Adding and subtracting within 20
Students solve story problems by adding and taking away, using objects, drawings, and number sentences. They learn that the equal sign means both sides match.
This is the year math stretches past ten and starts working in tens and ones. Students add and subtract within 20, count all the way to 120, and learn that the two digits in a number like 47 stand for four tens and seven ones. They also measure objects with a row of paper clips, tell time on a clock to the hour and half-hour, and name shapes by what makes them that shape. By spring, students can solve a short word problem on paper and split a circle or rectangle into halves and fourths.
Students solve story problems by adding and taking away, using objects, drawings, and number sentences. They learn that the equal sign means both sides match.
Students build faster ways to add and subtract, like counting on, making a ten, and using one fact to figure out another. Small numbers start to feel automatic.
Students count, read, and write numbers up to 120. They see that a two-digit number is made of tens and ones, and compare numbers using greater than and less than.
Students add within 100 using place value, including adding tens to tens and ones to ones. They find ten more or ten less in their head and subtract multiples of ten.
Students compare lengths and measure objects with same-size units laid end to end. They tell time to the hour and half-hour on analog and digital clocks, and sort information into simple charts.
Students identify what makes a shape a shape, like the number of sides, and put shapes together to make new ones. They split circles and rectangles into halves and fourths.
Students read a math problem, figure out what it's actually asking, and keep trying even when the first approach doesn't work.
Students take a real problem (like sharing 8 crayons between 2 kids) and turn it into numbers, then check that the answer still makes sense in real life.
Students explain why their math answer makes sense and listen to how classmates solved the same problem. Then they say whether they agree and why.
Students use drawings, numbers, or simple equations to show how a real-world situation works. A picture of apples on a table becomes a math problem they can solve.
Students learn to pick the right tool for the job, whether that means counting on their fingers, grabbing a ruler, or drawing a picture. They think about which tool actually helps before they start.
Students say exactly what they mean with numbers and math words. They label units like inches or cents, write symbols correctly, and check that their answers make sense.
Students learn to spot patterns and rules hiding in plain sight, like noticing that adding zero never changes a number. That habit helps them solve new problems by recognizing something familiar.
Students notice when the same steps keep working the same way, like adding zero never changes a number. They use that pattern as a shortcut instead of starting from scratch each time.
| Standard | Definition | Code |
|---|---|---|
| Make sense of problems and persevere in solving them | Students read a math problem, figure out what it's actually asking, and keep trying even when the first approach doesn't work. | CCSS.Math.Practice.MP1 |
| Reason abstractly and quantitatively | Students take a real problem (like sharing 8 crayons between 2 kids) and turn it into numbers, then check that the answer still makes sense in real life. | CCSS.Math.Practice.MP2 |
| Construct viable arguments and critique the reasoning of others | Students explain why their math answer makes sense and listen to how classmates solved the same problem. Then they say whether they agree and why. | CCSS.Math.Practice.MP3 |
| Model with mathematics | Students use drawings, numbers, or simple equations to show how a real-world situation works. A picture of apples on a table becomes a math problem they can solve. | CCSS.Math.Practice.MP4 |
| Use appropriate tools strategically | Students learn to pick the right tool for the job, whether that means counting on their fingers, grabbing a ruler, or drawing a picture. They think about which tool actually helps before they start. | CCSS.Math.Practice.MP5 |
| Attend to precision | Students say exactly what they mean with numbers and math words. They label units like inches or cents, write symbols correctly, and check that their answers make sense. | CCSS.Math.Practice.MP6 |
| Look for and make use of structure | Students learn to spot patterns and rules hiding in plain sight, like noticing that adding zero never changes a number. That habit helps them solve new problems by recognizing something familiar. | CCSS.Math.Practice.MP7 |
| Look for and express regularity in repeated reasoning | Students notice when the same steps keep working the same way, like adding zero never changes a number. They use that pattern as a shortcut instead of starting from scratch each time. | CCSS.Math.Practice.MP8 |
Students use pictures, objects, and simple equations to figure out addition and subtraction problems. They practice breaking apart and combining small groups of things to find a missing number.
Students read short story problems and figure out a missing number by adding or subtracting. The unknown can be the starting amount, the change, or the total, and the numbers stay at 20 or below.
Students add three small numbers together to solve a short story problem, like finding out how many apples are in three baskets combined. The total is always 20 or less.
Adding and subtracting follow predictable rules. Students learn that flipping the numbers in an addition problem gives the same answer, and that addition and subtraction are opposites they can use to check each other.
