What does a student learn in StateVirginia,GradeGrade 5,SubjectMathematics?

Students match fractions to their decimal form, like seeing that 1/4 and 0.25 are the same amount. They also put a mix of fractions and decimals in order from smallest to largest.

Students use drawings or physical objects to show why a fraction and a decimal represent the same amount, focusing on thirds, eighths, and fractions whose denominators divide evenly into 100.

Students match decimals like 0.375 to their fraction form using pictures or physical models. The focus is on thirds, eighths, and hundredths.

Students match fractions like one-third or three-eighths to their decimal form, such as 0.333 or 0.375. They practice both with visual models and without, building the number sense to move between the two forms fluently.

Students line up a mix of fractions and decimals, up to four numbers at once, from smallest to largest or largest to smallest. They use number lines, place value, or benchmark numbers to decide the order, then explain how they know they got it right.

Students learn which numbers can only be divided evenly by 1 and themselves (prime) and which can be broken into smaller factors (composite). They also write any whole number up to 100 as a multiplication of its prime building blocks.

Students sort numbers up to 100 into two groups: numbers that can only be divided evenly by 1 and themselves (prime), and numbers that have other divisors too (composite). They draw or build a model to show why a number belongs in each group.

Prime numbers can only be divided evenly by 1 and themselves. Composite numbers have more than two factors. Students sort whole numbers up to 100 into these two groups and explain the difference.

Students break a number (up to 100) down into all the prime numbers that multiply together to make it. For example, 12 breaks into 2 x 2 x 3.

Students solve word problems using whole numbers, with at least one step involving addition, subtraction, multiplication, or division. They also estimate answers first to check that their math makes sense.

Students round or adjust numbers in a word problem to get a ballpark answer before solving. This helps catch errors and check whether a final answer makes sense.

Students solve word problems using addition, subtraction, multiplication, and division of whole numbers. They show their work and explain how they got the answer, including problems where division leaves a remainder.

Students add, subtract, and multiply whole numbers in word problems where the answer stays below 100,000. Think totals, change, and quantities across two or more steps.

Multiplication word problems at this level use numbers no larger than a two-digit number times a three-digit number, such as 47 times 312.

Students solve word problems that involve dividing whole numbers, where the number they divide by is no larger than a two-digit number, such as 48 divided by 12.

Division problems at this grade top out at four-digit numbers (think 1,248 divided by something). Students are not yet expected to divide numbers in the ten-thousands or beyond.

When students divide in a word problem, they figure out what the leftover amount actually means. Sometimes the remainder changes the answer; sometimes it gets ignored.

Students add, subtract, and multiply fractions to solve word problems, including fractions with different bottom numbers. They show their work and explain how they got the answer, using drawings or number lines when it helps.

Finding the least common multiple means locating the smallest number that two denominators both divide into evenly. Students use that shared number to rewrite fractions so they have matching bottom numbers before adding or subtracting.

Students add and subtract fractions and mixed numbers, even when the bottom numbers differ. They find the exact answer, then simplify it down to its simplest form.

Students add and subtract fractions and mixed numbers to solve word problems, including fractions with different bottom numbers. Answers must be written in simplest form.

Students multiply a whole number by a fraction to solve a word problem, such as finding 2/3 of 9 objects. A model like a number line or drawing helps show the work, and the answer must be written in simplest form.

Students add, subtract, multiply, and divide decimal numbers to solve real problems, then explain why their answer makes sense. Multi-step problems are included, so students may need to run more than one operation to reach a solution.

Before solving a decimal problem, students use rounding or compatible numbers to predict whether their answer is in the right ballpark. That check catches big mistakes before they stick.

Students multiply two decimal numbers together, using estimation first to check that their answer makes sense. They practice this enough to do it reliably with the standard step-by-step method.

Students multiply decimal numbers where one of the numbers is a single digit, such as 2.3 times 4 or 0.08 times 0.9. They also check whether their answer is reasonable using estimation.

Students multiply a three-digit decimal by a single digit, such as 3.28 times 7. The focus is on setting up the problem correctly and placing the decimal point in the right spot in the answer.

Students multiply two decimal numbers together, like 0.85 times 3.7 or 9.2 times 3.5. Each number in the problem has up to two digits, and the answer will not go beyond the thousandths place.

Students divide a decimal number by a whole number, finding the exact answer and checking it with an estimate to make sure it's reasonable.

Students divide decimal numbers and whole numbers to find answers up to four digits long. Practice problems stay manageable so students can focus on placing the decimal point correctly.

When students divide decimal numbers, the answer can be a whole number or a decimal that goes to one, two, or three places after the decimal point.

Students divide decimal numbers by a single-digit whole number or a decimal like 0.3 or 0.7. They practice both estimating the answer and solving it exactly.

When dividing decimals, students add at most one placeholder zero to a number so the division works out evenly. This keeps the problems manageable without requiring multiple extra steps.

