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NCTM FOCAL POINTS AND SINGAPORE MATH SYLLABUS

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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 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 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

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 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

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 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

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 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

 

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 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

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

  

 


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