What does a student learn in StateNorth Carolina,GradeGrade 8,SubjectMathematics?

Students explore how flipping, turning, and sliding a shape produces an exact copy. Two shapes are congruent when one can be moved onto the other using those same moves, and students describe the steps that show why.

Students describe what happens to a shape's coordinates on a graph after it is stretched, slid, turned, or flipped. They practice each move separately and record how the corner points change.

Students learn that two shapes are "similar" when one can be transformed into the other by sliding, flipping, rotating, or scaling it up and down. They practice identifying and describing those steps between two given shapes.

Students figure out angle patterns in triangles and parallel lines, then use those patterns to solve problems. They also learn that two triangles are similar when two of their angles match.

Students learn why the Pythagorean Theorem works: in a right triangle, the two shorter sides squared and added together equal the longest side squared. They also learn to run that reasoning backward to check whether a triangle is a right triangle.

Students use the Pythagorean Theorem to find a missing side length in a right triangle, then apply that skill to real problems like finding the shortest path across a field or the height of a ramp.

Students use the Pythagorean Theorem to find the straight-line distance between two points plotted on a grid. They treat the horizontal and vertical gaps as the two short sides of a right triangle, then solve for the longest side.

Students use the volume formulas for cones, cylinders, and spheres, recognizing how those three formulas connect to each other. They apply that understanding to find the volume of real objects like cans, funnels, and balls.

Every number can be written as a decimal. Rational numbers produce decimals that end or repeat a pattern. Irrational numbers, like pi or the square root of 2, produce decimals that go on forever with no repeating pattern.

Students find where irrational numbers like square roots and pi land on a number line by estimating their decimal values. They round square roots and cube roots to the nearest tenth and pi to the nearest hundredth.

Exponent rules let students rewrite multiplication and division of powers as a single, simpler expression. Students practice collapsing something like 2 to the fifth times 2 to the third into one clean number.

Students find the square root or cube root of a number to solve equations like x² = 25 or x³ = 8. They work with perfect squares up to 400 and recognize what number was multiplied by itself to get the result.

Scientific notation is shorthand for writing very large or very small numbers using powers of 10. Students use it to compare those numbers, like figuring out how many times bigger the distance to the sun is than the distance across a city.

Multiply and divide very large or very small numbers written in scientific notation. Students solve real-world problems, switching between scientific notation and decimal form as needed.

Students solve equations and inequalities with one unknown, like 3x + 5 = 20 or 2x - 1 > 7. They learn that an equation can have one answer, no answer, or infinite answers, and practice solving problems where the variable appears on both sides.

Students work with two straight-line equations at once and find where they cross on a graph. That crossing point is the answer because it is the only spot that fits both equations at the same time.

Students plot two quantities on a graph to see if they move together, for example whether more study time connects to higher test scores. They look for patterns like clusters, outliers, and whether the relationship follows a straight line or a curve.

Students draw a best-fit line through a scatter plot and judge how well it matches the data by checking how close the dots are to that line.

A line drawn through a scatterplot has two key numbers: its slope (how fast one quantity changes as the other grows) and where it crosses the vertical axis. Students use those numbers to answer real questions, like predicting a price from a weight.

Students sort survey data into a two-way table that crosses two categories, like grade level and favorite sport. They then use the row and column percentages to decide whether the two categories are connected.

A function is a rule where each input has exactly one output. Students learn to spot functions in tables, lists of coordinate pairs, and graphs, where every x-value lines up with one y-value and nothing more.

Students look at two lines shown in different forms, such as an equation, a graph, or a table, and compare their slopes and starting points to say which is steeper or where each one crosses zero.

Reading a table, equation, or graph, students decide whether a relationship between two values is linear. That means checking whether the rate of change stays the same throughout.

Students learn to write and graph equations in the form y = mx + b to describe straight-line patterns. They identify the starting value and the rate of change from a table, a graph, or two points, and explain what those numbers mean in context.

Students read a graph to spot where a line rises, falls, or curves, then sketch a rough graph to match a real-world situation like a bike ride or a filling bathtub.