Big numbers and place value
Students read, write, and compare numbers into the hundred thousands. They round to any place and start to see that each digit is worth ten times the one to its right.
This is the year math stretches into bigger numbers and finer parts. Students multiply and divide larger numbers, work through word problems with more than one step, and start to see fractions as pieces they can add, compare, and even multiply by a whole number. They also begin reading decimals like 0.7 and 0.25. By spring, students can solve a multi-step word problem and explain why 2/4 and 1/2 name the same amount.
Students read, write, and compare numbers into the hundred thousands. They round to any place and start to see that each digit is worth ten times the one to its right.
Students multiply larger numbers and divide with remainders, then use those skills in multi-step word problems. They also find factor pairs and decide whether a number is prime or composite.
Students learn that the same fraction can be written many ways, like 1/2 and 2/4. They compare fractions, add and subtract fractions with the same bottom number, and multiply a fraction by a whole number.
Students connect fractions like 7/10 to decimals like 0.7 and compare decimals to the hundredths. They also convert between units such as feet and inches, and solve problems about time, money, and liquid amounts.
Students measure angles with a protractor and sort shapes by their sides and angles. They spot right, acute, and obtuse angles, and find lines of symmetry in everyday figures.
Students add, subtract, multiply, and divide whole numbers to solve real problems, like figuring out how many items fit in equal groups or how much is left after sharing.
Students learn that multiplication equations describe how many times bigger one number is than another. For example, 35 = 5 x 7 means 35 is five times as many as 7, and students write equations to match that kind of comparison.
Word problems ask students to figure out when one amount is a set number of times bigger than another. Students decide whether to multiply or divide, then write an equation to find the missing number.
Students read multi-step story problems, write an equation using a letter for the missing number, and solve using addition, subtraction, multiplication, or division. Then they check whether the answer makes sense by estimating or rounding.
Factors are numbers that divide evenly into a larger number. Multiples are what you get when you skip-count by a number. Students learn to find both for any whole number up to 100.
Students find every pair of numbers that multiply to make a given number, then decide whether that number is prime (only divisible by 1 and itself) or composite (divisible by smaller numbers too).
Students create a repeating or growing pattern, like a number sequence or shape arrangement, then explain the rule behind it.
Students follow a rule to build a number or shape pattern, then notice things about that pattern the rule never mentioned. For example, a rule might produce numbers that are always even, even though "even" was never part of the instructions.
| Standard | Definition | Code |
|---|---|---|
| Use the four operations with whole numbers to solve problems | Students add, subtract, multiply, and divide whole numbers to solve real problems, like figuring out how many items fit in equal groups or how much is left after sharing. | 4.OA.A |
| Interpret a multiplication equation as a comparison, e.g., interpret 35 = 5 × 7… | Students learn that multiplication equations describe how many times bigger one number is than another. For example, 35 = 5 x 7 means 35 is five times as many as 7, and students write equations to match that kind of comparison. | 4.OA.1 |
| Multiply or divide to solve word problems involving multiplicative comparison… | Word problems ask students to figure out when one amount is a set number of times bigger than another. Students decide whether to multiply or divide, then write an equation to find the missing number. | 4.OA.2 |
| Solve multistep word problems posed with whole numbers and having whole-number… | Students read multi-step story problems, write an equation using a letter for the missing number, and solve using addition, subtraction, multiplication, or division. Then they check whether the answer makes sense by estimating or rounding. | 4.OA.3 |
| Gain familiarity with factors and multiples | Factors are numbers that divide evenly into a larger number. Multiples are what you get when you skip-count by a number. Students learn to find both for any whole number up to 100. | 4.OA.B |
| Find all factor pairs for a whole number in the range 1–100 | Students find every pair of numbers that multiply to make a given number, then decide whether that number is prime (only divisible by 1 and itself) or composite (divisible by smaller numbers too). | 4.OA.4 |
| Generate and analyze patterns | Students create a repeating or growing pattern, like a number sequence or shape arrangement, then explain the rule behind it. | 4.OA.C |
| Generate a number or shape pattern that follows a given rule | Students follow a rule to build a number or shape pattern, then notice things about that pattern the rule never mentioned. For example, a rule might produce numbers that are always even, even though "even" was never part of the instructions. | 4.OA.5 |
Students add, subtract, multiply, and round numbers in the thousands and beyond by using what they know about how place value works. Big numbers follow the same rules as small ones.
