Counting and writing numbers
Students learn to count out loud to 100 and write numbers from 0 to 20. They practice counting groups of objects and saying how many are there.
This is the year numbers become real tools, not just words in a song. Students count to 100, write numbers up to 20, and figure out which group has more by matching and counting. They start adding and taking away small amounts using fingers, drawings, or objects, and they learn that a teen number like 14 is really one ten plus a few more. By spring, students can count out 15 objects, add and subtract within 5 without stopping to think, and name shapes like circles, triangles, and cubes around the house.
Students learn to count out loud to 100 and write numbers from 0 to 20. They practice counting groups of objects and saying how many are there.
Students figure out which group has more, less, or the same. They start comparing two written numbers between 1 and 10 to see which is bigger.
Students put groups together and take them apart using fingers, drawings, and small objects. They solve simple word problems and start to add and subtract quickly within 5.
Students see that numbers like 13 or 18 are made of one ten and some extra ones. This is the first step toward place value in later grades.
Students describe objects by length and weight and compare two things directly to see which is longer or heavier. They also sort objects into groups and count each group.
Students name flat shapes like circles and triangles and solid shapes like cubes and spheres. They describe where objects are using words like above, below, and next to, and build bigger shapes from smaller ones.
Students learn the names of numbers and practice counting in order. They say numbers from 1 to 100 and understand that each number has a fixed place in the sequence.
Students count out loud from 1 to 100, one number at a time, then practice again skipping ahead by tens: 10, 20, 30, all the way to 100.
Starting from any number, students count forward without going back to 1 first. A teacher might say "start at 6" and students continue: 7, 8, 9, 10.
Students write the numbers 0 through 20 and match each one to a group of objects. Zero means the group is empty.
Students count a group of objects and say how many there are. They match each object to a number as they count, and the last number they say is the total.
Counting a group of objects means the last number said tells you how many there are total. Students practice this by counting things out loud and stopping at the right number.
Counting means saying one number for each object, no skipping and no counting the same thing twice. Students point to each item as they count so every object gets exactly one number.
When counting a group of objects, the last number said is the total. It doesn't matter how the objects are arranged or what order students count them in.
Each new counting number is one more than the one before it. Students learn that saying "six" means one more object than "five," building the understanding that numbers go up by exactly one each time.
Students count up to 20 objects arranged in a row, a grid, or a circle, and up to 10 objects scattered randomly. They also hear a number and count out exactly that many objects.
Students look at two groups of objects and say which group has more, which has fewer, or whether they match.
Students look at two groups of objects and decide which group has more, which has fewer, or whether both groups have the same amount. They check by counting or pairing objects one to one.
Students look at two written numbers, both between 1 and 10, and decide which is greater, which is smaller, or whether they are equal.
| Standard | Definition | Code |
|---|---|---|
| Know number names and the count sequence | Students learn the names of numbers and practice counting in order. They say numbers from 1 to 100 and understand that each number has a fixed place in the sequence. | CCSS.Math.Content.K.CC.A |
| Count to 100 by ones and by tens | Students count out loud from 1 to 100, one number at a time, then practice again skipping ahead by tens: 10, 20, 30, all the way to 100. | CCSS.Math.Content.K.CC.A.1 |
| Count forward beginning from a given number within the known sequence | Starting from any number, students count forward without going back to 1 first. A teacher might say "start at 6" and students continue: 7, 8, 9, 10. | CCSS.Math.Content.K.CC.A.2 |
| Write numbers from 0 to 20 | Students write the numbers 0 through 20 and match each one to a group of objects. Zero means the group is empty. | CCSS.Math.Content.K.CC.A.3 |
| Count to tell the number of objects | Students count a group of objects and say how many there are. They match each object to a number as they count, and the last number they say is the total. | CCSS.Math.Content.K.CC.B |
| Understand the relationship between numbers and quantities | Counting a group of objects means the last number said tells you how many there are total. Students practice this by counting things out loud and stopping at the right number. | CCSS.Math.Content.K.CC.B.4 |
| When counting objects, say the number names in the standard order, pairing each… | Counting means saying one number for each object, no skipping and no counting the same thing twice. Students point to each item as they count so every object gets exactly one number. | CCSS.Math.Content.K.CC.B.4a |
| Understand that the last number name said tells the number of objects counted | When counting a group of objects, the last number said is the total. It doesn't matter how the objects are arranged or what order students count them in. | CCSS.Math.Content.K.CC.B.4b |
| Understand that each successive number name refers to a quantity that is one… | Each new counting number is one more than the one before it. Students learn that saying "six" means one more object than "five," building the understanding that numbers go up by exactly one each time. | CCSS.Math.Content.K.CC.B.4c |
| Count to answer "how many?" questions about as many as 20 things arranged in a… | Students count up to 20 objects arranged in a row, a grid, or a circle, and up to 10 objects scattered randomly. They also hear a number and count out exactly that many objects. | CCSS.Math.Content.K.CC.B.5 |
| Compare numbers | Students look at two groups of objects and say which group has more, which has fewer, or whether they match. | CCSS.Math.Content.K.CC.C |
| Identify whether the number of objects in one group is greater than, less than | Students look at two groups of objects and decide which group has more, which has fewer, or whether both groups have the same amount. They check by counting or pairing objects one to one. | CCSS.Math.Content.K.CC.C.6 |
| Compare two numbers between 1 and 10 presented as written numerals | Students look at two written numbers, both between 1 and 10, and decide which is greater, which is smaller, or whether they are equal. | CCSS.Math.Content.K.CC.C.7 |
Addition means combining two groups of things. Subtraction means splitting a group or taking some away. Students practice both using small numbers, objects, and simple drawings.
