What does a student learn in StateNew Mexico,GradeGrade 7,SubjectMathematics?

Students draw, measure, and describe shapes, then explain how those shapes relate to each other. That includes scaling a figure up or down, slicing a solid to see its cross-section, and working with angles formed by intersecting lines.

Scale drawings work like maps: a small measurement on paper stands for a larger real-world distance. Students read a scale to find actual lengths and areas, then redraw the same figure at a new scale.

Students draw triangles using given angle and side measurements, then figure out whether those measurements can only produce one triangle, could produce several, or make a triangle impossible to build.

Cutting through a 3-D shape like a box or pyramid reveals a flat cross-section. Students figure out what that flat shape looks like depending on where and how the cut is made.

Students solve everyday problems involving angles, area, and volume. That means calculating the size of shapes, the space inside a box, or the angle where two lines meet.

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 related.

Students find missing angles in diagrams by using the relationships between angle pairs. For example, two angles on a straight line always add up to 180 degrees, so if one is known, students can write a simple equation to find the other.

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

Proportional relationships show up in unit prices, speed, and recipes. Students learn to recognize and calculate those relationships, then use them to solve real problems with numbers that scale together.

Finding a unit rate means figuring out the cost, speed, or amount for exactly one unit. Students work with fractions on both sides of the ratio, like miles per fraction of an hour, and simplify down to a single clean rate.

Two quantities are proportional when they grow (or shrink) at the same steady rate. Students identify that relationship in a table, graph, or equation, then use it to solve problems like finding the better price or predicting a distance.

Students check whether two quantities grow at the same steady rate by looking at a table of values or a graph. If the graph forms a straight line through the origin, the relationship is proportional.

In a proportional relationship, one number always changes by the same multiplier. Students find that steady multiplier, called the unit rate, whether it shows up in a table, a graph, an equation, or a word problem.

Students write an equation to show how two quantities change together at a constant rate. For example, if each item costs $3, they write y = 3x to capture that relationship.

Students read a graph of a proportional relationship and explain what each plotted point means in context. They pay close attention to why the line passes through (0, 0) and what the point at x = 1 reveals about the unit rate.

Students use ratios and percentages to solve everyday problems like calculating a sale price, figuring out a tip, or finding how much tax gets added to a purchase. The math often takes more than one step.

Students practice adding, subtracting, multiplying, and dividing with negative numbers, fractions, and decimals. This builds on the fraction work from earlier grades and extends it to numbers on both sides of zero.

Adding and subtracting positive and negative numbers, including fractions and decimals. Students place these values on a number line to show what happens when they combine or take away amounts that can fall above or below zero.

Adding opposite numbers always lands at zero. Students learn to recognize when two quantities cancel each other out, like earning $5 and spending $5, or climbing 3 floors and descending 3.

Adding a positive number moves right on a number line; adding a negative moves left. Students learn that any number plus its opposite always equals zero, and practice connecting those moves to real situations like temperatures rising and falling.

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 rational numbers gets easier when students use number properties as shortcuts. Students learn to rearrange or regroup numbers in an expression to make the math simpler, rather than working left to right every time.

Multiplying and dividing with negative numbers, fractions, and decimals. Students learn the rules that govern these operations and apply them to solve problems with any kind of rational number.

Multiplying negative numbers follows the same rules fractions do. Students learn why a negative times a negative gives a positive, and practice making sense of those products using real situations like debt or temperature.

Dividing one whole number by another always produces a rational number (a fraction or integer), as long as the divisor is not zero. Students also learn that a negative sign on a fraction can sit in front, in the numerator, or in the denominator and mean the same thing.

Multiplying and dividing with negative numbers, fractions, and decimals follows the same rules as whole numbers. Students use those familiar rules as shortcuts to work through trickier calculations.

Dividing a fraction's top number by its bottom number turns it into a decimal. That decimal will either stop completely or repeat the same digits in a pattern forever.

Word problems with positive numbers, negative numbers, and fractions that mix all four operations: addition, subtraction, multiplication, and division. Students work through problems drawn from real situations, like temperature changes or money.

Students rewrite math expressions into simpler or different forms without changing what they equal. They use rules like combining like terms or the distributive property to make expressions easier to work with.

Students combine and simplify algebraic expressions using operations like factoring and distribution. For example, they recognize that 2(x + 3) and 2x + 6 mean the same thing, or combine 3x + 5 + x into 4x + 5.

Rewriting a math expression a different way can reveal something useful, like seeing that 1.2x means "the original amount plus a 20% increase" without doing two separate calculations.

Students use equations and expressions to solve real problems, like figuring out how long a trip takes or how much something costs after a discount.

Students solve real-world problems that mix whole numbers, fractions, and decimals, including negatives. They pick the most efficient form for each number, switch between forms when it helps, and check whether the answer makes sense before finishing.

Students turn a word problem into an equation or inequality with a variable, then solve it to find the unknown quantity, like a missing price or distance.

Students set up and solve one-step and two-step equations from word problems, then check whether the algebra matches the arithmetic they could do by hand.

Students solve word problems that produce an inequality instead of a single answer, then plot the range of solutions on a number line and explain what those numbers mean in the real situation.

Students learn to survey a small group and use those results to make reasonable predictions about a much larger group. The key idea is that the sample has to be chosen randomly, not hand-picked.

Surveying a small, randomly chosen group can reveal patterns about a much larger group. Students learn why random selection matters and what makes a sample trustworthy enough to draw conclusions from.

Students use survey or experiment results from a small random group to make predictions about a much larger group. They repeat the sampling process several times to see how much their predictions shift.

Students compare two groups of data, like test scores from two different classes, and draw conclusions about how the groups differ or what they have in common.

Students look at two dot plots or box plots side by side and describe how much the groups overlap. They measure the gap between the midpoints of each group and express that gap as a multiple of the spread.

Students compare two groups using averages and spread to draw conclusions. For example, they might use survey data to decide whether seventh graders or eighth graders typically sleep longer.

Students learn what makes an event likely or unlikely, then build simple models to predict how often it should happen and check those predictions against real results.

Probability is a number from 0 to 1 that describes how likely something is to happen. A probability near 0 means it rarely happens, near 1 means it almost always happens, and around 1/2 means it could go either way.

Students run an experiment many times, such as flipping a coin or rolling a die, and use the results to estimate how likely the event is. The more trials they run, the closer their estimate gets to the true probability.

Students build a simple model to predict how often something will happen, like flipping a coin, then compare those predictions to what actually happens and explain any differences.

When every outcome is equally likely, like rolling a number cube, students figure out the chance of any result by dividing one outcome by the total number of outcomes.

Students collect real data from an experiment, like rolling a die or drawing cards, then use the results to estimate how likely each outcome actually is rather than assuming all outcomes are equally likely.

Students find the chances of two or more events happening together, like flipping a coin and rolling a die at the same time. They use lists, tables, or branching diagrams to map 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 all possible outcomes.

Students list every possible outcome of two combined events, like rolling two dice, using a table or branching diagram. Then they circle or identify which outcomes match the specific result they're looking for.

Students design a simulation, like flipping a coin or rolling a die, to estimate how often two events happen together. Running the simulation many times gives a picture of the real odds.