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

A ratio compares two quantities, like 3 red tiles for every 5 blue tiles. Students write and read ratios in different forms and explain what the comparison means in context.

Students learn what it means when a rate is expressed "per one" of something, like miles per hour or cost per item, then practice using that language to describe real comparisons.

Students use ratios and rates to solve everyday problems, like finding the best price per item or converting inches to feet. They work with tables, diagrams, and equations to show the same relationship different ways, including percents.

Dividing a fraction by another fraction gives a quotient students can find using a diagram or equation. Students apply that skill to solve word problems, such as figuring out how many quarter-cup servings fit in three-eighths of a cup.

Long division with big numbers. Students divide numbers like 4,536 by 12, choosing a method that works and getting the right answer.

Adding, subtracting, multiplying, and dividing numbers with decimal points, like prices or measurements. Students choose a reliable method and get the right answer every time.

Students find the largest number that divides evenly into two numbers, and the smallest number both can divide into. They also rewrite addition problems by pulling out a shared factor, turning something like 12 + 8 into 4 x (3 + 2).

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

Students plot positive and negative numbers, including fractions and decimals, on a number line and on a coordinate grid. They also learn that flipping a number's sign twice lands back at the original number.

Students learn to place positive and negative numbers on a number line, compare which is bigger or smaller, and figure out how far any number is from zero. This shows up in real life when comparing temperatures or understanding debt.

Students plot points anywhere on a coordinate grid, not just the positive section, then use those coordinates to measure the distance between two points that share a row or column.

Students practice writing and solving expressions with exponents, like 2 to the 4th power, without reaching for a calculator every step. The focus is on doing it accurately and knowing when to take shortcuts.

Students learn to read and write math expressions that use letters as stand-ins for numbers, like writing "subtract y from 5" as 5 - y. They also swap in real numbers for those letters to calculate answers, including with everyday formulas.

Students rewrite math expressions in a simpler or different form using rules like the distributive property. For example, 3(x + 4) becomes 3x + 12. Both versions say the same thing, just written differently.

Two expressions are equivalent when they always produce the same answer, no matter what number you plug in. Students learn to spot when two algebraic expressions are just different ways of writing the same thing.

Students test whether a number makes an equation or inequality true by plugging it in and checking both sides. This is how solving works: finding the value that fits.

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 figuring out how many miles are left in a trip.

Students write and solve simple equations to answer real-world questions, like finding an unknown price or distance. They practice problems where a number is added to an unknown value, or an unknown value is multiplied by a number.

Students write inequalities like x > 5 or x < 10 to describe real-world limits, such as a speed limit or a minimum age. They also plot all the possible answers on a number line, recognizing there is no single solution but a whole range of them.

Students pick two changing quantities in a real situation, like distance and time, and write an equation that connects them. Then they check whether a graph and a table tell the same story as the equation.

Students find the area of triangles, quadrilaterals, and other flat shapes by splitting them into simpler pieces or fitting them into rectangles. They use those methods to solve real problems involving floor plans, plots of land, and similar situations.

Students find the volume of a box that has measurements like 2 1/2 inches on a side. They practice both filling the box with small cubes and multiplying the three side lengths to confirm both methods give the same answer.

Students plot points on a grid to draw shapes, then measure side lengths by comparing the coordinates of two corners that share the same row or column.

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 piece to find the total surface area.

Students learn to take a set of numbers and display them visually on a number line using dot plots, histograms, or box plots. Each chart type shows the same data differently, helping students spot patterns like clusters, gaps, and spread.

Students summarize a set of numbers by finding the middle value or average, measuring how spread out the numbers are, and spotting any values that look unusually high or low compared to the rest.

Students come up with questions worth investigating, then identify real data sources like weather databases, government websites, or phone sensors that could answer them.

Students gather real information using tools like spreadsheets or apps, then describe what the data shows. They also learn that data can come from their own collection or from an outside source like a government database or published study.

Students read dot plots and box plots to describe where data clusters, how spread out it is, and whether the shape leans one way or bunches in the middle.

Students use data they collected and analyzed to answer a question they set out to investigate. They explain what the numbers show and why it matters, with some help from the teacher.