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

Ratios compare two amounts, like 3 cups of juice to 1 cup of water. Students use that relationship to scale recipes, read maps, and solve real problems where two quantities stay in proportion.

Students learn to compare two quantities, like 3 cups of juice to 2 cups of water, and write that relationship three ways: as a fraction, with the word "to," or with a colon.

A unit rate is a ratio simplified to "per one" (like 60 miles per hour or $3 per apple). Students use unit rates to compare and solve ratio problems, such as finding the better deal or calculating distance at a steady speed.

Students use ratios and rates to solve everyday problems, like converting measurements or figuring out percents. They work through these problems using tables, diagrams, and equations to find and check their answers.

Dividing fractions builds on what students already know about multiplication and division. Students learn why dividing by a fraction is the same as multiplying by its reciprocal, then use that shortcut to solve problems with fractions.

Students divide fractions by fractions, using drawings or number lines to show why the answer makes sense. They connect the picture to an equation so the math isn't just a rule to memorize.

Students divide one fraction by another to solve real problems, like splitting a recipe or measuring a length. They interpret what the quotient means in context, not just as a number on the page.

Students practice long division, multi-digit multiplication, and finding shared factors or multiples between two numbers. These are the building blocks for working with fractions later in the year.

Long division with big numbers, done reliably and quickly. Students use the standard step-by-step method to divide numbers like 4,896 by 32, working through real problems that actually require it.

Students practice adding, subtracting, multiplying, and dividing numbers with decimal points using the step-by-step written methods taught in class, like long division or column addition, rather than estimating or using shortcuts.

Students rewrite an addition problem by pulling out a shared factor. For example, 12 + 8 becomes 4 x (3 + 2), because 4 divides evenly into both numbers.

Finding the GCF means figuring out the largest number that divides evenly into two numbers. Finding the LCM means finding the smallest number both can divide into. Students practice both skills with whole numbers.

Students break a number down into its prime building blocks. For example, 12 becomes 2 x 2 x 3, showing every prime number that multiplies together to make it.

Rational numbers include fractions, decimals, and negative numbers. Students move between these forms, choosing whichever version fits the problem they're solving.

Positive and negative numbers show opposite ideas, like earning money versus spending it, or climbing above sea level versus diving below it. Students use these signed numbers to describe real situations where direction or value matters.

Students place whole numbers, fractions, and decimals on a number line, reading both positive and negative values. This is the same skill used to read a thermometer or timeline.

Opposites are two numbers that sit on different sides of zero but the same distance away from it. For example, 3 and -3 are opposites because both are exactly 3 steps from zero on a number line.

Students explain what zero means in context: zero degrees means no change from the freezing point, zero dollars means an account is empty, and so on. The meaning of zero shifts depending on the situation.

Students plot points on a grid using positive and negative numbers. They locate ordered pairs like (3, -2) by moving left or right on the horizontal line, then up or down on the vertical line.

Students look at the positive or negative signs of two coordinates and use that to name which of the four sections of a grid the point sits in.

Points like (3, 5) and (3, -5) are mirror images across the horizontal axis of a coordinate grid. Students find both points and explain why flipping a point's vertical value gives its reflection.

Points like (3, 5) and (-3, 5) are mirror images across the vertical axis on a coordinate grid. Students identify pairs like these as reflections, where the y-value stays the same but the x-value flips to its opposite.

Students plot points anywhere on a coordinate grid, positive or negative, and find the distance between two points that share a row or column.

Absolute value is the distance a number sits from zero on a number line, ignoring whether it's positive or negative. Students find and explain the absolute value of fractions, decimals, and whole numbers using everyday situations like temperature or debt.

Students compare and order fractions, decimals, and negative numbers, using a number line when it helps. Absolute value tells how far a number sits from zero, and students use that distance to solve real-world problems.

Reading and writing algebraic expressions is using letters to stand in for unknown numbers, then solving the expression once the values are known. Students connect the arithmetic they already know to equations that use variables.

Students learn what it means when a number has a small raised number next to it, like 2 to the power of 3. They write those expressions, calculate the value, and compare results to see which is larger.

Students use letters to stand in for unknown numbers, then write and solve expressions based on real situations, like figuring out total cost or distance traveled.

A variable is a letter that stands in for a number students don't know yet. Students learn to read expressions like x + 5 as "some unknown number, plus five," where x could be any value the problem allows.

Students turn word problems and real-life situations into math expressions using variables. For example, "three more than a number" becomes x + 3.

