Singapore Math

Dimensions Textbooks 7A & 7B and Dimensions Textbooks 8A & 8B

perfect squares and cubes

Dimensions 7A

Chapter 1: Factors and Multiples

1.5 Square Roots and Cube Roots

1. Square Roots
2. Cube Roots

square and cube roots

Dimensions 7A

Chapter 1: Factors and Multiples

1.5 Square Roots and Cube Roots

1. Square Roots
2. Cube Roots

percents less than 1 and greater than 100 (decimal and fractional percents)

Dimensions 7A

Chapter 7: Percentage

7.1 Meaning of Percentage

1. Introduction
2. Expressing One Quantity as a Percentage of Another

7.2 Reverse Percentages

7.3 Percentage Increase and Decrease

1. Percentage Increase
2. Percentage Decrease

7.4 Discount and Sales Tax A. Discount

1. Sales Tax In A Nutshell

numerical proportional reasoning (rates, ratio, proportions, and percent)

Dimensions 7A

Chapter 6: Ratio, Rate, and Speed

6.1 Ratios Involving Rational Numbers

1. Meaning of Ratio
2. Simplification of Ratios
3. Ratio of Three Quantities
4. Problems Involving Ratios

6.2 Average Rate

6.3 Speed

1. Uniform Speed and Average Speed
2. Conversion of Units In A Nutshell

Chapter 7: Percentage 7.1 Meaning of Percentage A. Introduction

1. Expressing One Quantity as a Percentage of Another 7.2 Reverse Percentages

7.3 Percentage Increase and Decrease A. Percentage Increase

1. Percentage Decrease 7.4 Discount and Sales Tax A. Discount
2. Sales Tax In A Nutshell

Dimensions 7B

Chapter 14: Proportions

14.1 Scale Drawing

14.2 Map Scale and Calculation of Area

1. Map Scale
2. Calculation of Area

14.3 Direct Proportion

14.4 Inverse Proportion In A Nutshell

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

Dimensions 7A

Chapter 5: Simple Equations in One Variable

5.3 Simple Fractional Equations

Problems In A Nutshell

Dimensions 8A

Chapter 5: Simple Algebraic Fractions

5.1 Simplifying Simple Algebraic Fractions

5.2 Multiplication and Division of Algebraic Fractions

5.3 Addition and Subtraction of Algebraic Fractions

5.4 Fractional Equations A. Solving Equations Involving Algebraic Fractions

1. Problem Solving Involving Fractional Equations

5.5 More about Formulas A. Finding the Value of an Unknown Quantity in a Formula

1. Changing the Subject of a Formula In A Nutshell

Review Exercise 5

discrete linear relations (extended to larger numbers, limited to integers)

Dimensions 7A

Chapter 5: Simple Equations in One Variable 5.1 Simple Linear Equations in One Variable

5.2 Equations Involving Parentheses

5.3 Simple Fractional Equations

5.4 Forming Linear Equations to Solve Problems In A Nutshell

Dimensions 8A

Chapter 2: Linear Equations in Two Variables 2.1 Linear Equations in Two Variables A. Review of Linear Equations in One Variable

1. 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

expressions- writing and evaluating using substitution

Dimensions 7A

Chapter 5: Simple Equations in One Variable 5.1 Simple Linear Equations in One Variable

5.2 Equations Involving Parentheses

5.3 Simple Fractional Equations

5.4 Forming Linear Equations to Solve Problems In A Nutshell

two-step equations with integer coefficients, constants, and solutions

Dimensions 8A

Chapter 2: Linear Equations in Two Variables 2.1 Linear Equations in Two Variables A. Review of Linear Equations in One Variable

1. 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

surface area and volume of regular solids, including triangular and other right prisms and cylinders

