The mathematics (algebra) course for the 7th grade of secondary school is part of the continuous mathematics curriculum of the educational system developed by L.G. Peterson.
This course links students' math learning from preschool to high school or vocational education. Its goal is to boost learning, develop their minds and morals, and maintain their health. It ensures all students have a strong math foundation for their personal growth. This knowledge is key for high school and vocational courses in tech and teaching.
The course uses the activity-based teaching method by L.G. Peterson, a practical approach vital for kids' development. It focuses on understanding math models and applying the results to real life.
Students first solve practical problems.
They build on their math skills, making math more interesting.
The course includes physics problems to reinforce new methods and demonstrate real-world applications.
Students learn about functions by solving problems and applying them to practical situations.
In each topic, students solve problems step by step, starting with known methods and progressing to discover new methods through observation and experimentation. Their work is compared to examples in the textbook.
The course offers a mix of tasks, including Olympiad-style problems, designed to match teenagers' needs and cater to adolescents' tendencies to daydream.
The curriculum goes beyond traditional math, covering logic, linear equations, and applications like information coding to prepare students for professional education.
Math topics are divided into seven lines, starting from preschool and continuing to high school, including modeling, logic, and geometry.
In elementary school, the numerical line covers various topics such as natural numbers, fractions, negative numbers, and rational numbers. Students also learn about number divisibility, prime and composite numbers, and the fundamental theorem of arithmetic.
Students explore the axiomatic method, congruences, and arithmetic of remainders.
Divisibility theory is emphasized for its aesthetic appeal and systematic review of properties, aiding in problem-solving skills for math competitions and Olympiads.
The course offers a comprehensive and progressive approach to math education, ensuring students are well-prepared for higher levels of mathematical study.
Algebraic Line
As part of the study of the algebraic line in the 5th and 6th grades, students learned to use symbolic notation to formulate and prove general statements. This enabled them to prove properties and criteria of divisibility, properties of proportions, and more. Students gained an understanding of numerical and symbolic expressions, their reading, writing, and the purpose of using variables. They found the values of symbolic expressions for given values of variables and performed transformations when solving equations. Thus, a solid foundation was laid for students to study the algebraic content of the 7th-grade curriculum.
Let's consider how the algebraic line develops in the 7th grade, highlighting the following directions:
In 7th grade, students dive into the world of algebra with a strong foundation that equips them with essential skills and knowledge. Let's explore some key topics covered in this grade:
Equivalent Expressions and Transformations:
Review and organize arithmetic laws
Create rules for equivalent manipulations
Apply rules to symbolic expressions
Operations on Polynomials:
Adding and subtracting polynomials
Multiplying monomials and polynomials
Multiplication Formulas:
Square of a sum and a difference
Difference of squares
Cube of a sum and a difference
Sum and difference of cubes
Factorization:
Finding common factors
Special formulas
Applying extra techniques
Exponentiation:
Understanding natural exponents
Performing operations with exponents
Exponentiation with rational numbers
Equations and Inequalities:
Solving equations through equivalent manipulations
Understanding linear equations
Grasping inequalities and their transformations
For advanced students, the curriculum offers opportunities to delve deeper into algebraic concepts, such as:
Pascal's Triangle:
Raising a binomial to an arbitrary natural power
Linear Equations in Two Variables:
Plotting graphs and finding solutions
Solving systems of equations using algebraic methods
Rational Equations:
Tackling quadratic and biquadratic equations
Exploring algebraic fractions and solving fractional-rational equations
By the end of the course, students will have a comprehensive understanding of algebraic manipulations, equations, and inequalities. With a solid grasp of these concepts, they will be well-prepared for more advanced mathematical challenges in the future.
Modeling Line
Most of the studied algorithms for solving equations and inequalities are applied by students when solving word problems. The particular feature of the course is that the motivation for studying a new type of equation (or inequality) arises from the need to solve practical problems.
In 7th grade, students use skills from grades 1-6 for problem-solving. They employ methods like diagrams and tables to apply mathematical modeling and refine their strategies. They learn to represent models with equations, inequalities, and relationships. These methods show how quantities in a problem are connected, whether directly or indirectly.
Functional Line
Let's consider how the functional line of the course develops in the 7th grade, highlighting the following directions:
By 7th grade, students learn about variables and graphs. They understand how variables link quantities and can be shown in formulas, tables, and graphs. They know about direct and inverse relationships and their graphs. In 6th grade, they see how quantities are connected. So, in 7th grade, they learn about functions. They see its importance for predicting events and coding. They also learn its name. A function, to them, is a rule that connects elements from two sets.
This method introduces new functions by looking at real problems. They start with direct proportionality, linear, and piecewise-linear functions. Studying piecewise linear functions in 7th grade builds on graph work, which began in 4th grade.
Each function studied is examined, its graph is constructed, and its properties are identified.
Logical line
Significant attention is devoted to developing the logical line in the course. In grades 5-6, students follow a logical path. They start with math language and move on to statements, proof, and methods. Next, come definitions, equivalent statements, and more. By 7th grade, they review these steps. They sharpen their definition skills and learn about proof by contradiction. Additionally, they explore logical reasoning with Euler-Venn diagrams. They also explore the reasons and types of logical errors.
Stochastic Line
Starting from the early school years, the stochastic line aims to develop information literacy among students. Seventh-grade students learn to gather and organize information. They then use this knowledge for practical tasks. Teachers encourage them to continue this in class and through projects. They might make presentations, problem sets, or brochures. Through this activity, students can develop computer skills necessary for learning in school and modern life.
In the 7th grade, students are also introduced to elements of combinatorics, statistics, and probability theory.
In the early grades and later in grades 5-7, students develop the experience of systematic exploration of possibilities using logical selection, tables, and decision trees. They use these methods to justify reasoning through exploration and solve tricky problems. As usual, the usefulness of constructing new mathematical tools is revealed through reflective analysis of practical problems. During the solution process, the inadequacy of existing exploration tools becomes apparent.
In the 7th grade, students encounter the issue of statistical characteristics of processes and become familiar with the following statistical measures: mean, mode, median, and range of a data set.
General Recommendations for Teachers
| Private Lessons | | | Group Lessons |
For a secondary school teacher who starts working with the 7th-grade materials, it is important to be familiar with the curriculum of the 5th and 6th grades for the same subject.
It's important to understand the materials for the 5th and 6th grades and the benchmarks from primary school.
Assessment System
In new lessons, self-study, and creative tasks, only success is measured. Mistakes are noted and corrected by looking at their causes, like insufficiently learned rules. Self-assessment happens in reflection lessons. Marks are given by the student.
Marks for tests are given to all students, with the difficulty level adjusted so that approximately 75% of the class can achieve grades A and B.
It should be noted that the goal of the course is not for every student to complete all the tasks in the course. The minimum required learning outcomes according to the curriculum are determined by educational standards.
Homework
Homework consists of two parts:
Considering the age characteristics of the students, it is recommended to involve them in selecting their homework assignments.
Students must do self-assessment, error correction, and marking in the notebooks. They can do this at the start of the lesson using a sample provided by the teacher. In this case, the teacher evaluates only the accuracy of the self-assessment. The additional part of the homework is recommended to be assessed individually. Only positive marks are given when evaluating these tasks.
Conclusion
L.G. Peterson's 7th-grade algebra course aims to build a strong math foundation for secondary students. It focuses on hands-on learning, boosting problem-solving and critical thinking. The topics include numbers, divisions, and algebra basics. Students work independently, solving practical problems and applying math to physics. This approach shows the value of math in real life. It also prepares them well for future math studies and careers.
| Private Lessons | | | Group Lessons |
