Adding and subtracting within 20
Students solve story problems about joining groups, taking some away, and comparing amounts. They learn quick recall for sums and differences up to ten and use strategies like counting on for bigger numbers.
This is the year math grows past counting into thinking in groups of ten. Students add and subtract within 20 until the small facts feel automatic, then use tens and ones to work with numbers up to 100. They also start measuring with a ruler, telling time on a clock, and naming coins. By spring, students can read a number like 47 as four tens and seven ones, and split a shape into halves or fourths.
Students solve story problems about joining groups, taking some away, and comparing amounts. They learn quick recall for sums and differences up to ten and use strategies like counting on for bigger numbers.
Students learn that the equal sign means both sides match, not just where the answer goes. They check whether number sentences are true and find the missing number in problems like 8 + ? = 13.
Students count past 100, read and write larger numbers, and skip count by twos, fives, and tens. They start to see a two-digit number as a bundle of tens plus some leftover ones.
Students add two-digit numbers up to 100 using blocks, drawings, and mental math. They compare numbers with the symbols for greater than and less than, and find ten more or ten less without counting.
Students measure objects by lining up smaller units end to end with no gaps. They tell time to the hour and half hour on analog and digital clocks, and learn the value of pennies, nickels, dimes, and quarters.
Students build and draw flat shapes and solid shapes, and put smaller shapes together to make new ones. They split circles and rectangles into halves and fourths and learn that more pieces means smaller pieces.
Students read a math problem carefully, figure out what it's asking, and keep trying even when the first approach doesn't work.
Students learn to move between a real-world problem and the numbers that represent it. They ask what the numbers mean, not just what they equal.
Students explain why their math answer makes sense, then listen to a classmate's explanation and say whether they agree or disagree.
Students use drawings, numbers, or objects to show a real-life situation, like splitting snacks into equal groups or counting coins to find a total.
Students learn which tools help solve a problem, such as a ruler, a number line, or their fingers, and when to reach for each one. The goal is knowing which tool fits, not just grabbing the nearest one.
Students say exactly what they mean in math. They use the right words, label their answers (like "3 apples" instead of just "3"), and check that their work is correct before finishing.
Students notice patterns in math, like how numbers can be broken apart and put back together, and use those patterns as shortcuts to solve problems.
Students notice when the same steps keep working the same way and use that pattern as a shortcut. For example, adding zero to any number always leaves it unchanged, so students stop recalculating and just know it.
| Standard | Definition | Code |
|---|---|---|
| Make sense of problems and persevere in solving them | Students read a math problem carefully, figure out what it's asking, and keep trying even when the first approach doesn't work. | MP.1 |
| Reason abstractly and quantitatively | Students learn to move between a real-world problem and the numbers that represent it. They ask what the numbers mean, not just what they equal. | MP.2 |
| Construct viable arguments and critique the reasoning of others | Students explain why their math answer makes sense, then listen to a classmate's explanation and say whether they agree or disagree. | MP.3 |
| Model with mathematics | Students use drawings, numbers, or objects to show a real-life situation, like splitting snacks into equal groups or counting coins to find a total. | MP.4 |
| Use appropriate tools strategically | Students learn which tools help solve a problem, such as a ruler, a number line, or their fingers, and when to reach for each one. The goal is knowing which tool fits, not just grabbing the nearest one. | MP.5 |
| Attend to precision | Students say exactly what they mean in math. They use the right words, label their answers (like "3 apples" instead of just "3"), and check that their work is correct before finishing. | MP.6 |
| Look for and make use of structure | Students notice patterns in math, like how numbers can be broken apart and put back together, and use those patterns as shortcuts to solve problems. | MP.7 |
| Look for and express regularity in repeated reasoning | Students notice when the same steps keep working the same way and use that pattern as a shortcut. For example, adding zero to any number always leaves it unchanged, so students stop recalculating and just know it. | MP.8 |
Students use pictures, objects, and number sentences to figure out addition and subtraction problems. They practice breaking apart small numbers and putting them back together to find a missing amount.
