Numbers up to 1,000
Students read, write, and compare bigger numbers using hundreds, tens, and ones. They place numbers on a number line and find 10 more, 10 less, 100 more, or 100 less without counting one by one.
This is the year math stretches from counting to thinking in hundreds. Students read, write, and compare numbers up to 1,000, and they learn that 100 is just ten tens stacked together. They add and subtract two-digit numbers, count coins up to a dollar, and start splitting shapes into halves, thirds, and fourths. By spring, they can tell time to the quarter hour and read a simple bar graph.
Students read, write, and compare bigger numbers using hundreds, tens, and ones. They place numbers on a number line and find 10 more, 10 less, 100 more, or 100 less without counting one by one.
Students learn their basic facts up to 20 by heart and start adding and subtracting two-digit numbers in word problems. They also estimate answers and check if a result makes sense.
Students find and extend patterns with numbers and shapes, and count mixed coins up to a dollar. They also use arrays and repeated addition, which is the first taste of multiplication.
Students sort flat and solid shapes, measure with a ruler to the nearest whole unit, and tell time to the quarter hour on both analog and digital clocks. They also learn the difference between a.m. and p.m.
Students share things fairly into halves, thirds, and fourths, and name those parts as fractions. They also read bar graphs and pictographs and answer questions using the data.
Reading and writing numbers up to 1,000, understanding that the position of each digit (hundreds, tens, ones) determines its value. Students compare two numbers and show which is greater, lesser, or equal.
Students read and write numbers up to 1,000 and show what those numbers mean using pictures, number lines, tally marks, and other hands-on tools.
Students place a number on a blank number line by thinking about where it falls between numbers they already know, like 10s and 50s. This builds a sense of how far apart numbers are.
Students break numbers like 347 into hundreds, tens, and ones, then write them out in different ways. They also know that 10 ones make a ten, and 10 tens make a hundred.
Starting from any three-digit number, students add or subtract 10 or 100 in their head. For example, 10 more than 342 is 352, and 100 less than 342 is 242.
Students sort real objects into pairs to figure out if a number is even or odd. If nothing is left over, the number is even. If one is left over, it's odd.
Students practice rounding numbers to the nearest ten or hundred, like deciding that 47 rounds to 50 or that 352 rounds to 400. They also learn when rounding makes sense in everyday life, such as estimating a price or a distance.
Students look at numbers up to 1,000 and decide which is greater, which is smaller, or which falls in between, using symbols like > and <. They lean on place value, hundreds, tens, and ones, to make that call.
Students add and subtract numbers up to 99 to solve everyday problems, like figuring out how many items are left in a store or how many more points one team scored than another.
Adding and subtracting are two sides of the same fact. Students use that connection to solve number problems up to 20, recognizing that knowing 8 + 7 = 15 also means knowing 15 - 7 = 8.
Students practice adding and subtracting numbers until they can get answers up to 20 quickly and without counting on their fingers. Think 7 + 8 or 15 - 6, recalled from memory.
Students make a quick guess at the answer to an addition or subtraction problem before solving it. For example, they might round to the nearest ten to check whether an answer is in the right ballpark.
Students add and subtract two-digit numbers by thinking about tens and ones, not just counting up or down. They use what they know about how numbers are built to solve problems efficiently.
Students add and subtract numbers up to 99, using word problems and equations. This is the core arithmetic of second grade: putting numbers together and taking them apart with confidence.
Repeated addition and arrays (like rows of chairs or dots in a grid) lay the groundwork for multiplication. Students use physical objects and visual patterns to see what it means to add the same number again and again.
Students begin working with fractions by splitting shapes and groups into equal parts and naming those parts, like halves and fourths.
Students split shapes or groups of objects into equal sections and name each section as a half, a third, or a fourth. They recognize that the sections must be the same size for the fraction to be correct.
Students divide shapes, groups of objects, or lengths into equal parts. They practice splitting things into halves, thirds, and fourths so every portion is exactly the same size.
Students figure out the total value of a group of coins, such as quarters, dimes, nickels, and pennies. It's the math behind counting change at a store.
