What does a student learn in StateNevada,GradeGrade 7,SubjectMathematics?

Students draw and describe shapes, then explain how those shapes relate to each other. This includes scaling figures up or down, slicing solids, and working out what changes and what stays the same.

Scale drawings work like a map: every measurement on paper stands for a larger (or smaller) real-world distance. Students read the scale, calculate actual lengths and areas, and redraw the figure at a new scale.

Students draw triangles using given angle and side measurements, then figure out whether those measurements produce exactly one triangle, several possible triangles, or no triangle at all.

Students slice through 3-D shapes, like boxes and pyramids, and identify the flat shape left behind. A vertical cut through a box gives a rectangle; a diagonal cut through a pyramid might give a triangle.

Students solve everyday problems that involve measuring angles, finding the area of flat shapes, and calculating the volume or surface area of 3-D objects like boxes and cylinders.

Students learn the two key circle formulas: area (pi times radius squared) and circumference (pi times diameter). Then they use those formulas to solve real problems and explain why the two formulas are connected.

When two or more angles share a corner or a straight line, students use what they know about how those angles relate to set up a simple equation and find the missing angle.

Students find the area, volume, or surface area of shapes built from triangles, rectangles, and other polygons. This includes flat figures and 3-D objects like boxes and prisms.

Proportional relationships show up whenever two quantities change together at a constant rate, like price per item or miles per hour. Students learn to spot that pattern, set up the math, and use it to solve real problems.

Students figure out the rate for one unit when both numbers in a ratio are fractions. For example, if a recipe uses half a cup of oil for a quarter pound of meat, students calculate how much oil is needed per pound.

Two quantities are proportional when they grow or shrink at the same steady rate. Students identify whether a relationship is proportional, then represent it as a table, graph, or equation.

Students check whether two quantities grow together at a steady rate by looking for matching ratios in a table or seeing if a graph forms a straight line through zero.

In a proportional relationship, one number always grows at the same rate as another. Students find that fixed rate, such as $3 per item or 55 miles per hour, whether it appears in a table, a graph, or an equation.

Students write an equation to describe a proportional relationship, such as y = 7x to show that a sandwich costs $7 per person. The equation makes it easy to find any value in the pattern.

Students read a graph showing a proportional relationship and explain what each plotted point means in real life. They pay close attention to why the line starts at zero and what the point at x = 1 reveals about the rate per single unit.

Students solve real-world problems involving percents, such as figuring out a sale price, calculating a tax, or finding how much interest a loan adds up to over time.

Students use what they already know about fractions to add, subtract, multiply, and divide any rational number, including negatives. That means working with numbers like -3, 1/2, or -0.75 on a number line or in equations.

Adding and subtracting positive numbers, negative numbers, and fractions by placing them on a number line. Students use the number line to show why moving left means subtracting and moving right means adding.

Opposite numbers cancel each other out. Students learn to recognize real situations where this happens, like a bank account where a $10 deposit and a $10 withdrawal leave a zero balance.

Adding a positive number moves right on a number line; adding a negative moves left. Students show that opposite numbers like 3 and -3 always cancel out to zero, then connect that idea to real situations like debt or temperature.

Subtracting a number is the same as adding its opposite. Students use this idea to find the distance between two numbers on a number line, like the gap between a temperature below zero and one above it.

Adding and subtracting fractions, decimals, and negative numbers gets easier when students use known rules, like how changing the order or grouping of numbers doesn't change the sum. Students apply those shortcuts to solve problems faster and with fewer errors.

Multiplying and dividing with negative numbers, fractions, and decimals. Students learn the rules for working with these numbers and apply them to solve real problems.

Multiplying negative numbers follows the same rules as multiplying fractions. Two negatives multiply to a positive, and students connect that pattern to real situations like debt or temperature dropping.

Dividing one whole number by another always produces a fraction or whole number, never an undefined answer (dividing by zero is the one exception). A negative sign on a division problem can sit in front of the fraction, on top, or on the bottom and the result stays the same.

