What does a student learn in StateVirginia,GradeGrade 4,SubjectMathematics?

Reading and writing numbers up to 999,999,999. Students identify what each digit means based on its position, so they know the 4 in forbid 4,000 stands for four thousand, not just four.

Students read a number like 423,615,208 and write out every word: four hundred twenty-three million, six hundred fifteen thousand, two hundred eight.

Hear a number spoken aloud or see it written in words, then write it out using digits. Students practice this with numbers up to the hundred millions place.

Reading a nine-digit number, students name what each digit is worth based on its position. In 568,165,724, the 8 sits in the millions place, so its value is 8,000,000.

Reading and comparing large numbers, up to the millions place. Students look at each digit's position to decide which number is bigger, smaller, or equal, then put a group of numbers in order from least to greatest or greatest to least.

Students compare two large numbers, up to seven digits each, and decide which is greater, which is smaller, or whether they are equal. They show that comparison using words or symbols like > and <.

Students put up to four large numbers in order from smallest to biggest or biggest to smallest. The numbers can be as large as 9,999,999, think of figures like city populations or national records.

Students place fractions, improper fractions, and mixed numbers in order from smallest to largest, and explain why one fraction is bigger or smaller than another. Denominators go up to 12.

Students compare and order up to four fractions that share the same bottom number by looking at the top numbers. They explain which fraction is largest or smallest using words, writing, or a drawing.

Students line up fractions that share the same top number but have different bottom numbers, deciding which is biggest or smallest by thinking about how large each equal piece is. They explain their reasoning out loud, in writing, or by drawing a picture.

Students use familiar reference points like 0, one-half, and 1 to decide which of up to four fractions is smallest or largest. Then they explain their reasoning out loud, in writing, or by drawing a picture.

Students compare two fractions or mixed numbers and decide which is greater, lesser, or equal, then explain why. They use the symbols >, <, and = and back up their answer with words, a drawing, or a number line.

Students show that two fractions with different bottom numbers can name the same amount, using pictures, fraction strips, or numbers alone.

Students break apart and rebuild fractions and mixed numbers using smaller pieces. For example, 3/4 can be shown as 1/4 plus 2/4, or as three separate 1/4 parts.

Students learn that a fraction is just a division problem written in a different form. If 3 muffins are split equally among 5 kids, each child gets 3/5 of a muffin, and that fraction means the same as 3 divided by 5.

Students read, write, and compare decimal numbers down to the thousandths place, like 0.375. They put decimals in order from least to greatest and explain how they know which is larger.

Students use blocks and charts to see how ten ones make a ten, ten tenths make one whole, and ten hundredths make one tenth. Each step up the place value chart is worth exactly ten times the step below it.

Reading and writing decimal numbers like 0.375, students connect the digits to pictures and physical objects that show tenths, hundredths, and thousandths as equal parts of a whole.

Students read and write decimal numbers like 0.375, matching digits to place values up to the thousandths spot. They connect the written number to drawings or base-ten blocks that show the same amount.

Given a decimal like 0.385, students name the exact position of each digit (tenths, hundredths, thousandths) and say what that digit is actually worth as a number.

Students line up decimals like 0.3, 0.25, and 0.175 from smallest to largest (or largest to smallest) using place value or a number line, then explain in words or with a drawing why their order is correct.

Students match fractions and decimals that name the same amount, like seeing that one-half and 0.5 are two ways to say the same thing. They work with halves, fourths, fifths, tenths, and hundredths.

Students write fractions as decimals, and decimals as fractions, using halves, fourths, fifths, tenths, and hundredths. For example, one-half is the same as 0.5, and one-fourth is the same as 0.25.

Students match fractions and decimals that mean the same amount, like seeing that one-half and 0.5 are the same number. They practice this with common fractions: halves, fourths, fifths, tenths, and hundredths.

Students look at a shaded grid or number line and write both the fraction and decimal that name the same amount. For example, a grid with 25 squares shaded out of 100 becomes both 1/4 and 0.25.

Students add and subtract whole numbers to solve everyday problems, then explain how they got the answer. Some problems take more than one step to work through.

Students decide whether a rough answer or an exact answer makes more sense for a given problem, then fine-tune that rough answer using phrases like "closer to" or "a little more than."

Students practice making quick estimates before solving addition and subtraction problems with large numbers. They round to the nearest hundred or thousand to check whether an answer is in the right ballpark.

Students add and subtract whole numbers up to 10,000 using the standard written method or other strategies, such as thinking about place value or number patterns.

