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Recently, much has been written about the successes of Singapore’s students in the area of mathematics. Singapore’s mathematics system includes: highly logical national mathematics standards; mathematically rich problem-based textbooks; challenging mathematics assessments; highly qualified mathematics teachers whose pedagogy centers on teaching to mastery; and special assistance from an expert teacher to its mathematically slower students, along with an alternative framework.
The National Council for Teachers of Math (NCTM) created a comparison chart of the NCTM focal points with the Singapore Math Syllabus, pre-K through grade 8. The comparison for grades 1-4 is included on the following pages and illustrates significant differences. The Singapore math syllabus is clear and specific in comparison to the NCTM focal points, at times.
The full chart is available online at:
www.edinformatics.com/math_science/nctm_singapore_math.htm.
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 ...”
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About the Singapore Math Syllabus:
Listed below are the mathematics topics for each grade level.
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Grade 1 Curriculum Focal Points |
Primary 1: |
Number and Operations and Algebra
Develop an understanding 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
Develop an understanding of whole number relationships, including grouping in tens and ones.
- Compare and order whole numbers
(at least to 100)
Geometry
Compose and decompose geometric shapes.
- Compose and decompose plane and solid figures
- Initial understandings of such properties as congruence and symmetry
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Whole Numbers
- Number and notation and place values
- Cardinal and ordinal numbers
- Compare and order numbers
- Addition and subtraction of single and two-digit numbers
- Multiplication (multiplication of numbers whose product is not great than 40
- Division: dividing numbers not greater than 20
Money and Measures
- Measurement of length and mass
- Time
- Money
Statistics
Geometry
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Grade 2 Curriculum Focal Points |
Primary 2: |
Number and Operations
Develop an understanding of the base-10 numeration system and place-value concepts.
- Count in units and multiples of hundreds, tens, and ones, as well as a grasp of number relationships
- Understand multi-digit numbers in terms of place value
Number and Operations and Algebra
Develop quick recall of addition facts and related subtraction facts and fluency with multi-digit addition and subtraction.
- Develop, discuss and use efficient, accurate and generalizable methods to add and subtract multi-digit whole numbers
- Develop fluency with efficient procedures, including standard algorithms, for adding and subtracting whole numbers
Measurement
Develop 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
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Whole Numbers
- Number notation and place values
- Addition and subtraction of two numbers up to three digits
- Multiplication and division within the 2,3,4,5 and 10 times table
- Word problems (solving one-step word problems involving the four operations)
Money and Measures
- Measurement of length, mass and volume: estimate and measure using metric system of measures
- Addition and subtraction of length, mass and volume
- Time: tell and write time from the clock
- Addition and subtraction of money
- One-step word problems involving length, mass, volume and money
Statistics
- Pictures and graphs using scale representations; solve problems using information in picture graphs
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Grade 3 Curriculum Focal Points |
Primary 3: |
Number and Operations and Algebra
Develop an understanding 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
Develop an understanding of fractions and fraction equivalence.
- Solve problems that involve comparing and ordering fractions
Geometry
Describe and analyze properties of two-dimensional shapes.
- Investigate, describe and reason about decomposing, combining, and transforming polygons to make other polygons
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Whole Numbers
- Number notation and place values: read and write numbers up to 10,000
- Addition and subtraction of number up to four digits
- Multiplication tables up to 10 x 10
- Multiplication and division by a one-digit number
- Odd and even numbers
- Word problems using two steps and the four operations on whole numbers
Money and Measures
- Units of measures: standard numbers and measuring in compound units for length, mass, time, area and volume, conversions of units
- Addition and subtraction of length, mass, volume and time
- Addition and subtraction of money and measures in compound units using decimal notation
- Word problems using two steps involving money and measures
- Perimeter of a rectilinear figure
- Area and perimeter of a square and a rectangle
Statistics
Fractions
- Equivalent fractions
- Comparing and ordering fractions
Geometry
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Grade 4 Curriculum Focal Points |
Primary 4: |
Number and Operations and Algebra
Develop 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
Develop an understanding of decimals, including the connections between fractions and decimals.
- Relate the 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
Develop 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
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Whole Numbers
- Number and notation and place value up to 100,000
- Approximation and estimation to nearest 10 and 100, estimations involving addition, subtraction and multiplication
- Factors and multiples up to 100
- Multiplication by a number up to two digits
- Division by a one-digit number and by 10
- Word problems using three steps involving whole numbers
Money and Measures
- Multiplication and division of length, mass, volume and time
- Multiplication and division of money
- Units of measure for volume
- Volume of a cube/cuboid and liquid
- Area and perimeter of a square, rectangle and related figures
- Word problems involving volume
Statistics
- Tables
- Bar graphs
- Word problems using data from bar graphs
Fractions
- Addition and subtraction
- Product of a proper fraction and a whole number
- Mixed numbers and improper fractions
- Word problems: two-step word problems involving fractions
Decimals
- Number notation and place value
- Addition and subtraction
- Multiplication and division decimals up to two decimal places and one-digit whole numbers
- Conversion between decimals and fractions
- Approximation and estimation
- Word problems involving decimals
Geometry
- Perpendicular and parallel lines
- Angles in degrees
- Symmetry
- Geometric figures: understanding different triangles and quadrilateral figures
- Properties of a square and rectangle
- 2-D representation of a 3-D solid
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