Counting and naming numbers
Students learn to count out loud to 100 and write the numbers 0 to 20. They match each number they say to one object so the count actually matches the pile.
This is the year numbers start to mean something. Students learn to count to 100, write numbers up to 20, and understand that the last number they say tells how many objects are in the group. They begin adding and taking away within 10 using fingers, drawings, and small story problems. By spring, a student can count out 15 objects, tell you which pile has more, and name a penny, nickel, dime, and quarter.
Students learn to count out loud to 100 and write the numbers 0 to 20. They match each number they say to one object so the count actually matches the pile.
Students name circles, squares, triangles, rectangles, and hexagons, plus solid shapes like cubes, cones, and spheres. They start describing where things are using words like above, below, and next to.
Students compare groups of objects and numbers up to 10 using greater than, less than, and equal to. They also sort objects into groups and compare which group has more.
Students use fingers, drawings, and small objects to add and take away within 10. They start to see that a number like 5 can be broken into pairs such as 2 and 3 or 4 and 1.
Students see that numbers from 11 to 19 are a group of ten plus some extra ones. This is the first step toward understanding how bigger numbers work later on.
Students compare objects by length, height, and weight using words like longer, taller, and heavier. They also learn to tell pennies, nickels, dimes, and quarters apart and name what each one is worth.
Students learn the names of numbers and how to say them in order. Counting from 1 to 100 is the foundation everything else in math builds on.
Students count out loud to 100, moving by ones, fives, or tens. They also count backward from 10 to 0.
Students practice counting up from any number, not just from 1. If you say "start at 6," they keep going: 7, 8, 9.
Students write the numbers 0 through 20 and use those numbers to show how many objects are in a group. If there are 7 crayons on the table, students write the number 7.
Students find the repeating piece inside a pattern, such as red-blue-red-blue, and use blocks or shapes to keep it going or build one from scratch.
Students count a group of objects and say how many there are. They match each object to one number as they count, then name the total.
Students count a group of objects and know the last number they say tells how many there are in total. Counting up to 20 things, students match each object to exactly one number as they go.
Students count up to 20 objects by touching or pointing to each one while saying its number out loud. Each object gets exactly one number, and students don't skip or double-count anything.
The last number you say when counting a group tells you how many are in that group. It doesn't matter if the objects are in a line or a pile, or which one you counted first.
Counting up means adding one more each time; counting back means taking one away. Students learn that numbers in order always change by exactly one, whether moving forward or backward.
Students count up to 20 objects arranged in a line, a circle, or a grid, and up to 10 objects scattered randomly. They can also grab the right number of objects when given a number between 1 and 20.
Students look at two groups of objects and decide which has more, which has fewer, or whether they match. This is the first step toward understanding how numbers relate to each other.
Students look at two groups of objects and decide which group has more, which has fewer, or whether both groups have the same amount.
Students look at two numbers up to 10 and say which is greater, which is less, or whether they are equal. No symbols needed yet, just the words.
| Standard | Definition | Code |
|---|---|---|
| Know number names and the counting sequence | Students learn the names of numbers and how to say them in order. Counting from 1 to 100 is the foundation everything else in math builds on. | K.CC.A |
| Count to 100 by ones, fives | Students count out loud to 100, moving by ones, fives, or tens. They also count backward from 10 to 0. | K.CC.A.1 |
| Count forward by ones beginning from any given number within the known sequence | Students practice counting up from any number, not just from 1. If you say "start at 6," they keep going: 7, 8, 9. | K.CC.A.2 |
| Write numbers from 0 to 20 | Students write the numbers 0 through 20 and use those numbers to show how many objects are in a group. If there are 7 crayons on the table, students write the number 7. | K.CC.A.3 |
| Recognize, describe, extend | Students find the repeating piece inside a pattern, such as red-blue-red-blue, and use blocks or shapes to keep it going or build one from scratch. | K.CC.A.4 |
| Count to tell the number of objects | Students count a group of objects and say how many there are. They match each object to one number as they count, then name the total. | K.CC.B |
| Understand the relationship between numbers and quantities | Students count a group of objects and know the last number they say tells how many there are in total. Counting up to 20 things, students match each object to exactly one number as they go. | K.CC.B.5 |
| When counting objects 1-20, say the number names in the standard order, using… | Students count up to 20 objects by touching or pointing to each one while saying its number out loud. Each object gets exactly one number, and students don't skip or double-count anything. | K.CC.B.5.a |
| Recognize that the last number name said tells the number of objects counted | The last number you say when counting a group tells you how many are in that group. It doesn't matter if the objects are in a line or a pile, or which one you counted first. | K.CC.B.5.b |
| Recognize that each successive number name refers to a quantity that is one… | Counting up means adding one more each time; counting back means taking one away. Students learn that numbers in order always change by exactly one, whether moving forward or backward. | K.CC.B.5.c |
| Count to answer "how many?" questions about as many as 20 things arranged in a… | Students count up to 20 objects arranged in a line, a circle, or a grid, and up to 10 objects scattered randomly. They can also grab the right number of objects when given a number between 1 and 20. | K.CC.B.6 |
| Compare numbers | Students look at two groups of objects and decide which has more, which has fewer, or whether they match. This is the first step toward understanding how numbers relate to each other. | 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. | K.CC.C.7 |
| Compare two given numbers up to 10, when written as numerals, using the terms… | Students look at two numbers up to 10 and say which is greater, which is less, or whether they are equal. No symbols needed yet, just the words. | K.CC.C.8 |
Students practice adding and subtracting small numbers by counting objects, drawing pictures, or acting out simple story problems.
