Counting and adding within 10
Students count, read, and write numbers and get quick with small addition and subtraction facts. They learn that counting on from a number is faster than starting at one every time.
This is the year numbers start working in groups of ten. Students count past one hundred, see that a number like 47 means four tens and seven ones, and use that idea to add and subtract. They also start measuring with a ruler, telling time on the hour and half-hour, and counting coins. By spring, students can solve a word problem about adding or taking away within twenty and explain their thinking.
Students count, read, and write numbers and get quick with small addition and subtraction facts. They learn that counting on from a number is faster than starting at one every time.
Students solve short story problems about adding to, taking from, and comparing groups. They learn that the equal sign means both sides match, and they find the missing number in a simple equation.
Students see that a two-digit number is made of tens and ones. They bundle ten into a group, compare numbers using greater than and less than, and find ten more or ten less in their head.
Students add within 100 using place value, including a two-digit number plus a one-digit number. They also subtract friendly numbers like 60 minus 30 and explain how they got the answer.
Students put objects in order by length and measure with paper clips or cubes laid end to end. They tell time to the hour and half hour on both kinds of clocks and count a handful of pennies, nickels, dimes, or quarters.
Students build and draw shapes, then put smaller shapes together to make bigger ones. They split circles and rectangles into halves and fourths and notice that more shares 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 move between a real-world problem and the math behind it. They set up equations from a story, then check that the answer still makes sense in the real world.
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, objects, or simple equations to show a real-life situation, like splitting crayons into groups or counting coins. The math becomes a picture of something they already know.
Students learn which tools (a ruler, a number line, counters) help solve a given problem, and when to reach for one instead of doing it in their head.
Students choose words and numbers carefully when explaining their math thinking. They label answers with the right units, like "3 apples" instead of just "3," and check that their work says exactly what they mean.
Students notice patterns in math, like how adding zero leaves a number unchanged or how a shape can be split into smaller familiar shapes. Spotting those patterns helps students solve new problems faster.
When students notice that adding zero always leaves a number unchanged, or that counting by twos always skips odd numbers, they are using that pattern to solve new problems faster and with more confidence.
| 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 move between a real-world problem and the math behind it. They set up equations from a story, then check that the answer still makes sense in the real world. | 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, objects, or simple equations to show a real-life situation, like splitting crayons into groups or counting coins. The math becomes a picture of something they already know. | MP.4 |
| Use appropriate tools strategically | Students learn which tools (a ruler, a number line, counters) help solve a given problem, and when to reach for one instead of doing it in their head. | MP.5 |
| Attend to precision | Students choose words and numbers carefully when explaining their math thinking. They label answers with the right units, like "3 apples" instead of just "3," and check that their work says exactly what they mean. | MP.6 |
| Look for and make use of structure | Students notice patterns in math, like how adding zero leaves a number unchanged or how a shape can be split into smaller familiar shapes. Spotting those patterns helps students solve new problems faster. | MP.7 |
| Look for and express regularity in repeated reasoning | When students notice that adding zero always leaves a number unchanged, or that counting by twos always skips odd numbers, they are using that pattern to solve new problems faster and with more confidence. | MP.8 |
Students learn to add and subtract by working through simple word problems. They figure out how many objects are left, added together, or still needed, using pictures, counters, or equations.
Students read short story problems and figure out the missing number by adding or subtracting. The unknown can be at the start, middle, or end of the problem, and numbers stay at 20 or below.
Students add three small numbers together to solve a short story problem, like figuring out how many apples there are across three baskets. The total is always 20 or less.
Adding and subtracting are mirror images of each other. Students learn that if 3 + 4 = 7, then 7 - 4 = 3, and use that connection to solve problems faster.
Adding numbers in any order gives the same answer. Students practice flipping pairs around (3 + 5 is the same as 5 + 3) and grouping numbers differently to make adding easier.
Subtraction is just addition with a missing piece. Students solve 10 minus 7 by asking "what number plus 7 equals 10?" This connects subtraction to addition facts they already know.