Multiplying and dividing with negative numbers, fractions, and decimals follows the same rules as whole numbers. Students use those rules as shortcuts to solve problems faster, rather than working from scratch each time.

Dividing the top number by the bottom number turns any fraction into a decimal. That decimal either stops or falls into a repeating pattern, and students learn to spot which one they have.

Real-world math problems often mix whole numbers, fractions, negatives, and decimals. Students solve those problems using addition, subtraction, multiplication, and division, choosing the right operation for the situation.

Students rewrite math expressions into simpler or different forms using rules like the distributive property or combining like terms. The value of the expression stays the same; only the way it looks changes.

Students rearrange and simplify algebraic expressions by adding, subtracting, factoring, and expanding them. The numbers involved can be fractions or decimals, not just whole numbers.

Rewriting a math expression a different way can reveal a shortcut or make a hidden relationship easier to see. Students practice recognizing when a rewritten form makes a problem simpler to solve.

Students use equations and expressions to solve real problems, like figuring out a fair price split or how long a trip takes. The math moves from numbers alone to working with unknowns.

Students solve real-world problems that mix whole numbers, fractions, and decimals, including negatives. They choose efficient calculation methods, switch between number forms when it helps, and check whether their answer makes sense before moving on.

Students write equations or inequalities using a variable to stand in for an unknown number, then solve for it. The problems come from real situations, like figuring out how many hours of work it takes to earn a certain amount.

Students set up and solve one-step and two-step equations from word problems, then check whether the algebra and the arithmetic got there the same way.

Students solve word problems where the answer is a range of values, not a single number. They plot that range on a number line and explain what it means in the context of the problem.

Students learn to survey a small group and use those results to make reasonable guesses about a much larger group. The key idea is that the sample needs to be chosen randomly so the results are fair.

Surveying a small, randomly chosen group can reveal patterns about a much larger group, but only if the sample is a fair cross-section. Students learn why random selection matters and what makes a survey result trustworthy.

Students use survey or experiment data from a small random group to make predictions about a much larger population. By repeating the sample multiple times, students see how much their estimates can shift from one sample to the next.

Students compare two groups using real data, like survey results or measurements, and draw conclusions about which group tends to be higher, more spread out, or more consistent. The comparison is informal, not a formal proof.

Students look at two dot plots or box plots side by side and judge how much the groups overlap. They measure the gap between the two midpoints and describe it in terms of how spread out the data is.

Students compare two groups using their averages and spread of data to draw conclusions. For example, they might use survey results to decide which grade tends to spend more time on homework.

Students learn what makes an event likely or unlikely, then build and test simple models to predict how often it should happen.

Probability is a number from 0 to 1 that shows how likely something is to happen. Close to 0 means it probably won't happen, close to 1 means it probably will, and around 1/2 means it's a coin flip.

Students run an experiment many times, then use the results to estimate how likely an event is to happen. They can also work the other way: given a probability, predict how often something will occur over many tries.

Students build a simple model to predict how often something should happen, like rolling a die, then compare those predictions to what actually happens. When the results don't match, students explain why.

When every outcome is equally likely, like rolling a fair number cube, students figure out the chances of something happening by dividing favorable outcomes by total outcomes.

Students collect real data from a repeated experiment, like flipping a coin or spinning a spinner, then use the results to estimate how likely each outcome actually is.

Students figure out the chances of two or more things happening together, like flipping a coin and rolling a die at the same time. They use lists, tables, or branching diagrams to map out every possible outcome.

When two things happen together (like flipping a coin and rolling a die), students find the probability by counting how many combined outcomes match what they want, then dividing by the total number of possible combinations.

Students list every possible outcome for two-part events, like rolling two dice, using a table or branching diagram. Then they identify which combinations match a specific result, such as both dice landing on six.

Students design a simulation (like flipping a coin or rolling a die repeatedly) to estimate how often two or more events happen together. They run the experiment, collect the results, and use the data to predict real-world probabilities.