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

Ratios compare two quantities, like 3 red tiles to 5 blue tiles. Students use that relationship to solve real problems, such as scaling a recipe or finding a unit price.

A ratio compares two quantities, like 3 red tiles for every 5 blue tiles. Unlike a fraction, a ratio doesn't always show part of a whole. Students learn to read and write these comparisons using ratio language.

Students figure out what one unit costs, travels, or produces when given a relationship between two quantities. For example, if a car goes 150 miles on 3 gallons, students find the miles per gallon.

Solving everyday problems with ratios means figuring out things like how much ingredients to use if you double a recipe, or how fast a car is traveling. Students use tables, diagrams, and equations to find missing values when two quantities are always in the same proportion.

Students build tables of equivalent ratios, fill in missing values, and plot the pairs on a graph. They use those tables to compare two ratios side by side.

Students figure out the price per item or the speed per hour when given a real-world situation. They use that single-unit rate to answer questions like how much 7 items cost or how far a car travels in 3 hours.

Students figure out what percent means in real life, like finding 30% of a price or working backward to find the full amount when they only know a piece of it and the percent.

Students use multiplication or division to switch between units in the same measurement system, like converting inches to feet or centimeters to meters. The ratio between units stays the same; only the numbers change.

Dividing a fraction by another fraction builds on what students already know about multiplication and division. Students learn to split fractional amounts into equal parts and find how many times one fraction fits into another.

Students divide a fraction by another fraction and explain what the answer means in a real situation, like figuring out how many half-cup servings fit in three-quarters of a cup.

Students practice long division, multiplication, and other operations with large numbers. They also find shared factors and multiples, which helps simplify fractions and solve problems with groups of unequal sizes.

Students practice long division with large numbers until they can work through the steps accurately and at a reasonable speed, without a calculator.

Students add, subtract, multiply, and divide decimal numbers like 3.75 or 12.4 using the standard written method, working quickly and accurately without a calculator.

Finding the greatest common factor means identifying the largest number that divides evenly into two given numbers. Students also find the smallest number two values share as a multiple, then use those skills to rewrite addition problems in a simpler grouped form.

Rational numbers include positives, negatives, and zero. Students use what they already know about whole numbers and fractions to place these numbers on a number line, compare them, and solve problems that involve negative values like temperature or debt.

Positive and negative numbers show opposites: money earned vs. spent, temperature above vs. below zero. Students read and write these numbers in real situations and explain what zero means in each one, such as breaking even or standing at sea level.

Students learn that numbers can be negative and place them on a number line or a grid. Finding a point like -4 or (-3, 2) works the same way as with positive numbers, just extending the line in the opposite direction.

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 at the original number.

Two points like (3, 4) and (-3, 4) are mirror images across an axis on a grid. Students learn to read the positive or negative signs in a coordinate pair to figure out which section of the grid a point lands in.

Students place whole numbers, fractions, and negatives on a number line and locate points on a grid using two coordinates. Both skills connect the idea that numbers have an exact position in space.

Students place positive and negative numbers in the right order on a number line and understand that absolute value measures how far a number is from zero, regardless of direction.

Reading a number line tells students which of two numbers is bigger or smaller. Students look at where each number sits on the line and use that position to explain what an inequality like, 3 < 2 actually means.

Students look at two numbers on a number line and explain in plain language which is greater and why. For example, they explain why a temperature of -3 degrees is colder than -1 degree, even though -3 looks like the bigger number.

Absolute value is how far a number sits from zero on a number line, ignoring which direction. Students learn why a number's distance from zero is different from saying which number is bigger or smaller, using real situations like temperature or debt.

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

Students start turning number sentences into expressions with variables, using what they already know about addition, multiplication, and other operations to work with unknowns for the first time.

Students learn what it means when a number has a small raised number next to it, like 2 to the power of 3. They calculate the result by multiplying the base number by itself that many times.

Variables are letters that stand in for unknown numbers. Students write, read, and solve expressions like 3x + 5 by swapping the letter for a given number and calculating the result.