Students solve word problems that involve adding and subtracting numbers up to one million. They also check whether their answers make sense by estimating before or after they calculate.

Students solve multiplication and division word problems, explain how they got their answers, and work toward knowing their times tables up to 12 x 12 from memory.

Students decide whether a problem needs an exact answer or a rough estimate, then explain why. They also sharpen that estimate using phrases like "closer to" or "a little more than" to get as close to the real answer as possible.

Students know their times tables up to 12 x 12 cold, with no counting on fingers or long pauses. They also know the matching division facts, like knowing 63 divided by 9 is 7 because they know 9 x 7.

Students write equations that show two different math expressions are equal, like proving that 4 × 3 and 2 × 6 both equal 12. Both sides of the equation balance, even when one side uses multiplication and the other uses subtraction.

Students decide whether two math expressions are equal or not, then write = or not-equal between them. For example, they check whether 4 x 12 gives the same result as 8 x 6 before choosing the right symbol.

Students find every pair of whole numbers that multiply together to make a given number up to 100. For example, the factor pairs of 12 are 1 and 12, 2 and 6, and 3 and 4.

Finding the greatest common factor means identifying the largest number that divides evenly into two or three given numbers. Students list the factors of each number, then find the biggest one they share.

Students multiply two whole numbers together, using tools like rounding or place value to check whether the answer makes sense. The focus is on picking a reliable method and knowing when an estimate is close enough.

Students multiply a two-digit number by a one-digit number, such as 34 × 6, and explain how they got the answer. This builds toward solving real-world problems that use multiplication.

Students multiply a three-digit number by a one-digit number, such as 347 times 6, and show how they got the answer.

Students multiply two 2-digit numbers together, like 34 times 27, and show how they got the answer. This builds toward solving real-world problems that use larger multiplication.

Students solve word problems that require multiplying whole numbers, then explain how they got the answer. Problems may take more than one step.

Students practice dividing two- and three-digit numbers by a single-digit number, finding exact answers and remainders. They also learn to estimate quotients by rounding before dividing.

Students solve one-step word problems using division, then explain how they got the answer. Problems use real situations, like splitting a group of objects into equal shares.

When dividing in a word problem, students figure out what the leftover amount actually means in real life, such as whether it rounds the answer up, gets ignored, or matters on its own.

Students add, subtract, and multiply fractions that share the same bottom number, then check whether their answer makes sense. Problems often come from real situations, like splitting a pizza or measuring ingredients.

Students add and subtract fractions that share the same bottom number, like 3/8 + 3/8 or 2 1/5 + 4/5, then simplify the answer. Problems may include mixed numbers and require regrouping.

Students add and subtract fractions and mixed numbers that share the same bottom number, like halves, thirds, or eighths. They solve word problems, check whether answers make sense, and simplify results when possible.

Students solve word problems that multiply a whole number by a simple fraction, like 6 times one-third. They use pictures or diagrams to show their work and find the answer.

Students use pictures or fraction models to show that multiplying a whole number by its matching unit fraction always equals 1. For example, 4 times one-fourth equals one whole.

Students add and subtract decimal numbers, like prices or measurements, going as small as thousandths. They also check whether their answer is reasonable before calling it done.

Students add and subtract decimal numbers up to the thousandths place, using rounding or other strategies to check whether their answer makes sense.

Students add and subtract decimal numbers, like prices or measurements written to three places after the decimal point. They solve real-world problems and show their work.

Addition and subtraction problems stay within four-digit numbers, so the largest value students work with looks like 9,999. Decimals go to the thousandths place, like $3.475.

Students add and subtract decimal numbers, like prices or measurements, to solve word problems. They also check whether their answer is reasonable before they're done.

Students measure real things, like the length of a desk, the weight of a backpack, or the amount of water in a bottle, using both everyday U.S. units (inches, pounds, cups) and metric units (centimeters, grams, liters). They use those measurements to solve word problems.

Choosing the right unit before measuring saves time and avoids confusion. Students decide whether a given length, weight, or liquid volume calls for a small unit like an inch or ounce, or a larger one like a foot or gallon.

Students measure how long or far something is, choosing the right unit for the job. A finger might be measured in inches or centimeters; a road in miles or kilometers.

Students practice converting and comparing weights using everyday units like ounces, pounds, grams, and kilograms. They work with both the U.S. system and the metric system.

Students measure and convert liquid amounts using everyday units like cups, quarts, and gallons, as well as metric units like milliliters and liters.

