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

Ratios compare two amounts, like 3 red tiles to 5 blue tiles. Students use that relationship to solve problems involving rates, prices, speeds, and other real-world comparisons.

A ratio compares two quantities, like 3 red tiles to 5 blue tiles. Students write and read these comparisons using words, fractions, or the colon notation 3:5.

Students build a table of equivalent ratios, fill in any missing values, then plot each pair on a coordinate grid to see the relationship as a line of points.

Students find out how much of something there is per one unit, like miles per hour or price per item, then use that single-unit rate to answer real questions about speed, cost, or distance.

Students figure out percent problems: finding a percent of a number, calculating what percent one number is of another, or working backward to find the original amount. Think sale prices, tips, or test scores.

Students practice switching between units like inches and centimeters, or miles and kilometers. They use ratios to set up the conversion and solve it.

Dividing a fraction by another fraction. Students learn why the "flip and multiply" shortcut works, then use it to solve real problems like splitting half a pizza into quarter-slice servings.

Students divide one fraction by another to solve real problems, like figuring out how many quarter-cup servings fit in two-thirds of a cup. They set up the problem, flip the second fraction, and multiply to find the answer.

Students add, subtract, multiply, and divide large whole numbers by hand. They also find which factors two numbers share and what multiples they have in common.

Students rewrite a addition problem like 12 + 8 as 4 x (3 + 2) by pulling out the shared factor both numbers divide into evenly. It's a way of reorganizing numbers to make them easier to work with.

Rational numbers include every whole number, fraction, and negative number on the number line. Students place, compare, and calculate with all of them, including numbers below zero.

Positive and negative versions of the same number sit on opposite sides of zero on a number line. For example, 3 and -3 are the same distance from zero, just in opposite directions.

Absolute value is how far a number sits from zero on a number line, regardless of which direction. Students learn that -5 and 5 are both a distance of 5 from zero, so they share the same absolute value.

Students convert the same number between its fraction, decimal, and percent forms. For example, one-half shows up as 0.5 and 50%, and one-third shows up as roughly 0.33 and 33%.

Algebra builds on arithmetic. Students learn to write and read expressions that use letters to stand in for unknown numbers, the same way they used to write equations with just digits.

An expression is a math phrase with numbers and symbols but no equal sign. An equation sets two expressions equal to each other, like 3x + 2 = 14. Students learn to tell the difference and use each correctly.

Students write expressions like 3x + 5 using variables and numbers, then find the value by swapping the variable for a given number and doing the arithmetic.

A variable is a letter that stands for an unknown number in a real situation. Students learn to read an expression like 3x and ask what x actually represents, such as hours worked or dollars saved.

Students rewrite expressions like 3(x + 4) into 12 + 3x and confirm the two versions always produce the same result. They use properties such as the distributive law to show why two expressions that look different are actually equal.

Students figure out the value of an unknown number in equations and inequalities, then check whether their answer makes the equation or inequality true.

Solving an equation or inequality means finding the number (or numbers) that make it true. Students check whether a value belongs in the solution set by substituting it in and seeing if both sides balance.

Students write equations with a letter standing in for an unknown number, then solve for what that letter must equal. The letter isn't abstract math shorthand; it represents something real, like a missing price or a distance.

Students learn to spot how two quantities are connected, like how total cost changes as the number of items changes. They practice writing and interpreting equations that show how one value depends on another.

Students write an equation that shows how one number changes based on another, like how total cost changes as the number of items bought increases.

Reading a table, graph, or equation that shows how two quantities are connected, then explaining how all three versions show the same relationship. For example, as hours worked increase, total pay increases at the same rate across all three.

Students find the area of flat shapes, the surface area of 3-D objects like boxes and prisms, and the volume of those same figures. The problems ask them to set up and solve real calculations, not just name formulas.

Reading a coordinate plane, students figure out which of the four sections a point sits in by checking whether its two numbers are positive or negative.

Two points that share the same numbers but have opposite signs are mirror images across the x-axis, the y-axis, or both. Students identify where each point lands on a coordinate grid and explain what changed.

Students find the distance between two points on a coordinate grid when they share the same x-value or the same y-value. Instead of measuring with a ruler, they subtract the coordinates.

Students plot points on a grid to draw shapes such as triangles, rectangles, and other polygons. They use the x- and y-axis to place each corner precisely and connect them to form the complete shape.

Students learn why data sets spread out differently and what that spread means. They compare groups by looking at how consistent or scattered the numbers are, not just what the average is.

A set of data has a pattern to it. Students learn to describe that pattern by finding the center (a typical value), the spread (how far apart the values are), and the overall shape of the data when displayed in a graph.

Students learn to describe a set of data by looking at its shape, center, and spread. They explain what the numbers mean as a group, not just one at a time.

Students look at a set of numbers, decide whether the data is spread out or bunched to one side, and choose the best measure (mean, median, or range) to describe it. The shape of the data and what it represents both matter.