Grade 8 Math Curriculum
Equations
Equations are mathematical statements that state the equality between two expressions. Eighth grade math students will learn different strategies like transposing and balancing methods to solve equations.
Basics of equations
An equation is essentially a way of expressing equality between two expressions. This section talks about the properties and the operations that can be used to solve them.
Solving multi-step equations using different operations
Some equations cannot be solved in a single step. In such cases, we need to solve it using multiple steps by performing different operations.
Solving equations with variables on both sides
Here, eighth grade math students will learn about solving equations that have variables on both sides.
Rewriting equations and formulas
Rewriting equations and formulas help students translate eighth grade math word problems into solvable math equations. This section discusses the aspects to consider while rewriting equations.
Transformations
Manipulating and playing with shapes and figures makes learning math a fun experience. Transformations allow us to manipulate and study geometric figures’ movement.
Concept of translation
Translation is a type of transformation in which a geometric figure is moved by a given distance in a particular direction. Here, students will learn how to translate shapes with the help of some examples.
Concept of reflection
Reflection is a type of transforming geometric figures. The reflection of a figure is basically the mirror image of the shape. Here, students will learn the significance of the line of reflection by observing various examples.
Concept of rotation
Rotation is a method of transformation in which a figure or the object is rotated around a point. This section discusses rotation of objects with the help of some real-life examples.
Concept of dilation
Dilation is another type of geometric transformation in which a figure is resized using a scaling factor. Here, eighth grade students will learn the concept of dilation, and how it can be used to create similar figures
Congruent figures
Congruent figures are geometric figures that have the same shape and size. In other words, congruent figures share same properties. Learners will learn how to determine if given two shapes are congruent.
Similar figures
Similar figures are the figures that have the same shape but different in size. Eighth graders will learn examples of similar figures and their relation to transformations.
Perimeters and areas of similar figures
Perimeter and area are terms used to describe the essential qualities of two-dimensional figures. In this section, students will learn about the perimeter and area of similar figures.
Angles and Triangles
An angle is a figure formed when two lines or two rays intersect. An angle has two arms and a common vertex. We can use a combination of angles to construct shapes. A triangle is the simplest closed 2-dimensional shape that can be constructed.
Parallel lines and transversals
Any two lines that never intersect are known as parallel lines. A third line that passes through a set of parallel lines is known as a transversal. Here, students will learn some interesting relations between the angles formed by parallel lines and transversals.
Alternate interior angles
Angles of triangles
A triangle is a closed shape made up of three sides and three angles. The combination of angles gives triangles some unique properties. Eighth grade math students will learn these properties to find relationships between angles of triangles.
Angles of polygons
Polygons are closed shapes that have at least three straight sides. Triangles, quadrilaterals, and pentagons are examples of polygons. Polygons have a specific set of properties depending on their features like number of equal angles, sides and number of parallel sides etc. Students will learn about the angles of polygons here with the help of eighth grade math problems.
Sum of interior angles of a polygon
Similar triangles
The triangles that have the same shape but different size are known as similar triangles. The sides of similar triangles are in proportion. Here, eighth graders will learn different methods to prove the similarity between two triangles.
Corresponding angle
Graphing and Writing Linear Equations
Linear equations are algebraic equations in which there has an exponent of one. The graph of a linear equation is a straight line. Students will learn how to form a linear equation and plot the equation on a graph.
Graphing linear equations and proportional relationships
The graph of a linear equation is always a straight line. But each linear equation will produce a different straight line on graph paper. Students use the concept of ordered pairs to graph linear equations and identify proportional relationships.
Finding the slope of a line
The slope of a line describes the steepness of a line. We can calculate the slope of a line using different methods. Eighth graders will learn about each method in detail in different pages here.
Finding the slope of a line (using graphing method)
We can calculate the slope of a line from its plot on graph paper. This is a straightforward method that can be used to solve eighth grade math problems.
Graphing linear equations (slope-intercept form)
A linear equation can be written in different forms. But its graph is always a straight line. This section discusses the steps involved in graphing a linear equation which is in the slope-intercept form.
Graphing linear equations (standard form)
Here, eighth grade math students will learn how to graph a linear equation that is in the standard form.
Writing equations (slope and a point)
Eighth grade math students will learn how to write the equation of a line when its slope and a point on the line are known.
Systems of Linear Equations
Now that students have learned the fundamental concepts of linear equations, it is time to progress to the next by solving a system of linear equations. A system of linear equations is a set of multiple equations having more than one variable.
Solution of a system of linear equation using graphical method
There are multiple ways to solve a system of linear equations. Eighth graders will first learn to solve a system of linear equations using the graphical method. This will help students gain a clear visual understanding of what the solution means.
Solving systems of linear equations by substitution
Now that students know what the solution of a system of linear equations means, they will learn the substitution method of solving linear equations. This method of solving linear equations is carried out by writing one variable in terms of the others and by using simple arithmetic operations.
Solving systems of linear equations by elimination
The next method of solving a system of linear equations is by eliminating one of the variables. In this method, students will learn to solve linear equations by manipulating them using simple operations like addition, subtraction, multiplication, and division.
Solving special systems of linear equations
A system of linear equations can be classified on the basis of the nature of its solutions. This section discusses the factors that determine the nature of solutions of a system of linear equations. Eighth grade math students will learn to solve these special systems of linear equations as well.
Data Analysis and Displays
Data is a collection of information that may include numbers, words, measurements, observations, and so on. We collect data to observe various things in the real world. But we need ways to display the data to make it more comprehensible. Eighth grade math students will learn data analysis and display methods in this chapter.
Plotting data in linear form
In this section, eighth grade math students will learn to display data in a linear form; i.e., by plotting lines on a graph.
