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

Students find the area of shapes like triangles and rectangles, figure out how much surface wraps around a 3-D object, and calculate how much space fits inside it. Problems use real measurements, not just textbook numbers.

Students figure out the area of triangles and irregular shapes by breaking them into simpler pieces, like rectangles or triangles, then adding the parts together. This skill shows up in real problems, not just on paper.

Students find the volume of a box whose sides include fraction measurements, such as 2 and a half inches. They confirm that multiplying length times width times height gives the same answer as filling the box with small equal cubes.

Students plot shapes on a grid using coordinate pairs, then measure side lengths by reading the distance between points that share a row or column. This skill shows up in problems like finding the perimeter of a mapped area.

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

Ratios compare two quantities, like 3 red tiles for every 5 blue ones. 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. Students learn to read and write these comparisons and use ratio language to describe real relationships between two amounts.

A unit rate boils a ratio down to "per one." Students learn to say things like "15 miles per hour" or "$3 per apple" and explain what that single-unit price or speed actually means.

Students use ratio reasoning to solve everyday problems, like figuring out how many cups of juice to mix if the recipe scales up. They work with ratio tables, diagrams, and equations to find missing values.

Students build a table of equivalent ratios, fill in any missing numbers, and then plot those pairs as points on a graph. They use the table to compare two ratios side by side.

Given a price per item or a speed, students figure out the total cost or distance by scaling that rate up or down. For example: if a car travels 55 miles per hour, how far does it go in three hours?

Students figure out what a percent means in real life: 30% of 60 is the same as 30 out of every 100, so 18. They also work backward, finding the full amount when they only know a piece of it and the percent.

Converting between units like inches and feet or miles and kilometers comes down to ratios. Students use multiplication or division to switch from one unit to another without changing what's actually being measured.

Dividing a fraction by another fraction. Students learn to split a fraction into equal-sized fractional pieces, building on what they already know about multiplying and dividing whole numbers.

Students learn to divide one fraction by another and find the answer, then use that skill to solve real word problems. They might draw a picture or write an equation to show their thinking.

Students practice long division, multiplication, and other operations with large numbers. They also find what numbers divide evenly into two values and what multiples two numbers share.

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

Students add, subtract, multiply, and divide decimal numbers accurately and without relying on a calculator. The numbers can have digits on both sides of the decimal point.

Students find the largest number that divides evenly into two numbers and the smallest number both numbers share as a multiple. They also rewrite addition problems by factoring out what two numbers have in common.

Rational numbers include every whole number, fraction, and negative number on a number line. Students learn how these numbers connect and how to work with all of them, including numbers below zero.

Positive and negative numbers describe opposites: money earned versus money spent, temperature above zero versus below it. Students read and write these numbers in real situations and explain what zero means in each one.

Students learn that every number, including negatives, has a specific spot on a number line or a grid. They practice plotting both positive and negative numbers on those lines and grids.

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, so -(-3) is just 3, and zero stays zero no matter what.

Ordered pairs like (3, 4) and (-3, 4) land in different quadrants of a coordinate grid. When only the signs change, the points mirror each other across one or both axes.

Students place whole numbers, fractions, and negatives on a number line, then locate points on a coordinate grid using two numbers to pinpoint an exact location.

Students compare and order numbers on a number line, including negatives, and learn that absolute value measures how far a number sits from zero regardless of direction.

Negative numbers, fractions, and decimals all have a place on the number line. Students read an inequality like -3 < 1 and explain what it means by pointing to where each number sits and which one is farther left or right.

Students read and write comparisons like "negative 8 degrees is colder than negative 3 degrees" using real situations. They explain what the inequality actually means, not just which symbol points which way.

Absolute value is how far a number sits from zero on a number line, ignoring which direction. Students use this to make sense of real situations, like a temperature 8 degrees below zero still being "8 degrees away" from zero.

Absolute value measures distance from zero, not which number is bigger. Students learn to keep those two ideas separate: a number can be farther from zero and still be less than another number.

Students plot points anywhere on a coordinate grid, including negative regions, then use those points to measure distances between locations that share the same horizontal or vertical position.

Students start turning arithmetic they already know into algebra. They learn to read and write expressions with variables, like using x instead of an unknown number, and evaluate those expressions when given a value.

Students write and solve expressions that use exponents, like 2 to the 4th power, and figure out what they equal. It's the math behind repeated multiplication written in a compact form.

Letters like x or n stand in for unknown numbers. Students write, read, and calculate the value of these expressions once they know what the letter equals.

Students write math expressions using numbers and letters, like writing "3x + 5" to mean "3 times some number, plus 5." The letter holds the place of a number they don't know yet.

Students learn the vocabulary for reading math expressions: what makes something a term, a factor, a coefficient, or a product. They also learn to treat a chunk of an expression as one unit when it's useful to do so.

Students plug a number into an expression and calculate the result, following the standard order of operations (like multiplying before adding) when no parentheses tell them what to do first.

Students rewrite expressions like 3(x + 4) into 12 + 3x, or combine like terms so that 2x + 5x becomes 7x. Different forms, same value.

Two expressions are equivalent when they produce the same result no matter what number you plug in. Students learn to spot when two different-looking math expressions are secretly identical.

Students learn to solve equations and inequalities that have one unknown value, like finding what number makes 3x = 12 true. They also figure out when a value makes an inequality work and show those solutions on a number line.

Students test whether a given number makes an equation or inequality true by plugging it in and checking both sides. It's the "does this number work?" step before solving.

Students learn that a letter like x can stand in for a number they don't know yet. They use that letter to write math expressions that describe a real situation, like a price or a distance.

Students write and solve simple equations like x + 6 = 15 or 3x = 24 to answer real-world math questions. The numbers involved are positive, and students find the missing value by working backward.

Students write inequalities like x > 5 or x < 10 to describe real-world limits, such as a height requirement or a speed limit. They show all the values that work by shading a number line.

Students learn to find the rule connecting two changing quantities, like figuring out how total cost changes as the number of items goes up. They write that rule as an equation and use it to predict values.

Students pick two quantities that change together (like hours worked and money earned), write an equation connecting them, then check whether the equation matches a table or graph of the same data.

Students learn that data sets don't all look the same. They study why data spreads out, clusters together, or centers around a typical value, and what that variation tells you about a real question.

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

A data set has patterns you can describe: where values tend to cluster, how spread out they are, and what shape the whole group makes. Students learn to read those patterns instead of just listing numbers.

A single number like the mean or median can represent a whole set of data. A different number, like the range, shows how spread out or bunched together those values are.

Students read a set of data and describe its shape, center, and spread. They explain what the numbers tell you, including where values cluster and how spread out they are.

Students learn to organize a set of numbers into visual charts like dot plots, histograms, and box plots. Each type of chart shows the same data a different way, helping readers spot patterns and outliers at a glance.

Numerical data sets are collections of numbers gathered to answer a question, like survey results or measurements. Students learn to describe what those numbers show by reporting how many values there are, what a typical value looks like, and how spread out the numbers are.

Students count and record how many data points are in a data set before analyzing it. Knowing that total helps make sense of graphs, tables, and any patterns found in the data.

Students explain what was measured in a data set and how it was measured. For example, they describe whether heights were recorded in inches or centimeters, or whether survey responses were counted or estimated.

Students find the middle value or average of a data set, then measure how spread out the numbers are. They also explain what the pattern means in plain terms and call out any numbers that look surprisingly high or low.

Students learn when to use the mean versus the median to describe a data set, and when to pair it with range or a spread measure. The choice depends on the shape of the data and what the numbers are actually measuring.