Introduction to Algebra 1 in 7th Grade BYOM | Russian Math Tutors
EN - USD

#### Write For Us

We are constantly looking for writers and contributors to help us create great content for our blog visitors.

BYOM Program

# Introduction to Algebra in 7th Grade BYOM

2023-05-26 |    0

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.

### Overview of the Course

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.

### Teaching Methodology

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.

### Approach to Learning

• 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.

### Problem-Solving Approach

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.

### Course Content

• 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.

### Numerical Line

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.

### Conclusion

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:

1. Performing equivalent manipulations on expressions.
2. Understanding the concept of exponentiation and applying its properties.
3. Solving equations.
4. Solving inequalities.

## Algebraic Foundations in 7th Grade

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:

• 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:

• 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:

• The concept of a function;
• Types of functions studied;
• Properties of functions studied;
• Numerical sequences as functions of a natural argument;

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:

1. The mandatory part includes 2-3 manageable tasks for each student and requires approximately 30 minutes of independent work.

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.