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

Shapes are congruent when they match exactly and similar when one is a scaled copy of the other. Students use hands-on tools to test these relationships by flipping, sliding, and resizing figures.

Students physically test what happens to lines, angles, and shapes when they are flipped, turned, or slid across a surface. The goal is to see that the shape stays the same size and its parts keep their measurements.

When a shape is flipped, slid, or rotated, any straight line or segment in it stays straight and keeps the same length. The transformation changes position, not size.

When a shape is flipped, slid, or rotated, its angles stay exactly the same size. Students learn that moving a figure around the page never changes how wide or narrow its corners are.

When two lines run side by side and never meet, any rotation, reflection, or slide keeps them that way. Students learn that these transformations never cause parallel lines to cross or converge.

Two shapes are congruent when one can be flipped, turned, or slid to land exactly on top of the other. Students identify whether that kind of move connects two figures, with no stretching or shrinking allowed.

Students learn how sliding, spinning, flipping, or stretching a shape changes the location of its points on a graph. They practice tracking exactly where each corner lands after the move.

Two shapes are similar if one can be slid, flipped, turned, or scaled up and down to match the other. Students identify which of those moves connect two figures and explain why the shapes are similar even if they're different sizes.

Students figure out rules about triangle angles and parallel lines by reasoning through what they see, not by memorizing formulas. They also use two matching angles to prove that two triangles have the same shape.

Students use the Pythagorean Theorem to find missing side lengths in right triangles. They also figure out the straight-line distance between two points on a grid.

Students explain why the Pythagorean Theorem works, not just how to use it. They use diagrams or models to show why the two shorter sides of a right triangle are related to the longest side.

Students use the rule that connects the three sides of a right triangle (a² + b² = c²) to find a missing side length. This shows up in real problems like finding the diagonal of a room or the distance between two points.

Students find the straight-line distance between two points on a grid by treating the gap as the longest side of a right triangle and using the Pythagorean Theorem to calculate it.

Students use formulas to find the volume of rounded 3-D shapes like cans, ice cream cones, and balls. They apply those formulas to real problems, not just textbook exercises.

Students use the volume formulas for cones, cylinders, and spheres to solve practical problems, like figuring out how much a can holds or how much sand fills a cone-shaped funnel.

Irrational numbers like pi or the square root of 2 cannot be written as simple fractions. Students learn to recognize these numbers and place them on a number line by finding the closest fraction or decimal that fits.

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

Students learn to place numbers like the square root of 2 or pi on a number line by finding the closest fraction or decimal that fits. This lets them compare and estimate values that never round out evenly.

Students learn what a function is, practice calculating outputs for given inputs, and compare how two different functions behave. Think of it as reading and interpreting rules that connect one number to exactly one result.

A function is a rule where every input has exactly one output. Students read graphs, tables, and equations to check whether each starting value produces a single result.

Students look at two functions shown in different forms, such as an equation and a graph, then compare how they behave. They find which grows faster, starts higher, or hits a specific value first.

Students learn that y = mx + b always graphs as a straight line, making it a linear function. They also identify functions whose graphs curve or bend, which tells them the relationship is not linear.

Students use equations and graphs to show how one quantity changes as another changes, like how distance grows as time passes. They choose the right type of function to fit real-world data and explain what it means.

Students find the starting value and rate of change for a straight-line relationship, whether it comes from a word problem, a table, or a graph, then explain what those numbers mean in context.

Students look at a graph and describe in words what's happening between two quantities, like where a line rises, falls, or curves. They also draw a rough graph from a verbal description.

Students practice writing very large and very small numbers using exponents, and learn what it means to square or cube a number. They also learn to read and use scientific notation, which is how scientists write numbers like 0.000003 or 93,000,000.

Exponent rules let students rewrite multiplication and division problems written with powers. Students use those rules to simplify expressions like 3 to the fourth divided by 3 squared down to a single, cleaner number.

Students solve equations by finding square roots and cube roots of numbers. They know that the square root of 4 is 2, the cube root of 8 is 2, and that the square root of 2 is a decimal that never ends or repeats.

Scientific notation is shorthand for writing very large or very small numbers, like the distance to a star or the size of a cell. Students learn to compare those numbers and say, for example, that one is a thousand times bigger than the other.

Students add, subtract, multiply, and divide numbers written in scientific notation, such as the distance to a star or the size of a cell. They also read scientific notation displayed on a calculator screen and pick units that fit the scale of what they are measuring.

Proportional relationships, straight-line graphs, and linear equations all describe the same kind of change. Students learn to move between these three forms and explain what they have in common.

Students graph proportional relationships and identify the slope as the unit rate. They compare two proportional relationships even when one is shown as a table and the other as a graph or equation.

Students use matching triangle shapes on a graph to show why a straight line keeps a steady slope no matter where you measure it. From that idea, they write the equation that describes any line.

Students figure out the value of an unknown in a linear equation and work out problems that involve two equations at once, finding the one pair of numbers that satisfies both.

Students solve equations with one unknown, like 3x + 5 = 20, finding the exact value that makes the equation true. This includes equations that may have one solution, no solution, or solutions that work for any number.

Solving a one-variable equation can end three ways: one answer, no answer, or any number works. Students simplify the equation step by step until they can tell which case they have.

Students solve equations that include fractions or decimals, distributing and combining terms to find the value of the variable.

Two equations with two unknowns can be solved together to find a single answer that satisfies both. Students find that one point by graphing, substituting, or eliminating a variable.

When two lines are graphed on the same grid, the point where they cross is the answer to both equations at once. Students learn to read that intersection as the solution that makes both rules true.

Students solve two equations together to find a single pair of numbers that satisfies both at once. They use algebra or a graph to find the answer, and sometimes spot the solution just by looking.

Students solve everyday problems that involve two unknowns at once, like finding the price of two items when you only know the total. They set up two equations and find the one answer that satisfies both.

Students look at two sets of data together, such as height and shoe size, to find out if a pattern connects them. They use scatter plots and tables to spot trends and describe what the relationship looks like.

Students read scatter plots to spot patterns between two sets of numbers, such as whether taller students tend to weigh more. They identify clusters, outliers, and whether the relationship follows a line or curves.

When a scatter plot's dots form a rough diagonal pattern, students draw a straight line through the middle of them. They then judge how well the line fits by checking how close most dots land to it.

Students use the equation of a trend line on a scatter plot to answer real questions, like predicting a person's height from their shoe size. They explain what the slope and starting point of the line mean in plain terms.

A two-way table sorts the same group of people by two categories at once, like sport played and grade level. Students build these tables, calculate percentages across rows or columns, and use those numbers to spot whether the two categories are connected.