Students translate word problems and number sentences into math expressions using variables. A phrase like "five more than a number" becomes x + 5.

Students learn the vocabulary for reading math expressions: a number multiplied by a variable is a coefficient, numbers or variables separated by addition are terms, and a multiplication result is a product. They treat groups of symbols as one unit when solving.

Students plug a given number into an expression and calculate the result, following the standard order of operations: exponents first, then multiplication and division, then addition and subtraction.

Students rewrite math expressions in a simpler or different form using rules like multiplying across parentheses. The value stays the same even when the expression looks different.

Two expressions are equivalent when they give the same result no matter what number you plug in. Students learn to spot when two different-looking expressions are actually the same thing in disguise.

Students learn to set up and solve simple equations and inequalities with one unknown, like finding what number makes 3x = 18 true or deciding which values satisfy x > 5.

Students plug a number into an equation or inequality to check whether it makes the statement true. It's the same logic as guessing a price and checking the receipt.

A variable is a letter that stands in for a number students don't know yet. Students use variables to write math expressions that describe real situations, like finding a missing price or distance.

Students write a simple equation to model a real-world situation, then solve for the missing number. The problems use addition, subtraction, multiplication, or division, with positive numbers only.

Students write inequalities like x > 5 or x < 12 to describe real-world limits, such as a height requirement or a spending cap. They also plot all the possible values that make an inequality true on a number line.

Students learn to find the rule connecting two related quantities, like how total cost changes as the number of items bought changes. They practice showing that relationship in a table, equation, or graph.

Students pick two changing quantities in a real situation, like hours worked and money earned, and use a variable for each to show how one affects the other.

Students write an equation like y = 3x to show how two quantities are connected, where one number changes based on the other. For example, if each ticket costs $3, they write an equation to find the total cost for any number of tickets.

Students read a graph or table to see how one value changes when another changes, then connect that pattern to an equation that describes the same relationship.

Students find the area of flat shapes, the surface area of 3-D objects like boxes and pyramids, and the volume of figures that take up space. They apply these skills to real situations, not just practice problems.

Students find the area of triangles, rectangles, and other flat shapes by breaking them apart or combining them into simpler pieces. They use those methods to solve real problems, like figuring out how much flooring or fabric a shape would cover.

Students find the volume of a box that has fractional side lengths, like 2 and a half inches by 3 and a half inches. They use the formula length times width times height and apply it to real problems.

Students plot points on a graph to draw shapes, then calculate the length of the sides by reading the coordinates. This skill shows up in problems like finding the perimeter of a floor plan or a mapped plot of land.

Students unfold a 3-D shape, like a box or a pyramid, into a flat pattern of rectangles and triangles. Then they add up the area of each face to find how much surface the shape has in total.

Students learn why data sets rarely line up perfectly. They practice spotting how spread out or bunched together a set of numbers is and what that spread actually means.

A statistical question expects different answers from different people or situations, 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 shape, a center, and a spread. Students learn to describe that shape using the mean, median, mode, and range so they can say where most values cluster and how spread out the data actually is.

A single number like an average tells you the middle of a data set, but it doesn't tell the whole story. Students also learn to describe how spread out the numbers are, so they can see whether values cluster tightly or scatter widely.

Students look at a set of data and describe what they see: where the numbers cluster, how spread out they are, and whether any values stand far from the rest.

Students learn to display a set of numbers as a dot plot, box plot, pie chart, or stem plot. Each format helps readers spot patterns in the data at a glance.

Students look at a set of numbers, such as test scores or temperatures, and describe what the data shows: how many values there are, what's typical, and how spread out the numbers are.

Students count how many data points are in a set and report that total. This tells anyone reading the data how many responses, measurements, or values were collected.

Students explain what a data set is actually measuring and how it was measured. For example, they note whether heights were recorded in inches or centimeters, or whether survey answers were yes/no choices.

Students find the middle value or average of a data set, then note how spread out the numbers are. They explain what those numbers mean for the real situation being measured.

Students learn when to use the mean versus the median to describe a data set, based on whether the numbers are spread out evenly or skewed by a few extreme values.