What Do You Learn In 8th Grade Math? Eighth grade math builds upon previous knowledge, introducing more complex concepts like algebra, geometry, and data analysis; at LEARNS.EDU.VN, we provide comprehensive resources to ensure students master these critical skills and prepare for future math success. Through structured lessons, practice problems, and real-world applications, students gain a deeper understanding of mathematical principles, fostering both confidence and proficiency, ultimately enhancing their analytical capabilities and problem-solving skills.
1. Understanding the Core Areas of 8th Grade Math
What do you learn in 8th grade math regarding its core components? In 8th grade math, students delve into essential areas such as number systems, algebra, geometry, and data analysis. A strong foundation in these areas ensures success in higher-level math courses, developing analytical and problem-solving skills crucial for academic and real-world applications.
1.1. Mastering Number Systems
What do you learn in 8th grade math about number systems? The study of number systems in 8th grade math involves understanding rational and irrational numbers, scientific notation, and absolute value. These concepts are fundamental for more advanced math topics, providing students with a deeper understanding of how numbers work and relate to one another.
1.1.1. Rational and Irrational Numbers
What do you learn in 8th grade math regarding rational and irrational numbers? Rational numbers can be expressed as a fraction, while irrational numbers cannot. Understanding the difference between these types of numbers is essential for performing operations and solving equations accurately.
Rational numbers include integers, fractions, and terminating or repeating decimals. Examples of rational numbers are:
- 2 (which can be written as 2/1)
- -3/4
- 0.5 (which can be written as 1/2)
- 0.333… (which can be written as 1/3)
Irrational numbers, on the other hand, are numbers that cannot be expressed as a simple fraction. They have non-repeating, non-terminating decimal expansions. Common examples include:
- √2 (square root of 2) ≈ 1.41421356…
- π (pi) ≈ 3.14159265…
- e (Euler’s number) ≈ 2.71828182…
LEARNS.EDU.VN offers detailed modules that break down the properties of rational and irrational numbers, providing examples and practice problems to solidify understanding. This knowledge forms the base for tackling more complex algebraic and geometric problems.
1.1.2. Scientific Notation
What do you learn in 8th grade math regarding scientific notation? Scientific notation is a way to express very large or very small numbers in a more manageable form. It is written as a × 10^b, where a is a number between 1 and 10, and b is an integer.
For example:
- 5,000,000 can be written as 5 × 10^6
- 0.00004 can be written as 4 × 10^-5
Scientific notation is particularly useful in scientific and engineering fields where dealing with extremely large or small numbers is common. LEARNS.EDU.VN provides interactive exercises and real-world examples to help students master this essential skill.
1.1.3. Absolute Value
What do you learn in 8th grade math about absolute value? The absolute value of a number is its distance from zero on the number line, regardless of direction. It is denoted by |x|, where x is the number.
For example:
- |5| = 5
- |-5| = 5
Understanding absolute value is crucial for solving equations and inequalities involving distance and magnitude. At LEARNS.EDU.VN, students will find clear explanations and practice problems that reinforce the concept of absolute value and its applications.
1.2. Algebra: Building Foundations
What do you learn in 8th grade math about algebra? Algebra in 8th grade math introduces students to solving linear equations, understanding systems of equations, and working with expressions and variables. These skills are crucial for higher-level math courses and provide a foundation for problem-solving in various contexts.
1.2.1. Solving Linear Equations
What do you learn in 8th grade math regarding solving linear equations? Solving linear equations involves finding the value of a variable that makes the equation true. This requires understanding operations like addition, subtraction, multiplication, and division and applying them to isolate the variable.
For example, to solve the equation 2x + 3 = 7:
- Subtract 3 from both sides: 2x = 4
- Divide both sides by 2: x = 2
LEARNS.EDU.VN offers step-by-step guides and practice problems to help students become proficient in solving linear equations. Understanding this concept is essential for tackling more complex algebraic problems.
1.2.2. Systems of Equations
What do you learn in 8th grade math about systems of equations? Systems of equations involve solving two or more equations simultaneously to find the values of the variables that satisfy all equations. Common methods for solving systems of equations include substitution and elimination.