Students read short story problems and figure out whether to add or subtract to find the missing number, using drawings, objects, or equations. Problems stay within 20 and the missing number can appear anywhere in the problem.
Students add three numbers together to solve a short story problem, keeping the total at 20 or under. They might use blocks, drawings, or written equations to find the answer.
Adding and subtracting are two sides of the same idea. Students learn that if 3 + 4 = 7, then 7 - 4 = 3, and practice flipping problems around to check their work.
Adding in any order gets the same answer. Students learn that 3 + 5 equals the same as 5 + 3, and that adding zero to any number leaves it unchanged.
Subtraction can be solved by thinking about addition instead. If students know that 9 + 4 = 13, they can use that to figure out 13 - 9 without counting backward.
Students practice adding and subtracting with numbers up to 20. They work toward knowing these facts from memory, the way they'll eventually know that 7 + 8 is 15 without stopping to count.
Counting up or back is one way to add or subtract. Students practice moving from counting on their fingers to using that same counting pattern as a faster math strategy.
Students practice adding and subtracting numbers up to 10 until the answers come quickly, then use those skills to tackle bigger problems up to 20.
Students practice writing and solving simple addition and subtraction equations, learning that the equals sign means both sides of the number sentence have the same value.
Students learn that the equal sign means "the same amount on both sides," not just "the answer goes here." They look at simple addition and subtraction equations and decide whether both sides actually match.
Students find the missing number in addition and subtraction problems, whether that number is at the start, middle, or end. For example: ___ + 4 = 9, or 5 + ___ = 9, or 5 + 4 = ___.
| Standard | Definition | Code |
|---|---|---|
| Represent and solve problems involving addition and subtraction | Students use pictures, objects, and number sentences to figure out addition and subtraction problems. They practice breaking apart small numbers and putting them back together to find a missing amount. | 1.OA.A |
| Solve addition and subtraction word problems within 20 involving situations of… | Students read short story problems and figure out whether to add or subtract to find the missing number, using drawings, objects, or equations. Problems stay within 20 and the missing number can appear anywhere in the problem. | 1.OA.A.1 |
| Solve word problems that call for addition of three whole numbers whose sum is… | Students add three numbers together to solve a short story problem, keeping the total at 20 or under. They might use blocks, drawings, or written equations to find the answer. | 1.OA.A.2 |
| Understand and apply properties of operations and the relationship between… | Adding and subtracting are two sides of the same idea. Students learn that if 3 + 4 = 7, then 7 - 4 = 3, and practice flipping problems around to check their work. | 1.OA.B |
| Apply properties of operations to add | Adding in any order gets the same answer. Students learn that 3 + 5 equals the same as 5 + 3, and that adding zero to any number leaves it unchanged. | 1.OA.B.3 |
| Restate a subtraction problem as a missing addend problem using the… | Subtraction can be solved by thinking about addition instead. If students know that 9 + 4 = 13, they can use that to figure out 13 - 9 without counting backward. | 1.OA.B.4 |
| Add and subtract within 20 | Students practice adding and subtracting with numbers up to 20. They work toward knowing these facts from memory, the way they'll eventually know that 7 + 8 is 15 without stopping to count. | 1.OA.C |
| Relate counting to addition and subtraction | Counting up or back is one way to add or subtract. Students practice moving from counting on their fingers to using that same counting pattern as a faster math strategy. | 1.OA.C.5 |
| Demonstrate fluency for addition and subtraction within ten, use strategies to… | Students practice adding and subtracting numbers up to 10 until the answers come quickly, then use those skills to tackle bigger problems up to 20. | 1.OA.C.6 |
| Work with addition and subtraction equations | Students practice writing and solving simple addition and subtraction equations, learning that the equals sign means both sides of the number sentence have the same value. | 1.OA.D |
| Understand the meaning of the equal sign | Students learn that the equal sign means "the same amount on both sides," not just "the answer goes here." They look at simple addition and subtraction equations and decide whether both sides actually match. | 1.OA.D.7 |
| Determine the unknown whole number in an addition or subtraction equation… | Students find the missing number in addition and subtraction problems, whether that number is at the start, middle, or end. For example: ___ + 4 = 9, or 5 + ___ = 9, or 5 + 4 = ___. | 1.OA.D.8 |
Students count forward past 100 and backward from any starting number. This builds the foundation for adding and subtracting bigger numbers later.
