What does a student learn in StateNorth Carolina,GradeGrade 6,SubjectMathematics?

A ratio compares two amounts, like 3 red tiles for every 5 blue tiles. Students write and read ratios using "for every," "to," and fraction notation to describe how two quantities relate.

A ratio compares two quantities by multiplication, not just subtraction. Students explain why 3 cups of juice to 2 cups of water means the juice is 1.5 times the water, not just "1 more cup."

Students show the same ratio in more than one way, such as a table, a diagram, or an equation. The goal is to see that each representation tells the same story about how two quantities relate.

A unit ratio simplifies a comparison to "per one," like miles per gallon or dollars per item. Students find both versions of that "per one" relationship in a problem and explain what each version means in context.

Ratio reasoning means using a known relationship between two quantities to find missing values. Students apply this thinking to real problems, like figuring out how many cups of juice to mix if the batch size changes.

Students build a table to line up two related quantities, like cups of juice to cups of water, then read across the rows to see if the amounts stay in the same proportion.

Students fill in a table where some numbers are missing by figuring out the relationship between the values in each row or column. It's a core skill for working with rates, prices, and other real-world comparisons.

Students find a unit ratio (like 3 miles per 1 hour) and use it to scale up or down, solving problems that ask how much of one thing goes with a given amount of another.

Students convert between units (feet to inches, minutes to hours) by setting up and solving ratios. They use the same method to rescale any measurement when a conversion rate is given.

Students take two related numbers, such as cups of flour and batches of cookies, and plot each pair as a point on a grid. Reading the graph shows how the two amounts grow together.

Percents are ratios compared to 100. Students use that idea to solve everyday problems, like figuring out a discount, a tax amount, or what score 18 out of 25 really means.

Percent means "out of 100." Students find a percent of a number by treating it as a ratio, so 30% of 200 means 30 out of every 100, which gives 60.

Students use simple percents like 50% or 25% as building blocks to find a piece of any number. For example, to find 15% of 80, they combine 10% and 5%.

Students figure out the full amount when they know a piece of it and what percent that piece represents. For example, if 30 students are 60% of the class, they work backward to find the total number of students.

Dividing a fraction by another fraction can seem abstract, so students use pictures and shared denominators to make the math visible before writing it as a number sentence.

Dividing one fraction by another gives a quotient, just like dividing whole numbers does. Students practice computing those quotients and explain what the answer means in a real situation, such as how many half-cup servings fit in three-quarters of a cup.

Students divide fractions to solve real problems, like splitting half a pizza equally among three people. They work through the math and explain what the answer actually means in the situation.

Students divide large numbers using long division, with at least four digits on top. They also explain what the answer and any leftover amount actually mean in the real problem.

Students add, subtract, multiply, and divide decimal numbers using the standard written steps. This builds on what students already know about place value so they can work with dollars, measurements, and other real-world numbers that aren't whole.

Prime factorization breaks a whole number down into the prime numbers that multiply together to make it. Students use that breakdown to find the greatest common factor and least common multiple of two numbers.

Breaking a whole number down into its prime building blocks. Students find the one combination of prime numbers that multiplies together to make that number, like writing 12 as 2 x 2 x 3.

Students find the largest number that divides evenly into two numbers, like figuring out the biggest equal group size that works for both 36 and 48. This is called the greatest common factor.

Finding the greatest common factor lets students rewrite a sum like 36 + 48 as 12(3 + 4). Students factor out the largest shared number and rewrite the addition in a simpler form.

Finding the least common multiple means figuring out the smallest number that two numbers both divide into evenly. Students use that shared number to rewrite fractions so they have the same bottom number, making addition and subtraction possible.

Rational numbers include positives, negatives, and zero. Students use them to describe real situations like owing money, measuring below sea level, or tracking temperature changes above and below freezing.

Negative numbers and positive numbers point in opposite directions. Students learn that owing $5 and earning $5 are opposites, and that numbers on either side of zero describe real situations pulling in different directions.

Students explain what zero means in a real-world situation, such as sea level, freezing temperature, or a zero balance in a bank account. Zero marks the dividing point between opposite values.

Absolute value is how far a number sits from zero on a number line, ignoring direction. A temperature of -8 degrees and a temperature of 8 degrees are both 8 steps from zero, so both have an absolute value of 8.

