7年生の数学の授業の準備はできました!

Your learner is currently enrolled in a course that introduces the fundamental concepts of algebra. This course is designed to cater to students with diverse backgrounds and learning styles. It’s structured in a way that each new topic builds upon the material that has been previously covered. This approach is aimed at demonstrating the interconnectedness and structure of mathematics.

The students in this course, which includes Basic Mathematics and Pre-algebra, often present a unique set of challenges. Many of them have had difficulties in their previous math classes. This could be due to a misconception where they believe they have a good grasp of some mathematical concepts, while in reality, their foundational knowledge might have gaps.

In addition to the course content, these students also need to learn other essential skills such as study techniques, time management, and strategies to cope with math anxiety. These skills are crucial for their overall academic success and are a key focus in our teaching approach.

Addressing gaps in foundational knowledge is crucial for helping students succeed in algebra. Here are some strategies that I use and have found to be effective:

Diagnostic Assessments: Start with diagnostic tests to identify specific areas where students have gaps. This helps tailor instruction to their needs.

Scaffolded Learning: Break down complex concepts into smaller, more manageable parts. Use scaffolding techniques to gradually build up students’ understanding.

Differentiated Instruction: Adapt teaching methods to cater to different learning styles. Use a mix of visual aids, hands-on activities, and interactive lessons to engage all students.

Frequent Review and Practice: Regularly review previously covered material to reinforce learning. Incorporate practice problems that revisit foundational concepts.

Peer Tutoring and Group Work: Encourage collaborative learning through peer tutoring and group activities. This allows students to learn from each other and gain different perspectives.

Use of Technology: Integrate educational technology tools, such as math apps and online tutorials, to provide additional practice and interactive learning experiences.

Real-World Applications: Show how algebra is used in real-life situations to make the material more relevant and interesting. This can help students see the value in what they are learning.

Building Study Skills: Teach effective study habits, time management, and organizational skills. These are essential for academic success and can help students manage their workload better.

Addressing Math Anxiety: Create a supportive classroom environment where mistakes are seen as learning opportunities. Use positive reinforcement and stress-reduction techniques to help students feel more confident in their abilities.

Regular Feedback: Provide timely and constructive feedback on assignments and assessments. This helps students understand their progress and areas that need improvement.

By implementing these strategies, I have found that I can help students build a strong foundation in mathematics, making it easier for them to grasp more advanced algebraic concepts.

Coverage and Scope
Pre-algebra takes a distinctive and innovative approach to presenting its material. The course starts with a series of small, manageable steps, each carefully crafted to boost students’ confidence in their ability to succeed. The topics are arranged in a meticulously planned sequence that emphasizes the logical progression of concepts, ensuring that each new idea builds seamlessly on the previous ones. This thoughtful method allows students to develop a profound and comprehensive understanding of each concept as they advance through the course.

This approach offers several key benefits for students:

Boosts Confidence: By starting with small, manageable steps, students gain confidence in their abilities early on. This positive reinforcement encourages them to tackle more challenging concepts with a sense of achievement.

Logical Progression: The meticulously planned sequence of topics ensures that each new concept builds on the previous one. This logical flow helps students see the connections between ideas, making it easier to understand and remember the material.

Deep Understanding: By focusing on a thorough understanding of each concept before moving on, students develop a solid foundation. This depth of knowledge is crucial for mastering more advanced topics later on.

Reduces Overwhelm: Breaking down the material into smaller steps prevents students from feeling overwhelmed. This gradual approach makes learning more manageable and less intimidating.

Encourages Critical Thinking: As students progress through the course, they are encouraged to think critically about how each concept fits into the larger picture. This fosters analytical skills and a deeper appreciation for the subject.

Individualized Learning: This method allows for adjustments based on individual student needs. Teachers can identify and address gaps in foundational knowledge, ensuring that each student progresses at their own pace.

Overall, this approach creates a supportive and effective learning environment that helps students build confidence, understand concepts deeply, and develop critical thinking skills.

