What does a student learn in StateWest Virginia,GradeGrade 4,SubjectMathematics?

Multiplication can mean "this many groups of that many." Students learn to read 4 x 6 as four groups of six, then write their own real-world situations that match a multiplication or division equation.

Students learn to read a multiplication equation as a comparison. For example, 35 = 5 x 7 means 35 is five times as large as 7, and they practice turning phrases like "three times as many" into multiplication equations.

Students solve word problems where one number is a set number of times bigger or smaller than another. They also learn to tell the difference between "three times as many" and "three more than."

Students solve word problems that take two or more steps, using addition, subtraction, multiplication, or division. They write equations with a letter for the missing number and check whether their answer makes sense by estimating.

Students learn which numbers divide evenly into a given number and which numbers are its multiples. For example, 3 is a factor of 12, and 12 is a multiple of 3.

Students find every pair of numbers that multiply together to reach a given number, then decide whether that number is divisible by smaller numbers or can only be divided evenly by itself and one.

Students spot a number or shape pattern, figure out the rule behind it, and use that rule to say what comes next.

Students follow a counting rule, like "add 3 starting at 1," to build a number sequence. Then they look for surprises in the pattern, such as the numbers alternating between odd and even, and explain why that keeps happening.

Students learn how each position in a number is worth ten times the position to its right. A 3 in the hundreds place is worth ten times more than a 3 in the tens place.

Each position in a number is worth ten times more than the spot to its right. The 4 in 400 is worth ten 4s in 40, and students use that pattern to compare, multiply, and divide bigger numbers.

Students read, write, and compare large whole numbers. They show a number like 4,briefing or 52,300 in digits, words, and expanded form, then use >, =, and < to say which number is bigger, smaller, or equal.

Rounding means deciding which "neat" number a given number is closest to. Students practice rounding to the nearest ten, hundred, thousand, or beyond using what they know about place value.

Students add, subtract, and multiply numbers in the hundreds and thousands by using what they know about place value. A student solving 346 + 278 thinks about hundreds, tens, and ones separately before combining them.

Students add and subtract large numbers quickly and correctly using the step-by-step written method taught in class, carrying and borrowing across columns as needed.

Students multiply numbers as large as 9,999 by a single digit, and multiply pairs of two-digit numbers together. They show their work by breaking numbers apart, drawing area models, or writing partial products so the steps are visible.

Students divide numbers up to four digits by a single digit and find any remainder left over. They show how they got the answer using drawings, arrays, or step-by-step partial quotients.

Fractions can name the same amount even when they look different. Students learn to spot when two fractions are equal and to put fractions in order from smallest to largest.

Two fractions can look different but cover the same amount. Students use pictures and diagrams to see why, then write or identify other fractions that match.

Students compare two fractions with different top and bottom numbers to decide which is larger, smaller, or equal. They draw a picture to prove it and record their answer using >, =, or <.

Students use what they know about adding and multiplying whole numbers to build fractions out of smaller pieces. For example, three-fourths is just three copies of one-fourth added together.

Fractions are built by adding smaller equal pieces together. If a fraction has 3 on top and 4 on bottom, that means three one-fourth pieces stacked up, so students practice seeing any fraction as a count of equal-sized slices.

Adding and subtracting fractions with the same bottom number. Students combine or remove equal-sized pieces of the same whole, the way they would add or subtract regular numbers.

Students break a fraction into smaller same-bottom-number pieces in more than one way, then write an equation to show each split. For example, 3/8 can be split as 1/8 + 2/8 or as 1/8 + 1/8 + 1/8.

Adding and subtracting mixed numbers means combining whole numbers and fractions like 2 1/4 plus 1 3/4. Students convert those mixed numbers into single fractions to add or subtract them, and they practice locating a mixed number between two whole numbers on a number line.

Students solve story problems that add or subtract fractions with the same bottom number, drawing a picture or writing an equation to show their work.

Multiplying a fraction by a whole number means finding the total when the same fraction repeats. Students learn that 3 x 1/4 is the same as adding 1/4 three times, then use that idea to solve problems with larger numbers.

Students learn that a fraction like 5/4 is just a unit fraction (1/4) counted multiple times. They use diagrams to show that 5/4 means five one-fourth pieces, written as 5 x (1/4).

Students learn that multiplying a whole number by a fraction is the same as counting up equal-sized pieces. For example, 3 times 2/5 means six one-fifth pieces, which equals 6/5.

Students solve story problems by multiplying a fraction by a whole number, such as figuring out how much food is needed for a group. They use drawings or fraction models to show their work and check which two whole numbers the answer falls between.

Students read and write fractions like 3/10 as decimals like 0.3, then compare two decimals to figure out which is larger.

Students learn to turn a fraction like 3/10 into 30/100 so they can add it to another fraction that already uses hundredths. It is the same idea as knowing that 3 dimes equal 30 cents.

Students write fractions with 10 or 100 on the bottom as decimals. For example, 62 out of 100 becomes 0.62, the way you'd read a price tag or a measurement on a ruler.

Students compare two decimal numbers, like 0.4 and 0.35, and use the symbols >, =, or < to show which is larger or smaller. They back up their answer with a number line or grid to show why the comparison makes sense.

Students practice converting measurements, like turning hours into minutes or feet into inches. They learn that smaller units give a more precise count of the same length, weight, or time.

Students learn how units of measurement relate to each other, like knowing 1 foot equals 12 inches or 1 kilogram equals 1,000 grams. They convert a larger unit into smaller ones and record the pairs in a two-column table.

Students solve story problems about miles, minutes, cups, coins, and grams, converting bigger units into smaller ones when needed. They draw number lines to show their work.

Students use multiplication to find the missing side of a rectangle when they know the area and one side length. A real-world problem might ask: if a floor covers 48 square feet and one wall is 8 feet long, how wide is the room?

Students read and answer questions about bar graphs, line plots, and picture graphs. They figure out totals, differences, and what the data shows overall.

Students record measurements like half-inch or quarter-inch lengths on a dot plot, then add or subtract those fractions to answer questions about the data, such as finding the difference between the longest and shortest item in a set.

Students learn what an angle is and how to measure it in degrees. They use a protractor to find angles in shapes and figures, and they add or subtract angle measures to solve problems.

An angle is the opening formed where two straight lines meet at a point. Students learn to measure that opening in degrees, the same way a clock's hands form a wider or narrower gap depending on the time.

An angle is a turn. Students learn that a full circle has 360 equal turns called degrees, and any angle is just a fraction of that full turn.

Angles are measured in degrees. An angle that makes one full one-degree turn for each degree in its measure, so a 90-degree angle turns through exactly 90 of those one-degree steps.

Students learn to read a protractor and measure angles in whole-number degrees. They also draw angles to a given size, like 45 or 120 degrees.

When a big angle is split into smaller angles, the pieces add up to the whole. Students use addition and subtraction to find a missing angle size, the same way they'd find a missing piece of a puzzle.