Students count forward and backward to 120, skip count by twos, fives, and tens, and write the numerals that match a group of objects.
Students learn that where a digit sits in a number determines its value. The "1" in 14 means one ten, not one one.
Reading a number like 24 means seeing two separate ideas at once: the tens digit (how many groups of ten) and the ones digit (how many singles left over). Students use this to make sense of every two-digit number they meet.
The number 10 is one full group of ten single ones. Students learn to see 10 not just as a number but as a bundle, which is the first step toward understanding how two-digit numbers are built.
Teens numbers (11 through 19) are built from one group of ten plus some leftover ones. So 14 means one full group of ten and four more, not just a 1 and a 4 sitting side by side.
Counting by tens means 30 is three groups of ten, 70 is seven groups of ten, and so on. Students learn that the tens digit tells exactly how many groups of ten are packed into a number like 20 or 80.
Students look at two numbers and decide which is bigger, smaller, or equal by checking the tens place first, then the ones. They record the answer using the symbols >, =, or <.
Students use what they know about tens and ones to add and subtract numbers. They learn that breaking a number into tens and ones makes adding and subtracting easier to work out.
Students add two numbers up to 100, such as 47 + 6, by thinking about tens and ones. They might use blocks, drawings, or written steps to show how they got the answer.
Students add a two-digit number (like 34) and a one-digit number (like 7) to get a sum. This is an early step in learning to add numbers that require carrying into the tens place.
Students add a two-digit number to a round number like 10, 20, or 30. They practice seeing how the tens place changes while the ones place stays the same.
Adding two two-digit numbers means adding the tens together and the ones together. Sometimes the ones add up to 10 or more, so students regroup them into a new ten.
Students look at a number like 43 and figure out in their head that ten more is 53, or ten less is 33, without counting up or back. They also put into words how they knew.
Students subtract round numbers by tens, like 70 minus 40, and explain how they got the answer. They use blocks, drawings, or number sentences to show their thinking.
| Standard | Definition | Code |
|---|---|---|
| Extend the counting sequence | Students count forward past 100 and backward from any starting number. This builds the foundation for adding and subtracting bigger numbers later. | 1.NBT.A |
| Starting at a given number, count forward and backwards within 120 by ones | Students count forward and backward to 120, skip count by twos, fives, and tens, and write the numerals that match a group of objects. | 1.NBT.A.1 |
| Understand place value | Students learn that where a digit sits in a number determines its value. The "1" in 14 means one ten, not one one. | 1.NBT.B |
| Understand that the two digits of a two-digit number represent amounts of tens… | Reading a number like 24 means seeing two separate ideas at once: the tens digit (how many groups of ten) and the ones digit (how many singles left over). Students use this to make sense of every two-digit number they meet. | 1.NBT.B.2 |
| 10 can be thought of as a bundle of ten ones — called a "ten." | The number 10 is one full group of ten single ones. Students learn to see 10 not just as a number but as a bundle, which is the first step toward understanding how two-digit numbers are built. | 1.NBT.B.2.a |
| The numbers from 11 to 19 are composed of a ten and one, two, three, four… | Teens numbers (11 through 19) are built from one group of ten plus some leftover ones. So 14 means one full group of ten and four more, not just a 1 and a 4 sitting side by side. | 1.NBT.B.2.b |
| The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four… | Counting by tens means 30 is three groups of ten, 70 is seven groups of ten, and so on. Students learn that the tens digit tells exactly how many groups of ten are packed into a number like 20 or 80. | 1.NBT.B.2.c |
| Compare two two-digit numbers based on meanings of the tens and ones digits… | Students look at two numbers and decide which is bigger, smaller, or equal by checking the tens place first, then the ones. They record the answer using the symbols >, =, or <. | 1.NBT.B.3 |
| Use place value understanding and properties of operations to add and subtract | Students use what they know about tens and ones to add and subtract numbers. They learn that breaking a number into tens and ones makes adding and subtracting easier to work out. | 1.NBT.C |
| Add whole numbers within 100 by using physical, visual | Students add two numbers up to 100, such as 47 + 6, by thinking about tens and ones. They might use blocks, drawings, or written steps to show how they got the answer. | 1.NBT.C.4 |