Students count a small pile of coins and write the total using the cent symbol. The total stays at one dollar or under.
Students figure out how to make an exact amount of money using pennies, nickels, dimes, and quarters. The total stays at one dollar or under.
| Standard | Definition | Code |
|---|---|---|
| Compare and represent whole numbers up to 1,000 with an emphasis on place value… | Reading and writing numbers up to 1,000, understanding that the position of each digit (hundreds, tens, ones) determines its value. Students compare two numbers and show which is greater, lesser, or equal. | 2.N.1 |
| Read, write, discuss | Students read and write numbers up to 1,000 and show what those numbers mean using pictures, number lines, tally marks, and other hands-on tools. | 2.N.1.1 |
| Use knowledge of number relationships to locate the position of a given whole… | Students place a number on a blank number line by thinking about where it falls between numbers they already know, like 10s and 50s. This builds a sense of how far apart numbers are. | 2.N.1.2 |
| Use place value to describe whole numbers between 10 and 1,000 in terms of… | Students break numbers like 347 into hundreds, tens, and ones, then write them out in different ways. They also know that 10 ones make a ten, and 10 tens make a hundred. | 2.N.1.3 |
| Find 10 more or 10 less than a given three-digit number | Starting from any three-digit number, students add or subtract 10 or 100 in their head. For example, 10 more than 342 is 352, and 100 less than 342 is 242. | 2.N.1.4 |
| Use objects to determine whether a number is even or odd | Students sort real objects into pairs to figure out if a number is even or odd. If nothing is left over, the number is even. If one is left over, it's odd. | 2.N.1.5 |
| Use place value understanding to round numbers to the nearest ten and nearest… | Students practice rounding numbers to the nearest ten or hundred, like deciding that 47 rounds to 50 or that 352 rounds to 400. They also learn when rounding makes sense in everyday life, such as estimating a price or a distance. | 2.N.1.6 |
| Use place value to compare and order whole numbers up to 1,000 using… | Students look at numbers up to 1,000 and decide which is greater, which is smaller, or which falls in between, using symbols like > and <. They lean on place value, hundreds, tens, and ones, to make that call. | 2.N.1.7 |
| Add and subtract one- and two-digit numbers in real-world and mathematical… | Students add and subtract numbers up to 99 to solve everyday problems, like figuring out how many items are left in a store or how many more points one team scored than another. | 2.N.2 |
| Use the relationship between addition and subtraction to generate basic facts… | Adding and subtracting are two sides of the same fact. Students use that connection to solve number problems up to 20, recognizing that knowing 8 + 7 = 15 also means knowing 15 - 7 = 8. | 2.N.2.1 |
| Demonstrate fluency with basic facts of addition and subtraction with sums and… | Students practice adding and subtracting numbers until they can get answers up to 20 quickly and without counting on their fingers. Think 7 + 8 or 15 - 6, recalled from memory. | 2.N.2.2 |
| Estimate sums and differences up to 100 | Students make a quick guess at the answer to an addition or subtraction problem before solving it. For example, they might round to the nearest ten to check whether an answer is in the right ballpark. | 2.N.2.3 |
| Use strategies and algorithms based on knowledge of place value and equality to… | Students add and subtract two-digit numbers by thinking about tens and ones, not just counting up or down. They use what they know about how numbers are built to solve problems efficiently. | 2.N.2.4 |
| Solve addition and subtraction problems involving whole numbers up to two… | Students add and subtract numbers up to 99, using word problems and equations. This is the core arithmetic of second grade: putting numbers together and taking them apart with confidence. | 2.N.2.5 |
| Use concrete models and structured arrangements, such as repeated addition… | Repeated addition and arrays (like rows of chairs or dots in a grid) lay the groundwork for multiplication. Students use physical objects and visual patterns to see what it means to add the same number again and again. | 2.N.2.6 |
| Explore the foundational ideas of fractions | Students begin working with fractions by splitting shapes and groups into equal parts and naming those parts, like halves and fourths. | 2.N.3 |
| Identify the parts of a set and area that represent fractions for halves, thirds | Students split shapes or groups of objects into equal sections and name each section as a half, a third, or a fourth. They recognize that the sections must be the same size for the fraction to be correct. | 2.N.3.1 |
| Construct equal-sized portions through fair sharing | Students divide shapes, groups of objects, or lengths into equal parts. They practice splitting things into halves, thirds, and fourths so every portion is exactly the same size. | 2.N.3.2 |
| Determine the value of a set of coins | Students figure out the total value of a group of coins, such as quarters, dimes, nickels, and pennies. It's the math behind counting change at a store. | 2.N.4 |
| Determine the value of a collection of coins up to one dollar using the cent… | Students count a small pile of coins and write the total using the cent symbol. The total stays at one dollar or under. | 2.N.4.1 |
| Use a combination of coins to represent a given amount of money up to one… | Students figure out how to make an exact amount of money using pennies, nickels, dimes, and quarters. The total stays at one dollar or under. | 2.N.4.2 |
Students find a pattern in a row of numbers or shapes and use that pattern to figure out what comes next or solve a simple problem.
