# What Do You Study in 8th Grade Math? A Complete Guide

## What Do You Study in 8th Grade Math?

In 8th-grade math, students study advanced algebraic concepts, geometry, real and irrational numbers, probability, and functions, and apply these skills to practical scenarios. They also explore transformations, exponents, and equations with radicals, and strengthen their problem-solving abilities in preparation for high school math.

Eighth grade marks a pivotal point in a student’s mathematical journey, where they delve even deeper into the world of mathematics, building on the solid foundation laid in previous years.

This comprehensive guide explores the diverse and challenging terrain of 8th-grade math, highlighting the key areas of focus and providing examples to illustrate the depth and breadth of the curriculum. From algebraic expressions to geometric transformations, and from statistical analysis to advanced equations, 8th-grade math equips students with the knowledge and skills necessary to tackle complex mathematical concepts and prepares them for the rigors of high school math.

## Algebraic Concepts

In 8th-grade math, students expand their algebraic knowledge. They learn to work with expressions, equations, and inequalities of increasing complexity. Let’s solve an example:

### Example

Solve for in the equation .

### Solution

Start by isolating the variable . Subtract 2 from both sides to get , which simplifies to .

Now, divide both sides by 3 to find :

x =

gives .

### Example

Solve for in the equation

### Solution

To solve for in the equation , we need to isolate on one side of the equation. Here are the steps to do so:

Step 1: Start by simplifying both sides of the equation by combining like terms. We want to get all the terms on one side and constants on the other side.

Subtract from both sides to move all -related terms to the left side:

This simplifies to:

Step 2: Next, isolate the -related terms on one side by adding 5 to both sides of the equation:

Step 3: Finally, divide both sides by 5 to solve for :

8/5 = 5x/5

8/5

So, the solution to the equation is or .

## Geometry and Transformations

Geometry becomes more intricate as students explore congruence, similarity, and geometric transformations. Here’s an example:

### Example

Perform a 90-degree clockwise rotation transformation on point A(2, 3) on the coordinate plane.

### Solution

To perform a 90-degree clockwise rotation, switch the x and y coordinates and negate the new x-coordinate. So, A(2, 3) becomes A'(-3, 2).

## Real Numbers and Irrational Numbers

Students work with real numbers and encounter irrational numbers. Let’s compute an example:

### Example

Calculate $\sqrt(2)$ × 3.

### Solution

Multiply the square root by 3: $\sqrt(2)$ × 3 = .

## Probability and Statistics

Probability and statistics play a significant role. Here’s an example related to probability:

### Example

You have a bag of colored marbles. There are 4 red marbles, 3 blue marbles, and 5 green marbles in the bag. What is the probability of randomly selecting a blue marble from the bag?

### Solution

To calculate the probability of randomly selecting a blue marble from the bag, you need to determine the ratio of the number of favorable outcomes (blue marbles) to the total number of possible outcomes (all marbles). Here’s how you do it:

Step 1: Find the total number of marbles in the bag, which is the sum of the different colors:

Total marbles = 4 (red) + 3 (blue) + 5 (green) = 12 marbles

Step 2: Find the number of favorable outcomes, which is the number of blue marbles:

Favorable outcomes (blue marbles) = 3 blue marbles

Step 3: Calculate the probability by dividing the number of favorable outcomes by the total number of possible outcomes:

Probability (P) = Favorable outcomes / Total outcomes

Probability (P) = 3 blue marbles / 12 marbles

Now, calculate the probability:

Probability (P) = 3/12

To simplify the fraction, you can divide both the numerator and denominator by their greatest common divisor, which is 3:

Probability (P) = (3÷3)/(12÷3)

Probability (P) = 1/4

So, the probability of randomly selecting a blue marble from the bag is 1/4 or 25%.

## Functions

Students are introduced to functions. Let’s represent a linear function graphically:

### Example

Represent the linear function graphically on a coordinate plane.

### Solution

Choose several values for , calculate for each, and plot the points. For example, when , , so one point on the graph is (0, 3). Do this for multiple values of to create the linear graph.

## Advanced Ratios and Proportions

Building on earlier concepts, students tackle more complex ratio and proportion problems. Here’s an example:

### Example

Given two similar triangles with a ratio of side lengths of 3:5, find the length of a missing side if the other is 9 inches.

### Solution

Use the proportion 3/5 = 9/x

where is the length of the missing side. Cross-multiply to get , and then divide both sides by 3: inches.

## Exponents and Scientific Notation

Exponents and scientific notation are vital skills. Let’s convert a number into scientific notation:

### Example

Express 500,000 in scientific notation.

### Solution

To express 500,000 in scientific notation, we need to move the decimal point five places to the left, which gives 5×$10^5$.

in scientific notation is 5×$10^5$.

## Equations with Radicals

Students encounter equations with radicals. Let’s solve one:

### Example

Solve for in the equation .

### Solution

To isolate , square both sides:

.

## Coordinate Plane and Graphing

Students deepen their understanding of the coordinate plane. Let’s graph a linear equation:

### Example

Graph the equation of a line, , on a coordinate plane.

### Solution

Choose various values of , calculate the corresponding values using the equation, and plot the resulting points on the coordinate plane. Connect the points to create a linear graph.

## Practical Applications

Math is applied to real-world scenarios throughout 8th-grade math. Here’s an example:

### Example

Calculate the total cost of a shopping trip with discounts and taxes, incorporating various mathematical concepts.

### Solution

Determine the cost of each item, apply discounts as percentages, sum the costs, and then calculate taxes as a percentage of the total cost to find the final cost.

## Conclusion

Eighth-grade math is a rich and diverse subject that challenges students to think critically and apply mathematical concepts to various scenarios. It provides a solid foundation for high school mathematics and equips students with valuable problem-solving skills that extend beyond the classroom.