| Add a two-digit number and a one-digit number | Students add a two-digit number (like 34) and a one-digit number (like 7) to get a sum. This is an early step in learning to add numbers that require carrying into the tens place. | 1.NBT.C.4.a |
| Add a two-digit number and a multiple of ten | Students add a two-digit number to a round number like 10, 20, or 30. They practice seeing how the tens place changes while the ones place stays the same. | 1.NBT.C.4.b |
| Understand that when adding two-digit numbers, combine like base-ten units such… | Adding two two-digit numbers means adding the tens together and the ones together. Sometimes the ones add up to 10 or more, so students regroup them into a new ten. | 1.NBT.C.4.c |
| Given a two-digit number, mentally find ten more or ten less than the number… | Students look at a number like 43 and figure out in their head that ten more is 53, or ten less is 33, without counting up or back. They also put into words how they knew. | 1.NBT.C.5 |
| Subtract multiples of ten in the range 10 – 90 from multiples of ten in the… | Students subtract round numbers by tens, like 70 minus 40, and explain how they got the answer. They use blocks, drawings, or number sentences to show their thinking. | 1.NBT.C.6 |
Students learn to measure how long something is by lining up small same-size objects end to end and counting them. They also compare lengths when two objects can't be placed side by side.
Line up three objects from shortest to longest. Students also figure out which of two objects is longer by comparing each one to a third object, like a piece of string or a pencil.
Students measure how long something is by lining up small objects, like paper clips, from one end to the other and counting them. The total number of clips is the length.
Students read clocks and write what time they show, starting with hours and half-hours on both digital and analog clocks.
Students read a clock and say or write the time, working with whole hours (like 3:00) and half-hours (like 3:30). They practice with both the traditional clock face and the number display on a digital clock.
Students collect simple information, like favorite colors or how many teeth they've lost, then organize it into a picture or tally chart so the class can read the results at a glance.
Students sort objects or answers into groups, count how many are in each group, and compare the groups. They answer questions like "How many more picked dogs than cats?"
Students count coins and small bills to find a total amount. They practice making change and comparing prices using real-world values.
Students learn to recognize quarters, dimes, and nickels by sight and understand what each coin is worth in pennies. A nickel equals five pennies, a dime equals ten, and a quarter equals twenty-five.
| Standard | Definition | Code |
|---|---|---|
| Measure lengths indirectly and by iterating | Students learn to measure how long something is by lining up small same-size objects end to end and counting them. They also compare lengths when two objects can't be placed side by side. | 1.MD.A |
| Order three objects by length | Line up three objects from shortest to longest. Students also figure out which of two objects is longer by comparing each one to a third object, like a piece of string or a pencil. | 1.MD.A.1 |
| Express the length of an object as a whole number of length units by laying… | Students measure how long something is by lining up small objects, like paper clips, from one end to the other and counting them. The total number of clips is the length. | 1.MD.A.2 |
| Tell and write time | Students read clocks and write what time they show, starting with hours and half-hours on both digital and analog clocks. | 1.MD.B |
| Tell and write time in hours and half-hours using analog and digital clocks | Students read a clock and say or write the time, working with whole hours (like 3:00) and half-hours (like 3:30). They practice with both the traditional clock face and the number display on a digital clock. | 1.MD.B.3 |
| Represent and interpret data | Students collect simple information, like favorite colors or how many teeth they've lost, then organize it into a picture or tally chart so the class can read the results at a glance. | 1.MD.C |
| Organize, represent, and interpret data with up to three categories | Students sort objects or answers into groups, count how many are in each group, and compare the groups. They answer questions like "How many more picked dogs than cats?" | 1.MD.C.4 |
| Work with money | Students count coins and small bills to find a total amount. They practice making change and comparing prices using real-world values. | 1.MD.D |
| Identify quarters, dimes | Students learn to recognize quarters, dimes, and nickels by sight and understand what each coin is worth in pennies. A nickel equals five pennies, a dime equals ten, and a quarter equals twenty-five. | 1.MD.D.5 |
Students sort and describe shapes by their sides, corners, and size. They learn to see what makes a square different from a triangle, or a circle different from a rectangle.