Changing the order of two numbers being added gives the same answer. Students learn to use this idea as a shortcut, so 3 + 5 and 5 + 3 both equal 8 and only one needs to be memorized.
Subtraction is just addition in reverse. Students learn that 10 minus 7 equals 3 by asking "what number added to 7 makes 10?" instead of counting backward.
Adding and subtracting with numbers up to 20. Students practice both operations until they can work through problems like 14 minus 6 or 9 plus 8 without losing track.
Adding and subtracting small numbers by counting up or back on a number line or with fingers. For example, to solve 7 + 2, students count up two steps from 7 instead of starting over from 1.
Students add and subtract numbers up to 20, and do it quickly and confidently up to 10. They use tricks like counting on, breaking numbers apart, or leaning on a fact they already know to find the answer faster.
Students practice writing and solving addition and subtraction equations, learning that the equals sign means both sides of a number sentence balance out.
The equal sign means "the same amount on both sides." Students look at addition and subtraction equations and decide if both sides actually balance out.
Students find the missing number in an equation like 5 + ? = 9 or 12 - ? = 7. They use what they know about adding and subtracting to figure out what makes the equation balance.
| Standard | Definition | Code |
|---|---|---|
| Represent and solve problems involving addition and subtraction | Students use pictures, objects, and simple equations to figure out addition and subtraction problems. They practice breaking apart and combining small groups of things to find a missing number. | CCSS.Math.Content.1.OA.A |
| Use addition and subtraction within 20 to solve word problems involving… | Students read short story problems and figure out a missing number by adding or subtracting. The unknown can be the starting amount, the change, or the total, and the numbers stay at 20 or below. | CCSS.Math.Content.1.OA.A.1 |
| Solve word problems that call for addition of three whole numbers whose sum is… | Students add three small numbers together to solve a short story problem, like finding out how many apples are in three baskets combined. The total is always 20 or less. | CCSS.Math.Content.1.OA.A.2 |
| Understand and apply properties of operations and the relationship between… | Adding and subtracting follow predictable rules. Students learn that flipping the numbers in an addition problem gives the same answer, and that addition and subtraction are opposites they can use to check each other. | CCSS.Math.Content.1.OA.B |
| Apply properties of operations as strategies to add and subtract | Changing the order of two numbers being added gives the same answer. Students learn to use this idea as a shortcut, so 3 + 5 and 5 + 3 both equal 8 and only one needs to be memorized. | CCSS.Math.Content.1.OA.B.3 |
| Understand subtraction as an unknown-addend problem | Subtraction is just addition in reverse. Students learn that 10 minus 7 equals 3 by asking "what number added to 7 makes 10?" instead of counting backward. | CCSS.Math.Content.1.OA.B.4 |
| Add and subtract within 20 | Adding and subtracting with numbers up to 20. Students practice both operations until they can work through problems like 14 minus 6 or 9 plus 8 without losing track. | CCSS.Math.Content.1.OA.C |
| Relate counting to addition and subtraction | Adding and subtracting small numbers by counting up or back on a number line or with fingers. For example, to solve 7 + 2, students count up two steps from 7 instead of starting over from 1. | CCSS.Math.Content.1.OA.C.5 |
| Add and subtract within 20, demonstrating fluency for addition and subtraction… | Students add and subtract numbers up to 20, and do it quickly and confidently up to 10. They use tricks like counting on, breaking numbers apart, or leaning on a fact they already know to find the answer faster. | CCSS.Math.Content.1.OA.C.6 |
| Work with addition and subtraction equations | Students practice writing and solving addition and subtraction equations, learning that the equals sign means both sides of a number sentence balance out. | CCSS.Math.Content.1.OA.D |
| Understand the meaning of the equal sign | The equal sign means "the same amount on both sides." Students look at addition and subtraction equations and decide if both sides actually balance out. | CCSS.Math.Content.1.OA.D.7 |
| Determine the unknown whole number in an addition or subtraction equation… | Students find the missing number in an equation like 5 + ? = 9 or 12 - ? = 7. They use what they know about adding and subtracting to figure out what makes the equation balance. | CCSS.Math.Content.1.OA.D.8 |
Students count past 100 and read and write numbers up to 120. They practice counting forward from any number, not just from one.
Count forward to 120 starting from any number, not just from 1. Students also read and write those numbers and match a written number to a group of objects.
Students learn that the position of a digit in a number tells you its value. A 2 in the tens place means twenty, not two.