Students add, subtract, and multiply decimal numbers to solve word problems. They use estimation and standard steps to check that answers make sense.

Students solve word problems that require dividing decimal numbers, such as splitting a dollar amount evenly among a group. They use estimation or models to check their work, then apply the standard long-division steps.

Students learn the rules for which math operations to do first when a problem has a mix of addition, subtraction, multiplication, and division. Getting the order right is what makes everyone's answer match.

Students follow a set sequence of steps (multiply and divide before adding and subtracting) to solve a math expression that mixes multiple operations. The answer changes if the steps are done out of order, so sequence matters.

Students solve math expressions that may include one set of parentheses, following the correct order of steps so the answer comes out right every time.

Students solve math expressions that mix addition, subtraction, multiplication, and division, following the correct order of steps. Each problem uses up to five whole numbers and four operations.

Expressions use only two-digit whole numbers (99 or smaller). Students practice applying the order of operations to calculations that stay manageable without a calculator.

Expressions use only parentheses, not brackets or fraction bars. Students simplify step by step in the correct order: parentheses first, then multiplication and division, then addition and subtraction.

Students look at a math problem that mixes addition, multiplication, or parentheses and explain the order in which each step gets solved. They describe which operation happens first, which comes second, and which comes third.

Students measure length, weight, and liquid volume using metric units like centimeters, kilograms, and liters. They apply those measurements to solve word problems, including ones set in real-world situations.

Choosing the right metric unit matters. Students look at a real-world measurement problem and decide whether centimeters, meters, grams, kilograms, milliliters, or liters makes the most sense for what is being measured.

Students measure lengths using metric units, from millimeters for tiny objects up to kilometers for long distances. They choose the right unit for the job and convert between them to solve problems.

Students weigh objects in grams and kilograms, choosing the right unit based on whether something is light (like a paperclip) or heavy (like a bag of flour).

Students measure liquid volume using milliliters and liters, choosing the right unit for the job. A small spoonful calls for milliliters; a full water bottle calls for liters.

Students estimate and measure length, mass, and liquid volume using metric units like centimeters, kilograms, and liters to solve real-world problems. The focus is on choosing the right unit and getting close to the actual measurement before checking with a ruler or scale.

Students measure length in millimeters, centimeters, and meters, choosing the right unit for the job. A fingernail is about a centimeter; a hallway is measured in meters.

Students weigh objects in grams and kilograms, deciding which unit fits best. A paperclip is measured in grams; a backpack in kilograms.

Students measure liquids using milliliters and liters, choosing the right unit based on the size of the container. A small medicine dropper holds milliliters; a large water bottle holds liters.

Students use one known conversion (such as 100 centimeters in a meter) to figure out an equivalent measurement in a different metric unit, like converting a length in centimeters into meters to solve a word problem.

Students measure lengths in metric units, from millimeters for small objects up to kilometers for long distances. They choose the right unit for the job and convert between them.

Students weigh objects in grams and kilograms, the metric units used on nutrition labels and in science class. A paperclip is about one gram; a bag of flour is about one kilogram.

Students measure liquids in milliliters and liters, choosing the right unit for the amount. A small spoonful of medicine calls for milliliters; a full water bottle calls for liters.

Students find the distance around a shape, the space inside it, or the space a 3-D object fills, then solve real-world problems using those measurements. They show their thinking in more than one way.

Students figure out how to calculate the area of a right triangle by exploring the relationship between the triangle and a rectangle. They arrive at the formula on their own through investigation, not memorization.

Students find the area of a right triangle by multiplying the base times the height, then dividing by two. The answer is written in square units, like 16 square inches.

Volume measures how much space fits inside a 3-D object, like how many cubes would fill a box or how many gallons fill a fish tank. Students explain what volume means and give real-life examples of when it matters.

Students figure out the formula for volume by stacking and counting unit cubes inside box-shaped objects. The goal is to see why multiplying length times width times height works, not just memorize it.

Students find the volume of a box-shaped object by multiplying its length, width, and height. They practice with real objects and diagrams before using the formula, then write the answer in cubic units like 12 cubic inches.

Students decide whether a problem calls for measuring around the outside of a shape, covering its surface, or filling its space. They practice recognizing which type of measurement fits before they calculate anything.

Students apply perimeter, area, and volume formulas to solve real-world problems, working with standard units like inches, feet, and cubic centimeters. The numbers come from actual situations, not just practice exercises.

Students sort triangles by their angles and side lengths, then measure angles using a protractor. They also solve real-world problems that involve missing angle sizes.

Students sort angles by size: right angles form a perfect corner, acute angles are smaller than that corner, obtuse angles are wider, and straight angles form a flat line. Students explain how they know which is which.

Students sort triangles by their angles (sharp, square, or wide) and by their sides (all equal, two equal, or none equal), then explain how they know.