Students practice adding and subtracting with numbers up to 20. They build speed and accuracy so those basic facts become second nature before bigger math arrives.
Counting up or back on a number line is the same move as adding or subtracting. Students practice starting at one number and counting forward to add or backward to subtract, rather than starting over from one each time.
Students add and subtract numbers up to 20 without counting on fingers, using mental tricks like breaking a number apart or building up to 10 first. The goal is quick, confident recall for any combination up to 10.
Students practice writing and solving addition and subtraction number sentences, learning that the equals sign means both sides of the equation 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 an addition or subtraction problem, like figuring out what goes in the blank in 5 + __ = 9. They practice this with both addition and subtraction.
| Standard | Definition | Code |
|---|---|---|
| Represent and solve problems involving addition and subtraction | Students learn to add and subtract by working through simple word problems. They figure out how many objects are left, added together, or still needed, using pictures, counters, or equations. | 1.OA.A |
| Use addition and subtraction within 20 to solve word problems involving… | Students read short story problems and figure out the missing number by adding or subtracting. The unknown can be at the start, middle, or end of the problem, and numbers stay at 20 or below. | 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 figuring out how many apples there are across three baskets. The total is always 20 or less. | 1.OA.A.2 |
| Understand and apply properties of operations and the relationship between… | Adding and subtracting are mirror images of each other. Students learn that if 3 + 4 = 7, then 7 - 4 = 3, and use that connection to solve problems faster. | 1.OA.B |
| Apply properties of operations to add and subtract | Adding numbers in any order gives the same answer. Students practice flipping pairs around (3 + 5 is the same as 5 + 3) and grouping numbers differently to make adding easier. | 1.OA.B.3 |
| Understand subtraction as an unknown-addend problem | Subtraction is just addition with a missing piece. Students solve 10 minus 7 by asking "what number plus 7 equals 10?" This connects subtraction to addition facts they already know. | 1.OA.B.4 |
| Add and subtract within 20 | Students practice adding and subtracting with numbers up to 20. They build speed and accuracy so those basic facts become second nature before bigger math arrives. | 1.OA.C |
| Relate counting to addition and subtraction | Counting up or back on a number line is the same move as adding or subtracting. Students practice starting at one number and counting forward to add or backward to subtract, rather than starting over from one each time. | 1.OA.C.5 |
| Add and subtract within 20, demonstrating fluency for addition and subtraction… | Students add and subtract numbers up to 20 without counting on fingers, using mental tricks like breaking a number apart or building up to 10 first. The goal is quick, confident recall for any combination up to 10. | 1.OA.C.6 |
| Work with addition and subtraction equations | Students practice writing and solving addition and subtraction number sentences, learning that the equals sign means both sides of the equation 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 an addition or subtraction problem, like figuring out what goes in the blank in 5 + __ = 9. They practice this with both addition and subtraction. | 1.OA.D.8 |
Students count forward and backward past 100, reading and writing numbers in order. This builds the number sense they'll use for every math skill that follows.
Students count, read, and write numbers up to 120, starting from any number, not just 1. They also look at a group of objects and write the number that shows how many.
Students learn that the position of a digit in a number tells you its value. A 3 in the tens place means thirty, not three.
A two-digit number like 47 is made of tens and ones. The left digit counts the groups of ten, and the right digit counts the leftover ones.
Students learn that 10 single objects grouped together make one unit called a "ten." That idea is the foundation for how our whole number system works.
Numbers 11 through 19 each have one group of ten plus some leftover ones. So 14 means one ten and four ones, not fourteen separate things counted one by one.
Counting by tens means trading ten single blocks for one group of ten. A number like 40 means exactly four of those groups, with nothing left over.
Students look at two numbers (like 47 and 52) and decide which is bigger, smaller, or equal by thinking about 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. This is the foundation for all the addition and subtraction work in first grade.
Students add numbers up to 100, like 47 + 6 or 47 + 30, by thinking about tens and ones. This is the start of the mental math they will use for the rest of elementary school.
