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

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.

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.