Students show what adding and taking away mean using fingers, drawings, or small objects. They don't just say the answer; they show how they got there.
Adding and subtracting with numbers up to 10, students solve simple story problems like "3 birds join 4 birds, how many now?" They show their thinking with drawings, objects, or a number sentence.
Students break a small number into two groups in different ways, like splitting 7 into 3 and 4 or 5 and 2. They sketch or write an equation to show each split.
Given a number from 1 to 9, students figure out what to add to reach 10. They show their answer with a drawing or a simple equation like 6 + 4 = 10.
Students practice adding and subtracting small numbers in their head until the answers come quickly, without counting on fingers or using objects. The goal is fluency with any combination up to 10.
| Standard | Definition | Code |
|---|---|---|
| Represent and solve problems involving addition and subtraction | Students practice adding and subtracting small numbers by counting objects, drawing pictures, or acting out simple story problems. | K.OA.A |
| Represent addition and subtraction with objects, fingers, drawings, acting out… | Students show what adding and taking away mean using fingers, drawings, or small objects. They don't just say the answer; they show how they got there. | K.OA.A.1 |
| Add and subtract within 10 to solve contextual problems with result/total… | Adding and subtracting with numbers up to 10, students solve simple story problems like "3 birds join 4 birds, how many now?" They show their thinking with drawings, objects, or a number sentence. | K.OA.A.2 |
| Decompose numbers less than or equal to 10 into addend pairs in more than one… | Students break a small number into two groups in different ways, like splitting 7 into 3 and 4 or 5 and 2. They sketch or write an equation to show each split. | K.OA.A.3 |
| Find the number that makes 10, when added to any given number, from 1 to 9… | Given a number from 1 to 9, students figure out what to add to reach 10. They show their answer with a drawing or a simple equation like 6 + 4 = 10. | K.OA.A.4 |
| Use mental strategies flexibly to develop fluency in addition and subtraction… | Students practice adding and subtracting small numbers in their head until the answers come quickly, without counting on fingers or using objects. The goal is fluency with any combination up to 10. | K.OA.A.5 |
Numbers 11 through 19 are made of a ten and some leftover ones. Students practice building and breaking apart these numbers to get ready for place value in later grades.
Numbers 11 to 19 are made of one group of ten plus a few extras. Students use blocks or drawings to show that, then write it as an equation like 18 = 10 + 8.
| Standard | Definition | Code |
|---|---|---|
| Work with numbers 11–19 to gain foundations for place value | Numbers 11 through 19 are made of a ten and some leftover ones. Students practice building and breaking apart these numbers to get ready for place value in later grades. | K.NBT.A |
| Compose and decompose numbers from 11 to 19 into a group of ten ones and some… | Numbers 11 to 19 are made of one group of ten plus a few extras. Students use blocks or drawings to show that, then write it as an equation like 18 = 10 + 8. | K.NBT.A.1 |
Students look at two objects and talk about which is taller, heavier, or longer. This is the start of measurement: noticing what can be compared and putting words to the difference.
Students pick up an everyday object and describe what they notice about it: how long it is, how tall it is, or how heavy it feels.
Students pick up two objects and compare them directly, such as holding two pencils side by side to see which is longer or which is heavier. They put the difference into words.
Students identify coins by name and know the value each one stands for.
Students learn to tell a penny, nickel, dime, and quarter apart by size and color, and match each coin to its value.
Students sort everyday objects into groups by color, shape, or size, then count how many are in each group.