A two-digit number like 47 has two parts: the left digit counts groups of ten, and the right digit counts leftover ones. So 47 means four tens and seven ones.
Ten single things grouped together make one "ten." That idea is the foundation of how our number system works, and students use it to understand any number bigger than 9.
Numbers like 13 or 17 are built from one group of ten and some leftover ones. Students learn to see 14 not as a random number but as ten plus four.
Round numbers like 30 or 70 are made of tens with nothing left over. Students learn that 30 means 3 tens, 70 means 7 tens, and so on up to 90.
Students look at two numbers side by side and decide which is bigger, smaller, or equal by checking how many tens and ones each number has. They record the result using the symbols >, =, or <.
Students use what they know about tens and ones to add and subtract numbers. They learn shortcuts based on how our number system is built, like adding tens to tens or breaking a number apart to make the math easier.
Adding two numbers up to 100, like 47 + 6 or 47 + 30, by grouping tens and ones. Students use blocks or drawings to show their thinking, then connect that to a written method.
Students pick a number like 34 and figure out in their head what it becomes when you add or subtract 10, without counting up or back. Then they explain 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 what they know about addition to make sense of the math.
| Standard | Definition | Code |
|---|---|---|
| Extend the counting sequence | Students count past 100 and read and write numbers up to 120. They practice counting forward from any number, not just from one. | CCSS.Math.Content.1.NBT.A |
| Count to 120, starting at any number less than 120 | Count forward to 120 starting from any number, not just from 1. Students also read and write those numbers and match a written number to a group of objects. | CCSS.Math.Content.1.NBT.A.1 |
| Understand place value | Students learn that the position of a digit in a number tells you its value. A 2 in the tens place means twenty, not two. | CCSS.Math.Content.1.NBT.B |
| Understand that the two digits of a two-digit number represent amounts of tens… | A two-digit number like 47 has two parts: the left digit counts groups of ten, and the right digit counts leftover ones. So 47 means four tens and seven ones. | CCSS.Math.Content.1.NBT.B.2 |
| 10 can be thought of as a bundle of ten ones — called a "ten." | Ten single things grouped together make one "ten." That idea is the foundation of how our number system works, and students use it to understand any number bigger than 9. | CCSS.Math.Content.1.NBT.B.2a |
| The numbers from 11 to 19 are composed of a ten and one, two, three, four… | Numbers like 13 or 17 are built from one group of ten and some leftover ones. Students learn to see 14 not as a random number but as ten plus four. | CCSS.Math.Content.1.NBT.B.2b |
| The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four… | Round numbers like 30 or 70 are made of tens with nothing left over. Students learn that 30 means 3 tens, 70 means 7 tens, and so on up to 90. | CCSS.Math.Content.1.NBT.B.2c |
| Compare two two-digit numbers based on meanings of the tens and ones digits… | Students look at two numbers side by side and decide which is bigger, smaller, or equal by checking how many tens and ones each number has. They record the result using the symbols >, =, or <. | CCSS.Math.Content.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 shortcuts based on how our number system is built, like adding tens to tens or breaking a number apart to make the math easier. | CCSS.Math.Content.1.NBT.C |
| Add within 100, including adding a two-digit number and a one-digit number | Adding two numbers up to 100, like 47 + 6 or 47 + 30, by grouping tens and ones. Students use blocks or drawings to show their thinking, then connect that to a written method. | CCSS.Math.Content.1.NBT.C.4 |
| Given a two-digit number, mentally find 10 more or 10 less than the number… | Students pick a number like 34 and figure out in their head what it becomes when you add or subtract 10, without counting up or back. Then they explain how they knew. | CCSS.Math.Content.1.NBT.C.5 |
| Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range… | Students subtract round numbers by tens, like 70 minus 40, and explain how they got the answer. They use blocks, drawings, or what they know about addition to make sense of the math. | CCSS.Math.Content.1.NBT.C.6 |
Students measure how long something is by lining up small same-size objects end to end, like placing blocks in a row to see how long a pencil is. They also compare lengths without putting two objects side by side.
Line up three objects from shortest to longest. Students also compare two objects they can't place side by side by measuring each one against a third object, like a piece of string.
Students measure how long something is by lining up small objects end to end, like placing paper clips in a row along a pencil. The count of those objects is the length.
Students read clocks and write the time they show, starting with hours and half-hours on an analog clock face.
Students read a clock and write times like 3:00 or 3:30. They practice with both the kind of clock that has hands and the kind that shows numbers.
