# Singapore Math

## Grade Nine Content

Singapore Dimensions (formerly Discovering) Mathematics Common Core Textbooks 7A & 7B and Texbooks 8A & 8B

*Dimensions 7A*

Chapter 2: Real Numbers

2.1 Idea of Negative Numbers and the Number Line A. Negative Numbers

- The Number Line
- Absolute Value

2.2 Addition and Additive Inverse

- Addition of Integers
- Additive Inverse

2.3 Subtraction and Absolute Value of the Difference

- Subtraction of Integers
- Absolute Value of the Difference

2.4 Multiplication, Division, and Combined Operations of Integers

- Multiplication of Integers
- Division of Integers
- Combined Operations of Integers

2.5 Rational Numbers

- Definition
- Addition and Subtraction of Rational Numbers
- Multiplication and Division of Rational Numbers

2.6 Real Numbers and Use of Calculators

- Real Numbers
- Use of Calculators

2.7 Rounding Numbers to Decimal Places

- Idea of Rounding
- Rounding Numbers to Decimal Places In A Nutshell

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*Dimensions 8A*

Chapter 1: Exponents and Scientific Notation

1.1 Positive Exponents and the Laws of Exponents

1.2 Zero and Negative Integer Exponents

1.3 Fractional Exponents A. nth root of a Positive Number

- Fractional Exponents

1.4 Comparing Exponents

1.5 Scientific Notation A. Representation of Very Small or Very Large Numbers

- Computation

1.6 Rounding Numbers to a Specified Number of Significant Figures

1.7 Estimations and Accuracy of Calculators

- Estimations
- Estimation and Irrational Numbers
- Accuracy in Calculators In a Nutshell

Review Exercise 1

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*Dimensions 7A*

Chapter 1: Factors and Multiples

- Exponential Notation

Chapter 3: Introduction to Algebra

- Exponential Notation

*Dimensions 8A*

Chapter 1: Exponents and Scientific Notation 1.1 Positive Exponents and the Laws of Exponents

1.2 Zero and Negative Integer Exponents

1.3 Fractional Exponents

- nth root of a Positive Number
- Fractional Exponents

1.4 Comparing Exponents

1.5 Scientific Notation

- Representation of Very Small or Very Large Numbers
- Computation

1.6 Rounding Numbers to a Specified Number of Significant Figures

1.7 Estimations and Accuracy of Calculators

- Estimations
- Estimation and Irrational Numbers
- Accuracy in Calculators In a Nutshell

Review Exercise 1

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*Dimensions 8A*

Chapter 3: Expansion and Factorization of Algebraic Expressions

3.1 Expansion of the Products of Algebraic Expressions

- Product of Single Terms
- Product of Two Expressions

3.2 Special Products More Properties of Inequalities

3.3 Factorization by using Special Products of Algebraic Expressions In A Nutshell

Review Exercise 3

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Chapter 4: Quadratic Factorization and Equations 4.1 Factorization of ax2 + bx +c

- x2 + bx + c
- ax2 + bx + c 4.2 Solving Quadratic Equations by Factorization

4.3 Problem Solving Involving Quadratic Equations In A Nutshell

Review Exercise 4

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*Dimensions 8A*

Chapter 2: Linear Equations in Two Variables

2.1 Linear Equations in Two Variables

- Review of Linear Equations in One Variable
- Meaning of Linear Equations in Two Variables 2.2 Solving Simultaneous Linear Equations in Two Variables using the Graphical Method

2.3 Solving Simultaneous Linear Equations in Two Variables using the Substitution Method

2.4 Solving Simultaneous Linear Equations in Two Variables using the Elimination Method

2.5 Solving Problems using Simultaneous Equations In A Nutshell

Review Exercise 2

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*Dimensions 8B*

Chapter 8: Graphs of Linear and Quadratic Functions 8.1 Linear Function

- Idea of Functions
- Linear Functions
- Rate of Change 8.2 Graphs of Quadratic Functions A. Graph of y = ax2 + bx + c, where a > 0
- Graph of y = ax2 + bx + c, where a < 0 In a Nutshell

Review Exercise 8

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Chapter 11: Coordinate Geometry

