What does a student learn in StateWest Virginia,GradeGrade 5,SubjectMathematics?

Students write math expressions like (3 + 4) x 2 using parentheses and order of operations, then explain in words what the expression means without actually solving it.

Students learn to read and write math expressions that include parentheses or brackets, then solve them in the correct order. Think of it as following the rules for which part of the problem to calculate first.

Students write math phrases like 2 x (8 + 7) to describe a calculation in order, then read an expression and describe what it means without solving it.

Students look at two number patterns side by side, spot the rule behind each one, and describe how the two patterns relate to each other.

Students follow two counting rules at the same time, list the number pairs they produce, and plot those pairs as dots on a grid. Then they describe what they notice about how the two lists relate to each other.

Each digit in a number is worth ten times more than the digit to its right. Students read, write, and compare numbers using that pattern, from billions down to thousandths.

Each digit in a number is worth 10 times more than the same digit one spot to its right, and 10 times less than the same digit one spot to its left. The 4 in 400 is worth ten 4s in 40.

Multiplying or dividing a number by 10, 100, or 1,000 shifts its digits left or right on a place value chart. Students explain why that shift happens and write powers of 10 using exponents like 10² or 10³.

Students read, write, and compare decimal numbers down to the thousandths place, like 3.047 or 12.519. They say which number is larger or smaller and put a group of decimals in order.

Students read and write decimal numbers out to the thousandths place three ways: as a standard number, in words, and broken into each digit's value (such as 3 hundreds + 4 tens + 7 ones + 3 tenths).

Students compare two decimal numbers out to the thousandths place by looking at the value of each digit and recording which number is greater, lesser, or equal using the symbols >, <, and =.

Students practice rounding whole numbers and decimals to a chosen place, like rounding 3.867 to the nearest tenth to get 3.9. The focus is on using place value to decide which way to round.

Students add, subtract, multiply, and divide large whole numbers and decimals like $4.75 or 12.30. This is the math behind making change, splitting a bill, or checking a receipt.

Students multiply large whole numbers (like 347 times 86) using the step-by-step written method taught in class. The goal is accuracy and speed, without a calculator.

Students divide large numbers (up to four digits) by a two-digit number and show how they got the answer. They might draw a grid, break the problem into smaller steps, or write out the math in equations.

Students add, subtract, multiply, and divide decimal numbers like $1.25 or $3.40. They use drawings or place-value thinking to solve the problem, then explain in writing why their method works.

Students find a common denominator so fractions share the same-size pieces, then add or subtract across the top. This is the core skill behind adding something like 1/2 and 1/3 without guessing.

Students learn to add and subtract fractions that have different bottom numbers, like 1/2 + 1/3, by rewriting them so the bottom numbers match first. It is the same idea as finding a common unit before combining two measurements.

Students add and subtract fractions with different denominators to solve word problems. They also check whether their answer makes sense by comparing it to familiar fractions like one-half or one-fourth.

Students multiply and divide fractions, including whole numbers times fractions and fractions divided by fractions. This builds on what they already know about multiplication and division with whole numbers.

Students learn that a fraction is just a division problem written in a different form: 3/4 means 3 divided by 4. They use diagrams or equations to solve word problems where splitting whole amounts into equal shares produces a fraction or mixed number as the answer.

Students multiply fractions by whole numbers and by other fractions. For example, they find what a half of three-quarters looks like and what that means as a single number.

Multiplying a fraction by a whole number or another fraction means splitting the second number into equal parts, then taking a portion of those parts. For example, (2/3) x 4 means splitting 4 into 3 equal parts and taking 2 of them.

Students figure out the area of a rectangle with fractional side lengths by multiplying the two fractions together. They also see why that multiplication works by picturing the rectangle divided into small equal pieces.

Scaling means stretching or shrinking a number. Students learn to predict whether multiplying by a fraction will give a larger or smaller result, before doing any calculation.

Students figure out whether an answer will be bigger or smaller than a starting number just by looking at what it's being multiplied by, without doing the actual math.

Students explain why multiplying a number by a fraction bigger than 1 makes it grow, and why multiplying by a fraction smaller than 1 makes it shrink. They connect that idea to what happens when you multiply a fraction by 1.

Students use drawings or equations to solve real-world fraction problems, like finding half of a recipe that calls for 2¾ cups of flour. Multiplying fractions and mixed numbers shows up in cooking, building, and other everyday situations.

Dividing a fraction like 1/2 by a whole number, or dividing a whole number by a fraction like 1/3, gets practiced here. Students work out how many pieces fit into a group or how a single piece splits further.

Students divide a simple fraction by a whole number, like splitting one-third of a pizza among 4 people. They draw a picture to show the answer and explain why it works using multiplication.

Students figure out how many small fractional pieces fit into a whole number. For example, dividing 4 by one-fifth means asking how many one-fifth slices fit into 4, and they use a picture or multiplication to check the answer.

Students solve everyday division problems that mix whole numbers and fractions, like splitting half a pound of chocolate among three people. They draw diagrams and write equations to show their thinking.

Students convert measurements inside the same system, changing feet to inches, kilograms to grams, or hours to minutes. They learn which unit fits the situation and how to move between them without switching systems.

Students practice switching between units in the same system, such as turning centimeters into meters or inches into feet, then use those conversions to solve real problems that take more than one step to figure out.

Students organize measurement data on a line plot, then answer questions about it by adding or subtracting the fractions shown on the plot.

Students record measurements given in fractions on a line plot, then use that data to solve problems, like figuring out how to split a total amount of liquid evenly across several containers.

Students learn what volume means: how much space a 3-D shape takes up inside. They figure out volume by counting unit cubes, then connect that counting to multiplication and addition.

Students learn that volume measures how much space fills a solid shape, like a box or a cube. They explore how that space is measured by counting unit cubes packed inside without gaps or overlaps.

A unit cube is a small cube where every side measures 1 unit. Students use it as the basic building block for measuring volume, the same way they use a single square to measure area.

Volume measures how much space a solid shape takes up. Students find volume by counting how many same-size cubes fill the shape completely, with no gaps or spaces left over.

Students count how many small cubes fit inside a 3-D shape to find its volume. They practice with standard cubes measured in centimeters, inches, or feet, and sometimes with informal stand-ins like sugar cubes or blocks.

Students find the volume of boxes and other rectangular shapes by multiplying length, width, and height, or by adding up the layers. They use that math to solve real problems, like figuring out how much a container holds.

Students figure out the volume of a box by imagining it packed with small cubes, then confirm that multiplying the three side lengths gives the same answer. It connects hands-on counting to the shortcut of multiplication.

Students use the formulas for volume to find how much space fits inside a box-shaped object. They multiply length times width times height, or multiply the base area times the height, to solve real problems with whole-number measurements.

Two boxes stacked or joined together have a total volume equal to the sum of their separate volumes. Students find the volume of each part, then add them to solve real problems like how much a storage unit holds.

Students plot points on a grid using two numbers, one for left-right and one for up-down, to solve math problems and answer real questions about data.

Students learn to plot points on a grid using two numbers, like (3, 5). The first number says how far to move sideways, the second says how far to move up.