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

Students find the area and circumference of circles using the standard formulas, then solve real-world problems with those results. They also explore why the two formulas are connected.

Students explore how 3-D shapes relate to each other, such as how a pyramid fits inside a prism of the same base and height. The goal is to see patterns in how volume and structure change across different solid figures.

Students learn that the volume of any prism or cylinder follows the same rule: multiply the area of the base shape by the height. Whether the base is a rectangle, triangle, or circle, that one formula covers it.

Students learn one formula that finds the total surface area of any prism or cylinder: double the base area, then add the area of all the sides wrapped around it. They apply it to shapes like cereal boxes and soup cans.

Students find the area of flat shapes like triangles and rectangles, then move to 3D shapes, calculating how much space a box or cylinder holds and how much material covers the outside.

A scale drawing shrinks or enlarges a real object by a set ratio. Students use that ratio to find actual lengths and areas from a map or diagram, and to redraw the same figure at a new scale.

Students see what solid shape appears when a flat rectangle or triangle spins around one of its edges. A spinning rectangle traces out a cylinder; a spinning triangle traces out a cone.

Cut straight through a box or a can and look at the flat shape left behind. Students identify what that cross-section looks like, whether it's a rectangle, circle, or other shape, depending on the angle of the cut.

Students find the rate for one unit when both numbers in a ratio are fractions. For example, they calculate miles per hour when the distance and time are each given as a fraction.

Two quantities are proportional when they grow (or shrink) at a constant rate. Students identify that relationship in tables, graphs, and equations, then use it to solve problems like finding unit price or converting measurements.

Students decide whether two quantities change at the same steady rate. They check by looking for matching ratios in a table or by graphing the values to see if the points form a straight line that passes through zero.

Students look at a table or graph and check whether every row or point shows the same rate, like $2 per mile or 3 cups per batch. That consistent rate is what makes the relationship proportional.

Students write an equation to describe a proportional relationship, such as total cost equals price times number of items, then use that equation to find missing values.

Students read a graph of a proportional relationship and explain what each plotted point means in real terms. The point (0, 0) means none in, none out, and the point where x is 1 shows the unit rate.

Students use percentages to solve real-world money problems: figuring out sales tax, tips, discounts, interest on a loan, or how much a price went up or down.

Students show addition and subtraction by moving left or right on a number line, including with negative numbers. A jump in the right direction means adding; a jump back means subtracting.

Positive and negative numbers that are the same distance from zero cancel each other out. Students learn that 5 and -5 add up to zero, and can spot real situations where that happens, like earning and spending the same amount.

Adding a negative number moves left on the number line; adding a positive moves right. Students show that p + q lands exactly |q| steps away from p, in whichever direction the sign of q points.

Subtracting a number gives the same result as adding its opposite. So 5 minus 3 is the same as 5 plus negative 3. Students use this idea to subtract any positive or negative number on a number line.

Subtracting two numbers tells you the distance between them on a number line. That distance is always positive, because distance doesn't go negative.

Adding and subtracting negative numbers gets easier with a few reliable rules. Students use properties like the commutative and associative rules to rearrange and simplify problems instead of brute-forcing every calculation.

Multiplying and dividing with negative numbers follows the same process as with positive ones. Students learn the sign rules (negative times negative equals positive, for example) and apply them to fractions and decimals too.

Multiplying negative numbers follows the same rules as multiplying positive ones. Students learn why a negative times a negative equals a positive, and practice applying sign rules to any multiplication problem with integers or fractions.

Students learn that dividing any two whole numbers (as long as you're not dividing by zero) always produces a fraction or integer. A negative sign on a division problem can sit in front of the fraction, on top, or on the bottom and the result is the same.

Multiplying and dividing with negative numbers follows the same rules as whole numbers, with one addition: two negatives make a positive. Students use those patterns as shortcuts instead of reworking the logic each time.

Students use long division to turn a fraction into a decimal. Every fraction either ends cleanly (like 0.25) or settles into a repeating pattern (like 0.333...), and students learn to tell the difference.

Real-world math problems often mix positive and negative numbers, fractions, and decimals. Students solve those problems using addition, subtraction, multiplication, and division, then explain what the answer actually means in context.

Students rearrange and simplify algebraic expressions by combining like terms, factoring, and expanding. The goal is to write the same expression in a different but equivalent form using whole-number and negative coefficients.

Rewriting a math expression in a different but equal form can reveal what's really happening in a problem. Students practice spotting those connections, like seeing that 1.05p and p + 0.05p both describe a 5% price increase.

Multi-step word problems often mix whole numbers, fractions, decimals, and negatives. Students solve those problems, switch between number forms when it helps, and check whether the answer makes sense before moving on.

Students translate a real-world situation into an equation or inequality with a variable, then solve it in two steps. Think: a starting price plus a fee equals a total, so what's the fee?

Word problems here involve setting up and solving equations with one unknown, like figuring out how many hours of work it takes to earn a certain amount. Students solve these efficiently and compare the algebra steps to what a plain number-crunching approach would look like.

Students solve word problems where the answer is a range of numbers, not a single value, then plot that range on a number line and explain what it means in the real situation.

Surveying every person in a group is rarely practical, so students learn to study a smaller sample and use what they find to draw conclusions about the whole group.

Surveying a small group only works if that group reflects the larger population. Students learn to spot whether a sample is truly representative and practice choosing samples that are.

Students look at a survey or sample and decide whether it fairly represents the whole group. They explain why the sample is trustworthy or why it might be skewed.

Students take a small random sample, use it to make a prediction about a larger group, then repeat the process with more samples to see how much their estimates shift from one sample to the next.

Students compare two sets of data on a graph to see how much they overlap and how far apart their centers are. The gap between the two groups gets measured in units of spread, not just raw numbers.

Students compare two groups using averages and spread, such as the typical score and how far apart the scores run, then draw a conclusion about which group tends to be higher, lower, or more consistent.

Students express how likely something is to happen as a number between 0 and 1. A result near 0 means it probably won't happen, near 1 means it probably will, and around one-half means it's a coin flip.

Flip a coin 10 times and heads might show up 3 times. Flip it 500 times and the results get closer to 50-50. Students run probability experiments to see how real results inch toward predicted results as the number of tries grows.

Students build a simple probability model (like predicting how often a coin lands heads) and then test it with real trials. If the prediction and the actual results don't match, students explain why.

Students learn that when every outcome has the same chance of happening, like rolling a number cube, they can find the probability of any result by dividing one outcome by the total number of 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 odds of two or more things happening together, like flipping a coin and rolling a die at the same time. They use lists, tables, and branching diagrams to map out every possible outcome.

Finding the chance of two events happening together works the same way as finding the chance of one event. Students count how many outcomes in the full list match what they're looking for, then write that as a fraction.

Students list every possible outcome for two-part events, like rolling two dice or flipping a coin and spinning a spinner, using a table or branching diagram. Then they pinpoint exactly which outcomes match the event they care about.

Students design a real or pretend experiment, like flipping coins or rolling dice, to estimate how often two events happen together. Running the experiment many times gives a picture of the actual odds.