Students read the tick marks and square corners drawn on a triangle to figure out which sides are the same length and where the right angles are.

Students sort triangles by their angles and side lengths, explaining how two triangles are alike or different. They learn that a triangle's angles and sides work together to give it its shape.

Students learn which tools to use when measuring or drawing angles, such as choosing a protractor the way they'd choose a ruler for a straight line.

Students use a protractor to measure angles and read the result in degrees. They practice identifying whether an angle is smaller than a corner, exactly a corner, wider than a corner, or a straight line.

Students cut or tear the corners off a paper triangle and fit them together to show they always form a straight line (180 degrees). Then they use that fact to find a missing angle when the other two are known.

Students find a missing angle by adding or subtracting the angles they already know. The problems use real diagrams where part of the picture is labeled and one piece is left to figure out.

Students gather data to answer a real question, then organize it into a line plot or stem-and-leaf plot and explain what the numbers show.

Students come up with a question that can only be answered by gathering real data, like "How many minutes do kids in our class spend reading each night?"

Students figure out what information they need to answer a question, then gather it through methods like polls, measurements, or simple experiments. They work with 30 or fewer pieces of data.

Students plot a set of data on a number line by marking an X or dot above each value, then label the axes and add a title. The data can include whole numbers, fractions, or decimals.

Students organize a set of numbers into a stem-and-leaf plot, splitting each value into its leading digit and trailing digit, then listing both in order from smallest to largest. The plot includes a title and a key explaining how to read it.

Students read line plots and stem-and-leaf plots to find patterns in data, then explain what the numbers show, in writing or out loud.

Students look at a completed line plot or stem-and-leaf plot and describe what the full set of data shows: where the values cluster, how spread out they are, and whether the shape is balanced or lopsided.

Students look at a finished dot plot or stem-and-leaf plot and draw a reasonable conclusion about what the data says, such as guessing that most students carry two to four books based on where the dots cluster.

Students read a stem-and-leaf plot to spot what stands out: which group had the highest scores, the lowest, or tied with another group. They explain in plain language what that pattern means.

Students look at a finished line plot or stem-and-leaf plot, decide what the data shows, and use that to predict what might happen next or answer the original question.

Students read a dot plot or stem-and-leaf plot, then use the numbers shown to solve addition and subtraction problems, sometimes in more than one step.

Students find the mean, median, or mode of a real data set (like test scores or temperatures) and use the range to describe how spread out the numbers are.

Mean is the "fair share" number. Students find it by spreading a set of values out evenly, so every group ends up with the same amount, like splitting 15 pieces of candy equally among 3 friends.

Students find the mean (average) of a data set by adding all the values and dividing by how many there are. It describes the center of the data, like a typical value for the group.

Finding the median means sorting a set of numbers from smallest to largest and identifying the middle value. Students use this to describe what's typical in real data, like test scores or temperatures.

Mode is the value that appears most often in a set of numbers. Students find the mode in real data sets, like survey results or collected measurements, and explain what it tells you about the group.

Range measures how spread out a set of numbers is. Students find it by subtracting the smallest value from the largest, then explain what that gap means in context, like the difference between the lowest and highest quiz scores in a class.

Students figure out how likely something is to happen by mapping out every possible outcome. They also use multiplication to count how many combinations are possible when making choices in a row.

Students list every possible result of a simple event, like flipping a coin twice or rolling a number cube, then use that list to find the chance of one outcome happening.

Students use multiplication to count the total number of possible outcomes when combining two or more choices. For example, 3 shirt colors and 4 pant options give 12 possible outfits.

Students look at a number sequence and figure out the rule that makes it grow or shrink, then use that rule to continue the pattern or build one of their own. Patterns can use whole numbers, fractions, or decimals.

Students look at a sequence of numbers, shapes, or a fill-in-the-blank table, figure out the rule that makes it grow or shrink, and use that rule to extend the pattern or build one from scratch.

Students look at a number pattern in a list or table, figure out the rule behind it (such as "add 7" or "divide by 3"), then use that rule to fill in missing numbers or continue the pattern.

Students follow a rule (like "multiply by 3" or "subtract 0.5") to fill in missing numbers in a pattern, using real-world setups such as a price table or a recipe that keeps growing or shrinking.

Students use letters to stand in for unknown numbers and solve simple real-world problems, like figuring out how many items are in a group when only the total is known.

A variable is a box, letter, or symbol that stands in for a number students don't know yet. Students learn to read and write expressions where that placeholder holds the place of a missing value.

Students read a word problem and write a single equation to solve it, using one unknown and one operation such as addition or division. The equation matches the situation described, not just the answer.

Writing expressions means swapping words for math symbols. Students translate a phrase like "5 more than a number" into something like y + 5, using a letter to stand in for the unknown value.

Students write a short story problem that matches an equation like x + 14 = 30. The story has to fit the math, not just use the same numbers.