For example, consider the following system of equations:
- x + y = 5
- 2x – y = 1
Using the substitution method, we can solve the first equation for x: x = 5 – y
Substitute this expression for x into the second equation:
2(5 – y) – y = 1
10 – 2y – y = 1
10 – 3y = 1
-3y = -9
y = 3
Now, substitute y = 3 back into the first equation:
x + 3 = 5
x = 2
Thus, the solution to the system of equations is x = 2 and y = 3.
LEARNS.EDU.VN provides detailed explanations and practice exercises to help students master the methods for solving systems of equations.
1.2.3. Expressions and Variables
What do you learn in 8th grade math regarding expressions and variables? Algebraic expressions are combinations of variables, constants, and operations. Variables are symbols (usually letters) that represent unknown values. Learning to simplify and evaluate expressions is crucial for solving algebraic equations.
For example, simplifying the expression 3x + 2y – x + 4y involves combining like terms:
3x – x + 2y + 4y = 2x + 6y
Evaluating the expression 2x + 6y when x = 2 and y = 3:
2(2) + 6(3) = 4 + 18 = 22
LEARNS.EDU.VN offers comprehensive modules that cover simplifying and evaluating algebraic expressions, providing students with a solid foundation in algebraic manipulation.
1.3. Geometry: Exploring Shapes and Spaces
What do you learn in 8th grade math about geometry? In 8th grade math, geometry focuses on understanding geometric properties, transformations, and the Pythagorean theorem. These concepts are crucial for developing spatial reasoning skills and understanding the relationships between shapes and spaces.
1.3.1. Geometric Properties
What do you learn in 8th grade math regarding geometric properties? Geometric properties include understanding parallelism, perpendicularity, and symmetry. These properties are essential for analyzing and solving problems involving geometric figures.
For example:
- Parallel lines never intersect and have the same slope.
- Perpendicular lines intersect at a 90-degree angle and have slopes that are negative reciprocals of each other.
- Symmetry refers to the property of a figure that remains unchanged under certain transformations like reflection or rotation.
LEARNS.EDU.VN offers interactive lessons and visual aids to help students understand and apply these geometric properties effectively.
1.3.2. Transformations
What do you learn in 8th grade math about transformations? Transformations involve changing the position or size of a geometric figure. Common types of transformations include reflection, translation, rotation, and dilation.
- Reflection: Flipping a figure over a line.
- Translation: Sliding a figure without changing its orientation.
- Rotation: Turning a figure around a fixed point.
- Dilation: Enlarging or reducing the size of a figure.
Understanding transformations helps students visualize and analyze how geometric figures can be manipulated in space. LEARNS.EDU.VN provides interactive tools that allow students to perform and analyze different transformations.
1.3.3. Pythagorean Theorem
What do you learn in 8th grade math regarding the Pythagorean Theorem? The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This is expressed as a^2 + b^2 = c^2, where a and b are the lengths of the legs, and c is the length of the hypotenuse.
The Pythagorean Theorem is used to find unknown side lengths in right triangles and has numerous applications in fields like engineering and architecture. LEARNS.EDU.VN offers detailed explanations and practice problems to help students master the Pythagorean Theorem and its applications.
1.4. Data Analysis: Interpreting Information
What do you learn in 8th grade math about data analysis? Data analysis in 8th grade math involves understanding sampling techniques, interpreting data representations, and calculating measures of central tendency. These skills are essential for making informed decisions based on data and understanding statistical concepts.
1.4.1. Sampling Techniques
What do you learn in 8th grade math regarding sampling techniques? Sampling techniques are methods used to select a subset of individuals from a larger population to estimate characteristics of the whole population. Different types of sampling techniques include random sampling, stratified sampling, and convenience sampling.
- Random sampling: Each member of the population has an equal chance of being selected.
- Stratified sampling: The population is divided into subgroups (strata), and random samples are taken from each subgroup.
- Convenience sampling: Selecting individuals who are easily accessible.
Understanding sampling techniques helps students collect and analyze data more effectively. LEARNS.EDU.VN provides resources that explain the pros and cons of different sampling methods and how to avoid bias.
1.4.2. Data Representations
What do you learn in 8th grade math regarding data representation? Data representations include various types of graphs and charts, such as circle graphs, line graphs, bar graphs, histograms, and box-and-whisker plots. Each type of representation is useful for displaying data in different ways and highlighting different aspects of the data.