11.1 Distance Between Two Points

11.2 Slope of a Straight Line

11.3 Equation of a Straight Line In a Nutshell

Review Exercise 11

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*Dimensions 8A*

Chapter 2: Linear Equations in Two Variables

2.1 Linear Equations in Two Variables

- Review of Linear Equations in One Variable
- Meaning of Linear Equations in Two Variables 2.2 Solving Simultaneous Linear Equations in Two Variables using the Graphical Method

2.3 Solving Simultaneous Linear Equations in Two Variables using the Substitution Method

2.4 Solving Simultaneous Linear Equations in Two Variables using the Elimination Method

2.5 Solving Problems using Simultaneous Equations In A Nutshell

Review Exercise 2

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*Dimensions 8B*

Chapter 8: Graphs of Linear and Quadratic Functions 8.1 Linear Function

- Idea of Functions
- Linear Functions
- Rate of Change

8.2 Graphs of Quadratic Functions

- Graph of y = ax2 + bx + c, where a > 0
- Graph of y = ax2 + bx + c, where a < 0 In a Nutshell

Review Exercise 8

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*Dimensions 8A*

Chapter 6: Congruence and Reflections

6.1 Congruence and Reflections

- Congruent Figures
- Reflections

6.2 Translations, Rotations and Combining Transformations

- Translations
- Rotations
- Combining Transformations

6.3 Similarity

6.4 Enlargements and Similarity

- Scale Factors
- Enlargements In A Nutshell

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Chapter 7: Parallel Lines and Angles in Triangles and Polygons 7.1 Angles formed by Parallel Lines and Transversals A. Angle Properties

- Parallel Lines and Transversals 7.2 Interior and Exterior Angles of a Triangle A. Angle Sum of a Triangle
- Exterior Angle of a Triangle 7.3 Angles Properties of Special Quadrilaterals

7.4 Polygons A. Types of Polygons

- Sum of Interior Angles of a Polygons
- Sum of Exterior Angles of a Polygons In A Nutshell

Review Exercise 7

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*Dimensions 7B*

Chapter 16: Probability of Simple Events

16.1 Set Notation

- Sets
- Equal Sets
- Subsets
- Universal Set and Empty Set
- Complement of a Set

16.2 The Meaning of Probability

- Introduction
- Terms and Definitions

16.3 Sample Space

- Sample Space
- Basic Properties of Probabilities In A Nutshell

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Chapter 17: Probability of Combined Events

17.1 Probability of Simple Combined Events

- Possibility Diagram
- Tree Diagram

17.2 The Meaning of Probability

17.3 Independent Events

17.4 Further Probabilities In A Nutshell

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Supplementation required – suggestions coming soon

## Curricular Competencies

### Reasoning/Analyzing

Supplementation required – suggestions coming soon

Use “*In A Nutshell*

*Review Exercise 3*

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addressed throughout

Use “*In A Nutshell*

*Review Exercise 3*

*Extend Your Learning Curve*

*Write In Your Journal*” to fulfil this competency

Use “*In A Nutshell*

*Review Exercise 3*

*Extend Your Learning Curve*

*Write In Your Journal*” to fulfil this competency

Supplementation required – suggestions coming soon

### Understanding/Solving

Use “*In A Nutshell*

*Review Exercise 3*

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Use “*In A Nutshell*

*Review Exercise 3*

*Extend Your Learning Curve*

*Write In Your Journal*” to fulfill this competency

Strongly addressed throughout

Use “*In A Nutshell*

*Review Exercise 3*

*Extend Your Learning Curve*

*Write In Your Journal*” to this competency

### Communicating/Representing

Use “*In A Nutshell*

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Use “*In A Nutshell*

*Review Exercise 3*

*Extend Your Learning Curve*

*Write In Your Journal*” to fulfill this competency

Use “*In A Nutshell*

*Review Exercise 3*

*Extend Your Learning Curve*

*Write In Your Journal*” to this competency

Use “*In A Nutshell*

*Review Exercise 3*

*Extend Your Learning Curve*

*Write In Your Journal*” to fulfill this competency

### Connecting/Reflecting

Use “*In A Nutshell*

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Use “*In A Nutshell*

*Review Exercise 3*

*Extend Your Learning Curve*

*Write In Your Journal*” to fulfill this competency