Students sort shapes by the features that actually define them, like the number of sides or corners, rather than by color or size. Then they draw or build shapes that match those rules.
Students fit basic shapes together, like triangles and squares, to build a new, bigger shape. Then they use that combined shape as a building block to make something new.
Students cut circles and rectangles into 2 or 4 equal pieces, like slicing a pizza or folding a piece of paper. They see that cutting something into more pieces makes each piece smaller.
Students learn to name equal pieces of a shape using words like "half," "quarter," and "fourth." Cutting a circle or square into two equal pieces gives you two halves; cutting it into four equal pieces gives you fourths or quarters.
Students split a shape into equal parts and describe the whole thing as "two halves" or "four fourths." The focus is on naming the whole by how many equal shares it is made of.
| Standard | Definition | Code |
|---|---|---|
| Reason with shapes and their attributes | Students sort and describe shapes by their sides, corners, and size. They learn to see what makes a square different from a triangle, or a circle different from a rectangle. | 1.G.A |
| Compare defining attributes and non-defining attributes of two- and… | Students sort shapes by the features that actually define them, like the number of sides or corners, rather than by color or size. Then they draw or build shapes that match those rules. | 1.G.A.1 |
| Compose two-dimensional | Students fit basic shapes together, like triangles and squares, to build a new, bigger shape. Then they use that combined shape as a building block to make something new. | 1.G.A.2 |
| Partition circles and rectangles into two and four equal shares | Students cut circles and rectangles into 2 or 4 equal pieces, like slicing a pizza or folding a piece of paper. They see that cutting something into more pieces makes each piece smaller. | 1.G.A.3 |
| Describe the shares using the words "halves," "fourths," and "quarters," and… | Students learn to name equal pieces of a shape using words like "half," "quarter," and "fourth." Cutting a circle or square into two equal pieces gives you two halves; cutting it into four equal pieces gives you fourths or quarters. | 1.G.A.3.a |
| Describe the whole as two of | Students split a shape into equal parts and describe the whole thing as "two halves" or "four fourths." The focus is on naming the whole by how many equal shares it is made of. | 1.G.A.3.b |
Students should add and subtract within 20, count to 120, and understand that a number like 47 means 4 tens and 7 ones. They should also tell time to the hour and half hour, measure with paper clips or cubes, and name coins like nickels, dimes, and quarters.
Use small objects like beans, cereal, or coins. Ask quick story questions: there are 8 grapes, students eat 3, how many are left? Five or ten minutes a few times a week builds the speed students need.
By the end of the year, students should know addition and subtraction within 10 quickly, without counting on fingers each time. Facts within 20 can still use strategies like making a ten. Flashcards or quick verbal quizzes during car rides help.
Most teachers start with counting and addition and subtraction within 10, then move into place value with tens and ones, then addition within 100. Measurement, time, money, and shapes work well in shorter units between the bigger number sense blocks.
Place value is the big one. Students often see 34 as the digits 3 and 4 instead of 3 tens and 4 ones. The equal sign is another sticking point, since many students read it as the answer comes next rather than both sides match.
Not at this age. Fingers are a real math tool and most students use them. The goal is for students to gradually move from counting every finger to knowing facts like 6 plus 4 without thinking. That shift happens with practice over the year.
Setting the table, sorting laundry, counting coins from a piggy bank, reading a clock to know when a show starts, and cutting a sandwich into halves or fourths all hit real math skills. Talking through the numbers out loud matters more than getting a worksheet done.
Ready students can add and subtract within 20 with reasonable speed, compare two-digit numbers using more than and less than, add a two-digit and one-digit number, and find ten more or ten less in their head. They can also tell time to the half hour and name halves and fourths.