Students learn the names for the parts of a math expression: a term, factor, coefficient, and so on. Given an expression like 3x + 5, they can point to the coefficient, name the sum, and explain what each part means.

Students solve math expressions that mix operations like multiplication, addition, and parentheses by working through them in the correct order. This includes expressions with absolute value or exponents.

Students rewrite an algebraic expression in a different but equal form by swapping the order of terms, grouping them differently, or distributing a number across parentheses. The result always equals the original.

Students decide whether two math expressions are equal in value, then explain why. They might simplify both sides or substitute numbers to prove the expressions always match or show where they differ.

Students write equations and inequalities to describe real situations, then solve them. Think of it as translating a word problem into math symbols and working out what value makes the statement true.

Students check whether a number solves an equation or inequality by plugging it in and seeing if both sides balance. It's the same logic as checking an answer: does this number actually make the statement true?

Students write a simple equation to model a real situation, like figuring out an unknown price or distance, then solve for the missing number. Both addition and multiplication equations are covered.

Students solve an equation and then explain what the answer actually means in the real situation. If x = 3, they say what that 3 represents, like 3 hours or 3 dollars, not just the number.

Students write an inequality to describe a real-world limit, like the minimum number of items needed or the maximum weight allowed, then find and graph all the values that make it true.

Students look at the answer to an inequality and explain what it means in real life. For example, if the solution says x is less than 10, they describe what that limit actually means for the situation in the problem.

Students plot the answer to an inequality on a number line, then explain why that answer isn't just one number but an endless range of values that all make the inequality true.

Students figure out which number in a relationship changes on its own and which one reacts to it. For example, the number of hours worked is independent; the pay earned depends on it.

Students look at two quantities that change together, like hours worked and dollars earned, and figure out how one affects the other. They describe that relationship using tables, graphs, or equations.

Students practice showing how two related quantities change together, using a table, a graph, or an equation to make the pattern visible.

Students look at real data sets, like survey results or game scores, and figure out what's typical. They also examine how spread out or bunched together the numbers are.

A statistical question expects different answers from different people or situations. Students practice telling apart questions that lead to varied data from ones with a single fixed answer.

Students find the middle, average, and most common value in a real data set, then measure how spread out the numbers are. They use those calculations to compare two data sets and explain what the difference means.

Students look at a set of real-world numbers and decide whether the mean, median, or mode gives the most accurate picture of the data.

Reading a data set's average or spread isn't enough. Students explain what those numbers actually mean for the situation, like why a wider range matters or what a typical value tells you about the group being studied.

Students learn to display a set of numbers as a visual chart, whether that means a dot plot, histogram, stem and leaf plot, or box plot. The goal is choosing the right picture to make the data easier to read.

Students look at a graph of data and describe what they see: where the values cluster, how spread out they are, whether the shape leans to one side, and whether any values stand out as unusually high or low.

Students read a bar graph, line plot, or histogram and explain what the real-world data in it actually means, not just what the numbers say.

Students plot shapes on a grid using coordinates, then use those coordinates to find side lengths, distances, or other measurements needed to solve a problem.

Students plot the corners of a shape on a grid, connect the points, and use the result to solve a problem, like finding the length of a fence or the area of a lot.

Students figure out the missing corner of a rectangle on a coordinate grid when two corners share the same row or column. They use what they know about opposite sides being equal to find the exact point.

Two points that share the same row or column on a grid sit a measurable distance apart. Students find that distance by subtracting one coordinate from the other, then apply that length to solve a real problem.

Students find the perimeter and area of shapes plotted on a grid, using the coordinates of each corner to measure side lengths. The shapes are aligned to the grid, so no diagonal sides are involved.

Students find the area of flat shapes, the surface area of 3-D objects, and the volume of containers by applying the right formula to real measurements.

Students find the area of shapes like triangles and irregular polygons by breaking them into simpler pieces, such as rectangles or right triangles, then adding those areas together.

Students break a complicated shape into simpler pieces, like rectangles or triangles, to figure out the total area. This comes up in real problems: flooring a room, covering a wall, or planning a garden layout.

Students unfold a 3-D shape (like a box or a pyramid) into a flat pattern of rectangles and triangles, then add up the area of each face to find the total surface area.

Students find the volume of a box-shaped object even when its side lengths include fractions. They multiply length, width, and height the same way they always have, just with numbers like 2 1/2 or 3/4 in the mix.

Students use cubes and diagrams to figure out how much space fits inside a box-shaped object. They practice two versions of the volume formula and compare the results across different prisms.