Chapter 1: Whole Numbers
Each of the four basic operations with whole numbers—addition, subtraction, multiplication, and division—is thoroughly modeled and explained. As we cover each operation, we also discuss algebraic notation and operation signs, translate algebraic expressions into word phrases, and explore practical applications of these operations.
Lesson 1 Part 1.1 Place Value and Rounding and Absolute Value
Lesson 2 Part 1.2 Numbers
Lesson 3 Part 1.3 Factoring
Lesson 4 Part 1.4 Exponents
Lesson 5 Part 1.5 Multiplying and Dividing by Powers of 10
Lesson 6 Part 1.6 Order of Operations
Lesson 7 Part 1.7 Greatest Common Factor
Lesson 8 Chapter 1 Review A Quiz
Lesson 9 Part 1.8 Least Common Multiple
Lesson 10 Part 1.9 Fraction Basics
Lesson 11 Part 1.10 Fraction Arithmetic
Lesson 12 Part 1.11 Decimal Equivalents of Fractions
Lesson 13 Part 1.12 Ratios
Lesson 14 Chapter 1 Review B Test

Chapter 2: Percents
Conversions between percents, fractions, and decimals are thoroughly explored. Practical applications of percents include calculating sales tax, commission, and simple interest. Additionally, the course covers proportions and solving percent equations using proportions.
Lesson 15 Part 2.1 Percent Basics
Lesson 16 Part 2.2 Percent with Fractions
Lesson 17 Part 2.3 Percentage
Lesson 18 Part 2.4 Finding Discounts
Lesson 19 Chapter 2 Review A Quiz
Lesson 20 Part 2.5 More or Less in Percent
Lesson 21 Part 2.6 Finding Percent
Lesson 22 Part 2.7 Finding the Percent of Change
Lesson 23 Part 2.8 Finding the Base
Lesson 24 Chapter 2 Review B Test 


Chapter 3: The Language of Signed Numbers and Algebra
Mathematical Vocabulary for Whole Numbers:
This section introduces essential terms related to whole numbers.
It covers concepts like addition, subtraction, multiplication, and division using whole numbers.
Variables in Algebra:
Algebra distinguishes itself from arithmetic by incorporating variables.
Variables represent unknown quantities and allow us to generalize mathematical relationships.
Arithmetic Concepts with Variables:
The chapter explores arithmetic concepts using both numeric expressions and variables.
Students practice calculations involving variables alongside regular numbers.
Expressions vs. Equations:
The difference between mathematical expressions (which don’t have an equal sign) and equations (which do) is explained.
Expressions describe relationships, while equations represent balance or equality.
Word Problems and Modeling:
Word problems are introduced, emphasizing real-world applications of math.
Students learn to translate verbal descriptions into mathematical expressions or equations.
Solving One-Step Equations:
The process for solving one-step equations is modeled.
Students learn to isolate the variable and find its value.
Lesson 25 Part 3.1 Properties of Arithmetic
Lesson 26 Part 3.2 Signed Numbers and the Number Line
Lesson 27 Part 3.3 Adding and Subtracting Signed Numbers 
Lesson 28 Chapter 3 Review A Quiz
Lesson 29 Part 3.4 Multiplying Signed Numbers
Lesson 30 Part 3.5 Dividing Signed Numbers 
Lesson 31 Part 3.6 Sequences
Lesson 32 Chapter 3 Review B Test
Lesson 33 Part 3.7 Introduction to Algebra
Lesson 38 Part 3.8 Algebraic Evaluation and Translation
Lesson 39 Chapter 3 Review C and Quarter 1 Test


Chapter 4: Geometry
The chapter begins with opportunities to solve “traditional” number, coin, and mixture problems. Geometry sections cover the properties of triangles, rectangles, trapezoids, circles, irregular figures, the Pythagorean
Theorem, and volume and surface areas of solids. Distance-rate-time problems and formulas are included as well.
Lesson 40 Part 4.1 Introduction to Geometry
Lesson 41 Part 4.2 Polygons
Lesson 42 Part 4.3 Perimeter
Lesson 43 Part 4.4 Angles
Lesson 44 Chapter 4 A Review Quiz
Lesson 45 Part 4.5 Triangles
Lesson 46 Part 4.6 Circles

Chapter 3: Integers
While introducing the basic operations with negative numbers, students continue to practice simplifying,
evaluating, and translating algebraic expressions. The Division Property of Equality is introduced and used to solve one-step equations.
Lesson 4 Friday, December 8, 2023 Part 3.1 Introduction to Integers
 Part 3.2 Add Integers
 Part 3.3 Subtract Integers

Lesson 5 Friday, December 15, 2023 Part 3.4 Multiply and Divide Integers
Part 3.5 Solve Equations Using Integers; Division Property of 
Equality

