What does a student learn in StateWest Virginia,GradeGrade 8,SubjectMathematics?

Irrational numbers like pi or the square root of 2 can't be written as a simple fraction. Students learn to place them on a number line by finding the closest fraction or decimal.

Some numbers, like 1/3, turn into decimals that repeat forever (0.333...). Others, like the square root of 2, never settle into a pattern. Students learn to tell the difference and convert repeating decimals back into fractions.

Rational numbers can be written as fractions; irrational numbers like pi or the square root of 2 cannot. Students practice telling the two apart and finding close fraction or decimal approximations for the irrational ones.

Students learn that some numbers, like the square root of 2 or pi, never settle into a repeating pattern. They practice pinning those numbers to an approximate spot on a number line by narrowing in on the value one decimal place at a time.

Students explain why adding or multiplying two fractions or whole numbers always gives a clean, predictable result, and why mixing a regular number with something like pi or a square root always gives a messier, never-repeating one.

Exponents are a shorthand for repeated multiplication. Students learn the rules that govern them, like what happens when you multiply or divide powers of the same number, and apply those rules to expressions with whole-number and negative exponents.

Students use exponent rules to simplify expressions with repeated multiplication, including negative exponents. For example, multiplying two powers of 3 might shrink down to a fraction like 1/27.

Students solve equations by finding square roots and cube roots, like figuring out what number times itself equals 25. They also learn that some roots, like the square root of 2, cannot be written as a clean fraction.

Students write huge or tiny numbers in scientific notation (like 3 × 10⁸ for 300 million) and use that shorthand to compare them, such as figuring out that one number is 20 times bigger than another.

Scientific notation is shorthand for writing very large or very small numbers. Students convert between standard numbers and scientific notation, pick sensible units for extreme measurements, and read the notation that calculators and spreadsheets produce.

Proportional relationships, straight-line graphs, and linear equations all describe the same kind of change. Students learn to move between those three forms and see why they say the same thing.

Students plot proportional relationships on a graph and read the slope as the unit rate. They compare two relationships shown in different forms, like a graph versus an equation, to figure out which one grows faster.

Similar triangles show why a straight line has the same steepness no matter which two points you measure. Students use that idea to write the equation of any straight line on a graph.

Students practice solving equations and inequalities with one unknown, like finding the value of x in 3x + 5 = 20. They also solve pairs of equations together to find one answer that works for both.

Students solve one-variable equations to answer real questions, like figuring out how long a trip takes or what a price will be. The equation has one unknown, and students find the value that makes it true.

Students sort equations into three buckets: one answer, no answer, or every number works. They simplify each equation step by step until it collapses into a clear form that shows which case they have.

Students solve equations where the numbers include fractions and decimals. That means distributing, combining similar terms, and finding the value of the unknown.

Students graph two straight lines on the same grid and find where they cross. That crossing point is the answer because it is the one spot that works for both equations at the same time.

Students solve a one-variable equation step by step and explain why each move keeps both sides balanced. Then they argue, in writing or out loud, why their method actually works.

Students solve real-world problems where the answer is a range of values, not a single number. They work through inequalities with fractions and decimals, distributing and combining terms to find every value that makes the inequality true.

Students take a formula like V = IR and rewrite it to solve for one specific variable. The steps work exactly like solving a regular equation: whatever you do to one side, you do to the other.

A function is a rule where each input gives exactly one output. Students learn to read a table, graph, or equation and decide whether it fits that rule, then compare two functions to see which grows faster or starts higher.

A function is a rule where every input has exactly one output. Students read graphs as a picture of that rule, where each point shows an input paired with its matching output.

Two functions can show up in different forms: one as a graph, another as an equation, a table, or a description. Students compare them to find which one grows faster or starts at a higher value.

The equation y = mx + b always draws a straight line on a graph. Students learn to recognize that pattern and contrast it with equations like A = s², where the graph curves instead of staying straight.

Students compare two functions shown in different formats, such as a table and a graph, and decide which one grows faster or starts higher. The skill is recognizing that the same type of relationship can be described more than one way.

Students write an equation that describes a straight-line relationship between two quantities, then explain what the slope and starting value mean in the real situation, whether they read those numbers from a graph, a table, or a word problem.

Students read a graph to describe how two quantities relate, noting where values rise, fall, or curve. They also sketch a rough graph from a verbal description, showing the same patterns by hand.

Shapes are congruent when they match exactly, and similar when they have the same shape but different sizes. Students use models or drawing tools to see how rotating, flipping, or sliding a shape changes its position without changing its size.

Rotations, reflections, and translations are the three ways to move a shape without changing its size or angles. Students test each move hands-on to confirm that the shape stays exactly the same after it slides, flips, or turns.

When two shapes are congruent, every line and segment maps exactly onto its matching line and segment in the other shape, with lengths staying equal. Students learn why size and position don't change what makes two figures the same.

When two shapes are congruent, every angle in one matches the exact same degree in the other. Students learn that flipping, sliding, or rotating a shape leaves all its angles unchanged.

When two parallel lines are moved, rotated, or flipped as part of a transformation, they stay parallel. Students learn that basic geometric relationships like this hold up under any rigid motion.

Two shapes are congruent when one can be flipped, turned, or slid to land exactly on the other. Students identify those moves and describe the steps that show why the two shapes match perfectly.

Students learn what happens to a shape's position and size on a grid when it's slid, turned, flipped, or scaled up and down. They describe each change using the coordinate pairs that mark the shape's corners before and after.

Two shapes are similar if one can be turned, flipped, slid, or resized to match the other exactly. Students identify those moves and describe them in order.

Students explore why a triangle's three angles always add up to 180 degrees and how cutting two parallel lines with a third line creates predictable angle pairs. They also use angle relationships to decide whether two triangles have the same shape.

Students use the Pythagorean Theorem to find a missing side length in a right triangle. If they know two sides, they can calculate the third using the relationship a² + b² = c².

Students calculate the volume of cylinders, cones, and spheres to solve real problems, like finding how much water fills a tank or how much ice cream fits in a cone.

Students learn the volume formulas for cones, cylinders, and spheres, then use those formulas to solve problems like figuring out how much water fills a tank or how much ice cream fits in a cone.

Students look at two sets of data at once, like height and shoe size, to see if a pattern connects them. They plot the points on a graph and describe what the relationship looks like.

Students plot two related measurements on a graph, such as height and shoe size, then describe what the pattern shows. They look for whether the dots cluster together, trend up or down, or curve in unexpected ways.

When two sets of numbers are plotted as dots on a graph, students draw a straight line through the middle of the pattern to show the relationship. They then judge how well the line fits by checking how close the dots are to it.

Students use a line's equation to answer real questions from two-column data, like height and age. The slope tells them how much one measurement changes for each unit increase in the other, and where the line crosses zero has meaning too.

Students organize survey data about two yes-or-no questions into a table, then use the percentages in each row or column to see whether the two things tend to go together.