Students practice adding and subtracting large numbers the same way every time, using the standard written method with carrying and borrowing. By the end of fourth grade, they should do this accurately without needing to stop and think through each step.
Students multiply large numbers (up to four digits) by a one-digit number, and multiply two two-digit numbers together. They show how the math works using diagrams like grids or rectangles, not just the answer.
Students divide numbers up to four digits by a single-digit number and find any remainder left over. They show how they got the answer using a drawing, a grid, or an equation.
Each place in a number is worth ten times more than the place just to its right. The 4 in 4,000 is worth ten times the 4 in 400.
Students read, write, and compare large numbers in three ways: as digits (4,593), as words (four thousand five hundred ninety-three), and broken apart by place value (4,000 + 500 + 90 + 3). They also compare two large numbers using the greater than, less than, or equal symbols.
Rounding a number means replacing it with a nearby "neat" number, like changing 4,739 to 4,700 or 5,000. Students learn to do this for any place in a multi-digit number by asking whether the digits to the right push the number up or keep it down.
| Standard | Definition | Code |
|---|---|---|
| Use place value understanding and properties of operations to perform… | Students add, subtract, multiply, and round numbers in the thousands and beyond by using what they know about how place value works. Big numbers follow the same rules as small ones. | 4.NBT.A |
| Fluently add and subtract multi-digit whole numbers using the standard… | Students practice adding and subtracting large numbers the same way every time, using the standard written method with carrying and borrowing. By the end of fourth grade, they should do this accurately without needing to stop and think through each step. | 4.NBT.4 |
| Multiply a whole number of up to four digits by a one-digit whole number | Students multiply large numbers (up to four digits) by a one-digit number, and multiply two two-digit numbers together. They show how the math works using diagrams like grids or rectangles, not just the answer. | 4.NBT.5 |
| Find whole-number quotients and remainders with up to four-digit dividends and… | Students divide numbers up to four digits by a single-digit number and find any remainder left over. They show how they got the answer using a drawing, a grid, or an equation. | 4.NBT.6 |
| Recognize that in a multi-digit whole number, a digit in one place represents… | Each place in a number is worth ten times more than the place just to its right. The 4 in 4,000 is worth ten times the 4 in 400. | 4.NBT.1 |
| Read and write multi-digit whole numbers using base-ten numerals, number names | Students read, write, and compare large numbers in three ways: as digits (4,593), as words (four thousand five hundred ninety-three), and broken apart by place value (4,000 + 500 + 90 + 3). They also compare two large numbers using the greater than, less than, or equal symbols. | 4.NBT.2 |
| Use place value understanding to round multi-digit whole numbers to any place | Rounding a number means replacing it with a nearby "neat" number, like changing 4,739 to 4,700 or 5,000. Students learn to do this for any place in a multi-digit number by asking whether the digits to the right push the number up or keep it down. | 4.NBT.3 |
Fractions can look different but mean the same thing. Students learn to recognize when two fractions are equal and to put fractions in order from smallest to largest.
Cutting a pizza into 8 equal slices instead of 4 doesn't change how much pizza you have. Students learn why fractions like 1/2 and 2/4 name the same amount, and how to find other fractions that are equal to a given one.
Students compare two fractions with different top and bottom numbers to decide which is larger, smaller, or equal. They use drawings, common denominators, or a benchmark like one-half, then record the result with >, =, or <.
Students learn to add and subtract fractions by building on what they already know about adding and subtracting whole numbers. The work centers on unit fractions, like 1/4 or 1/8, as the building blocks.
Adding fractions means combining copies of the same-sized piece. Students learn that 3/4 is just three 1/4 pieces added together, the same way 3 ones make the number 3.
Adding fractions means joining pieces of the same whole. Subtracting fractions means removing pieces from that same whole, the way students would add or remove slices from one pizza, not two different-sized ones.
Students break one fraction into smaller fractions that add up to the same amount, then write an equation showing the pieces. For example, 3/4 can be written as 1/4 + 1/4 + 1/4, or as 2/4 + 1/4.
Adding and subtracting mixed numbers means working with numbers like 2 1/2 or 3 3/4. Students add or subtract the whole parts and the fractions separately, or convert everything into a single fraction first.
Students solve story problems that involve adding or subtracting fractions with the same bottom number, like figuring out how much pizza is left after two people take a slice. They use drawings or equations to show their work.
Multiplying a fraction by a whole number works the same way as repeated addition. Students learn that 3 x (1/4) is just three one-fourth pieces added together, then use that idea to solve real problems with fractions.