Students sort a group of objects into two or more groups, then say which group has more and which has fewer.
| Standard | Definition | Code |
|---|---|---|
| Describe and compare measurable attributes | Students look at two objects and talk about which is taller, heavier, or longer. This is the start of measurement: noticing what can be compared and putting words to the difference. | K.MD.A |
| Describe the measurable attributes of an object, such as length | Students pick up an everyday object and describe what they notice about it: how long it is, how tall it is, or how heavy it feels. | K.MD.A.1 |
| Directly compare two objects with a measurable attribute in common, to describe… | Students pick up two objects and compare them directly, such as holding two pencils side by side to see which is longer or which is heavier. They put the difference into words. | K.MD.A.2 |
| Work with money | Students identify coins by name and know the value each one stands for. | K.MD.B |
| Identify the penny, nickel, dime | Students learn to tell a penny, nickel, dime, and quarter apart by size and color, and match each coin to its value. | K.MD.B.3 |
| Classify objects and count the number of objects in each category | Students sort everyday objects into groups by color, shape, or size, then count how many are in each group. | K.MD.C |
| Sort a collection of objects into a given category, with 10 or fewer in each… | Students sort a group of objects into two or more groups, then say which group has more and which has fewer. | K.MD.C.4 |
Students learn to name basic shapes and tell them apart by how they look, whether flat like a circle or solid like a cube.
Students name everyday shapes they see around them, like a clock (circle) or a window (rectangle), and describe where things are using words like above, below, beside, and behind.
Students name basic shapes and solids, like a triangle or a cylinder, no matter how big they are or which way they're turned. A sideways square or a tiny circle still gets the right name.
Students sort everyday shapes into two groups: flat ones like squares and circles, and solid ones like cubes and spheres that you can pick up and hold.
Students sort, compare, and build shapes by describing what makes each one different. They also put smaller shapes together to make new ones.
Students look at two shapes side by side and explain what makes them alike and what makes them different. A ball and a cube are both solid, but one rolls and one stacks.
Students build or draw shapes they see in real life, like a window square or a soup can cylinder. The goal is to connect flat pictures and solid objects to the shapes they already know by name.
Students put together circles, squares, and triangles to build a larger picture or object, then point out which smaller shapes make up the whole thing.
| Standard | Definition | Code |
|---|---|---|
| Identify and describe shapes and solids | Students learn to name basic shapes and tell them apart by how they look, whether flat like a circle or solid like a cube. | K.G.A |
| Describe objects in the environment using names of shapes and solids | Students name everyday shapes they see around them, like a clock (circle) or a window (rectangle), and describe where things are using words like above, below, beside, and behind. | K.G.A.1 |
| Correctly name shapes and solids | Students name basic shapes and solids, like a triangle or a cylinder, no matter how big they are or which way they're turned. A sideways square or a tiny circle still gets the right name. | K.G.A.2 |
| Identify shapes (squares, circles, triangles, rectangles | Students sort everyday shapes into two groups: flat ones like squares and circles, and solid ones like cubes and spheres that you can pick up and hold. | K.G.A.3 |
| Analyze, compare, create | Students sort, compare, and build shapes by describing what makes each one different. They also put smaller shapes together to make new ones. | K.G.B |
| Describe similarities and differences between two- and three-dimensional… | Students look at two shapes side by side and explain what makes them alike and what makes them different. A ball and a cube are both solid, but one rolls and one stacks. | K.G.B.4 |
| Model shapes/solids in the world by building or drawing them | Students build or draw shapes they see in real life, like a window square or a soup can cylinder. The goal is to connect flat pictures and solid objects to the shapes they already know by name. | K.G.B.5 |
| Compose a figure using simple shapes/solids and identify smaller shapes/solids… | Students put together circles, squares, and triangles to build a larger picture or object, then point out which smaller shapes make up the whole thing. | K.G.B.6 |
Students should count to 100 by ones, fives, and tens, write numbers 0 to 20, and add and subtract within 10. They should also name basic shapes, compare objects by size and weight, and identify a penny, nickel, dime, and quarter.
Count anything together: steps up the stairs, grapes on a plate, cars in the driveway. Once counting to 20 feels easy, try starting from a number other than 1, like counting from 7 up to 15.
Start with counting, one-to-one matching, and writing numbers to 10. Move into comparing groups and decomposing numbers, then build addition and subtraction within 10. Save the 11 to 19 work as ten and some more ones for later in the year, since it sets up first grade place value.
Yes, and it is the next thing to practice. Reciting numbers is different from counting real things. Put out 12 to 20 small objects and have students touch each one as they say the number. The last number said is the total.
Two areas tend to lag: one-to-one correspondence past 12, and decomposing numbers in more than one way (such as 6 as 4 and 2, or 5 and 1). Build in short, frequent practice with objects all year, not just during the unit.
Use real situations. Put 4 crackers on a plate, add 3 more, ask how many. Take 2 away, ask how many are left. Fingers, drawings, and objects all count. Speed is not the goal this year.
They can count out 20 objects accurately, compare two numbers up to 10, and solve simple add and take away stories within 10 using objects or drawings. They can also see a teen number like 14 as ten and four more.
Memorizing helps, but recognition matters more. Students should name squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres in any size or position. For coins, they should identify each one by sight and know its value.