【People's Education Press】Junior High School English Grade 7 First Semester

📚 Content Summary

This textbook serves as an introductory mathematics resource for first-year junior high school students, primarily covering four core modules: rational numbers, addition and subtraction of polynomials, linear equations in one variable, and basic geometry. By introducing abstract concepts such as negative numbers, number lines, and algebraic expressions, it helps students transition from arithmetic thinking to algebraic thinking, laying a solid foundation for middle school mathematics.

Open the door to algebra, building the cornerstone of rational thinking.

Author: Lin Qun

Acknowledgments: Approved by the Ministry of Education 2012, National Outstanding Textbook Award Second Prize

🎯 Learning Objectives

1. Master absolute value calculation and properties: Accurately compute the absolute value of any rational number and understand its geometric meaning (distance).
2. Skillfully compare sizes of rational numbers: Master using number lines and absolute values to compare the relative sizes of positive numbers, negative numbers, and zero.
3. Excel in rational number addition: Apply sign rules accurately in addition operations and flexibly use arithmetic laws to improve computational efficiency.
4. Accurately distinguish concepts: Identify monomials (coefficient, degree) and polynomials (terms, degree), and understand the meaning of polynomials.
5. Master operational rules: Skillfully apply the rule of combining like terms and the rule of removing parentheses to correctly perform addition and subtraction of polynomials.
6. Strengthen application modeling: Translate real-world problems (e.g., geometry, motion, data patterns) into algebraic expressions and simplify them for evaluation.
7. Master core skills: Understand and proficiently apply the two properties of equations, solving linear equations in one variable through standardized steps.
8. Develop modeling thinking: Identify equal relationships in real problems and master the problem-solving process: "set up variables, form equations, solve, check, answer."
9. Solve complex scenarios: Tackle practical problems involving profit-loss calculations, score table logic analysis, and optimal phone billing plan selection.
10. Recognize points, lines, planes, solids, and their interconversions; understand the correspondence between three-dimensional figures and their nets.

🔹 Lesson 1: Practice Class on Operations and Comparisons of Rational Numbers

Overview: This lesson aims to reinforce students’ understanding of the concept of absolute value in rational numbers and its application in comparing magnitudes, while also deepening mastery of rational number addition rules. Through practice, students will learn to interpret operations within the context of number lines and skillfully apply the commutative and associative laws of addition to simplify complex calculations, establishing a strong foundation for future algebraic studies.

Learning Outcomes:

• Master absolute value calculation and properties: Accurately compute the absolute value of any rational number and understand its geometric meaning (distance).
• Skillfully compare sizes of rational numbers: Master using number lines and absolute values to compare the relative sizes of positive numbers, negative numbers, and zero.
• Excel in rational number addition: Apply sign rules accurately in addition operations and flexibly use arithmetic laws to improve computational efficiency.

🔹 Lesson 2: Practice Class on Polynomial Addition and Subtraction with Algebraic Applications

Overview: This lesson aims to smoothly transition students from foundational knowledge of "rational numbers" to the core content of "addition and subtraction of polynomials." Key topics include definitions of monomials and polynomials, combining like terms, rules for removing parentheses, and comprehensive applications of polynomial addition and subtraction in real-life contexts (e.g., motion problems, geometric area, pattern exploration, spreadsheet calculations), fostering students' shift from numerical thinking to symbolic abstraction.

Learning Outcomes:

• Accurately distinguish concepts: Identify monomials (coefficient, degree) and polynomials (terms, degree), and understand the meaning of polynomials.
• Master operational rules: Skillfully apply the rule of combining like terms and the rule of removing parentheses to correctly perform addition and subtraction of polynomials.
• Strengthen application modeling: Translate real-world problems (e.g., geometry, motion, data patterns) into algebraic expressions and simplify them for evaluation.

🔹 Lesson 3: Specialized Class on Solving Linear Equations and Real-World Problems

Overview: This course enables students to master the standardized procedure for solving linear equations in one variable—eliminating denominators, removing parentheses, moving terms, combining like terms, and normalizing coefficients—based on the fundamental properties of equations. Simultaneously, it connects theory with practice, focusing on tackling typical application problems such as profit-loss calculations, sports scoring systems, engineering matching, and phone billing, thereby cultivating students’ ability to model real-world issues mathematically.

Learning Outcomes:

• Master core skills: Understand and proficiently apply the two properties of equations, solving linear equations in one variable through standardized steps.
• Develop modeling thinking: Identify equal relationships in real problems and master the problem-solving process: "set up variables, form equations, solve, check, answer."
• Solve complex scenarios: Overcome challenges involving profit-loss calculations, score table logic analysis, and optimal phone billing plan selection.

🔹 Lesson 4: Introductory Geometry and Practice Class on Segment and Angle Calculations

Overview: This course aims to help students consolidate their basic understanding of geometric figures through practice, covering transformations from three-dimensional figures (points, lines, planes, solids) to two-dimensional representations (nets), and emphasizing key concepts such as segment properties (midpoint, shortest distance) and special angle relationships (complementary and supplementary angles). Through hands-on manipulation of visual diagrams and numerical calculations, students will develop initial spatial awareness and logical reasoning abilities.

Learning Outcomes:

• Recognize points, lines, planes, solids, and their interconversions; understand the correspondence between three-dimensional figures and their nets.
• Skillfully master the definition of midpoint and the concept of distance between two points, and apply the principle “the shortest path between two points is a straight line” to solve real-world path problems.
• Understand the definitions and properties of complementary and supplementary angles (equal angles have equal complements/supplements), and perform sixty-based angle operations involving degrees, minutes, and seconds.