Students add a two-digit number to a one-digit or two-digit number by thinking about tens and ones, then write a number sentence that matches what they did and explain their thinking in words.
Adding two two-digit numbers means combining the tens together and the ones together. Sometimes the ones add up to ten or more, so students regroup them into a new ten.
Students pick a two-digit number and figure out what it looks like with one more or one fewer ten added to it, all in their head. No counting on fingers required.
Students subtract numbers like 70 minus 40 using blocks, drawings, or what they know about tens. Then they explain how they got the answer.
| Standard | Definition | Code |
|---|---|---|
| Extend the counting sequence | Students count forward and backward past 100, reading and writing numbers in order. This builds the number sense they'll use for every math skill that follows. | 1.NBT.A |
| Count to 120, starting at any number less than 120 | Students count, read, and write numbers up to 120, starting from any number, not just 1. They also look at a group of objects and write the number that shows how many. | 1.NBT.A.1 |
| Understand place value | Students learn that the position of a digit in a number tells you its value. A 3 in the tens place means thirty, not three. | 1.NBT.B |
| Understand that the two digits of a two-digit number represent amounts of tens… | A two-digit number like 47 is made of tens and ones. The left digit counts the groups of ten, and the right digit counts the leftover ones. | 1.NBT.B.2 |
| 10 can be thought of as a bundle of ten ones—called a "ten." | Students learn that 10 single objects grouped together make one unit called a "ten." That idea is the foundation for how our whole number system works. | 1.NBT.B.2.a |
| The numbers from 11 to 19 are composed of a ten and one, two, three, four… | Numbers 11 through 19 each have one group of ten plus some leftover ones. So 14 means one ten and four ones, not fourteen separate things counted one by one. | 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 trading ten single blocks for one group of ten. A number like 40 means exactly four of those groups, with nothing left over. | 1.NBT.B.2.c |
| Compare two two-digit numbers based on meanings of the tens and ones digits… | Students look at two numbers (like 47 and 52) and decide which is bigger, smaller, or equal by thinking about how many tens and ones each number has. They record the result 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. This is the foundation for all the addition and subtraction work in first grade. | 1.NBT.C |
| Add within 100, including adding a two-digit number and a one-digit number | Students add numbers up to 100, like 47 + 6 or 47 + 30, by thinking about tens and ones. This is the start of the mental math they will use for the rest of elementary school. | 1.NBT.C.4 |
| Use concrete models or drawings and strategies based on place value, properties… | Students add a two-digit number to a one-digit or two-digit number by thinking about tens and ones, then write a number sentence that matches what they did and explain their thinking in words. | 1.NBT.C.4.a |
| Understand that in adding two-digit numbers, one adds tens and tens, ones and… | Adding two two-digit numbers means combining the tens together and the ones together. Sometimes the ones add up to ten or more, so students regroup them into a new ten. | 1.NBT.C.4.b |
| Given a two-digit number, mentally find 10 more or 10 less than the number… | Students pick a two-digit number and figure out what it looks like with one more or one fewer ten added to it, all in their head. No counting on fingers required. | 1.NBT.C.5 |
| Subtract multiples of 10 in the range 10–90 from multiples of 10 in the range… | Students subtract numbers like 70 minus 40 using blocks, drawings, or what they know about tens. Then they explain how they got the answer. | 1.NBT.C.6 |
Students learn to measure how long something is by lining up same-size objects end to end and counting them. They also compare lengths of two objects by using a third object as a go-between.
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.
Students measure how long something is by lining up small objects, like paper clips, from one end to the other with no gaps. The total count of those objects is the length.
Students read clocks and write down the time they show. In first grade, this means reading both the hour and minute hands on an analog clock.
Students read a clock and write the time when the hour or half-hour hand points to a number. They practice with both the round face clock and the digital display.
Students collect simple information, like favorite colors or how many siblings classmates have, then organize it into a picture or tally chart 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 find which has more or fewer.
Students count coins and bills to find totals and make change. This is their first look at money as a math tool they'll use every day.
