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

Students write math expressions using parentheses and order of operations, then explain in words what those expressions mean. Think of it as translating between math notation and plain English.

Parentheses and brackets tell students which part of a math problem to solve first. Students practice writing and solving expressions like (3 + 4) x 2, following the standard rules for which operations to do in what order.

Students write math phrases like "add 8 then multiply by 4" as a number expression, and read expressions someone else wrote without solving them first.

Students look at two number patterns side by side and describe how they relate to each other. For example, they might notice that one sequence grows twice as fast as another and explain why.

Students follow two separate counting rules to build two lists of numbers, then compare the lists to spot what stays the same or changes between them.

Students look at two number patterns side by side and describe what connects them, such as noticing that one list is always twice as large as the other.

Students take two number patterns, pair up matching terms, and plot those pairs as points on a grid. The result is a graph that shows how the two patterns relate to each other.

Students learn how the position of a digit in a number determines its value, seeing why a 4 in the hundreds place means something very different from a 4 in the ones place.

Each place in a number is worth 10 times more than the spot to its right and 10 times less than the spot to its left. So the 4 in 400 is worth 10 fours, not one.

Multiplying by 10, 100, or 1,000 shifts the digits left and adds zeros. Dividing does the opposite, moving the decimal point right to left. Students explain why those patterns happen and write powers of 10 using exponents like 10² or 10³.

Students read, write, and compare decimal numbers out to the thousandths place using digits, words, and expanded form. They use the greater than, less than, and equal signs to show which decimal is larger or smaller.

Students round decimal numbers to the nearest whole number, tenth, or hundredth, then show their thinking on a number line to explain which way they rounded and why.

Students add, subtract, multiply, and divide large whole numbers and decimals like $4.75 or 12.50. The work builds the arithmetic students use in everyday situations involving money, measurement, and multi-step problems.

Students multiply large numbers by hand, like 342 times 1,508, quickly and accurately. They know the steps well enough to work through the problem without stopping to figure out what to do next.

Students divide large numbers (up to four digits) by a two-digit number and show how they got the answer using a drawing, a grid, or an equation. They explain their thinking, not just the result.

Students add, subtract, multiply, and divide numbers with decimal points, like $4.75 or $12.30. They check that their answers make sense by estimating first.

Students add and subtract fractions with different denominators by first converting them to a common denominator. Think of it as cutting two different-sized pieces of pie into matching slices so the math works out evenly.

Students add and subtract fractions that have different bottom numbers, like 1/2 + 1/3, by rewriting them so both fractions share the same bottom number first. This works with mixed numbers too, like 2 1/2 + 1 1/3.

Students add and subtract fractions with different denominators to solve real-world problems, like splitting a recipe or measuring wood. They also use familiar fractions like 1/2 to check whether their answer makes sense before moving on.

Students use what they already know about multiplication and division to work with fractions. That means multiplying a fraction by a whole number, by another fraction, and dividing fractions in straightforward problems.

A fraction is just a division problem in disguise. Students learn that 3/4 means 3 divided by 4, so a fraction bar works the same way as a division sign.

Multiplying a fraction by a whole number or by another fraction. Students find, for example, what half of three-quarters looks like and write the answer as a fraction.

Students learn two ways to multiply a fraction by a whole number: split the whole number into equal parts first and then scale up, or multiply first and then split the result. Both paths land on the same answer.

Students find the area of a rectangle whose sides are fractions by multiplying the two side lengths together. They also show why that multiplication works by filling the rectangle with small equal squares.

Multiplying by a fraction makes a number smaller. Students learn to predict whether an answer will be bigger or smaller than the starting number just by looking at what they're multiplying by, before doing any calculation.

Multiplying a number by a fraction less than 1 makes the result smaller, not bigger. Students learn to predict whether an answer will be larger or smaller than what they started with, before doing any math.

Multiplying a number by a fraction smaller than 1 shrinks it; multiplying by a fraction larger than 1 grows it. Students explain why this happens and connect that pattern to what it means to multiply by 1.

Students multiply fractions and mixed numbers to solve everyday problems, like finding the area of a garden or splitting a recipe. They draw models or write equations to show their thinking.

Students practice splitting a simple fraction (like 1/3) into equal groups, or dividing a whole number into fractional parts. They work through both directions: a fraction divided by a whole number, and a whole number divided by a fraction.

Dividing a fraction by a whole number means splitting it into even smaller pieces. Students figure out how much one share is when, say, 1/3 of a pizza gets split among 4 people.

Dividing a whole number by a fraction (like 4 divided by 1/2) asks how many of those fraction-sized pieces fit into the whole. Students figure out the answer and explain what it means.

Students solve everyday problems that involve dividing fractions by whole numbers or whole numbers by fractions. They draw diagrams and write equations to show their thinking.

Students practice converting bigger units into smaller ones within the same system, like turning 3 feet into 36 inches or 2 kilograms into 2,000 grams.

Students practice converting measurements like feet to inches or kilograms to grams, then use those conversions to solve real problems with distance, time, money, or weight. Problems often include fractions and decimals.

Students read and make graphs and line plots using data that includes fractions. They answer questions about what the data shows, like comparing totals or finding differences between measurements.

Students plot measurement data on a number line using fractions like 1/2 or 1/4, then add or subtract those fractions to answer questions about what the data shows.

Students learn what volume means and practice measuring how much space a 3-D shape holds. They connect volume to multiplication and addition, using those operations to find the answer instead of counting every cube.

Volume measures how much space a solid shape takes up. Students learn that volume is measured by counting how many same-size cubes fit inside a shape without gaps or overlaps.

A unit cube is a cube where each side measures 1 unit. Students use it as the basic building block for measuring how much space a 3-D shape takes up.

Packing small cubes into a box, with no gaps or overlaps, shows how volume works. The number of cubes that fit inside is the volume, measured in cubic units.

Students count small cubes packed inside a 3D shape to measure how much space it holds. Each cube represents one unit of volume, like a cubic inch or cubic centimeter.

Finding the volume of a box-shaped object means multiplying its length, width, and height together. Students use that idea to solve real problems, like figuring out how many unit cubes fill a fish tank or a storage crate.

Students find the volume of a box by imagining it filled with small equal cubes, then confirm that multiplying the three side lengths gives the same answer. Counting cubes and multiplying length times width times height always match.

Students use two formulas to find the volume of a box: multiply length times width times height, or multiply the area of the bottom face times the height. They practice both methods on real-world problems with whole-number measurements.

Students find the volume of an irregular solid by splitting it into two box-shaped pieces, calculating each piece separately, then adding the two numbers together.

Students plot and read points on a grid using two numbers, like coordinates on a map, to solve math problems and answer questions about real situations.

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

Students plot points on a grid to solve real problems, like tracking distance traveled or comparing two quantities. They also read what a plotted point means in context, such as what a dot at (3, 5) tells you about the situation.

Students sort flat shapes into groups based on what they have in common, like the number of sides or whether angles are right angles. A square fits into the rectangle group because it shares the same properties.

Shapes can belong to more than one category at once. A square is always a rectangle, and a rectangle is always a parallelogram, so every rule that applies to the bigger group applies to the smaller one too.