Data display
In this section, eighth grade math students will be introduced to different data display methods including pictographs, bar graphs, line graphs, histograms, stem and leaf plots, box and whiskers plots, pie charts, scatter plots, and line plots.
Functions
A function is an expression or a rule that defines the relationship between a value in a data set and a value in a different data set. It is important for eighth grade students to be thoroughly familiar with functions as it is a fundamental concept in calculus.
Relations and functions
Relations and functions are important math concepts in the 8th grade math curriculum. A relation is simply a depiction of inputs and outputs as an ordered pair. On the other hand, a function is a special type of relation in which each input has only one output.
Difference between relations and function
Representations of functions
A function can be represented using different methods. Writing the rule using a mathematical expression, creating a table, and plotting a graph are some of the ways in which we represent a function. Students will solve eighth grade math problems to practice different methods of representing a function.
Linear functions
A linear function is a function whose function rule consists of variables raised to the power of one. The graph of a linear function is always a straight line.
Comparing linear and nonlinear functions
In this section, 8th grade math students will learn the characteristics of linear functions and nonlinear functions. Here, they will learn how to derive and interpret linear functions.
Analyzing and sketching graphs
We use graphs to represent data in an easily comprehensible manner. Here, students will learn to analyze and sketch different types of graphs.
Exponents and Scientific Notation
An exponent is a mathematical representation which is symbolic of the number of times a number is multiplied by itself. We can use exponents instead of repetitive multiplication of the same number to shorten or simplify expressions. To simplify a term, we can use the concept of scientific notation, which will be discussed later in detail.
Laws of exponents
Difference between power and exponent
Product of powers property
Eighth graders will learn to evaluate expressions involving the multiplication of two powers using the product of powers property.
Quotient of powers property
Here, students will learn the quotient powers property which can be used to simplify the division of two powers.
Zero and negative exponents
A number can be raised to any value. So far, students have learned what happens when a number is raised to a positive exponent. Now, 8th grade math students will learn the meaning of raising a number to zero or a negative exponent.
Estimating quantities
Estimating quantities is an important skill that students need to strike off the eighth grade skill checklist. This will help them save time while solving math problems.
Scientific notation
Scientific notation of a number is a standard way of expressing a number using powers of 10. Eighth graders will learn to use scientific notation to express big and small numbers in a convenient manner. Students need to learn this notation to solve questions in math and science in higher grades.
Operations in scientific notation
In this section, 8th grade math students will learn to perform operations on scientific notations of numbers.
Real Numbers and the Pythagorean Theorem
The set of real numbers includes all natural numbers, whole numbers, integers, fractions, rational numbers, and irrational numbers. Eighth grade math students will learn different types of real numbers. Along with real numbers, students will also learn the Pythagoras theorem, which is an important topic in the 8th grade math curriculum.
Square roots
Here, 8th grade math students will learn to find the square root of a given perfect square number.
Perfect square
Square root tricks
Square roots: 1 to 100
Square root finder
Pythagorean theorem
The Pythagoras theorem relates the three sides of a right-angled triangle by deriving a relationship between their lengths. In any right-angled triangle, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides.
Converse of the Pythagorean theorem
The converse of the Pythagorean theorem states that if the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares on the other two sides, the angle opposite to the hypotenuse is a right angle.
Cube roots
A cube root is a number that gives a cube number when it is multiplied by itself three times. Here, 8th grade math students will learn to find cube roots of numbers with which they are already familiar.
Perfect cube of numbers
Rational numbers
A rational number is a number that can be expressed in the pq form, where q0. Eighth grade math students will learn the properties of a rational number in this section.
Irrational numbers
An irrational number is a number that cannot be expressed in the pq form. Students will learn how to recognize an irrational number by observing the digits on the right side of the decimal point.
Difference between rational and irrational numbers
Real numbers
Operations on real numbers
Volume and Similar Solids
We use the concept of volume to describe the size of three-dimensional figures. To be specific, the volume of a solid is the space occupied by the solid. Eighth grade math students will also learn the concept of similar solids and the properties associated with them.
Volumes of cylinders
Here, 8th grade math students will learn the formula used to calculate the volume of a cylinder. They will also solve eighth grade math problems to be thorough with the concept.
Cylinders
Volumes of cones
The volume of a cone is learned in relation to the volume of a cylinder with the same base. Students will learn to use this formula to solve math problems for eighth graders.
Cones
Volumes of spheres
A sphere is a perfectly round three-dimensional shape that gives a circular cross-section when cut along any axis. All points on the surface of a sphere are equidistant from its center.
Spheres
Surface areas and volumes of similar solids
In this section, 8th grade math students will learn to calculate the surface area and volume of similar solids. Students will also solve 8th grade math problems to understand the concepts thoroughly.
Oblique sketch
Finding area and perimeter of different shapes
Surface areas and volumes
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Most of the advanced concepts taught in higher grades will be based on the basic concepts taught in 8th grade, as 8th grade acts as a bridge between middle school and high school. Hence, it is important for all students to master all concepts taught in 8th grade.
8th grade math demands a lot of practice. Hence, students need to practice a lot of questions in order to improve their performance in eight grade math. Students can rely on the concept articles and questions available on BYJU’S Math to practice eighth grade math concepts.
We get a square number when we multiply a number by itself. Here, the original number is known as the square root of the square number. Similarly, we get a cube number when we multiply a number by itself thrice. In this case, the original number is the cube root of the cube number.
The power of a number is an operation that can be used instead of the repeated multiplication of a number. The exponent in a power refers to the number of times a number is multiplied by itself.
As the name suggests, the scientific notation of a number is mostly used in the scientific field. Scientists deal with numbers that are either too big or too small to write. Example, the speed of light. In such cases, they replace a number with its scientific notation to express the same value in an efficient way.