Students count a small group of the same coin, pennies or nickels or dimes or quarters, and find the total value up to 50 cents.
| Standard | Definition | Code |
|---|---|---|
| Measure lengths indirectly and by iterating length units | Students learn to measure how long something is by lining up same-size objects end to end and counting them. They also compare lengths of two objects by using a third object as a go-between. | 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. | 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 with no gaps. The total count of those objects is the length. | 1.MD.A.2 |
| Tell and write time | Students read clocks and write down the time they show. In first grade, this means reading both the hour and minute hands on an analog clock. | 1.MD.B |
| Tell and write time in hours and half-hours using analog and digital clocks | Students read a clock and write the time when the hour or half-hour hand points to a number. They practice with both the round face clock and the digital display. | 1.MD.B.3 |
| Represent and interpret data | Students collect simple information, like favorite colors or how many siblings classmates have, then organize it into a picture or tally chart so the class can read and compare the results. | 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 find which has more or fewer. | 1.MD.C.4 |
| Work with money | Students count coins and bills to find totals and make change. This is their first look at money as a math tool they'll use every day. | 1.MD.D |
| Determine the value of a collection of coins up to 50 cents | Students count a small group of the same coin, pennies or nickels or dimes or quarters, and find the total value up to 50 cents. | 1.MD.D.5 |
Students sort and describe shapes by their sides, corners, and size. They learn to see what makes a square a square or a triangle a triangle.
Students learn which features actually make a shape what it is. A triangle is always three-sided and closed, but its color or size don't define it. Students sort, build, and draw shapes based on the rules that count.
Students combine simple shapes like triangles, squares, and circles to build a new, larger shape. Then they keep going, using that new shape to build something bigger.
Students cut circles and rectangles into two or four equal pieces and name each piece a half, fourth, or quarter. They also see that cutting a shape into more pieces makes each piece smaller.
| 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 a square or a triangle a triangle. | 1.G.A |
| Distinguish between defining attributes | Students learn which features actually make a shape what it is. A triangle is always three-sided and closed, but its color or size don't define it. Students sort, build, and draw shapes based on the rules that count. | 1.G.A.1 |
| Compose two-dimensional shapes | Students combine simple shapes like triangles, squares, and circles to build a new, larger shape. Then they keep going, using that new shape to build something bigger. | 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 and name each piece a half, fourth, or quarter. They also see that cutting a shape into more pieces makes each piece smaller. | 1.G.A.3 |
Students should add and subtract within 20, know their facts within 10 by heart, count to 120, and add two-digit numbers within 100. They should also tell time to the hour and half-hour, measure with a ruler, name coins, and split shapes into halves and fourths.
Count steps to the car, ask how many forks are needed for dinner, or play quick games like rolling two dice and adding. Talking through the answer matters as much as getting it right. Five minutes a day adds up fast.
It means students can answer facts like 7 plus 3 or 8 minus 5 quickly and without counting on fingers every time. They still use strategies, but the common facts feel automatic. This frees up brainpower for harder problems later.
Start with counting to 120 and building teen numbers as a ten and some ones. Move into tens and ones for any two-digit number, then comparing numbers, then adding within 100. Save subtracting multiples of ten for the last stretch.
Not at first. Fingers are a fine tool while students are learning. The goal is to move from counting every finger to strategies like counting on from the bigger number or making a ten, so facts get faster over time.
The equal sign as a balance, not a signal to write the answer, trips up most students. Word problems with the unknown in the start or middle, and subtraction as a missing addend, also need extra time. Plan a second pass on each.
Read the problem together, then ask what is happening before asking for an answer. Have students draw a quick picture or use coins, beans, or buttons to act it out. The picture is often what unlocks the math.
They can solve word problems within 20 with the unknown in any spot, add two-digit and one-digit numbers using place value, tell time to the half-hour, and name coin values up to 50 cents. Solid fact fluency within 10 is the clearest signal.
Number work should hold the biggest share of time, roughly two thirds. Measurement, time, money, data, and shapes can be woven in as shorter units or as warm-ups and centers. They reinforce counting and comparing without crowding out core number work.