Chapter 4: Fractions
Fraction circles and bars are used to help make fractions real and to develop operations on them. Students
continue simplifying and evaluating algebraic expressions with fractions, and learn to use the Multiplication
Property of Equality to solve equations involving fractions.
Lesson 6 Friday, January 5, 2024 Part 4.1 Visualize Fractions
Part 4.2 Multiply and Divide Fractions

Lesson 7 Friday, January 12, 2024 Part 4.3 Multiply and Divide Mixed Numbers and Complex Fractions

Lesson 8 Friday, January 19, 2024 Part 4.4 Add and Subtract Fractions with Common Denominators
Part 4.5 Add and Subtract Fractions with Different Denominators
Part 4.6 Add and Subtract Mixed Numbers

Lesson 9 Friday, January 26, 2024 Part 4.7 Solve Equations with Fractions

Chapter 5: Decimals
Basic operations with decimals are presented, as well as methods for converting fractions to decimals and vice versa. Averages and probability, unit rates and unit prices, and square roots are included to provide opportunities to use and round decimals.
Lesson 10 Friday, February 2, 2024 Part 5.1 Decimals
Part 5.2 Decimal Operations
Part 5.3 Decimals and Fractions

Lesson 11 Friday, February 9, 2024 Part 5.4 Solve Equations with Decimals

Lesson 12 Friday, February 16, 2024 Part 5.5 Averages and Probability
Part 5.6 Ratios and Rate

Lesson 13 Friday, February 23, 2024 Part 5.7 Simplify and Use Square Roots



Lesson 15 Friday, March 8, 2024 6.4 Solve Simple Interest Applications

Lesson 16 Friday, March 15, 2024 6.5 Solve Proportions and their Applications

Chapter 7: The Properties of Real Numbers
The properties of real numbers are introduced and applied as a culmination of the work done thus far, and to prepare students for the upcoming chapters on equations, polynomials, and graphing.
Lesson 17 Friday, March 22, 2024 7.1 Rational and Irrational Numbers

Lesson 18 Friday, March 29, 2024 7.2 Commutative and Associative Properties
7.3 Distributive Property
7.4 Properties of Identity, Inverses, and Zero

Lesson 19 Friday, April 5, 2024 7.5 Systems of Measurement

Chapter 8: Solving Linear Equations
A gradual build-up to solving multi-step equations is presented. Problems involve solving equations with
constants on both sides, variables on both sides, variables and constants on both sides, and fraction and decimal coefficients.

Lesson 20 Friday, April 12, 2024 Part 8.1 Solve Equations Using the Subtraction and Addition Properties of Equality
Part 8.2 Solve Equations Using the Division and Multiplication Properties of Equality
Part 8.3 Solve Equations with Variable and Constants on Both Sides

Lesson 21 Friday, April 19, 2024 Part 8.4 Solve Equations with Fraction or Decimal Coefficients


Chapter 9: Graphs
This chapter is placed last so that all of the algebra with one variable is completed before working with linear equations in two variables. Examples progress from plotting points to graphing lines by making a table of solutions to an equation. Properties of vertical and horizontal lines and intercepts are included. Graphing linear equations at the end of the course gives students a good opportunity to review evaluating expressions and solving equations
Lesson 31 Part 9.1 Intro to Graphing
Lesson 32 Part 9.2 Translations
Lesson 33 Part 9.3 Slope
Lesson 34 Part 9.4 Linear Equations
Lesson 35 Part 9.5 Direct Variation
Lesson 36 Chapter 9 Review Test

Chapter 10: Polynomial Math and Radicals
Adding and subtracting polynomials is presented as an extension of prior work on combining like terms. Integer exponents are defined and then applied to scientific notation. The chapter concludes with a brief introduction to factoring polynomials.
Lesson 26 Part 10.1 Add and Subtract Polynomials Like Terms
Lesson 27 Part 10.2 Use Multiplication Properties of Like Terms
Lesson 28 Part 10.3 Scientific Notation
Lesson 29 Part 10.4 Multiply Polynomials
                  Part 10.4 Divide Monomials
Lesson 30 Part 10.5 Multiplying Polynomials
Lesson 31 Part 10.6 Dividing Polynomials
Lesson 32 Part 10.7 Factoring Polynomials
Lesson 33 Part 10.8 Introduction to Radicals