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

Students draw and build geometric figures, like triangles and angles, then explain how changing one shape affects another. The focus is on seeing the connections between shapes, not just naming them.

Scale drawings use a ratio to shrink or enlarge real objects, like a map where one inch stands for a mile. Students figure out real lengths and areas from those drawings, then 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, several possible triangles, or no triangle at all.

Cut a 3-D shape like a box or pyramid with an imaginary flat plane and name the 2-D shape left behind. Students learn that the angle of the cut changes what that flat cross-section looks like.

Students use formulas to find angles, area, and volume in shapes they'd see in real life, like a room, a box, or a ramp.

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

When two or more angles share a corner or a straight line, students use what they know about how those angles relate to write and solve an equation that finds the missing angle.

Students find the area, volume, or surface area of shapes made from triangles, rectangles, and other polygons, including boxes and prisms. Problems use real objects, not just diagrams.

Proportional relationships show up everywhere: recipe scaling, unit prices, speed. Students learn to spot them, set up ratios, and use those ratios to solve real problems with numbers.

Students figure out the rate for one unit when both numbers in the ratio are fractions, like finding miles per hour when each measurement is itself a fraction.

Two quantities are proportional when they change at a steady rate together, like doubling one doubles the other. Students identify that relationship in tables, graphs, and equations.

Students check whether two quantities stay in a constant ratio by scanning a table for equivalent fractions or plotting the data to see if the points form a straight line through zero.

In a proportional relationship, one value always changes by the same rate relative to the other. Students find that fixed rate, whether it appears in a table, a graph, an equation, or a written description.

Students write an equation to show how two quantities change together at a constant rate. For example, if every hour earns $9, they write an equation that finds the total for any number of hours.

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

Students use ratios and percentages to solve real-life problems across multiple steps, like figuring out a sale price after a discount, calculating sales tax, or finding simple interest on a loan.

Students build on what they know about fractions to add, subtract, multiply, and divide with negative numbers, decimals, and fractions. This is the math behind debt, temperature changes, and anything that moves in two directions.

Adding and subtracting positive and negative numbers, including fractions and decimals. Students use a number line to show why the math works, not just what the answer is.

Adding opposite numbers always lands at zero. Students learn to recognize this in real situations, like a temperature rising 5 degrees then dropping 5 degrees, or owing $10 and then earning $10 back.

Adding a positive number moves right on the number line; adding a negative moves left. Students learn that any number plus its opposite always equals zero, and they connect this 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 and to solve real problems involving negatives.

Adding and subtracting rational numbers gets easier when students use shortcuts like the commutative or associative properties. Instead of grinding through each problem from scratch, students rearrange or regroup numbers to make the math simpler.

Multiplying and dividing negative numbers, fractions, and decimals follows the same rules students already know from whole numbers. Students learn when the answer is positive, when it's negative, and why that pattern holds.

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

Dividing one whole number by another always produces a fraction or whole number, never a broken result. Students learn that a negative sign on a division problem can sit on the top number, the bottom number, or out front, and all three mean the same thing.

Multiplying and dividing fractions, decimals, and negative numbers follows the same rules as whole numbers. Students use those familiar properties (like order doesn't change the answer) to work through trickier calculations.

Dividing the top number by the bottom number turns any fraction into a decimal. That decimal either stops completely or settles into a repeating pattern of digits.

Adding, subtracting, multiplying, and dividing with fractions, decimals, and negative numbers shows up in everyday problems like splitting a bill or calculating a temperature drop. Students apply all four operations to solve those kinds of problems.

Students rewrite math expressions into simpler or different forms using rules like the distributive property and combining like terms. The goal is to make expressions easier to work with, not to solve for a variable.

Students rewrite expressions like 3x + 6 into 3(x + 2), or combine like terms to simplify. The goal is to rearrange an expression into an equivalent form without changing its value.

Rewriting a math expression in a different form can reveal shortcuts or connections that aren't obvious at first glance. Students practice spotting those equivalent forms and explaining what the new version shows about the problem.

Students practice turning everyday situations into equations and solving them. That means figuring out an unknown value, whether the problem comes from a word problem, a table, or a real-world scenario.

Students solve real-world problems that mix whole numbers, fractions, and decimals, including negatives. They pick the most useful form for each number, work through the math, 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. Think of it as translating a sentence like "twice a number minus 4 equals 10" into math and finding the missing value.

Students set up and solve equations with one unknown to answer real-world word problems, such as finding a missing price or distance. They also compare the algebraic steps to plain arithmetic to see why both paths reach the same answer.

Students solve word problems where the answer is a range of numbers, not just one. They show the solution on a number line and explain what that range means in the real situation.

Students learn to survey a small group and use those results to make reasonable predictions about a much larger group, like estimating how many kids in a school prefer a certain lunch by polling one class.

Surveying a small, randomly chosen group can reveal patterns about a much larger group, but only if the sample reflects the whole. Students learn why picking people at random matters and what makes a survey result trustworthy.

Students take a small random sample, like surveying 30 kids to estimate something about the whole school, then repeat the process with more samples to see how much the results shift each time.

Students compare two groups using real data, like test scores or heights, and draw conclusions about how the groups differ. They support their conclusions with what the numbers actually show, not just a guess.

Students compare two sets of data on a graph and describe how far apart the midpoints are, using the spread of the data as the measuring stick.

Students compare two groups using averages and spread. For example, they might look at test scores from two classrooms and decide which group tends to score higher or whose scores are more spread out.

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. A probability near 0 means it rarely happens, near 1 means it almost always happens, 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. If a coin is flipped 200 times, they can predict roughly how often heads will land.

Students build a simple probability model, like a coin flip or spinner, predict how often each outcome should happen, then compare those predictions to what actually happens and explain any big differences.

When every outcome has the same chance of happening (like rolling a fair number cube), students figure out the probability of a specific result by dividing one outcome by the total number of possible outcomes.

Students collect data from a real experiment, like flipping a coin or spinning a spinner, then use what actually happened to build a model that predicts how likely each outcome 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 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 outcome combinations make the event happen, then dividing by all possible combinations.

Students list every possible outcome for two-part events, like rolling two dice, using a table or branching diagram. Then they pinpoint exactly which combinations match a specific result.

Students build a simple experiment, like flipping coins or rolling dice, to act out situations where two or more things happen at once. They run it repeatedly and record the results to estimate how likely different outcomes are.