# Singapore Math

## Grade Seven Content

US Edition Book Textbook 6B and Dimensions books Textbooks 7A & 7B

#### multiplication and division facts to 100 (extending computational fluency)

Dimensions

Book 7A: Chapter 1: Factors and Multiples

1.1 Factors and Multiples

1. Factors
2. Multiples

1.2 Prime Factorization and Exponential Notation A. Prime Factorization

1. Exponential Notation

1.3 Greatest Common Factor (GCF)

1.4 Least Common Multiple (LCM)

1.5 Square Roots and Cube Roots

1. Square Roots
2. Cube Roots In A Nutshell

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

Dimensions

Book 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

2.2 Addition and Additive Inverse

1. Addition of Integers
2. Additive Inverse

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 A. Real Numbers

1. Use of Calculators

2.7 Rounding Numbers to Decimal Places A. Idea of Rounding

1. Rounding Numbers to Decimal Places In A Nutshell

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

Supplementation Required

#### relationships between decimals, fractions, ratios, and percents

Supplementation Required

#### discrete linear relations, using expressions, tables, and graphs

Dimensions

Book 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

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#### two-step equations with whole-number coefficients, constants, and solutions

Dimensions

Book 7A: Chapter 4: Algebraic Manipulation

4.1 Like Terms and Unlike Terms

4.2 Distributive Law, Addition and Subtraction of Linear Algebraic Expressions

1. Use of Parentheses
2. Addition and Subtraction of Linear Algebraic Expressions

4.3 Simplification of Linear Algebraic Expressions

4.4 Factorization by Extracting Common Factors

4.5 Factorization by Grouping Terms In A Nutshell

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#### circumference and area of circles

Primary book 6B

Unit 2: Circles: Radius and Diameter, Circumference, Area

#### volume of rectangular prisms and cylinders

Primary book 6B

Unit 4: Volume: Solving Problems

#### Cartesian coordinates and graphing

Dimensions

Book 7B: Chapter 10: Coordinates and Linear Graphs

10.1 Cartesian Coordinate System

10.2 Linear Graphs

10.3 Slopes of Linear Graphs

1. Positive Slopes
2. Negative Slopes
3. Special Cases In A Nutshell

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#### combinations of transformations

Dimensions

Book 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

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#### circle graphs

Primary book 6B

Unit 3: Graphs: Pie Charts

#### experimental probability with two independent events

Dimensions

Book 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

1. Introduction
2. Terms and Definitions

16.3 Sample Space

1. Sample Space
2. Basic Properties of Probabilities

In A Nutshell

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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

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#### financial literacy — financial percentage

Dimensions

Book 7A: Chapter 7: Percentage

7.4 Discount and Sales Tax A. Discount

1. Sales Tax In A Nutshell

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#### line graphs

Supplementation Required

#### single-outcome probability, both theoretical and experimental

Supplementation Required

#### financial literacy — simple budgeting and consumer math

Dimensions

Book 7A: Chapter 7: Percentage

7.4 Discount and Sales Tax A. Discount

1. Sales Tax In A Nutshell

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## Curricular Competencies

### Reasoning/Analyzing

#### Use logic and patterns to solve puzzles and play games

The “In A Nutshell, Extend Your Learning Curve, Write In Your Journal” could possibly meet this competency. Teacher to verify.

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

The “In A Nutshell, Extend Your Learning Curve, Write In Your Journal” could possibly meet this competency. Teacher to verify.

#### Estimate reasonably

Supplementation Required

#### Demonstrate and apply mental math strategies

Supplementation Required

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

The “In A Nutshell, Extend Your Learning Curve, Write In Your Journal” could possibly meet this competency. Teacher to verify.

#### Model mathematics in contextualized experiences

Supplementation Required

### Understanding/Solving

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

The “In A Nutshell, Extend Your Learning Curve, Write In Your Journal” could possibly meet this competency. Teacher to verify.

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

The “In A Nutshell, Extend Your Learning Curve, Write In Your Journal” could possibly meet this competency. Teacher to verify.

#### Visualize to explore mathematical concepts

Supplementation Required

#### 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

Dimensions

Book 7B: 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 A. Uniform Speed and Average Speed

1. Conversion of Units In A Nutshell

Extend Your Learning Curve

### Communicating/Representing

#### Use mathematical vocabulary and language to contribute to mathematical discussions

The “In A Nutshell, Extend Your Learning Curve, Write In Your Journal” could possibly meet this competency. Teacher to verify.

#### Explain and justify mathematical ideas and decisions

The “In A Nutshell, Extend Your Learning Curve, Write In Your Journal” could possibly meet this competency. Teacher to verify.

#### Communicate mathematical thinking in many ways

The “In A Nutshell, Extend Your Learning Curve, Write In Your Journal” could possibly meet this competency. Teacher to verify.

#### Represent mathematical ideas in concrete, pictorial, and symbolic forms

Supplementation Required

### Connecting/Reflecting

#### Reflect on mathematical thinking

The “In A Nutshell, Extend Your Learning Curve, Write In Your Journal” could possibly meet this competency. Teacher to verify.

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

Dimensions

Book 7A: 3.3 Writing Algebraic Expressions to Represent Real-world Situations

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

First Peoples perspectives are not covered