Absolute value is the distance a number sits from zero, regardless of direction. Students learn that -7 and 7 are both 7 steps from zero, which helps make sense of real situations like a debt of $7 and a gain of $7.

Absolute value measures distance from zero, not position on a number line. Students learn that -8 is farther from zero than -3, but -3 is still greater than -8 because it sits to the right.

Students place fractions, decimals, and negative numbers on a number line and locate points on a grid using two coordinates. Both skills build the foundation for graphing in later math.

Plotting positive and negative numbers on a number line, including fractions and decimals. Students place values on both sides of zero and understand that opposite numbers are the same distance from zero in different directions.

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.

Students place fractions, decimals, and negative numbers at the correct spot on a number line, whether it runs left to right or top to bottom.

Students plot and name points in all four sections of a coordinate grid, using positive and negative numbers for both the left-right and up-down positions. They also recognize that points like (3, -5) and (-3, -5) are mirror images across an axis.

Students learn that positive and negative signs in a coordinate pair tell you which section of a graph the point lands in. A positive x and positive y puts you in one corner; mix the signs and the point moves to a different section.

Two points on a grid that share the same numbers but with opposite signs are mirror images of each other. Flip across the horizontal axis, the vertical axis, or both, and the points land on top of each other.

Students plot pairs of numbers (like 3 and -3) on a coordinate grid to find and mark their exact locations. This builds on what students know about number lines and extends it to a full grid with four sections.

Students compare and order positive and negative numbers, including fractions and decimals, by placing them correctly on a number line. A temperature of -5 is less than 3, even though 5 looks bigger.

Students read an inequality like, 3 < 5 and explain what it means on a number line: which number sits further left, which sits further right, and why that position makes one value smaller or larger.

Students read a number line or chart and explain why one number sits above, below, or between another. For example, they compare temperatures, debts, or elevations and put them in order using less than or greater than.

Students plot and locate points anywhere on a coordinate grid, then use those coordinates to measure the distance between two points that share the same row or column.

Adding a positive number and its matching negative cancels out to zero. Students use this idea to add and subtract integers, including negative numbers on a number line or in real-life situations like temperature or debt.

Positive and negative numbers can cancel each other out. Students identify real-life situations where two opposite values, like earning $5 and spending $5, add up to zero.

Adding a negative number moves left on the number line; adding a positive moves right. Students also learn that a number and its opposite, like 3 and -3, cancel each other out and sum to zero.

Subtracting an integer is the same as adding its opposite. Students use a number line to show that the distance between two numbers equals the absolute value of their difference.

Students use number lines and counters to add and subtract positive and negative numbers. They connect the math to real situations, like owing money or measuring temperature changes.

Students write and calculate expressions that include exponents, such as 2 to the power of 3, and work out the correct answer when parentheses change the order of operations.

Reading and writing algebraic expressions means replacing a number with a letter (called a variable) to show an unknown value, then following the order of operations to find the answer when a number is plugged in.

Students write math expressions using numbers and letters, like 3x + 5 to mean "three times a number, plus five." Letters stand in for unknown values the way a blank line would on a worksheet.

Reading an expression like 2(3 + x), students name each piece: the coefficient, the sum inside the parentheses, the terms. They also recognize that a grouped part, like (3 + x), can act as one chunk.

Students plug a number into a formula, like swapping in a speed or a price, and calculate the result. This is how they move from abstract equations to answers that mean something in real life.

Students rewrite math expressions into simpler or different forms using rules like the distributive property. For example, 3(x + 4) becomes 3x + 12, and both mean the same thing.

Two expressions can look different but equal the same value. Students learn to recognize when that's true and explain why, using what they know about number properties and operations.

Plug a number into an equation to check if it makes both sides equal. Students test values from a list to find which one actually solves the equation.

Students write expressions like 3x or n + 5 to describe a real-world situation, such as finding the cost of several items or splitting a group evenly. The variable stands in for the unknown number.

Students write an equation to match a real-world situation, then solve for the unknown. The focus is on problems where the unknown is added to, subtracted from, multiplied by, or divided by a whole number or fraction.

Students solve equations like x + 7 = 15 by figuring out what number makes both sides equal. All numbers in the problem are positive, including fractions and decimals.

Students solve multiplication equations like 3 • x = 12 using positive whole numbers and fractions. They find the missing value by asking what number, multiplied by the one they know, gives the result.

