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

Scale drawings show a real object shrunk or enlarged by a set ratio. Students use that ratio to find the actual size of lengths and areas, then redraw the figure at a new scale.

Given three angle or side measurements, students draw triangles and figure out whether those numbers produce exactly one triangle, several possible triangles, or no triangle at all.

Slice through a 3-D shape like a box or pyramid and describe the flat shape the cut reveals. A straight slice through a box makes a rectangle; an angled slice through a pyramid might make a triangle.

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

When two angles share a line or a corner, their measures follow predictable rules. Students use those rules to write a short equation and solve for the missing angle in a diagram.

Students find the area, volume, or surface area of shapes built from triangles, rectangles, and other flat or solid figures. That means calculating how much carpet covers a floor or how much cardboard wraps a box.

Unit rates compare two measurements as a single "per one" number, like miles per hour or cost per ounce. Students calculate these rates even when the measurements involve fractions, such as half a mile walked in a quarter of an hour.

Two quantities are proportional when they grow (or shrink) at the same steady rate. Students identify whether a relationship is proportional, represent it as an equation or graph, and use it to make predictions.

Students check whether two quantities always change at the same rate, using a table of values or a graph to see if the relationship forms a straight line through zero.

Students find the unit rate hiding inside a table, graph, equation, or word problem. For example, if a car travels 150 miles in 3 hours, they pull out the 50 miles per hour that ties the whole relationship together.

Students write an equation to describe a proportional relationship, then check that the same pattern shows up in a table or graph. A constant rate connects every representation.

Students read a graph to explain what each plotted point means in a real situation. The point (1, r) shows the unit rate, such as miles per hour, and (0, 0) confirms the relationship starts at zero.

Students use ratios and percents to solve everyday problems with multiple steps, like calculating a sale price after a discount, figuring out how much tax is added, or finding the interest owed on a loan.

Students add and subtract positive and negative numbers, including fractions and decimals. They show what that looks like by plotting and moving along a number line.

Adding a number to its opposite always lands on zero. Students learn to spot this in real life, like a bank account that gains $15 and then loses $15, ending up exactly where it started.

Adding a positive number moves up the number line; adding a negative number moves down. Students connect this to real situations, like a bank balance rising or falling after a deposit or withdrawal.

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 solve real problems involving negatives, like temperatures or debt.

Students use shortcuts like grouping or reordering numbers to make adding and subtracting fractions, decimals, and negatives easier. The arithmetic is the same; the order just gets rearranged to simplify the work.

Multiplying and dividing with negative numbers, fractions, and decimals. Students learn the rules for when answers turn negative and practice switching between fractions, decimals, and percentages to express the same value.

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

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 without changing the value.

Multiplying and dividing with fractions, decimals, and negative numbers follows the same rules as whole-number math. Students name which property, such as the commutative or distributive property, they used to solve a problem.

Students use long division to turn a fraction into a decimal. Every fraction either stops cleanly (like 0.25) or repeats a pattern of digits that goes on forever (like 0.333...).

Students practice switching between fractions, decimals, and percents to express the same value in different forms. For example, knowing that 3/4, 0.75, and 75% all mean the same thing.

Word problems that mix whole numbers, fractions, negatives, and decimals ask students to add, subtract, multiply, or divide to find a real answer. Students apply the same fraction rules they already know, even when the numbers get messier.

Students simplify and rearrange expressions with fractions and negative numbers by combining like terms, factoring, and expanding. The goal is to rewrite a messy expression into a cleaner, equivalent form.

Rewriting a math expression in a different form can reveal something useful about the problem. For example, rewriting 1.05x as (1 + 0.05)x shows both the original amount and the 5% increase at the same time.

Students solve everyday problems with positive and negative numbers, fractions, and decimals across multiple steps. They also check whether their answer makes sense by estimating before or after they calculate.

Students use a letter to stand in for an unknown number, then build and solve equations or inequalities to answer real-world questions, like finding how many hours of work it takes to earn a certain amount.

Word problems here lead to a two-step equation, like "three times a number plus five equals twenty." Students learn to work backward through the math to find the unknown number.

Students write and solve inequalities from real-world word problems, then plot the answer on a number line and explain what the solution means in plain terms.

Surveying a small, randomly chosen group can reveal patterns about a much larger group. Students learn why the way a sample is chosen matters as much as its size.

Students collect random samples from a larger group to make reasonable guesses about the whole population. By comparing several samples of the same size, students see how much estimates can shift from one sample to the next.

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

Students compare two groups using averages and spread, like comparing the typical quiz score and score range in two classrooms, to draw conclusions about which group tends to perform differently and why.

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

Students run an experiment many times, like flipping a coin or rolling a die, to see how often each outcome actually happens. The more trials they run, the closer the results get to the true probability.

Students build a simple probability model (like a spinner or coin flip), predict how often an outcome should happen, then compare that prediction to what actually happens. If the numbers don't match, students explain why.

Students learn that when every outcome is equally likely (like rolling a fair die), each one gets the same share of the probability. They use that idea to figure out the chances of specific results.

Students collect real data from an experiment, like flipping a coin or spinning a spinner, then use those results to build a model that predicts how often each outcome is likely to happen.

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.

When two things happen together (like flipping a coin and rolling a die), students find the probability by counting the favorable combinations out of all possible combinations.

Students list every possible outcome for two combined events, like rolling two dice, using a chart or branching diagram. Then they pick out which outcomes match a specific result, such as both dice landing on six.

Students build a real-world model, like flipping coins or rolling dice, to figure out how often two or more chance events happen together. They run the simulation and record results instead of just calculating by hand.