- Circle graphs (pie charts): Show proportions of a whole.
- Line graphs: Show trends over time.
- Bar graphs: Compare quantities across different categories.
- Histograms: Show the distribution of numerical data.
- Box-and-whisker plots: Display the median, quartiles, and outliers of a dataset.
LEARNS.EDU.VN offers interactive modules that teach students how to interpret and create different types of data representations effectively.
1.4.3. Measures of Central Tendency
What do you learn in 8th grade math about measures of central tendency? Measures of central tendency include the mean, median, and mode, which are used to describe the typical value in a dataset.
- Mean: The average of all the values in the dataset.
- Median: The middle value when the data is arranged in order.
- Mode: The value that appears most frequently in the dataset.
Choosing the appropriate measure of central tendency depends on the nature of the data and the presence of outliers. LEARNS.EDU.VN provides practice problems and real-world scenarios to help students understand and apply these measures effectively.
2. Detailed 8th Grade Math Curriculum Breakdown
What do you learn in 8th grade math, specifically in each chapter? An 8th grade math curriculum typically covers topics from number systems to geometry and data analysis. Understanding the detailed breakdown ensures comprehensive learning and better preparation for advanced math courses.
2.1. Chapter 1: Number Systems
What do you learn in 8th grade math in Chapter 1? In Chapter 1, students learn about expressing numbers in scientific notation, identifying rational and irrational numbers, and understanding absolute value. These concepts are foundational for more advanced topics.
2.1.1. Lesson 1: Scientific Notation
What do you learn in 8th grade math about scientific notation? Students learn to express numbers between zero and one in scientific notation. This skill is crucial for handling very large and very small numbers efficiently.
For example, expressing 0.000075 in scientific notation involves moving the decimal point five places to the right, resulting in 7.5 × 10^-5. LEARNS.EDU.VN provides interactive exercises to practice converting numbers into scientific notation.
2.1.2. Lesson 2: Rational and Irrational Numbers
What do you learn in 8th grade math about rational and irrational numbers? This lesson focuses on identifying and describing rational and irrational numbers. Understanding the distinction is crucial for performing accurate calculations and solving equations.
Rational numbers can be expressed as a fraction, while irrational numbers cannot. Examples of rational numbers include 2, -3/4, and 0.5. Irrational numbers include √2, π, and e. LEARNS.EDU.VN offers modules that thoroughly explain the properties of each type of number.
2.1.3. Lesson 3: Absolute Value
What do you learn in 8th grade math about absolute value? Students learn to identify and explain absolute value, which is the distance of a number from zero on the number line.
For example, the absolute value of -7 is 7, denoted as |-7| = 7. Understanding absolute value is important for solving equations and inequalities involving distance. LEARNS.EDU.VN offers practice problems to reinforce this concept.
2.2. Chapter 2: Comparing Numbers with and Operations in Scientific Notation
What do you learn in 8th grade math in Chapter 2? Chapter 2 covers comparing large and small numbers in scientific notation, adding and subtracting numbers in scientific notation, and using scientific notation with technology.
2.2.1. Lesson 1: Comparing Large Numbers in Scientific Notation
What do you learn in 8th grade math regarding comparing large numbers in scientific notation? Students learn to compare large numbers expressed in scientific notation by comparing their exponents and coefficients.
For example, to compare 3 × 10^8 and 5 × 10^6, compare the exponents first. Since 8 is greater than 6, 3 × 10^8 is larger. LEARNS.EDU.VN provides comparison exercises to help students master this skill.
2.2.2. Lesson 2: Comparing Small Numbers in Scientific Notation
What do you learn in 8th grade math about comparing small numbers in scientific notation? This lesson teaches students how to compare small numbers in scientific notation by comparing their exponents and coefficients.
For example, to compare 2 × 10^-5 and 8 × 10^-7, compare the exponents. Since -5 is greater than -7, 2 × 10^-5 is larger. LEARNS.EDU.VN offers detailed modules to practice this comparison.
2.2.3. Lesson 3: Adding and Subtracting Numbers in Scientific Notation
What do you learn in 8th grade math about adding and subtracting numbers in scientific notation? Students learn to add and subtract numbers in scientific notation by ensuring they have the same exponent, then adding or subtracting the coefficients.
