What does a student learn in StateWest Virginia,GradeGrade 7,SubjectMathematics?

Students figure out whether two quantities change at a constant rate together, like speed and distance, then use that relationship to solve problems with real numbers.

Students figure out how fast, how far, or how much per single unit when the numbers involved are fractions. For example, walking half a mile in a quarter hour works out to 2 miles per hour.

Two quantities are proportional when they grow (or shrink) at a constant rate together. Students identify that relationship in tables, graphs, and equations, then use it to solve problems like comparing prices or mixing recipes.

Students look at a table of numbers or a graph to decide whether two quantities grow at the same steady rate. If the graph forms a straight line through the origin, or every ratio in the table simplifies to the same number, the relationship is proportional.

Students find the unit rate hiding in a table, graph, equation, or word problem. That single number shows how two quantities change together at a steady pace.

Students write an equation to show a proportional relationship, such as total cost equals price times number of items. This turns a real-world pattern into a formula they can use to solve problems.

Reading a graph of a proportional relationship, students explain what each point means in context. They pay close attention to (0,0), which shows that zero input gives zero output, and (1,r), which shows the unit rate directly.

Students use ratios and percents to solve everyday money problems: calculating sales tax, a restaurant tip, a discount, or how much a price went up or down.

Adding, subtracting, multiplying, and dividing with negative numbers, fractions, and decimals. Students take the fraction skills they already know and apply them to numbers on both sides of zero.

Adding and subtracting positive and negative numbers, including fractions and decimals. Students place those values on a number line to show what the math looks like visually.

Opposite numbers add up to zero. Students identify real situations where this happens, like a $5 gain and a $5 loss leaving a balance of zero.

Adding a positive number moves right on the number line; adding a negative moves left. Students use this to add fractions, decimals, and integers, and explain why a number and its opposite always add up to zero.

Subtracting a number is the same as adding its opposite. 7 minus 3 gives the same result as 7 plus negative 3, and the gap between any two numbers on a number line equals the absolute value of their difference.

Adding and subtracting positive and negative numbers follows the same rules as whole-number arithmetic. Students use those rules as shortcuts to reorder or regroup numbers and make calculations easier.

Multiplying and dividing with negative numbers, fractions, and decimals. Students learn the rules for working with those number types together and use them to solve real problems.

Multiplying negative numbers follows the same rules as multiplying fractions. Students learn why a negative times a negative equals a positive, then connect that idea to real situations like debt or temperature change.

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

Students use shortcuts like the commutative and distributive properties to multiply and divide fractions, decimals, and negative numbers more efficiently. The same rules that worked with whole numbers still apply.

Students use long division to turn a fraction into a decimal. Every fraction either stops cleanly (like 0.25) or settles into a repeating pattern (like 0.333...). There are no other options.

Students solve everyday problems using positive and negative numbers, fractions, and decimals together. That means adding, subtracting, multiplying, and dividing across all four operations in situations that come from real life.

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

Rewriting an expression like 3(x + 4) as 3x + 12, or reversing that process, is the core skill here. Students use rules like the distributive property to rewrite addition and subtraction problems with fractions or decimals into simpler, equivalent forms.

Rewriting a math expression in a new form can reveal a shortcut or show how two quantities connect. For example, adding a 5% tip and multiplying the total by 1.05 give the same result.

Rewriting an expression in different forms, such as turning a+0.05a into 1.05a, to show how the parts relate. Students use this to spot what a rewritten expression tells them about the original situation.

Students solve word problems that mix whole numbers, fractions, and decimals, including negatives. They switch between number forms when it helps, then check whether the answer makes sense using a quick mental estimate.

Students translate a real-world situation into an equation or inequality with a variable, then solve it by thinking through what the numbers actually mean.

Students set up and solve two-step equations from word problems, then explain why their algebra steps match the arithmetic they could have done in their head. A rectangle's perimeter problem is a good example.

Students write and solve inequalities from word problems, then plot the answer on a number line and explain what it means. For example: how many sales does a worker need to earn at least $100 this week?

Scale drawings use a ratio to shrink or enlarge real objects onto paper. Students create and interpret these drawings, figuring out actual measurements from a map or diagram.

Scale drawings use a fixed ratio to shrink or enlarge real shapes on paper. Students read a map or blueprint, calculate the actual size of a room or distance, and redraw the same figure at a new scale.

