Singapore Math

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

operations with rational numbers (addition, subtraction, multiplication, division, and order of operations)

Dimensions 7A

Chapter 2: Real Numbers

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

1. The Number Line
2. Absolute Value

2.3 Subtraction and Absolute Value of the Difference

1. Subtraction of Integers
2. Absolute Value of the Difference

2.4 Multiplication, Division, and Combined Operations of Integers

1. Multiplication of Integers
2. Division of Integers
3. Combined Operations of Integers

2.5 Rational Numbers

1. Definition
2. Addition and Subtraction of Rational Numbers
3. Multiplication and Division of Rational Numbers

2.6 Real Numbers and Use of Calculators

1. Real Numbers
2. Use of Calculators

2.7 Rounding Numbers to Decimal Places

1. Idea of Rounding
2. Rounding Numbers to Decimal Places In A Nutshell

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

1. Fractional Exponents

1.4 Comparing Exponents

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

1. Computation

1.6 Rounding Numbers to a Specified Number of Significant Figures

1.7 Estimations and Accuracy of Calculators

1. Estimations
2. Estimation and Irrational Numbers
3. Accuracy in Calculators In a Nutshell

Review Exercise 1

exponents and exponent laws with whole-number exponents

Dimensions 7A

Chapter 1: Factors and Multiples

1. Exponential Notation

Chapter 3: Introduction to Algebra

1. 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

1. nth root of a Positive Number
2. Fractional Exponents

1.4 Comparing Exponents

1.5 Scientific Notation

1. Representation of Very Small or Very Large Numbers
2. Computation

1.6 Rounding Numbers to a Specified Number of Significant Figures

1.7 Estimations and Accuracy of Calculators

1. Estimations
2. Estimation and Irrational Numbers
3. Accuracy in Calculators In a Nutshell

Review Exercise 1

operations with polynomials, of degree less than or equal to 2

Dimensions 8A

Chapter 3: Expansion and Factorization of Algebraic Expressions

3.1 Expansion of the Products of Algebraic Expressions

1. Product of Single Terms
2. 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

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

1. x2 + bx + c
2. ax2 + bx + c 4.2 Solving Quadratic Equations by Factorization

4.3 Problem Solving Involving Quadratic Equations In A Nutshell

Review Exercise 4

two-variable linear relations, using graphing, interpolation, and extrapolation

Dimensions 8A

Chapter 2: Linear Equations in Two Variables

2.1 Linear Equations in Two Variables

1. Review of Linear Equations in One Variable
2. 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

Dimensions 8B

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

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

Review Exercise 8

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

multi-step one-variable linear equations

Dimensions 8A

Chapter 2: Linear Equations in Two Variables

2.1 Linear Equations in Two Variables

1. Review of Linear Equations in One Variable
2. 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

Dimensions 8B

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

1. Idea of Functions
2. Linear Functions
3. Rate of Change

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

Review Exercise 8

spatial proportional reasoning

Dimensions 8A

Chapter 6: Congruence and Reflections

6.1 Congruence and Reflections

1. Congruent Figures
2. Reflections

6.2 Translations, Rotations and Combining Transformations

1. Translations
2. Rotations
3. Combining Transformations

6.3 Similarity

6.4 Enlargements and Similarity

1. Scale Factors
2. Enlargements In A Nutshell

Review Exercise 6

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

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

7.4 Polygons A. Types of Polygons

1. Sum of Interior Angles of a Polygons
2. Sum of Exterior Angles of a Polygons In A Nutshell

Review Exercise 7

statistics in society

Dimensions 7B

Chapter 16: Probability of Simple Events

16.1 Set Notation

1. Sets
2. Equal Sets
3. Subsets
4. Universal Set and Empty Set
5. Complement of a Set

16.2 The Meaning of Probability

1. Introduction
2. Terms and Definitions

16.3 Sample Space

1. Sample Space
2. Basic Properties of Probabilities In A Nutshell

Chapter 17: Probability of Combined Events

17.1 Probability of Simple Combined Events

1. Possibility Diagram
2. Tree Diagram

17.2 The Meaning of Probability

17.3 Independent Events

17.4 Further Probabilities In A Nutshell

financial literacy — simple budgets and transactions

Supplementation Required

Curricular Competencies

Reasoning/Analyzing

Use logic and patterns to solve puzzles and play games

Supplementation Required

Use reasoning and logic to explore, analyze, and apply mathematical ideas

Use “In A Nutshell

Review Exercise 3

Write In Your Journal” to fulfill this competency

Demonstrate and apply mental math strategies

Use “In A Nutshell

Review Exercise 3

Write In Your Journal” to fulfil this competency

Use tools or technology to explore and create patterns and relationships, and test conjectures

Use “In A Nutshell

Review Exercise 3

Write In Your Journal” to fulfil this competency

Model mathematics in contextualized experiences

Supplementation Required

Understanding/Solving

Apply multiple strategies to solve problems in both abstract and contextualized situations

Use “In A Nutshell

Review Exercise 3

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Develop, demonstrate, and apply mathematical understanding through play, inquiry, and problem solving

Use “In A Nutshell

Review Exercise 3

Write In Your Journal” to fulfill this competency

Engage in problem-solving experiences that are connected to place, story, cultural practices, and perspectives relevant to local First Peoples communities, the local community, and other cultures

Use “In A Nutshell

Review Exercise 3

Write In Your Journal” to   this competency

Communicating/Representing

Use mathematical vocabulary and language to contribute to mathematical discussions

Use “In A Nutshell

Review Exercise 3

Write In Your Journal” to fulfill this competency

Explain and justify mathematical ideas and decisions

Use “In A Nutshell

Review Exercise 3

Write In Your Journal” to fulfill this competency

Communicate mathematical thinking in many ways

Use “In A Nutshell

Review Exercise 3

Write In Your Journal” to   this competency

Represent mathematical ideas in concrete, pictorial, and symbolic forms

Use “In A Nutshell

Review Exercise 3

Write In Your Journal” to fulfill this competency

Connecting/Reflecting

Reflect on mathematical thinking

Use “In A Nutshell

Review Exercise 3

Write In Your Journal” to fulfill this competency

Connect mathematical concepts to each other and to other areas and personal interests

Use “In A Nutshell

Review Exercise 3