For example, to add 2 × 10^4 and 3 × 10^4, add the coefficients: (2 + 3) × 10^4 = 5 × 10^4. If the exponents are different, adjust the numbers to have the same exponent before adding. LEARNS.EDU.VN offers step-by-step guides for these operations.
2.2.4. Lesson 4: Using Scientific Notation with Technology
What do you learn in 8th grade math about using scientific notation with technology? This lesson covers using calculators and other technological tools to perform calculations with numbers in scientific notation.
Calculators can handle scientific notation using the EE or EXP button. Students learn to input and interpret results in scientific notation. LEARNS.EDU.VN provides tutorials on using technology for scientific notation.
2.3. Chapter 3: Real Numbers
What do you learn in 8th grade math in Chapter 3? In Chapter 3, students learn to convert repeating decimals to fractions, work with roots, solve equations using roots, and compare and order real numbers.
2.3.1. Lesson 1: Repeating Decimals to Fractions
What do you learn in 8th grade math regarding converting repeating decimals to fractions? Students learn to convert repeating decimals into fractions using algebraic methods.
For example, to convert 0.333… to a fraction:
- Let x = 0.333…
- 10x = 3.333…
- Subtract the first equation from the second: 9x = 3
- Solve for x: x = 3/9 = 1/3
LEARNS.EDU.VN offers detailed explanations and practice problems to master this conversion.
2.3.2. Lesson 2: Roots
What do you learn in 8th grade math about roots? This lesson focuses on calculating and approximating principal square roots. Understanding roots is crucial for solving algebraic equations and simplifying expressions.
For example, the principal square root of 25 is 5, denoted as √25 = 5. LEARNS.EDU.VN provides exercises to practice finding square roots.
2.3.3. Lesson 3: Using Roots to Solve Equations
What do you learn in 8th grade math about using roots to solve equations? Students learn to use roots to solve equations involving squares and other powers.
For example, to solve the equation x^2 = 16, take the square root of both sides: x = ±4. LEARNS.EDU.VN offers step-by-step guides for solving equations using roots.
2.3.4. Lesson 4: Compare and Order
What do you learn in 8th grade math about comparing and ordering real numbers? This lesson covers comparing and ordering numbers in various forms, including fractions, decimals, scientific notation, absolute value, and radicals.
For example, to compare 1/2, 0.6, √0.25, and |−0.4|:
- Convert all numbers to decimal form: 0.5, 0.6, 0.5, 0.4
- Order the numbers: 0.4, 0.5, 0.5, 0.6
LEARNS.EDU.VN provides exercises to practice comparing and ordering real numbers.
2.3.5. Lesson 5: Estimation
What do you learn in 8th grade math about estimation? Students learn to use estimation for situations involving real numbers. This skill is useful for checking the reasonableness of answers and making quick approximations.
For example, estimating the value of √50: Since √49 = 7 and √64 = 8, √50 is approximately 7.1. LEARNS.EDU.VN offers practice problems to enhance estimation skills.
2.3.6. Lesson 6: Properties
What do you learn in 8th grade math about properties? This lesson focuses on applying properties such as the commutative, associative, and distributive properties to solve problems with real numbers.
For example, using the distributive property: 2(x + 3) = 2x + 6. LEARNS.EDU.VN provides modules explaining these properties in detail.
2.3.7. Lesson 7: Real Number Operations
What do you learn in 8th grade math about real number operations? Students learn to simplify numerical expressions with real numbers, including addition, subtraction, multiplication, and division.
For example, simplifying the expression 3 + 2 × (5 – 1):
- Perform the operation inside the parentheses: 5 – 1 = 4
- Multiply: 2 × 4 = 8
- Add: 3 + 8 = 11
LEARNS.EDU.VN offers practice problems to master real number operations.
2.4. Chapter 4: Number Theory
What do you learn in 8th grade math in Chapter 4? Chapter 4 covers divisibility rules, representing numbers in different bases, and identifying prime and composite numbers.
2.4.1. Lesson 1: Divisibility Rules
What do you learn in 8th grade math regarding divisibility rules? Students learn to use divisibility rules to solve problems. Divisibility rules are shortcuts to determine whether a number is divisible by another number without performing division.
For example:
- A number is divisible by 2 if its last digit is even.