Students show adding and subtracting in different ways: counting out blocks, drawing pictures, acting out a story, or writing a number sentence like 3 + 2 = 5.
Students solve simple story problems about combining or removing small groups of things, using fingers, drawings, or objects to find answers up to 10.
Students break a small number into two groups in different ways. For example, 5 can be split into 4 and 1, or into 2 and 3, and students draw or write an equation to show each split.
Students figure out what number pairs with a given number to make 10. If you have 6, what do you need to reach 10? Students work this out with counters, drawings, or a simple number sentence.
Adding and subtracting with numbers up to 5 is something students can do quickly, without counting on their fingers. Think 2 + 3 or 4 minus 1, answered right away from memory.
| Standard | Definition | Code |
|---|---|---|
| Understand addition as putting together and adding to | Addition means combining two groups of things. Subtraction means splitting a group or taking some away. Students practice both using small numbers, objects, and simple drawings. | CCSS.Math.Content.K.OA.A |
| Represent addition and subtraction with objects, fingers, mental images… | Students show adding and subtracting in different ways: counting out blocks, drawing pictures, acting out a story, or writing a number sentence like 3 + 2 = 5. | CCSS.Math.Content.K.OA.A.1 |
| Solve addition and subtraction word problems | Students solve simple story problems about combining or removing small groups of things, using fingers, drawings, or objects to find answers up to 10. | CCSS.Math.Content.K.OA.A.2 |
| Decompose numbers less than or equal to 10 into pairs in more than one way… | Students break a small number into two groups in different ways. For example, 5 can be split into 4 and 1, or into 2 and 3, and students draw or write an equation to show each split. | CCSS.Math.Content.K.OA.A.3 |
| For any number from 1 to 9, find the number that makes 10 when added to the… | Students figure out what number pairs with a given number to make 10. If you have 6, what do you need to reach 10? Students work this out with counters, drawings, or a simple number sentence. | CCSS.Math.Content.K.OA.A.4 |
| Fluently add and subtract within 5 | Adding and subtracting with numbers up to 5 is something students can do quickly, without counting on their fingers. Think 2 + 3 or 4 minus 1, answered right away from memory. | CCSS.Math.Content.K.OA.A.5 |
Numbers 11 through 19 get broken into ten and some leftover ones. Students learn to see 14, for example, as a group of ten plus four more, which is the first step toward understanding how our number system works.
Students learn that numbers like 13 or 17 are made of a group of ten and a few leftovers. They practice breaking those numbers apart and writing it as a simple addition, like 13 = 10 + 3.
| Standard | Definition | Code |
|---|---|---|
| Work with numbers 11—19 to gain foundations for place value | Numbers 11 through 19 get broken into ten and some leftover ones. Students learn to see 14, for example, as a group of ten plus four more, which is the first step toward understanding how our number system works. | CCSS.Math.Content.K.NBT.A |
| Compose and decompose numbers from 11 to 19 into ten ones and some further… | Students learn that numbers like 13 or 17 are made of a group of ten and a few leftovers. They practice breaking those numbers apart and writing it as a simple addition, like 13 = 10 + 3. | CCSS.Math.Content.K.NBT.A.1 |
Students look at everyday objects and compare them by size, length, or weight. They practice saying which crayon is longer or which block is heavier.
Students pick up an object and describe more than one thing about it: how long it is, how heavy it feels, or how tall it stands. One block can be both heavy and short at the same time.
Students pick two objects and compare them directly, like holding two pencils side by side to find which one is longer or shorter. They put the difference into words.
Students sort a group of objects into categories (by color, shape, or size) and count how many are in each group.
Students sort a group of objects into categories (like color or shape), count how many are in each group, and then put the groups in order from smallest to largest.
| Standard | Definition | Code |
|---|---|---|
| Describe and compare measurable attributes | Students look at everyday objects and compare them by size, length, or weight. They practice saying which crayon is longer or which block is heavier. | CCSS.Math.Content.K.MD.A |
| Describe measurable attributes of objects, such as length or weight | Students pick up an object and describe more than one thing about it: how long it is, how heavy it feels, or how tall it stands. One block can be both heavy and short at the same time. | CCSS.Math.Content.K.MD.A.1 |
| Directly compare two objects with a measurable attribute in common, to see… | Students pick two objects and compare them directly, like holding two pencils side by side to find which one is longer or shorter. They put the difference into words. | CCSS.Math.Content.K.MD.A.2 |
| Classify objects and count the number of objects in each category | Students sort a group of objects into categories (by color, shape, or size) and count how many are in each group. | CCSS.Math.Content.K.MD.B |
| Classify objects into given categories | Students sort a group of objects into categories (like color or shape), count how many are in each group, and then put the groups in order from smallest to largest. | CCSS.Math.Content.K.MD.B.3 |
Students name everyday shapes like squares, circles, and triangles, and describe what makes each one look the way it does. They also recognize 3D shapes like cubes and spheres in the real world.