Fractions are just multiples of a unit fraction. If the unit fraction is 1/4, then 2/4 is two of those pieces, 3/4 is three of them, and so on. Students use this idea to make sense of any fraction.
Multiplying a fraction by a whole number means counting up that fraction repeatedly. Students learn that 3 x (2/5) is the same as six one-fifth pieces, then write the result as a single fraction.
Word problems ask students to multiply a fraction by a whole number, like figuring out how many cups are in 4 servings of a half-cup recipe. Students use drawings or equations to show their thinking and find the answer.
Fractions like 1/10 and 1/100 can be written as decimals like 0.1 and 0.01. Students read, write, and compare those decimal numbers, including on a number line.
Students learn that 3/10 is the same as 30/100, then use that idea to add fractions with tenths and hundredths together. This builds the groundwork for working with decimals and money.
Students write fractions with a 10 or 100 on the bottom as decimals. A fraction like 3/10 becomes 0.3, and 25/100 becomes 0.25.
Comparing decimals like 0.3 and 0.27 to decide which is larger, then writing the answer using >, =, or <. Students use grids or number lines to show why one decimal is bigger, smaller, or equal to the other.
| Standard | Definition | Code |
|---|---|---|
| Extend understanding of fraction equivalence and ordering | Fractions can look different but mean the same thing. Students learn to recognize when two fractions are equal and to put fractions in order from smallest to largest. | 4.NF.A |
| Explain why a fraction a/b is equivalent to a fraction | Cutting a pizza into 8 equal slices instead of 4 doesn't change how much pizza you have. Students learn why fractions like 1/2 and 2/4 name the same amount, and how to find other fractions that are equal to a given one. | 4.NF.1 |
| Compare two fractions with different numerators and different denominators… | Students compare two fractions with different top and bottom numbers to decide which is larger, smaller, or equal. They use drawings, common denominators, or a benchmark like one-half, then record the result with >, =, or <. | 4.NF.2 |
| Build fractions from unit fractions by applying and extending previous… | Students learn to add and subtract fractions by building on what they already know about adding and subtracting whole numbers. The work centers on unit fractions, like 1/4 or 1/8, as the building blocks. | 4.NF.B |
| Understand a fraction a/b with a > 1 as a sum of fractions 1/b | Adding fractions means combining copies of the same-sized piece. Students learn that 3/4 is just three 1/4 pieces added together, the same way 3 ones make the number 3. | 4.NF.3 |
| Understand addition and subtraction of fractions as joining and separating… | Adding fractions means joining pieces of the same whole. Subtracting fractions means removing pieces from that same whole, the way students would add or remove slices from one pizza, not two different-sized ones. | 4.NF.3.a |
| Decompose a fraction into a sum of fractions with the same denominator in more… | Students break one fraction into smaller fractions that add up to the same amount, then write an equation showing the pieces. For example, 3/4 can be written as 1/4 + 1/4 + 1/4, or as 2/4 + 1/4. | 4.NF.3.b |
| Add and subtract mixed numbers with like denominators, e.g., by replacing each… | Adding and subtracting mixed numbers means working with numbers like 2 1/2 or 3 3/4. Students add or subtract the whole parts and the fractions separately, or convert everything into a single fraction first. | 4.NF.3.c |
| Solve word problems involving addition and subtraction of fractions referring… | Students solve story problems that involve adding or subtracting fractions with the same bottom number, like figuring out how much pizza is left after two people take a slice. They use drawings or equations to show their work. | 4.NF.3.d |
| Apply and extend previous understandings of multiplication to multiply a… | Multiplying a fraction by a whole number works the same way as repeated addition. Students learn that 3 x (1/4) is just three one-fourth pieces added together, then use that idea to solve real problems with fractions. | 4.NF.4 |
| Understand a fraction a/b as a multiple of 1/b | Fractions are just multiples of a unit fraction. If the unit fraction is 1/4, then 2/4 is two of those pieces, 3/4 is three of them, and so on. Students use this idea to make sense of any fraction. | 4.NF.4.a |
| Understand a multiple of a/b as a multiple of 1/b | Multiplying a fraction by a whole number means counting up that fraction repeatedly. Students learn that 3 x (2/5) is the same as six one-fifth pieces, then write the result as a single fraction. | 4.NF.4.b |
| Solve word problems involving multiplication of a fraction by a whole number… | Word problems ask students to multiply a fraction by a whole number, like figuring out how many cups are in 4 servings of a half-cup recipe. Students use drawings or equations to show their thinking and find the answer. | 4.NF.4.c |
| Understand decimal notation for fractions | Fractions like 1/10 and 1/100 can be written as decimals like 0.1 and 0.01. Students read, write, and compare those decimal numbers, including on a number line. | 4.NF.C |
| Express a fraction with denominator 10 as an equivalent fraction with… | Students learn that 3/10 is the same as 30/100, then use that idea to add fractions with tenths and hundredths together. This builds the groundwork for working with decimals and money. | 4.NF.5 |
| Use decimal notation for fractions with denominators 10 or 100 | Students write fractions with a 10 or 100 on the bottom as decimals. A fraction like 3/10 becomes 0.3, and 25/100 becomes 0.25. | 4.NF.6 |
| Compare two decimals to hundredths by reasoning about their size | Comparing decimals like 0.3 and 0.27 to decide which is larger, then writing the answer using >, =, or <. Students use grids or number lines to show why one decimal is bigger, smaller, or equal to the other. | 4.NF.7 |
Reading and making sense of information shown in charts, graphs, and tables. Students collect measurements or counts, display them visually, and answer questions about what the data shows.