- A number is divisible by 3 if the sum of its digits is divisible by 3.
- A number is divisible by 5 if its last digit is 0 or 5.
LEARNS.EDU.VN provides resources that explain and illustrate these rules.
2.4.2. Lesson 2: Multiple Representations
What do you learn in 8th grade math regarding multiple representations? This lesson focuses on representing numbers in base ten in other bases (two, five, and eight) and vice versa.
For example, converting the base-ten number 10 to base two:
- 10 ÷ 2 = 5 remainder 0
- 5 ÷ 2 = 2 remainder 1
- 2 ÷ 2 = 1 remainder 0
- 1 ÷ 2 = 0 remainder 1
- Reading the remainders in reverse order: 1010 (base two)
LEARNS.EDU.VN offers exercises to practice number base conversions.
2.4.3. Lesson 3: Prime and Composite
What do you learn in 8th grade math about prime and composite numbers? Students learn to identify numbers as relatively prime. Prime numbers have only two factors: 1 and themselves, while composite numbers have more than two factors.
For example, 7 is a prime number, while 12 is a composite number (factors: 1, 2, 3, 4, 6, 12). LEARNS.EDU.VN provides modules on identifying prime and composite numbers.
2.5. Chapter 5: Ratio, Proportion, and Percent
What do you learn in 8th grade math in Chapter 5? Chapter 5 covers rate of change, proportions, solving percent problems, and comparing proportional relationships.
2.5.1. Lesson 1: Rate of Change
What do you learn in 8th grade math about rate of change? Students learn to describe and use rate of change to solve problems. Rate of change is the ratio of the change in one quantity to the change in another.
For example, if the temperature increases from 20°C to 30°C in 2 hours, the rate of change is (30 – 20) / 2 = 5°C per hour. LEARNS.EDU.VN provides practice problems to calculate rate of change.
2.5.2. Lesson 2: Proportions
What do you learn in 8th grade math about proportions? This lesson focuses on using proportional relationships to find measures of length, weight or mass, and capacity or volume.
For example, if 2 apples cost $1, then 6 apples will cost $3, using the proportion 2/1 = 6/x. LEARNS.EDU.VN offers exercises to solve proportional problems.
2.5.3. Lesson 3: Percents
What do you learn in 8th grade math about percents? Students learn to solve real-world problems involving percents greater than 100.
For example, if a store marks up an item by 150%, and the original price is $20, the new price is $20 + (1.50 × $20) = $50. LEARNS.EDU.VN provides practice problems for solving percent problems.
2.5.4. Lesson 4: Comparing Two Proportional Relationships
What do you learn in 8th grade math regarding comparing two proportional relationships? Students learn to compare two proportional relationships represented in different ways, such as tables, graphs, and equations.
For example, comparing two lines on a graph to determine which has a greater slope. LEARNS.EDU.VN offers modules on comparing proportional relationships.
2.6. Chapter 6: Real World Computation
What do you learn in 8th grade math in Chapter 6? Chapter 6 covers solving real-world problems with rational numbers, ratios, rates, proportions, and percents, including multi-step problems.
2.6.1. Lesson 1: Operations
What do you learn in 8th grade math about operations? Students learn to solve real-world problems with rational numbers, including integers, decimals, and fractions.
For example, calculating the total cost of items with different prices and quantities. LEARNS.EDU.VN provides practice problems involving real-world scenarios.
2.6.2. Lesson 2: Real World Problems
What do you learn in 8th grade math about real-world problems? This lesson focuses on solving real-world problems with ratios, rates, proportions, and percents.
For example, determining the sale price of an item after a percentage discount. LEARNS.EDU.VN offers exercises to solve these types of problems.
2.6.3. Lesson 3: Multi-Step Problems
What do you learn in 8th grade math about multi-step problems? Students learn to solve real-world two- or three-step problems with integers, decimals, fractions, ratios, rates, proportions, and percents.
For example, calculating the final price of an item after a discount and sales tax. LEARNS.EDU.VN provides step-by-step solutions for multi-step problems.
2.7. Chapter 7: Expressions and Equations
What do you learn in 8th grade math in Chapter 7? Chapter 7 covers substituting rational numbers into expressions, translating word expressions into algebraic expressions, and simplifying and evaluating algebraic expressions.