Students work with number patterns that grow bigger or get smaller, like counting up by fives or back by twos. They spot the rule, continue the pattern, and use it to solve simple real-world problems.
Students find a pattern made of repeating shapes, such as circle-square-circle-square, and describe what comes next. They show the pattern using drawings, objects, or symbols.
Students figure out a missing number in a simple equation, like 5 + ? = 12, by connecting the math to a real situation. This is the beginning of solving for unknowns.
Students use counters or a number line to show what a math equation means. This helps them see why the numbers on both sides of the equal sign balance out.
Students look at a math equation and draw a picture or describe a real-world situation that matches it. They also work the other way: turning a story or picture into a number sentence.
Students use shortcuts like "order doesn't matter in addition" to figure out what number fills a blank in a math sentence, then decide if the full sentence is true or false.
| Standard | Definition | Code |
|---|---|---|
| Describe the relationship found in patterns to solve real-world and… | Students find a pattern in a row of numbers or shapes and use that pattern to figure out what comes next or solve a simple problem. | 2.A.1 |
| Represent, create, describe, complete | Students work with number patterns that grow bigger or get smaller, like counting up by fives or back by twos. They spot the rule, continue the pattern, and use it to solve simple real-world problems. | 2.A.1.1 |
| Represent and describe repeating patterns involving shapes in a variety of… | Students find a pattern made of repeating shapes, such as circle-square-circle-square, and describe what comes next. They show the pattern using drawings, objects, or symbols. | 2.A.1.2 |
| Use number sentences involving unknowns to represent and solve realworld and… | Students figure out a missing number in a simple equation, like 5 + ? = 12, by connecting the math to a real situation. This is the beginning of solving for unknowns. | 2.A.2 |
| Use objects and number lines to represent number sentences | Students use counters or a number line to show what a math equation means. This helps them see why the numbers on both sides of the equal sign balance out. | 2.A.2.1 |
| Generate models and situations to represent number sentences and vice versa | Students look at a math equation and draw a picture or describe a real-world situation that matches it. They also work the other way: turning a story or picture into a number sentence. | 2.A.2.2 |
| Apply the commutative property, identity property | Students use shortcuts like "order doesn't matter in addition" to figure out what number fills a blank in a math sentence, then decide if the full sentence is true or false. | 2.A.2.3 |
Students sort, compare, and describe shapes like squares, triangles, and cubes by looking at their sides, corners, and faces. They start to notice rules that apply to whole groups of shapes, not just one at a time.
Students learn to spot trapezoids and hexagons in the world around them, including versions that look slightly different from the textbook shape. A trapezoid has one pair of parallel sides; a hexagon has six sides.
Students sort and compare flat shapes by counting sides, corners, and angles. A triangle has three sides; a rectangle has four right corners. Students group shapes by what they have in common.
Students put together and take apart flat shapes, such as fitting two triangles to form a square or breaking a hexagon into smaller pieces.