Reading an inequality like x > 5 and explaining what it means in a real situation. Students also plot the solution on a number line and understand that inequalities have many correct answers, not just one.

Students test whether a number makes an inequality true by plugging it in and checking. For example, does 4 make x + 3 > 6 true? Students try the number and see if the statement holds.

Students write an inequality like x > 5 or x < 10 to describe a real-world limit, such as a speed limit or a minimum age. The inequality captures the condition in math symbols.

Students learn that an inequality like x > 5 has no single answer. Any number greater than 5 works, so the solution is a whole range of values shown as an arrow on a number line.

Students write an inequality like x > 4 or x < 10, then mark its solution on a number line using an open or closed dot and a shaded ray. The number line shows every value that makes the inequality true.

Students identify which number in a pair changes on its own (like days passing) and which one responds to it (like money earned). They write an equation to show that relationship and use a table or graph to see the pattern.

Students pick two quantities that change together, like hours worked and money earned, and use variables to show how one depends on the other.

Students look at the same math relationship shown four different ways (a word problem, an equation, a table, and a graph) and explain how the numbers connect across each one.

Find the area of triangles, quadrilaterals, and other polygons by composing or decomposing them into known shapes. Students apply these skills to real problems, like calculating how much flooring or fabric a space requires.

Finding the area of a triangle by fitting it inside a rectangle or splitting it into right triangles. Students use what they know about rectangle area to figure out how much space a triangle takes up.

Students find the area of unusual shapes by cutting them into triangles or rectangles, then adding those areas together. It's the math behind figuring out how much flooring or paint a room with an odd layout would need.

Finding the volume of a box when its length, width, or height is a fraction, like 2 and a half inches. Students multiply the three side lengths together and use that calculation to solve real problems.

Drawing shapes on a grid and using the coordinates of their corners to find side lengths, perimeters, or distances between points.

Students plot points on a grid using coordinate pairs, connect them, and draw shapes like triangles or rectangles. The focus is on using the coordinates accurately to form the correct polygon.

Students use coordinate grids to measure the length of a horizontal or vertical line segment by finding the distance between two points that share the same x- or y-value.

Students unfold the faces of a box or pyramid into a flat pattern, then add up the area of each face to find the total surface area. Problems connect this to real situations like wrapping a gift or covering a shape with material.

A statistical question expects different answers from different people or sources, not one single answer. Students learn to tell the difference between "How old am I?" and "How old are the students in this school?"

A set of data has a pattern to it. Students learn to describe that pattern by finding where values cluster in the middle, how spread out the values are, and what the overall shape of the data looks like on a graph.

Reading a set of numbers means looking at two things: a middle value (like an average) and how spread out the numbers are. Both together give a fuller picture than either one alone.

Finding the center of a data set means picking one number that best represents the whole group. Students learn to calculate the mean or median so a set of values can be summarized at a glance.

The mean (average) shows where a set of numbers "balances out," like finding a fair split among a group. One unusually high or low number can pull the mean away from what most of the data actually shows.

The median is the middle number in a list sorted from smallest to largest. Students find it by ordering all the values and locating the one in the center.

Two graphs can show the same average but tell very different stories. Students compare data displays to see how spread out or tightly packed the values are, even when the midpoints look identical.

Students organize numbers by placing them on a dot plot, histogram, or box plot. Each display makes it easier to spot where data clusters, where gaps appear, and how spread out the values are.

Students learn to display a set of numbers as a dot plot, histogram, or box plot. Each graph type shows the same data differently, so students choose the one that makes patterns easiest to read.

Students look at the same set of data shown in two different graphs or displays and explain what each one makes easy to see and what each one hides.

Students summarize a set of numbers by reporting how many values there are, what the numbers measure, and which average or spread best describes the data. They explain why their chosen summary fits the situation.

Reporting what a data set is about: how many values it includes, what was measured, and how the measurement was done.

Students count and report how many data points appear in a dot plot or histogram. This is the first step in making sense of what a graph is actually showing.

Students explain what they measured, how they measured it, and what units they used, such as inches or minutes. This gives the data context so the numbers make sense.

Describing what a set of numbers measures, why it was collected, and how many values are in it, before drawing any conclusions about patterns or spread.

Students find the average or median of a data set, describe how spread out the values are, and point out anything unusual, like a number that falls far outside the rest.

Students look at whether data is spread evenly or skewed to one side, then explain why the mean or median is the better summary number for that shape.