Students collect measurements in fractions (like 1/2 inch or 1/4 inch), plot them on a number line chart, then add and subtract those fractions to answer questions about the data.
Students practice converting bigger units of measurement into smaller ones, like turning hours into minutes or feet into inches, then use those conversions to solve word problems.
Students learn how units within the same system relate to each other, like how many centimeters fit in a meter or minutes in an hour. They practice converting a larger unit into smaller ones and recording those pairs in a table.
Word problems ask students to add, subtract, multiply, or divide measurements like miles, minutes, cups, pounds, and dollars. Students also convert larger units into smaller ones and use number lines to show their work.
Students use formulas to find how much space a rectangle covers and how far it is around the outside. They apply this to real situations, like figuring out how much carpet a room needs or how much fencing surrounds a yard.
Students learn what an angle is and how to measure it in degrees, the way a clock's hands form different openings throughout the day. They use a protractor to find the size of angles in real shapes.
An angle is the opening formed when two straight lines meet at a point. Students learn to measure that opening in degrees, the way a clock's hands spread apart from the center.
A degree is one tiny slice of a full circle, cut into 360 equal pieces. Students use those slices to measure how wide an angle opens, the same way a clock face is divided into hours.
Angles are measured in degrees. Students learn that a 90-degree angle is made up of 90 one-degree turns, so the total number of those small turns is the angle's measure.
Students use a protractor to measure angles in whole-number degrees, then draw new angles to match a given measurement.
When a large angle is split into smaller angles, the parts add up to the whole. Students find missing angle sizes by writing addition or subtraction equations, the same way they would find a missing number in any math problem.
| Standard | Definition | Code |
|---|---|---|
| Represent and interpret data | Reading and making sense of information shown in charts, graphs, and tables. Students collect measurements or counts, display them visually, and answer questions about what the data shows. | 4.MD.A |
| Make a line plot to display a data set of measurements in fractions of a unit | Students collect measurements in fractions (like 1/2 inch or 1/4 inch), plot them on a number line chart, then add and subtract those fractions to answer questions about the data. | 4.MD.4 |
| Solve problems involving measurement and conversion of measurements from a… | Students practice converting bigger units of measurement into smaller ones, like turning hours into minutes or feet into inches, then use those conversions to solve word problems. | 4.MD.B |
| Know relative sizes of measurement units within one system of units including… | Students learn how units within the same system relate to each other, like how many centimeters fit in a meter or minutes in an hour. They practice converting a larger unit into smaller ones and recording those pairs in a table. | 4.MD.1 |
| Use the four operations to solve word problems involving… | Word problems ask students to add, subtract, multiply, or divide measurements like miles, minutes, cups, pounds, and dollars. Students also convert larger units into smaller ones and use number lines to show their work. | 4.MD.2 |
| Apply the area and perimeter formulas for rectangles in real world and… | Students use formulas to find how much space a rectangle covers and how far it is around the outside. They apply this to real situations, like figuring out how much carpet a room needs or how much fencing surrounds a yard. | 4.MD.3 |
| Geometric measurement | Students learn what an angle is and how to measure it in degrees, the way a clock's hands form different openings throughout the day. They use a protractor to find the size of angles in real shapes. | 4.MD.C |
| Recognize angles as geometric shapes that are formed wherever two rays share a… | An angle is the opening formed when two straight lines meet at a point. Students learn to measure that opening in degrees, the way a clock's hands spread apart from the center. | 4.MD.5 |
| An angle is measured with reference to a circle with its center at the common… | A degree is one tiny slice of a full circle, cut into 360 equal pieces. Students use those slices to measure how wide an angle opens, the same way a clock face is divided into hours. | 4.MD.5.a |
| An angle that turns through n one-degree angles is said to have an angle… | Angles are measured in degrees. Students learn that a 90-degree angle is made up of 90 one-degree turns, so the total number of those small turns is the angle's measure. | 4.MD.5.b |
| Measure angles in whole-number degrees using a protractor | Students use a protractor to measure angles in whole-number degrees, then draw new angles to match a given measurement. | 4.MD.6 |
| Recognize angle measure as additive | When a large angle is split into smaller angles, the parts add up to the whole. Students find missing angle sizes by writing addition or subtraction equations, the same way they would find a missing number in any math problem. | 4.MD.7 |
Students sort shapes by their sides and corners, spotting right angles, parallel lines, and whether edges meet or stay apart. It's the geometry behind every square, triangle, and rectangle they already know.