Dimensions 7B

Chapter 13: Volumes and Surface Areas of Solids

13.1 Volumes and Total Surface Areas of a Cube and a Cuboid A. Nets of Cube, Cuboid, and Other Prisms

1. Cube
2. Cuboid

13.2 Volume and Total Surface Area of a Prism A. Prism

1. Volume of Prism
2. Surface Area of Prism

13.3 Volumes and Surface Areas of Composite Solids

1. Conversion between Different Units
2. Composite Solids In A Nutshell

Pythagorean theorem

Dimensions 8B

Chapter 10: Pythagorean Theorem

10.1 Pythagorean Theorem

10.2 The Converse of Pythagorean Theorem

1. Definition
2. Determination of Right-Angled Triangles

10.3 Applications of Pythagoras Theorem In a Nutshell

Review Exercise 10

construction, views, and nets of 3D objects

Dimensions 7B

Chapter 13: Volumes and Surface Areas of Solids 13.1 Volumes and Total Surface Areas of a Cube and a Cuboid

1. Nets of Cube, Cuboid, and Other Prisms
2. Cube
3. Cuboid

13.2 Volume and Total Surface Area of a Prism A. Prism

1. Volume of Prism
2. Surface Area of Prism

13.3 Volumes and Surface Areas of Composite Solids

1. Conversion between Different Units
2. Composite Solids In A Nutshell

Dimensions 8B

Chapter 12: Mensuration of Pyramids, Cylinders, Cones and Spheres

12.1 Pyramids

1. Introducing Pyramids
2. Nets and Surface Areas of Pyramids
3. Volumes of Pyramids

12.2 Cylinders

1. Volume and Surface Area of a Cylinder

12.3 Cones

1. Introducing Cones
2. Net and Surface Area of a Cone
3. Volume of a Cone

12.4 Spheres

1. Introducing Spheres
2. Volume of a Sphere
3. Surface Area of a Sphere In a Nutshell

Review Exercise 12

central tendency

Supplementation Required

theoretical probability with two independent events

Dimensions 7B

Chapter 16: Probability of Simple Events 16.1 Set Notation A. Sets

1. Equal Sets
2. Subsets
3. Universal Set and Empty Set
4. Complement of a Set 16.2 The Meaning of Probability A. Introduction
5. Terms and Definitions 16.3 Sample Space A. Sample Space
6. Basic Properties of Probabilities In A Nutshell

Chapter 17: Probability of Combined Events 17.1 Probability of Simple Combined Events A. Possibility Diagram

1. Tree Diagram 17.2 The Meaning of Probability

17.3 Independent Events

17.4 Further Probabilities In A Nutshell

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

Any of the journal writing and “extend your learning curve activities” can be used as a platform to meet this competency, with the support of a teacher.

Estimate reasonably

Dimension 8A

1.7 Estimations and Accuracy of Calculators A. Estimations

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

Demonstrate and apply mental math strategies

Any of the journal writing and “extend your learning curve activities” can be used as a platform to meet this competency, with the support of a teacher.

Model mathematics in contextualized experiences

Supplementation Required

Understanding/Solving

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

Dimensions 7A

Chapter 3: Introduction to Algebra

3.3 Writing Algebraic Expressions to Represent Real-world Situations In A Nutshell

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

Any of the journal writing and “extend your learning curve activities” can be used as a platform to meet this competency, with the support of a teacher.

Visualize to explore mathematical concepts

Any of the journal writing and “extend your learning curve activities” can be used as a platform to meet this competency, with the support of a teacher.

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

Any of the journal writing and “extend your learning curve activities” can be used as a platform to meet this competency, with the support of a teacher.

Communicating/Representing

Use mathematical vocabulary and language to contribute to mathematical discussions

Any of the journal writing and “extend your learning curve activities” can be used as a platform to meet this competency, with the support of a teacher.

Explain and justify mathematical ideas and decisions

Any of the journal writing and “extend your learning curve activities” can be used as a platform to meet this competency, with the support of a teacher.

Communicate mathematical thinking in many ways

Any of the journal writing and “extend your learning curve activities” can be used as a platform to meet this competency, with the support of a teacher.

Represent mathematical ideas in concrete, pictorial, and symbolic forms

Supplementation Required

Connecting/Reflecting

Reflect on mathematical thinking

Supplementation Required

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

Dimensions 7A

Chapter 3: Introduction to Algebra

3.3 Writing Algebraic Expressions to Represent Real-world Situations In A Nutshell

Incorporate First Peoples worldviews and perspectives to make connections to mathematical concepts

First Peoples perspectives are not covered