Students collect simple information, like favorite colors or how many siblings classmates have, then sort it into a chart or picture graph so the class can read and compare the results.
Students sort objects or answers into groups, count how many are in each group, and compare the groups to answer questions like "which has more?" and "how many more?"
| Standard | Definition | Code |
|---|---|---|
| Measure lengths indirectly and by iterating length units | Students measure how long something is by lining up small same-size objects end to end, like placing blocks in a row to see how long a pencil is. They also compare lengths without putting two objects side by side. | CCSS.Math.Content.1.MD.A |
| Order three objects by length | Line up three objects from shortest to longest. Students also compare two objects they can't place side by side by measuring each one against a third object, like a piece of string. | CCSS.Math.Content.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 end to end, like placing paper clips in a row along a pencil. The count of those objects is the length. | CCSS.Math.Content.1.MD.A.2 |
| Tell and write time | Students read clocks and write the time they show, starting with hours and half-hours on an analog clock face. | CCSS.Math.Content.1.MD.B |
| Tell and write time in hours and half-hours using analog and digital clocks | Students read a clock and write times like 3:00 or 3:30. They practice with both the kind of clock that has hands and the kind that shows numbers. | CCSS.Math.Content.1.MD.B.3 |
| Represent and interpret data | Students collect simple information, like favorite colors or how many siblings classmates have, then sort it into a chart or picture graph so the class can read and compare the results. | CCSS.Math.Content.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 to answer questions like "which has more?" and "how many more?" | CCSS.Math.Content.1.MD.C.4 |
Students sort and describe shapes by their sides and corners. They build new shapes by combining simpler ones.
Students learn which features make a shape what it is. A triangle is always three-sided and closed, but its color or size don't matter. Students sort, draw, and build shapes based on the rules that actually define them.
Students put simple shapes together to build a bigger shape, then use that bigger shape to build something new. Think of it like shape puzzles made from triangles, squares, and rectangles.
Students cut circles and rectangles into two or four equal pieces, then name those pieces using words like halves, fourths, and quarters. They also see that the more pieces you cut, the smaller each piece gets.
| Standard | Definition | Code |
|---|---|---|
| Reason with shapes and their attributes | Students sort and describe shapes by their sides and corners. They build new shapes by combining simpler ones. | CCSS.Math.Content.1.G.A |
| Distinguish between defining attributes | Students learn which features make a shape what it is. A triangle is always three-sided and closed, but its color or size don't matter. Students sort, draw, and build shapes based on the rules that actually define them. | CCSS.Math.Content.1.G.A.1 |
| Compose two-dimensional shapes | Students put simple shapes together to build a bigger shape, then use that bigger shape to build something new. Think of it like shape puzzles made from triangles, squares, and rectangles. | CCSS.Math.Content.1.G.A.2 |
| Partition circles and rectangles into two and four equal shares, describe the… | Students cut circles and rectangles into two or four equal pieces, then name those pieces using words like halves, fourths, and quarters. They also see that the more pieces you cut, the smaller each piece gets. | CCSS.Math.Content.1.G.A.3 |
Students add and subtract within 20, count to 120, and work with tens and ones in numbers up to 100. They also tell time to the hour and half hour, measure with a ruler, and name shapes by their parts.
Count coins in a jar, set the kitchen timer on the half hour, or ask quick story problems at dinner like "You had 8 grapes and ate 3, how many are left?" Five minutes a day adds up fast.
Students answer sums and differences within 10 quickly and without finger counting on every problem. They still use strategies for harder facts within 20, like making a ten or counting on from the bigger number.
Start with counting on and number bonds to 10, then build making-ten and doubles strategies for facts within 20. Save two-digit addition and ten more or ten less for the second half of the year, after place value is solid.
Not yet. Finger counting is a normal step in first grade. The goal is for students to move from counting every finger to strategies like "8 and 2 makes 10, then 4 more is 14." Practice with dot cards and ten frames helps.
Place value with teen numbers and word problems with the unknown in the start position are the two big ones. Students also need repeated practice with the equal sign meaning "the same as," not "the answer comes next."
Read the problem twice, then ask the student to act it out with buttons, cereal, or small toys. Have them say which number is the whole and which is a part before writing anything down.
Look for quick recall of sums within 10, confident two-digit addition with a model, and accurate counting and writing of numbers to 120. Students should also explain their thinking out loud, not just give an answer.
Memorizing helps, but understanding comes first. By spring, students should know sums within 10 from memory and have reliable strategies for facts up to 20. Flashcards work better after the strategies are in place.