and by 10 6) Word problems using 3 steps involving
whole numbers Money
and Measures 1)Multiplication
and division of length, mass, volume and time 2) Multiplication and division
of money 3) Units of measure for volume 4)Volume of a cube/'cuboid and liquid 5)
Area and Perimeter of a square, rectangle and related figures 6) Word problems
involving volume Statistics 1)
Tables 2) Bar Graphs 3) Word Problems using data from bar graphs Fractions 1)
Addition and Subtraction 2) Product of a proper fraction and a whole number 3)
Mixed numbers and improper fractions 4) Word problems  2step word problems
involving fractions Decimals 1)
Number notation and place value 2) Addition and Subtraction 3) Multiplication
and division decimals up to 2 decimal places and 1digit whole number 4) Conversion
between decimals and fractions 5) Approximation and estimation 6) Word
problems involving decimals Geometry 1)
Perpendicular and parallel lines 2)
Angles in degrees 3)
Symmetry 4) Geometric
Figures  understanding different triangles and quadrilateral figures 5)
Properties of a square and rectangle 6)
2D representation of a 3d solid  Grade
5 Curriculum Focal Points Number
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 decimals develop
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 threedimensional shapes and analyzing
their properties, including volume and surface area decompose
threedimensional shapes and find surface areas and volumes of prisms measure
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 EM1/2 Whole
Numbers 1)
Number notation and place values up to 10 million 2)
Multiplication and division
up to 4 digits by a 2digit number 3)
Factors and multiples 4)Order
of operations 5) Word problems using whole numbers Mensuration 1)Conversion
of measurements involving decimals and fractions 2) Volume of a cube/cuboid
 finding the edge of a cube 3) Area of a triangle Statistics 1)
Line graphs Fractions 1)
Addition and subtraction 2)
Product of fractions 3) Concept of fraction as division 4) Division of
a proper fraction by a whole number 5) Word problems involving fractions Decimals 1)
Multiplication and division of decimals up to 3 decimal places Geometry 1)
Angles 2) 8point
compass 3) Properties
of a parallelogram, rhombus, trapezium, and a triangle 4)
Geometrical Constructions 5)
Tessalations Average,
Rate and Speed 1)
Calculating averages 2)
Calculating rate 3)
Word problems involving average and rate Ratio
and Proportion 1)
Ratio recognition and interpretation, word problems using ratios Percentages 1)
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 quantity 3)
Two step problems using percentage  Curriculum
Focal Points and Connections for Grade 6 Number
and Operations: Developing an understanding of and fluency with multiplication
and division of fractions and decimals use
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 rates solve
a wide variety of problems involving ratios and rates. Algebra:
Writing, interpreting, and using mathematical expressions and equations solve
simple onestep equations by using number sense, properties of operations construct
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 Stream Mensuration 1)
Area and circumference of a circle 2) Area and perimeter of a figure related
to square, rectangle, triangle and circle 3) Volume of a solid made up of cubes/cuboids
and volume of liquids
Statistics 1)
Pie charts Geometry 1)
Angles in geometric figures 2) 2D representation of a 3D solid, visualize
a prism and pyramid from drawings 3) Nets, identify nets of cubes, prism, pyramid Average,
Rate and Speed
1)
Time using the 24 hour clock 2) Speed, distance and time 3) Word problems
using average, rate and speed Ratios
and Proportion 1)
Ratio and direct proportion
Percentage 1)
one quantity as a percentage of another Algebra 1)
Algebraic expression in one variable  Grade
7 Curriculum Focal Points Number
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 threedimensional shapes select
appropriate two and three dimensional shapes to model realworld 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 equations extend
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 Algebra
1)
Numbers and the four operations, negative numbers, rational numbers, using of
greater, less than symbols
2) Ratio, rate and proportions
3) Percentage
including expressing one quantity as a percentage of another, problems involving
percentages
4) Speed, concepts of speed, average speed, conversion of units
5)
Algebraic representation and formulae
6) Algebraic manipulation
7)
Functions and graphs
8) Solutions of equations and inequalities Geometry
and Measurement Angles,
triangles and polygons including classifications and constructions Statistics
and Probability Data
handling  Grade
8 Curriculum Focal Points Algebra:
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 threedimensional 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 system Data
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 O Numbers
and Algebra 1)
Ratio, rate and proportion including map scales and direct/indirect proportions 2)
Algebraic manipulation including factorization, addition, subtraction, multiplication
of fractions 3) Functions and graphs including quadratic functions 4) Solutions
of equations including simultaneous linear equations 5) Set language and notation Geometry
and Measurement 1)
Congruence and similarity 2) Pythagorean Theorem 3) Mensuration including
volume and surface area of pyramid, cone and sphere Statistics
and Probability 1)
Data analysis  mean, mode and median 2) Simple probability problems  Pre
16 Curriculum   Prekindergarten
Curriculum Focal Points Number
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 Points Number
and Operations: Representing, comparing, and ordering whole numbers and joining
and separating sets Geometry:
Describing shapes and space Measurement:
Ordering objects by measurable attributes
Explanations
and Connections
to the Focal Points
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
Primary School Mathematics Syllabus
SINGAPORE
Secondary School Mathematics Syllabus
  