Students name everyday objects by their shape and describe where they are. A block is a cube, the clock is a circle, and the crayon is beside the book.
Students learn to name a shape correctly whether it is big or small, upside down, or turned sideways. A triangle is still a triangle no matter how it sits on the page.
Students sort shapes into two groups: flat shapes like a square drawn on paper, and solid shapes like a ball or a block you can pick up and hold.
Students sort, compare, and build shapes by looking at how many sides they have and whether edges are straight or curved. They also fit smaller shapes together to make bigger ones.
Students look at shapes like squares, triangles, and boxes, then describe what makes them alike or different. They notice things like how many sides or corners a shape has, whether the sides are the same length, and whether the shape is flat or solid.
Students build and draw shapes using everyday materials like sticks and clay. This connects the flat shapes on paper to real objects they can touch and make.
Students put simple shapes together to build a bigger one, like fitting two triangles to make a square. This is the hands-on start of understanding how shapes relate to each other.
| Standard | Definition | Code |
|---|---|---|
| Identify and describe shapes | Students name everyday shapes like squares, circles, and triangles, and describe what makes each one look the way it does. They also recognize 3D shapes like cubes and spheres in the real world. | CCSS.Math.Content.K.G.A |
| Describe objects in the environment using names of shapes | Students name everyday objects by their shape and describe where they are. A block is a cube, the clock is a circle, and the crayon is beside the book. | CCSS.Math.Content.K.G.A.1 |
| Correctly name shapes regardless of their orientations or overall size | Students learn to name a shape correctly whether it is big or small, upside down, or turned sideways. A triangle is still a triangle no matter how it sits on the page. | CCSS.Math.Content.K.G.A.2 |
| Identify shapes as two-dimensional | Students sort shapes into two groups: flat shapes like a square drawn on paper, and solid shapes like a ball or a block you can pick up and hold. | CCSS.Math.Content.K.G.A.3 |
| Analyze, compare, create | Students sort, compare, and build shapes by looking at how many sides they have and whether edges are straight or curved. They also fit smaller shapes together to make bigger ones. | CCSS.Math.Content.K.G.B |
| Analyze and compare two- and three-dimensional shapes, in different sizes and… | Students look at shapes like squares, triangles, and boxes, then describe what makes them alike or different. They notice things like how many sides or corners a shape has, whether the sides are the same length, and whether the shape is flat or solid. | CCSS.Math.Content.K.G.B.4 |
| Model shapes in the world by building shapes from components | Students build and draw shapes using everyday materials like sticks and clay. This connects the flat shapes on paper to real objects they can touch and make. | CCSS.Math.Content.K.G.B.5 |
| Compose simple shapes to form larger shapes | Students put simple shapes together to build a bigger one, like fitting two triangles to make a square. This is the hands-on start of understanding how shapes relate to each other. | CCSS.Math.Content.K.G.B.6 |
Students should count to 100 by ones and tens, write numbers 0 to 20, and add and subtract small amounts up to 10. They should also name common shapes like circles, squares, and cubes, and compare two objects by size or weight.
Count real things during the day. Count steps to the car, grapes on a plate, or buttons on a shirt. Ask how many are left after eating one or two. Five minutes a day builds the habit better than a long session once a week.
Spend the first weeks on counting objects one by one and matching each count to a written number from 0 to 10. Strong one-to-one counting is the base for almost everything that comes later, so it pays to slow down here.
It is common and worth working on. Saying numbers in order is not the same as counting a pile of objects. Practice by moving each item as students say the number, so one object gets one number. Stop and ask how many are there now.
Start with real objects and stories before showing any equation. Put two blocks with three blocks, count the total, then write 2 plus 3 equals 5. Students should be fluent adding and subtracting within 5 by year end, and able to solve word problems within 10 using drawings or fingers.
It means showing the same number in different ways. Five can be 4 and 1, or 3 and 2, or 5 and 0. At home, hand a child five crackers and ask how many ways they can split them into two plates. This builds the thinking behind addition.
Numbers 11 to 19 are the first step into place value. Students learn that 14 is ten ones and four more ones, which sets up tens and hundreds in first grade. Use ten-frames or bundles of ten sticks so the ten is something students can see and touch.
They can count a group of 20 objects accurately, write numbers to 20, add and subtract within 5 without counting on fingers, and recognize teen numbers as ten and some more. They can also name basic shapes and compare two objects by length or weight.
Students name and describe flat shapes like triangles and hexagons, and solid shapes like cubes and cones. They also compare two objects directly, such as which pencil is longer or which bag is heavier. At home, point out shapes in signs, windows, and food.