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

Given three side lengths, students figure out whether those lengths can actually form a triangle. If the two shorter sides added together are longer than the third, a real triangle exists.

Given three angles that add to 180 degrees, students draw all the different triangles those angles allow and compare what they find.

Given three angle or side measurements, students decide whether a triangle can actually exist. Some combinations are impossible, and students explain why.

Students learn what shape appears when you slice through a box or pyramid, whether the cut runs straight across, top to bottom, or at an angle. A horizontal cut through a box, for example, gives a rectangle.

Students solve everyday problems using angles, areas, and volumes. They find how much paint covers a wall, how much space fits inside a box, or what angle a ramp makes with the ground.

Students learn the formulas for a circle's area and circumference, then use them to solve real problems. They also explore why those two formulas are connected to each other.

Given a figure with intersecting or connected lines, students find a missing angle by writing and solving an equation. They use angle relationships like opposite angles being equal or two angles adding up to 90 or 180 degrees.

Students find the area, surface area, or volume of shapes built from triangles, rectangles, and other polygons, including boxes and prisms. Problems come from real situations, not just textbook diagrams.

Random sampling means picking a group by chance so the results represent everyone fairly. Students use that sample to make reasonable guesses about a larger group, like estimating how many kids in a school prefer a certain lunch.

Surveying part of a group to draw conclusions about the whole group only works if that smaller group fairly represents everyone. Random sampling is the most reliable way to get a fair slice.

Students pick a small random sample from a larger group, use it to make a prediction about the whole group, then repeat the process a few times to see how much their estimates shift.

Students look at data from two groups and draw conclusions about how they compare. For example, they might decide whether one class reads more books per month than another based on a dot plot or histogram.

Students compare two sets of data and identify which group has a higher average and which group's numbers are more spread out. They use both pieces of information together to draw conclusions about the two groups.

Reading two sets of data side by side, students compare things like test scores or heights across two groups. They look at how the numbers spread out and where the middle falls to draw conclusions about what the data actually shows.

Students count how many data points are in each group before comparing the two groups. A larger sample usually gives a more reliable picture.

Students explain what a data set is actually measuring, such as height in inches or time in minutes, and describe how that measurement was collected. This gives context to any comparison made between two groups.

Students summarize data from two groups by finding the median or mean of each, then describe what those numbers reveal about the overall pattern. This helps compare the two groups side by side.

Students compare two data sets by measuring how spread out the numbers are, using tools like the range or interquartile range. They also call out anything unusual that doesn't fit the pattern.

Students learn when to use the mean or median to describe a data set and when to use range or spread, based on whether the data is balanced or skewed and what the numbers actually represent.

Students compare two sets of data on a dot plot and judge how far apart the groups are. They measure the gap between the two averages and describe it in terms of how spread out each group's data is.

Students compare two groups using averages and spread, like checking whether words in a seventh-grade textbook are typically longer than words in a fourth-grade one. The goal is to draw a reasonable conclusion from real data, not just guess.

Students compare two sets of data by looking at how spread out each set is, not just which average is higher. They use that spread to draw conclusions about which group performed differently.

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 0.5 means it's a coin flip.

Students roll a die or flip a coin many times, record what happens, and use those results to predict how often an outcome will occur in a large number of tries. The more trials they run, the closer the results get to the true probability.

Students build a simple probability model (like predicting how often a coin lands heads), then run the experiment and compare what they predicted to what actually happened. If the numbers don't match, they explain why.

When every outcome has the same chance of happening, students calculate the probability of a specific result. For example, if names are drawn from a hat, they find the fraction that represents one name or a whole group being picked.

Students collect real results from an experiment, like spinning a penny or tossing a cup, then use those results to estimate how likely each outcome is. The probability comes from what actually happened, not from assuming every outcome has an equal chance.

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 diagrams to map out every possible outcome.

Compound events combine two or more simple events, like flipping a coin and rolling a die together. Students find the probability by counting how many outcomes in the full list of possibilities match what they're looking for, then writing that as a fraction.

Students list every possible outcome of two combined events (like rolling two dice) using a table, chart, or branching diagram, then circle the specific outcomes that match a given result.

Students set up a simple experiment, like drawing cards or using a number generator, to estimate how often two or more chance events happen together. Then they use the results to answer real probability questions.