Students estimate and then measure real objects using U.S. Customary units (inches, feet, pounds, cups) and metric units (centimeters, kilograms, liters). They compare their estimate to the actual measurement to check their reasoning.

Students measure objects to the nearest fraction of an inch (down to one-eighth inch), foot, or yard, and also to the nearest millimeter, centimeter, or meter. They choose the right unit for the size of what they are measuring.

Students weigh objects using a scale and record the result in ounces or pounds, then do the same using grams or kilograms. They choose the unit that fits the size of the object and round to the nearest whole unit.

Students measure liquids using cups, pints, quarts, and gallons, and also using milliliters and liters. They read a measuring cup or container and record the amount to the nearest unit.

Students estimate a measurement first, then check it against the real measurement to see how close they were. This builds a feel for how long, heavy, or full something actually is.

Given a conversion fact (like 1 foot equals 12 inches), students figure out larger or smaller measurements in the same system. For example, they use that one fact to find how many inches are in 3 feet.

Students convert between inches, feet, and yards, deciding how many inches fit in a foot or how many feet make a yard.

Students practice choosing between ounces and pounds to weigh everyday objects, like deciding whether a sandwich or a bag of dog food is measured in which unit.

Students measure and convert liquid amounts using cups, pints, quarts, and gallons. They figure out how many cups fill a quart, or how many quarts make a gallon.

Students figure out how much time has passed between two events on a clock, like how long a movie runs or how many minutes are left before lunch. Problems use hours and minutes within a single 12-hour stretch.

Students figure out how much time has passed between two clock times, like from 9:15 a.m. to 11:45 a.m. Problems may stay within morning or afternoon, or cross from one to the other.

Students figure out how much time has passed between two events on a clock. Given a start time and an end time, they calculate the hours and minutes in between.

Students are given a start time and a number of hours and minutes that pass, then figure out what time the clock shows when that stretch of time is up.

Students figure out what time something started by counting backward from when it ended. For example, if a movie ends at 3:15 and ran for 90 minutes, students work back to find when it began.

Students measure the sides of rectangles and squares to find how much space they cover (area) and how far it is around the outside (perimeter). They use formulas to solve both types of problems in inches, feet, centimeters, and meters.

Students use tiles, graph paper, and drawings to figure out the rules for calculating the area and perimeter of rectangles and squares. They build the formula themselves instead of just memorizing it.

Students find the area and perimeter of a rectangle using just two side lengths, a width and a length, with or without a drawing to help.

Students find the area and perimeter of a square using just one side length. Because all four sides match, that one measurement is all they need.

Students use tiles, graph paper, and drawings to see how a rectangle's area (the space inside) and its perimeter (the distance around the edge) are related but not the same thing.

Students draw and compare rectangles that share the same perimeter but have different areas, or the same area but different perimeters. A long, thin rectangle and a nearly square rectangle can have the same distance around them but very different amounts of space inside.

Students use measurements to find the distance around and the total surface covered by rectangles and squares, then apply those calculations to real situations like fencing a yard or tiling a floor.

Students learn to recognize and draw basic geometry terms: a point, a ray, a line segment, an angle, and a full line. They also identify when two lines cross, run side by side without meeting, or meet at a right angle.

Students learn the basic building blocks of geometry: what makes a line different from a ray or a line segment, and how angles are formed at a vertex. They identify and describe each shape using its endpoints and corners.

Students explain what endpoints and vertices are: the exact spots where a line segment stops, a ray begins, or two lines meet to form an angle.

Students use a ruler to draw exact geometric figures: points, line segments, rays, angles, and lines. The ruler keeps the lines straight and the drawings accurate.

Students spot parallel, perpendicular, and intersecting lines inside shapes and real objects, like a stop sign, a book, or a brick wall, and name which lines cross, meet at a corner, or never touch.

Students learn the shorthand symbols mathematicians use to label lines, rays, angles, and segments on paper, and use those same symbols to show when two lines are parallel or meet at a right angle.

Students sort and describe four-sided shapes like squares, rectangles, and rhombuses by looking at their sides and angles. They learn which shapes share properties and how a square, for example, is also a rectangle.

Students sort shapes like rectangles, squares, and trapezoids into groups by examining their sides and corners, then put their findings into words as working definitions.

Students find and name the corners, sides, and angles inside four-sided shapes like squares and rectangles, explaining what makes each part a corner, a side, or an angle.

Students look at the sides of four-sided shapes and identify which sides run parallel, which cross each other, and which sides are the same length.