Students sort 3D shapes like cubes, cones, and pyramids by counting their flat faces, corners, and edges. A cube has 6 faces; a cone has 1. Sorting by those differences is the skill.
Students identify right angles (the square corners found on a piece of paper or a door frame) and decide whether other angles are more open or more closed than a right angle.
Students measure how long objects are using rulers or other tools, then compare lengths to figure out which is longer or shorter. They also explore how much liquid a container can hold.
Measuring with a small unit, like a paper clip, takes more units than measuring with a big unit, like a ruler length. Students learn why the unit size changes how many you need to count.
Students use a ruler to measure objects to the nearest inch or centimeter. The numbers on a ruler count equal-sized spaces, not just the lines, so the measurement tells how many of those spaces fit along the object.
Two containers that look completely different can hold the same amount. Students pour water or rice between differently shaped cups and bowls to see that size and shape do not always tell you which one holds more.
Students read a clock and say whether the time is on the hour, quarter past, half past, or quarter to the next hour.
Students learn that a.m. covers the hours from midnight to noon and p.m. covers noon to midnight. They use that difference to make sense of a daily schedule.
Students read and write times like 2:15 or 2:45 on both a standard clock with hands and a digital display. Quarter hours land at the 12, 3, 6, and 9 on the clock face.
| Standard | Definition | Code |
|---|---|---|
| Analyze attributes of two- and three-dimensional figures and develop… | Students sort, compare, and describe shapes like squares, triangles, and cubes by looking at their sides, corners, and faces. They start to notice rules that apply to whole groups of shapes, not just one at a time. | 2.GM.1 |
| Recognize regular and irregular trapezoids and hexagons | Students learn to spot trapezoids and hexagons in the world around them, including versions that look slightly different from the textbook shape. A trapezoid has one pair of parallel sides; a hexagon has six sides. | 2.GM.1.1 |
| Describe, compare, and classify two-dimensional figures according to their… | Students sort and compare flat shapes by counting sides, corners, and angles. A triangle has three sides; a rectangle has four right corners. Students group shapes by what they have in common. | 2.GM.1.2 |
| Compose and decompose two-dimensional shapes using triangles, squares… | Students put together and take apart flat shapes, such as fitting two triangles to form a square or breaking a hexagon into smaller pieces. | 2.GM.1.3 |
| Sort three-dimensional shapes based on attributes such as number of faces… | Students sort 3D shapes like cubes, cones, and pyramids by counting their flat faces, corners, and edges. A cube has 6 faces; a cone has 1. Sorting by those differences is the skill. | 2.GM.1.4 |
| Recognize right angles and classify angles as smaller or larger than a right… | Students identify right angles (the square corners found on a piece of paper or a door frame) and decide whether other angles are more open or more closed than a right angle. | 2.GM.1.5 |
| Understand length as a measurable attribute and explore capacity | Students measure how long objects are using rulers or other tools, then compare lengths to figure out which is longer or shorter. They also explore how much liquid a container can hold. | 2.GM.2 |
| Explain the relationship between the size of the unit of measurement and the… | Measuring with a small unit, like a paper clip, takes more units than measuring with a big unit, like a ruler length. Students learn why the unit size changes how many you need to count. | 2.GM.2.1 |
| Explain the relationship between length and the numbers on a ruler by using a… | Students use a ruler to measure objects to the nearest inch or centimeter. The numbers on a ruler count equal-sized spaces, not just the lines, so the measurement tells how many of those spaces fit along the object. | 2.GM.2.2 |
| Explore how varying shapes and styles of containers can have the same capacity | Two containers that look completely different can hold the same amount. Students pour water or rice between differently shaped cups and bowls to see that size and shape do not always tell you which one holds more. | 2.GM.2.3 |
| Tell time to the quarter hour | Students read a clock and say whether the time is on the hour, quarter past, half past, or quarter to the next hour. | 2.GM.3 |
| Distinguish between a.m | Students learn that a.m. covers the hours from midnight to noon and p.m. covers noon to midnight. They use that difference to make sense of a daily schedule. | 2.GM.3.1 |
| Read and write time to the quarter hour on an analog and digital clock | Students read and write times like 2:15 or 2:45 on both a standard clock with hands and a digital display. Quarter hours land at the 12, 3, 6, and 9 on the clock face. | 2.GM.3.2 |
Students gather information, sort it into a simple chart or graph, and answer questions about what the data shows.
