What does a student learn in
New York, Grade 6, Mathematics ?

Exponents are shorthand for repeated multiplication. Students write and solve expressions like 2 to the power of 4, reading the small raised number as instructions for how many times to multiply the base number by itself.

Students write and solve math expressions that use letters as stand-ins for unknown numbers. They learn the names for each part of an expression and follow the correct order of steps when calculating a final answer.

Students rewrite math expressions in a simpler or different form using rules like the distributive property. For example, they recognize that 3(x + 2) and 3x + 6 mean the same thing.

Two expressions can look different but equal the same value for any number plugged in. Students learn to spot when that's true and explain why the two forms match.

Solving an equation means finding which number makes both sides balance. Students test numbers by plugging them in one at a time to see if the equation or inequality works out.

Students use letters like x or n to stand in for unknown numbers, then write math expressions to describe real-world situations. The letter can mean one specific missing value or a whole range of possible values.

Students write a simple equation to match a real-world situation, then solve it. The unknown is one step away: add, subtract, or multiply using whole numbers and fractions.

Students write inequalities like x > 5 or x ≤ 12 to describe real-world limits, such as a minimum age or a speed cap. Then they plot every number that fits the rule on a number line.

Students pick two quantities that change together, like hours worked and money earned, and use a variable for each. They write an equation, then check whether a graph or table matches the pattern.

Students find the area of shapes like triangles and trapezoids by breaking them into simpler pieces or fitting them inside a rectangle. They use these methods to solve real problems, not just textbook exercises.

Students find the volume of box-shaped objects even when the sides have fractional measurements, like 2½ inches. They apply that skill to real problems, such as figuring out how much a container holds.

Students plot points on a grid to draw shapes, then measure the length of a side by comparing the coordinates of two corners that share a row or column. The skill shows up in map problems and area calculations.

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 flat piece to find the total surface area of the original shape.

Students use drawings of squares and boxes to see why some numbers are called perfect squares or perfect cubes. A 4-by-4 square shows why 16 is a perfect square; a 3-by-3-by-3 box shows why 27 is a perfect cube.

Students divide fractions by fractions and explain what the answer means. They apply that skill to word problems, like figuring out how many half-cup servings fit in a two-thirds cup container.

Students practice long division with large numbers until the steps feel automatic. They work through multi-digit problems using the standard written method, not just a calculator.

Students add, subtract, multiply, and divide numbers with decimal points, like 3.75 or 12.4, using the standard written steps for each operation. The goal is accuracy and speed without a calculator.

Students find the largest number that divides evenly into two numbers, and the smallest number that both can divide into. They also use those shared factors to rewrite addition problems in a simpler form.

Positive and negative numbers show opposite values, like money earned versus money owed, or floors above and below ground. Students use them to describe real situations and explain what zero means in each case.

A ratio compares two amounts, like 3 red tiles for every 5 blue tiles. Students read and write ratios to describe how two quantities in a real situation relate to each other.

A unit rate says how much of one thing you get per single unit of another, like 30 miles per gallon or $4 per pound. Students find that rate and describe it in plain language using words like "per" or "for every."

Students use ratios and rates to solve real problems: filling in tables, finding missing values, calculating percents, and converting units like inches to feet or ounces to pounds.

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

Mean, median, and mode each squeeze a whole data set into one summary number. A measure of variation, like range, shows how spread out those numbers are.

Students learn to show data visually by placing numbers on a number line, grouping them into a histogram, or marking each value as a dot. The goal is to read a dataset at a glance instead of staring at a list of numbers.

Students collect a set of numbers, find the range and average, and then describe what the pattern shows and whether any values stand out. They also explain why the shape of the data affects which measure of center makes the most sense.

Probability is a number from 0 to 1 that shows how likely something is to happen. A result near 0 means it rarely happens, near 1 means it almost always does, and around 0.5 means it could go either way.

Students run an experiment many times, like flipping a coin, and use the results to estimate how often something will happen. They can also work the other way: given a probability, predict how often the outcome should appear over many tries.

Students build a simple probability model, like a fair coin or a six-sided die, to predict how likely an outcome is. Then they compare those predictions to what actually happens when they run the experiment and explain why the results might not match.

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

Surveying a small group can reveal patterns about a much larger one, but only if that small group is a fair reflection of the whole. Students learn why a skewed or hand-picked sample gives unreliable answers about the bigger population.

How you collect data matters. Students learn why larger, well-chosen samples give a truer picture of a whole group, then compare multiple samples of the same size to see how estimates can shift from one sample to the next.