【People's Education Press】Middle School Math Grade 7 Part 2

📚 Content Summary

This textbook is a core component of middle school mathematics, covering intersecting and parallel lines, real numbers, the Cartesian coordinate system, systems of linear equations in two variables, inequalities and inequality systems, as well as data collection, organization, and description. Through this semester’s study, students will transition from basic geometric relationships to algebraic logic, establishing foundational thinking that integrates numbers and shapes.

Explore the mysteries of numbers and shapes, and develop rigorous mathematical logical thinking.

Author: Lin Qun

Acknowledgments: This book is a compulsory education textbook reviewed and approved by the Ministry of Education, compiled by the Middle School Mathematics Curriculum Research and Development Center of the Institute of Curriculum and Textbooks for Compulsory Education, People's Education Press.

🎯 Learning Objectives

1. Identify and calculate adjacent supplementary angles and vertical angles; master the property that vertical angles are equal, and understand the methods and characteristics of drawing perpendicular lines.
2. Understand the parallel postulate and apply relationships among corresponding angles, alternate interior angles, and same-side interior angles (the "three lines and eight angles" rule) to determine whether two lines are parallel.
3. Master the definition of translation and use the characteristic that connecting lines between corresponding points are parallel and equal in length to design simple geometric transformations.
4. Understand the concepts of arithmetic square root, square root, and cube root, and be proficient in performing square root and cube root operations.
5. Grasp the properties of square roots and cube roots (such as the characteristics of roots for positive numbers, negative numbers, and zero), and be able to identify irrational numbers.
6. Master the classification system of real numbers and apply estimation or properties of squaring/cubing to compare the sizes of real numbers.
7. Understand and master the fundamental concepts of the Cartesian coordinate system, accurately identifying the coordinate axes, origin, and four quadrants.
8. Grasp the rules of translation, skillfully compute new coordinates after horizontal and vertical translations of points or figures, and describe the translation process based on coordinate changes.
9. Apply coordinate methods, establish simple Cartesian coordinate systems to describe geographical locations or solve practical life problems involving the integration of numbers and shapes.
10. Master solution methods: Proficiently use substitution elimination and addition/subtraction elimination to solve systems of linear equations in two variables.

🔹 Lesson 1: Foundations and Geometric Proofs of Intersecting and Parallel Lines

Overview: This lesson covers the core foundations of middle school geometry, primarily focusing on the positional relationships between two lines in the same plane (intersecting and parallel). By studying the properties of adjacent supplementary angles, vertical angles, and perpendicular lines, students will begin to engage with geometric logic. Subsequently, through the criteria and properties of parallel lines, they will learn the basic expression forms of geometric proofs (because/therefore). Finally, through translation transformations, students will understand the invariance of figures during motion.

Learning Outcomes:

• Identify and calculate adjacent supplementary angles and vertical angles; master the property that vertical angles are equal, and understand the methods and characteristics of drawing perpendicular lines.
• Understand the parallel postulate and apply relationships among corresponding angles, alternate interior angles, and same-side interior angles (the "three lines and eight angles" rule) to determine whether two lines are parallel.
• Master the definition of translation and use the characteristic that connecting lines between corresponding points are parallel and equal in length to design simple geometric transformations.

🔹 Lesson 2: Definition, Operations, and Extended Properties of Real Numbers

Overview: This unit covers the core concepts involved in extending from the rational number system to the real number system, focusing on the definitions, operations, and properties of arithmetic square roots, square roots, and cube roots. Through learning about root extraction operations, students will understand the objective existence of non-repeating infinite decimals (irrational numbers), master the classification method of real numbers, and be able to compare the sizes of real numbers—laying a foundation for future algebraic studies.

Learning Outcomes:

• Understand the concepts of arithmetic square root, square root, and cube root, and be proficient in performing square root and cube root operations.
• Master the properties of square roots and cube roots (such as the characteristics of roots for positive numbers, negative numbers, and zero), and be able to identify irrational numbers.
• Master the classification system of real numbers and apply estimation techniques or properties of squaring/cubing to compare the sizes of real numbers.

🔹 Lesson 3: Cartesian Coordinate System and Preliminary Integration of Numbers and Shapes

Overview: This instructional design aims to guide seventh-grade students in transitioning from one-dimensional number lines to two-dimensional Cartesian coordinate systems. The focus lies in understanding how ordered pairs uniquely determine point positions, mastering the division rules of the four quadrants, and deeply exploring the logical patterns of coordinate changes during translation of points and figures—ultimately achieving a preliminary integration of “solving shapes using numbers” and “using shapes to aid numerical understanding.”

Learning Outcomes:

• Understand and master the fundamental concepts of the Cartesian coordinate system, accurately identifying the coordinate axes, origin, and four quadrants.
• Grasp the rules of translation, skillfully compute new coordinates after horizontal and vertical translations of points or figures, and describe the translation process based on coordinate changes.
• Apply coordinate methods, establish simple Cartesian coordinate systems to describe geographical locations or solve practical life problems involving the integration of numbers and shapes.

🔹 Lesson 4: Solution Methods and Application Modeling of Systems of Linear Equations in Two Variables

Overview: The core of this unit lies in using the concept of “elimination” to transform complex systems of two (or three) linear equations into familiar one-variable linear equations. Key teaching points include operational skills for substitution elimination and addition/subtraction elimination, as well as how to construct mathematical models for real-world problems (such as navigation, production, and geometry).

Learning Outcomes:

• Master solution methods: Proficiently use substitution elimination and addition/subtraction elimination to solve systems of linear equations in two variables.
• Mathematical modeling: Analyze quantitative relationships in real-world problems and set up systems of linear equations to solve application questions.
• Logical extension: Understand the logical approach to solving systems of three linear equations, i.e., repeatedly eliminating variables to reduce to a single-variable equation.

🔹 Lesson 5: Logic and Operations of Systems of Linear Inequalities

Overview: This lesson aims to guide students from the symmetric logic of equations to the asymmetric logic of inequalities. The course covers the basic properties of inequalities (especially the reversal of inequality signs when multiplying or dividing by negative numbers), standard solution methods for linear inequalities in one variable, visual representation of solution sets on number lines, and how to use inequality models to solve real-life problems involving maximum/minimum values and ranges. Finally, by finding the “common part” of multiple inequality solution sets, students will master the logical operations of systems of linear inequalities.

Learning Outcomes:

• Understand and master the three fundamental properties of inequalities, and accurately perform equivalent transformations of inequalities.
• Skillfully solve linear inequalities and systems of linear inequalities, correctly marking solution sets on number lines (distinguishing between open and closed circles).
• Based on keywords in real-world problems (such as “at least,” “exceed,” “not more than”), construct inequality models and solve them.

🔹 Lesson 6: Data Collection, Organization, and Descriptive Statistical Analysis

Overview: This course aims to guide seventh-grade students in mastering the basic methods of statistical investigation—from data collection (census vs. sampling) to data organization (frequency distribution tables) and data description (bar graphs, pie charts, histograms). Through the inquiry-based project “Talking About Water Conservation Through Data,” students will apply mathematical theory to real-world environmental issues, cultivating data analysis awareness and scientific decision-making skills.

Learning Outcomes:

• Distinguish between census and sampling surveys, and accurately identify population, individual, sample, and sample size.
• Skillfully draw bar and pie charts, and master the method for calculating central angles in pie charts.
• Master the steps for creating frequency distribution tables and histograms, and understand how class width and number of classes affect the description of data distribution.