2.7.1. Lesson 1: Expressions
What do you learn in 8th grade math about expressions? Students learn to substitute rational numbers into expressions and evaluate them.
For example, evaluating the expression 2x + 3 when x = 4: 2(4) + 3 = 11. LEARNS.EDU.VN offers practice problems for evaluating expressions.
2.7.2. Lesson 2: Expressions with Exponents
What do you learn in 8th grade math about expressions with exponents? This lesson focuses on substituting rational numbers into expressions with exponents and radicals.
For example, evaluating the expression x^2 + √y when x = 3 and y = 16: (3)^2 + √16 = 9 + 4 = 13. LEARNS.EDU.VN provides exercises involving exponents and radicals.
2.7.3. Lesson 3: Expressions and Equations
What do you learn in 8th grade math about expressions and equations? Students learn to translate word expressions and equations into algebraic expressions and equations, including those with one or more variables and exponents.
For example, translating “five more than twice a number” into the expression 2x + 5. LEARNS.EDU.VN offers modules on translating word problems.
2.7.4. Lesson 4: Expressions, Equations, and Inequalities
What do you learn in 8th grade math about expressions, equations, and inequalities? This lesson covers translating verbal expressions and sentences into algebraic inequalities and vice versa.
For example, translating “a number is less than 10” into the inequality x < 10. LEARNS.EDU.VN provides exercises involving inequalities.
2.7.5. Lesson 5: Real World Expressions
What do you learn in 8th grade math about real-world expressions? Students learn to use variables to represent unknown quantities in real-world situations.
For example, representing the cost of buying n notebooks at $2 each as 2n. LEARNS.EDU.VN offers modules on real-world applications of expressions.
2.7.6. Lesson 6: Simplify
What do you learn in 8th grade math about simplifying expressions? This lesson focuses on combining and simplifying algebraic expressions with a maximum of two variables.
For example, simplifying the expression 3x + 2y – x + 4y: 2x + 6y. LEARNS.EDU.VN provides practice problems for simplifying expressions.
2.7.7. Lesson 7: Substitution
What do you learn in 8th grade math regarding substitution? Students learn to evaluate algebraic expressions and equations by substituting integral values for variables and simplifying.
For example, evaluating the expression 2x + 3y when x = 2 and y = 3: 2(2) + 3(3) = 4 + 9 = 13. LEARNS.EDU.VN offers exercises involving substitution.
2.7.8. Lesson 8: Inequalities
What do you learn in 8th grade math regarding inequalities? Students learn to solve linear inequalities in one variable algebraically.
For example, solving the inequality 2x + 3 < 7:
- Subtract 3 from both sides: 2x < 4
- Divide both sides by 2: x < 2
LEARNS.EDU.VN provides step-by-step guides for solving inequalities.
2.8. Chapter 8: Identifying Solutions and Solving Equations
What do you learn in 8th grade math in Chapter 8? Chapter 8 covers identifying the number of solutions in a linear equation and solving equations with variables on both sides, requiring the distributive property or combining like terms.
2.8.1. Lesson 1: Identifying the Number of Solutions in a Linear Equation
What do you learn in 8th grade math about identifying the number of solutions in a linear equation? Students learn to identify whether a linear equation has one solution, no solution, or infinitely many solutions.
For example:
- 2x + 3 = 7 has one solution (x = 2).
- 2x + 3 = 2x + 5 has no solution.
- 2x + 3 = 2x + 3 has infinitely many solutions.
LEARNS.EDU.VN provides modules that explain how to determine the number of solutions.
2.8.2. Lesson 2: Solving Equations with Variables on Both Sides
What do you learn in 8th grade math about solving equations with variables on both sides? This lesson focuses on solving equations where the variable appears on both sides of the equation.
For example, solving the equation 3x + 5 = x + 9:
- Subtract x from both sides: 2x + 5 = 9
- Subtract 5 from both sides: 2x = 4
- Divide both sides by 2: x = 2
LEARNS.EDU.VN offers step-by-step guides for solving these types of equations.
2.8.3. Lesson 3: Solving Equations Requiring the Distributive Property
What do you learn in 8th grade math about solving equations requiring the distributive property? Students learn to solve equations that require using the distributive property to eliminate parentheses.