Students learn the basic building blocks of geometry: how to draw and name points, straight lines, line segments, rays, and angles (including right, sharp, and wide-open ones). They also spot parallel and perpendicular lines inside flat shapes.
Students sort flat shapes by checking whether their sides run parallel, meet at a corner, or form a right angle like the corner of a piece of paper. Right triangles get their own category because one of their angles is exactly that square corner.
Students learn to spot the fold line on a shape that creates two matching halves. They practice finding those lines on real shapes and drawing them in.
| Standard | Definition | Code |
|---|---|---|
| Draw and identify lines and angles | Students sort shapes by their sides and corners, spotting right angles, parallel lines, and whether edges meet or stay apart. It's the geometry behind every square, triangle, and rectangle they already know. | 4.G.A |
| Draw points, lines, line segments, rays, angles | Students learn the basic building blocks of geometry: how to draw and name points, straight lines, line segments, rays, and angles (including right, sharp, and wide-open ones). They also spot parallel and perpendicular lines inside flat shapes. | 4.G.1 |
| Classify two-dimensional figures based on the presence or absence of parallel… | Students sort flat shapes by checking whether their sides run parallel, meet at a corner, or form a right angle like the corner of a piece of paper. Right triangles get their own category because one of their angles is exactly that square corner. | 4.G.2 |
| Recognize a line of symmetry for a two-dimensional figure as a line across the… | Students learn to spot the fold line on a shape that creates two matching halves. They practice finding those lines on real shapes and drawing them in. | 4.G.3 |
Students should add and subtract large numbers quickly, multiply up to four digits by one digit, and divide with remainders. They should compare fractions, add fractions with the same bottom number, and work with simple decimals like 0.7 or 0.42. They should also measure angles and find the area of a rectangle.
Practice times tables in short bursts while cooking or driving. Ask comparison questions like, the dog is 4 times as heavy as the cat, so how much does the dog weigh? Five minutes a day beats a long weekend session.
Students learn that 3/4 is the same as 6/8 by seeing it on a number line or a folded strip of paper. They compare fractions, add ones with the same bottom number, and start to see that 0.5 and 1/2 mean the same amount. Pizza slices, measuring cups, and rulers all help.
Most teachers start with place value and multi-digit operations, then move into multiplicative comparison and factors. Fractions take the longest stretch, usually winter into spring. Measurement, angles, and geometry round out the year and pull the earlier work back in.
Long division with remainders, comparing fractions with unlike bottom numbers, and interpreting word problems with more than one step. Build in spiral review for these from the first week. Quick warm-ups beat full reteach lessons.
Read it together and ask what the question is really asking. Have students draw a picture or write a number sentence with a box for the unknown. Estimating first, even roughly, helps catch wild answers before they happen.
Students start by seeing an angle as a slice of a circle, then use a protractor to measure in degrees. They also learn that angle measures add up, so a 30 degree and 60 degree angle next to each other make 90 degrees. A simple protractor at home is enough to practice.
Students can multiply and divide multi-digit numbers with the standard methods, add and subtract fractions with the same bottom number, and write decimals to the hundredths. They can also solve multistep word problems and explain why their answer makes sense. End-of-unit work samples tell the story better than a single test.