Students sort and compare four-sided shapes by looking at their sides and corners. They learn what makes a square different from a rectangle, and a rhombus different from a parallelogram.

Students sort rectangles, squares, and other four-sided shapes by checking which sides run in the same direction and never meet, the way railroad tracks stay the same distance apart.

Students identify right-angle corners in shapes like rectangles and squares, recognizing that perpendicular sides meet at a perfect 90-degree angle, the same corner you see on a piece of notebook paper.

Students sort quadrilaterals by checking which sides are equal in length. A square has four equal sides, a rectangle has two pairs of equal sides, and a trapezoid may have none.

Students sort quadrilaterals by counting their right angles, the square corners you see on a piece of paper or a floor tile. A rectangle has four; a trapezoid may have two, one, or none.

Students learn to read the small marks drawn on shapes, the tick marks that show equal sides, the arrows that show parallel sides, and the little squares that show right angles.

Students learn to label the sides and corners of four-sided shapes using standard math symbols, writing something like AB for a side or angle B for a corner.

Students sort and describe flat shapes and 3-D objects by counting their corners, edges, and faces. They compare figures with and without a physical model in front of them.

Students identify 3-D shapes like cubes, rectangular prisms, pyramids, spheres, cones, and cylinders by looking at real objects and pictures of them.

Students learn to tell 3D shapes apart by counting their flat faces, edges, and corners. A cube has 6 square faces; a pyramid has triangular faces that meet at a point; a sphere has none of those features at all.

Students sort and compare flat shapes (circles, squares, triangles, rectangles) and 3D shapes (spheres, cubes, pyramids, rectangular prisms) by counting their sides, corners, edges, and faces.

Students gather real information, plot it on a line graph, and then explain what the graph shows. The focus is on reading trends over time, like how temperature changes across a week.

Students come up with a question that can only be answered by gathering real data, such as "How many books did our class read each month this year?"

Students figure out what information they need to answer a question, then gather it by observing, measuring, or running a simple experiment. The data set stays small, no more than 10 numbers.

Students create line graphs from a data set, giving the graph a title and labeling both axes with whole numbers. They practice this by hand and with digital tools.

Reading a line graph, students describe what changed over time, explain the trend in their own words, and share what the data shows in writing or out loud.

Students look at a line graph and explain what the data shows overall, such as when a temperature rose the fastest or which stretch of time saw the biggest change.

Students look at a line graph and spot what stands out: the highest point, the lowest point, or places where the line stays flat. Then they explain in plain words what that feature means in real life.

Students look at a line graph and draw a conclusion that goes beyond what the numbers say outright, like noticing a trend or predicting what might happen next.

Students look at a completed line graph and use its patterns to draw a conclusion or predict what might happen next, then explain how the data supports their answer.

Students read a line graph and use the numbers shown to solve addition and subtraction problems, sometimes in more than one step.

Students figure out how likely something is to happen, like rolling a certain number on a die or pulling a red tile from a bag. They use fractions or simple models to show that chance.

Students use words like "impossible," "unlikely," "equally likely," "likely," and "certain" to describe how probable an outcome is. For example, they decide whether spinning a color on a spinner is guaranteed, possible, or can never happen.

Students list every possible result of a simple chance event, like flipping a coin or spinning a spinner, when there are 24 or fewer outcomes. They use physical objects to build and check that list.

Students write the chance of something happening as a fraction, like 1/6 for rolling one number on a die. The bottom of the fraction shows how many things could happen; the top shows how many ways the event can occur.

Students decide how likely something is to happen and connect that chance to a number. A coin flip that could go either way is "equally likely," something that can never happen is zero, and something guaranteed to happen is one.

Students design a simple game or scenario where the chance of something happening matches a fraction they're given. If the probability is 1 out of 4, they build a spinner or word problem that shows exactly those odds.

Students find the rule in a number pattern and use it to extend or build their own. Patterns grow or shrink by adding, subtracting, or multiplying whole numbers.

Students look at a sequence of numbers or pictures, figure out the rule that makes it grow or shrink, and use that rule to fill in what comes next or create their own pattern.

Students look at a number pattern in a list or table, figure out the rule behind it (such as "add 6 each time" or "multiply by 3"), then use that rule to fill in missing numbers or continue the pattern.

Students start with a rule (like "multiply by 3") and build a number pattern from scratch, filling in a table to show what each input produces as an output.

Students follow a single rule (like "multiply by 3" or "subtract 5") to figure out what number comes next in a pattern, using a real-life situation as the context.