Reading a bar graph or pictograph means understanding that a longer bar or more pictures means more things were counted in that group. Students connect the size of what they see to the actual number it stands for.
Students sort collected information into up to four groups, then display it in a picture graph or bar graph. The bar scale counts by 1s, 2s, 5s, or 10s depending on how large the numbers get.
Students read a pictograph or bar graph and use the numbers in it to write and solve a simple addition or subtraction word problem. The data in the chart is the starting point, not just the answer.
Students look at a pictograph or bar graph and answer questions about what the data shows, then use the numbers to make a simple prediction about what might happen next.
| Standard | Definition | Code |
|---|---|---|
| Collect, organize, and interpret data | Students gather information, sort it into a simple chart or graph, and answer questions about what the data shows. | 2.D.1 |
| Explain that the length of a bar in a bar graph and the number of objects in a… | Reading a bar graph or pictograph means understanding that a longer bar or more pictures means more things were counted in that group. Students connect the size of what they see to the actual number it stands for. | 2.D.1.1 |
| Organize a collection of data with up to four categories using pictographs and… | Students sort collected information into up to four groups, then display it in a picture graph or bar graph. The bar scale counts by 1s, 2s, 5s, or 10s depending on how large the numbers get. | 2.D.1.2 |
| Write and solve one-step word problems involving addition or subtraction using… | Students read a pictograph or bar graph and use the numbers in it to write and solve a simple addition or subtraction word problem. The data in the chart is the starting point, not just the answer. | 2.D.1.3 |
| Draw conclusions and make predictions from information in a pictograph and bar… | Students look at a pictograph or bar graph and answer questions about what the data shows, then use the numbers to make a simple prediction about what might happen next. | 2.D.1.4 |
Students read, write, and compare numbers up to 1,000 using hundreds, tens, and ones. They add and subtract two-digit numbers, know addition and subtraction facts up to 20 by heart, tell time to the quarter hour, and count coins up to a dollar.
Count coins from a jar and ask how much is there. Read the clock together and ask how long until dinner. On a car ride, ask what is 10 more than 248, or 100 less than 615. Short and steady beats long sessions.
Fingers are fine early in the year. By spring, students should know sums and differences up to 20 quickly, without counting one by one. Practice a small set of facts each week using flashcards, dice games, or quick verbal quizzes at dinner.
Build numbers to 100 first with tens and ones, then extend to 1,000 with hundreds. Once students can name hundreds, tens, and ones, layer in 10 more, 10 less, 100 more, 100 less, then rounding and comparing. Expanded form fits naturally once the place names are solid.
Students answer addition and subtraction facts up to 20 in a few seconds, using strategies like making ten, doubles, and the link between addition and subtraction. Speed without strategy is brittle, so keep the strategies visible even during fact practice.
Fractions begin with fair sharing. Students split shapes, sets, and lengths into halves, thirds, and fourths, and name the parts. Cutting a sandwich into four equal pieces or sharing crackers fairly between three friends builds the idea before any symbols appear.
Two-digit subtraction with regrouping, telling time to the quarter hour, and counting mixed coins tend to need a second pass. Build in short review cycles every few weeks instead of one big unit, and pull these into morning warm-ups through the spring.
Students do not memorize times tables yet. They build groups using counters, arrays, and repeated addition, such as four rows of three cookies. The goal is to see multiplication as equal groups, which sets up the work next year.
By June, students should compare numbers to 1,000, add and subtract two-digit numbers with regrouping, know facts to 20 from memory, tell time to the quarter hour, count coins to a dollar, and read a simple bar graph or pictograph to answer a question.