What does a student learn in StateAlaska,GradeGrade 6,SubjectMathematics?

Students find the area of triangles, rectangles, and other flat shapes by splitting them into simpler pieces or combining them. They use these skills to solve real problems, like figuring out how much flooring or fencing a space needs.

Students calculate the volume of box-shaped figures using a formula, then examine how the shape of the base changes the overall figure. They also compare prisms and cylinders by looking at their faces and sides.

Students plot points on a grid to draw shapes, then measure the length of each side by counting units between corners that share a row or column. They use this to solve real problems involving distance and area.

Nets are flat, unfolded versions of 3D shapes like boxes or prisms. Students unfold those shapes on paper, then add up the area of each flat face to find the total surface area.

Students learn that a circle's diameter stretches all the way across the center, while the radius is just half that distance from center to edge. They compare these two measurements and describe how they relate.

Students write ratios to describe how two quantities relate, such as 3 cups of flour for every 2 cups of sugar or 4 red cars out of every 10 cars in a parking lot.

Unit rate means finding the cost, speed, or amount for exactly one of something. Students use division to simplify a ratio down to "per one" and then solve everyday problems like price per item or miles per hour.

Students use ratios and rates to solve everyday problems, like figuring out how far a car travels per gallon or how much ingredients to use when doubling a recipe. They work with tables, diagrams, and equations to find missing values.

Students build a table of equivalent ratios, fill in missing values, and plot those pairs as points on a graph. They use the table to compare ratios and spot which ones are equal.

Students figure out prices per item or speeds per hour by dividing one quantity by another. A typical problem might ask how much one apple costs or how far a car travels in a single minute.

Students figure out what a percent means in real numbers, like calculating 30% of a $50 gift card or working backward to find the full price when they know a discount amount and its percentage.

Students use ratios to convert between measurement systems, like turning kilometers into miles or pounds into kilograms. They keep track of which units cancel out so the answer lands in the right unit.

Dividing a fraction by another fraction gives a result students can picture and calculate. Students learn to split things like half a cup into quarter-cup portions and find out how many fit, using diagrams or equations to show their work.

Students multiply and divide large whole numbers by hand using the standard steps. They decide whether a leftover amount makes more sense as a remainder, a decimal, or a fraction based on what the problem is actually asking.

Students add, subtract, multiply, and divide numbers with decimal points using the standard written method. They also know what to do with a remainder: write it as a decimal or round it to a specific place.

Finding the greatest common factor means identifying the largest number that divides evenly into two given numbers. Finding the least common multiple means finding the smallest number both share as a multiple. Students also rewrite addition problems using shared factors to simplify them.

Positive and negative numbers show opposites: money earned vs. spent, degrees above vs. below freezing, ground level vs. underground. Students read and write these numbers in real situations and explain what zero means in each one.

Negative numbers have a place on the number line too, not just zero and the positives. Students learn to plot numbers like -3 or -7 on a number line and locate points with negative coordinates on a grid.

Negative and positive versions of the same number sit on opposite sides of zero on a number line. Flipping a number's sign twice lands back on the original number, and zero stays zero no matter how many times you flip it.

Two numbers pin a point on a grid. When you flip the sign on one or both numbers, the point mirrors across the grid's center line, landing the same distance away on the opposite side.

Students place whole numbers, fractions, and negatives on a number line and locate points on a grid using two coordinates. Reading a coordinate grid is the core skill here.

Students learn to place positive and negative numbers in the right order on a number line and to find how far any number sits from zero, regardless of which side it's on.

Students read an inequality like -3 < 5 and explain what it means on a number line: the number on the left sits further to the left. Position on the line is what makes one number less than another.

Students read a number line or a temperature chart and explain why one number is greater or less than another. They put that reasoning into words, not just a symbol.

Absolute value is how far a number sits from zero, regardless of which side. Students use this to make sense of real situations like debt or temperature, where the direction matters but the size of the gap matters more.

Absolute value measures how far a number is from zero, not which number is greater. Students learn to keep those two ideas separate: a negative number can have a large absolute value and still be less than a positive one.

Students plot points anywhere on a coordinate grid, including negative sides, then use those coordinates to calculate the distance between two points that share a row or column.

Exponents are shorthand for repeated multiplication. Students write and calculate expressions like 2 to the power of 4, meaning 2 times itself four times, and find the result.

Letters like x or n stand in for unknown numbers. Students write, read, and calculate the value of these expressions, the same way they'd solve a puzzle where a missing piece has a placeholder name.

Students write math expressions using numbers and letters, like 3x or 2 + n, to describe a calculation. The letter stands in for a number they don't know yet.

Students learn the vocabulary that names different parts of a math expression. Given something like 3x + 5, they can point to the coefficient, the term, or the sum and explain what each part means.

Students plug numbers into expressions and formulas, then calculate the answer in the right order: parentheses first, then exponents, then multiplication and division, then addition and subtraction.

Students rewrite math expressions into different but equal forms, like turning 3(x + 4) into 3x + 12. They use rules about how numbers and variables can be rearranged or grouped without changing the value.

Two expressions are equivalent when they produce the same result no matter what number you plug in. Students learn to recognize this pattern and confirm that two different-looking expressions are actually the same.

Students test whether a number makes an equation or inequality true by plugging it in and checking. It's the mathematical version of "does this value fit?"

Students learn that a letter like x can stand in for a number they don't know yet. They practice turning real-world problems into math expressions by swapping unknown values for a variable.

Students write and solve simple equations to answer real-world questions, like finding a missing price or distance. They practice two basic setups: adding a number to the unknown, or multiplying it.

Students write inequalities like x > 5 to describe real-world limits, such as needing more than five dollars. They then show all the values that work by marking them on a number line, which stretches on without end.

Students pick two quantities that change together (like hours worked and money earned), write an equation showing how one drives the other, then check whether a graph or table tells the same story.

A statistical question expects different answers from different people or sources. "How tall are students in our class?" is statistical. "How tall am I?" is not.

A data set tells a story about a group, and students learn to summarize that story three ways: where the middle falls, how spread out the values are, and what the overall pattern looks like.

Mean, median, and mode each collapse a whole set of numbers into one number that represents the middle or most common value. Range does the opposite: it shows how spread out those numbers are.

Students learn to show a set of numbers as a visual chart, such as a dot plot, histogram, or box plot, so patterns in the data are easier to spot.

Numerical data sets are collections of numbers gathered around a real question, like "How many minutes do students sleep?" Students learn to summarize those numbers by describing what's typical, how spread out the values are, and how the data was collected.

Students count how many data points are in a dataset and report that total. It is the first step in summarizing any set of numbers, like recording how many students were surveyed before analyzing the results.

Students explain what was being measured in a data set and how it was recorded. For example, they note whether the data tracks height in inches or time in minutes, so the numbers in the chart actually make sense.

Students find the middle value and average of a data set, measure how spread out the numbers are, and note any values that look unusually high or low. Then they explain what those numbers mean in real life.

Students decide whether the mean or median tells a more honest story about a set of data, based on how spread out the numbers are and what the data is actually measuring.

Students figure out whether a game is fair by calculating the chances of every possible result. If each player has an equal shot at winning, the game is fair. If not, they explain why one player has the advantage.

Students figure out how many different choices are possible when mixing and matching options, like picking one ice cream flavor and one topping. They multiply the number of options in each category to find the total combinations.