**
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.

**
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 base-ten numeration system
and place-value 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)
1-step 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 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

**
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 2-steps
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 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

**
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 1-digit 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 - 2-step 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 1-digit 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)
2-D representation of a 3-d 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 three-dimensional shapes and analyzing
their properties, including volume and surface area

decompose three-dimensional 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

**
Whole
Numbers**

1)
Number notation and place values up to 10 million

2)
Multiplication and division
up to 4 digits by a 2-digit 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) 8-point
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 one-step 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) 2-D representation of a 3-D 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 three-dimensional shapes

select 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 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 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

...Pyt
hagorean
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

**
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
1-6 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

**
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

**
SOURCE: See below for full explanation
of topics, outcomes and remarks.**

**
Note:**
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pdf files. They may load slowly, so be patient. It is worth your wait to view
them both.