What does a student learn in StateMissouri,GradeGrade 8,SubjectMathematics?

Students simplify expressions that use exponents and square roots, including negative and zero exponents. This builds the number skills they need for algebra and geometry in high school.

Exponent rules let students rewrite and simplify expressions like 3 to the 4th times 3 to the 2nd without multiplying everything out. Students practice applying those rules to show that two different-looking expressions are equal.

Proportional relationships, straight-line graphs, and linear equations all describe the same idea in different forms. Students learn to move between a table, a graph, and an equation to see how one quantity changes as another grows.

Students explain why the steepness of a straight line stays the same no matter which two points on it you measure. They use similar triangles on a coordinate grid to show why that ratio never changes.

Students figure out the rules behind straight-line graphs: why a line through the origin follows y = mx, and why shifting that line up or down adds the value b.

Students solve equations and inequalities with one unknown, then work with two equations at once to find values that satisfy both. This shows up in problems like finding where two rates meet or when two quantities are equal.

Students write and sort linear equations by how many answers they have: exactly one, none at all, or infinitely many. They learn to recognize which type an equation is before solving it.

Solving equations and inequalities where the numbers involved are fractions or decimals. Students distribute, combine like terms, and isolate the variable to find the solution.

Students graph two straight lines on the same coordinate plane and find where they cross. That crossing point is the solution to both equations at once.

Students find where two lines cross on a graph and explain why that crossing point is the answer to both equations at once.

Students learn why two lines on a graph can cross at one point, run parallel and never meet, or sit on top of each other and share every point. They explain which situation a given pair of equations produces and why.

Students find the one point where two straight-line equations cross, using substitution or elimination to get a single answer that satisfies both equations at once.

Students learn when two shapes are identical in size and angle, and when they are the same shape but different sizes. They use tracing, folding, or drawing tools to test whether figures match or scale up and down.

Students learn what happens to a shape's coordinates when it's flipped, slid, turned, or scaled up and down on a grid. They describe those changes using the before-and-after coordinate pairs.

Students use the Pythagorean Theorem to find a missing side of a right triangle. Given two side lengths, they calculate the third using the relationship between the sides.

Students use drawings or physical models to show why the Pythagorean Theorem works: in a right triangle, the two shorter sides squared and added together equal the longest side squared. They also work the rule in reverse to check whether a triangle is a right triangle.

Students figure out how much space fits inside pointed and rounded 3-D shapes like cones and spheres. They apply the right formula for each shape to solve real problems.

Students find the total area of every flat face on a pyramid, then add those areas together to get one number. That number tells how much material it would take to wrap or build the outside of the shape.

Students calculate how much space fits inside pointed and curved 3D shapes, like party hats, Egyptian pyramids, and basketballs. They use specific formulas for each shape.

Students learn what a function is, practice finding its output for a given input, and compare how two functions behave. Think of it as reading and interpreting rules that connect one number to another.

A relation is a function if each input has exactly one output. Students look at tables, graphs, or pairs of values and decide whether any input repeats with a different result.

Students compare two functions shown in different formats, such as reading one from a table and the other from a graph or equation, then explain which is growing faster or has a higher starting value.

Students use equations and graphs to show how one quantity changes as another changes, like how distance grows as time passes. They decide which type of function best fits a real situation and explain what the graph shows.

Students look at a real-world situation, like a phone bill that charges a flat fee plus a rate per minute, and explain what the slope and starting value actually mean in that context.

Reading a graph, students describe how one quantity changes as another increases or decreases. They can also work in reverse, sketching a graph that matches a written description of the relationship.

Students look at two sets of data together, such as height and shoe size, to find patterns or connections between them. They use scatter plots and tables to see whether one measurement tends to rise or fall as the other changes.

Students use the slope and starting value of a best-fit line on a scatter plot to answer real questions, like predicting how much a car's value drops each year based on actual data.

Students build a two-way table to show how two categories relate, like whether students in a survey own a pet and also play a sport. Then they read the table to spot patterns between the two categories.