For example, solving the equation 2(x + 3) = 10:
- Distribute the 2: 2x + 6 = 10
- Subtract 6 from both sides: 2x = 4
- Divide both sides by 2: x = 2
LEARNS.EDU.VN provides exercises to practice using the distributive property.
2.8.4. Lesson 4: Solving Equations Requiring Combining Like Terms
What do you learn in 8th grade math about solving equations requiring combining like terms? This lesson focuses on solving equations that require combining like terms before solving for the variable.
For example, solving the equation 3x + 2x + 5 = 15:
- Combine like terms: 5x + 5 = 15
- Subtract 5 from both sides: 5x = 10
- Divide both sides by 5: x = 2
LEARNS.EDU.VN offers modules on combining like terms in equations.
2.9. Chapter 9: Systems of Equations
What do you learn in 8th grade math in Chapter 9? Chapter 9 covers analyzing systems of equations and identifying the number of solutions in a linear equation.
2.9.1. Lesson 1: Analyzing Systems of Equations
What do you learn in 8th grade math about analyzing systems of equations? Students learn to analyze systems of equations to determine whether they have one solution, no solution, or infinitely many solutions.
For example:
- x + y = 5 and x – y = 1 has one solution.
- x + y = 5 and 2x + 2y = 10 has infinitely many solutions.
- x + y = 5 and x + y = 10 has no solution.
LEARNS.EDU.VN provides modules on analyzing systems of equations.
2.9.2. Lesson 2: Identifying the Number of Solutions in a Linear Equation
What do you learn in 8th grade math about identifying the number of solutions in a linear equation? This lesson focuses on determining the number of solutions a system of equations has based on its properties.
For example, parallel lines have no solution, intersecting lines have one solution, and coinciding lines have infinitely many solutions. LEARNS.EDU.VN offers exercises to practice identifying the number of solutions.
2.10. Chapter 10: Plane Geometry
What do you learn in 8th grade math in Chapter 10? Chapter 10 covers geometric properties, polygons, the Pythagorean theorem, congruence and similarity, and transformations.
2.10.1. Lesson 1: Geometric Properties
What do you learn in 8th grade math about geometric properties? Students learn to use properties of parallelism, perpendicularity, and symmetry to solve real-world problems.
For example, determining if two lines are parallel based on their slopes. LEARNS.EDU.VN provides resources on geometric properties.
2.10.2. Lesson 2: Polygons
What do you learn in 8th grade math about polygons? This lesson focuses on comparing and describing properties of convex and concave polygons.
Convex polygons have all interior angles less than 180 degrees, while concave polygons have at least one interior angle greater than 180 degrees. LEARNS.EDU.VN offers modules on polygon properties.
2.10.3. Lesson 3: Pythagorean Theorem
What do you learn in 8th grade math regarding the Pythagorean Theorem? Students learn to apply the Pythagorean theorem to solve real-world problems.
For example, finding the length of the hypotenuse of a right triangle with legs of lengths 3 and 4: c = √(3^2 + 4^2) = 5. LEARNS.EDU.VN provides practice problems on the Pythagorean theorem.
2.10.4. Lesson 4: Congruent and Similar
What do you learn in 8th grade math about congruent and similar figures? This lesson covers identifying congruence and similarity in real-world situations and providing justifications.
Congruent figures have the same shape and size, while similar figures have the same shape but different sizes. LEARNS.EDU.VN offers exercises to identify congruence and similarity.
2.10.5. Lesson 5: Transformations
What do you learn in 8th grade math about transformations? Students learn to identify and perform transformations (reflection, translation, rotation, and dilation) of a figure on a coordinate plane.
For example, reflecting a triangle over the x-axis. LEARNS.EDU.VN provides interactive tools to perform transformations.
2.10.6. Lesson 6: Proportional Relationships
What do you learn in 8th grade math regarding proportional relationships? This lesson focuses on identifying how changes in dimensions affect area and perimeter.
For example, doubling the side length of a square quadruples its area. learns.edu.vn offers modules on proportional relationships in geometry.
2.11. Chapter 11: Advanced Transformations
What do you learn in 8th grade math in Chapter 11? Chapter 11 covers transforming lines, angles, and parallel lines, understanding congruence and similarity
