What math should students know by the end of the year?

Students count out loud to 20, recognize written numbers 0 through 10, and count up to 10 objects one at a time. They also name circles, squares, rectangles, and triangles, and compare small groups using words like more and fewer.

How can families practice counting at home?

Count real things together: stairs going up, grapes on a plate, socks coming out of the dryer. Point to each item as students say the number. Five minutes a day builds the habit of matching one number to one object.

My child can say numbers to 20 but miscounts objects. Is that normal?

Yes. Saying the number words and actually counting objects are two different skills. Slow down and touch each item while saying the number. The last number said is the total, and that idea takes a lot of practice to click.

How should counting be sequenced across the year?

Start with counting aloud to 10 and matching one number to one object in a neat row. Move to counting up to 10 in rows or columns, then to scattered groups of up to 5. Saving scattered counting for later in the year prevents a lot of frustration.

What does zero mean at this age?

Students learn that zero is the number for none. Show an empty plate, an empty cup, or a bowl after the crackers are gone, and ask how many are left. Naming zero as a real count helps later when students compare groups.

How can shapes and patterns be practiced at home?

Go on a shape hunt around the kitchen: the clock is a circle, a window is a rectangle, a slice of pizza is a triangle. For patterns, clap-stomp-clap-stomp, or line up red-blue-red-blue blocks and ask what comes next.

Which skills usually need the most reteaching?

One-to-one correspondence and the idea that the last number said is the total. Many students recite numbers without connecting them to objects. Plan short, daily counting routines with real objects rather than worksheets.

How is data introduced at this age?

Students sort real objects into groups and line them up to compare. A simple example: have students place their shoe under a velcro or laces label, then count which row is longer. That is a real-object graph, and it builds the base for bar graphs later.

How do I know students are ready for Kindergarten math?

Students count to 20, recognize numbers 0 through 10, count up to 10 objects accurately, and compare two small groups using more, fewer, or same. They can also name the four basic shapes and copy a simple repeating pattern.

What does a student learn in ?

This is the year math begins with counting things students can touch. Students count aloud to 20, point to written numbers up to 10, and learn that the last number they say tells how many are in the pile. They also start noticing shapes like circles and squares, sorting buttons or blocks by color or size, and saying which stick is longer. By spring, students can count a small group of objects one by one and tell a grown-up which bowl has more.

Counting to 20
Number recognition
Comparing groups
Sorting
Shapes
Patterns
Measurement

Source: Oklahoma Oklahoma Academic Standards

Year at a glance

How the year usually goes. Every school and district set their own curriculum, so treat this as a guide, not official pacing.

1
Counting and number names
Students learn to count out loud up to 20 and start to recognize written numbers from 0 to 10. They also learn that zero means none at all.
2
How many in a group
Students point to objects one at a time as they count, up to 10. They learn that the last number they say is the total, even when the items are spread out.
3
Sorting and patterns
Students group objects by color, size, or shape and explain why those items go together. They also copy and continue simple patterns using blocks, sounds, or movements.
4
Shapes and sizes
Students name circles, squares, rectangles, and triangles. They compare two objects using words like bigger, longer, or heavier.
5
Comparing and graphing
Students look at two small groups and tell which has more, fewer, or the same. With help from a teacher, they line up real objects to make simple picture graphs.

Mastery Learning Standards

The required skills a student should display by the end of Pre-Kindergarten.

Pre-Kindergarten

Know number names and count in sequence

PK.N.1

Students learn the names of numbers and practice saying them in order: 1, 2, 3. This is the foundation for counting real objects later.
Count aloud forward in sequence by 1s to 20

PK.N.1.1

Students count out loud from 1 to 20, in order, without skipping a number.
Recognize and name written numerals 0-10

PK.N.1.2

Students look at a written number (like a 3, a 7, or a 0) and say its name out loud. This covers every numeral from zero to ten.
Recognize that 0 (zero) represents the count of no objects

PK.N.1.3

Zero means "none." Students learn that the number 0 stands for an empty group, like a plate with no cookies or a box with nothing inside.
Count to tell the number of objects

PK.N.2

Students count a small group of objects, like blocks or crayons, and say how many there are. The last number they say is the total.
Identify the number of objects, up to 10, in a row or column

PK.N.2.1

Students count a row or line of objects and say how many there are, up to ten. This is the first step toward understanding what numbers actually mean.
Use one-to-one correspondence in counting objects and matching groups of…

PK.N.2.2

Students count up to 10 objects by touching each one and saying one number at a time. They also match two groups to show the groups have the same amount.
Understand the last numeral spoken when counting aloud tells how many total…

PK.N.2.3

When students count a small group of objects out loud, the last number they say tells them how many are in the whole group. This is called the counting principle, and students practice it with groups of up to 10 objects.
Count up to 5 items in a scattered configuration, not in a row or column

PK.N.2.4

Students count up to 5 objects even when those objects are spread out randomly, not lined up. This builds the habit of counting what's there, not just what's neat.
Compare sets using numbers

PK.N.3

Students look at two groups of objects and say which group has more, which has fewer, or whether both groups have the same amount.
Compare two sets of 0-5 objects using comparative language such as "same,"…

PK.N.3.1

Students look at two small groups of objects and decide which group has more, which has fewer, or whether both groups are the same size.
Recognize, duplicate

PK.A.1

Students spot a repeating pattern (like red, blue, red, blue) and copy it or keep it going. This is the first step toward understanding how math rules work.
Sort and group up to 5 objects into a set based upon characteristics such as…

PK.A.1.1

Students sort small groups of objects by color, size, or shape, then say out loud what makes them alike.
Recognize, duplicate

PK.A.1.2

Students spot a repeating pattern, like red-blue-red-blue, then copy it and keep it going. They practice with objects, claps, or movements.
Identify common shapes

PK.GM.1

Students name everyday shapes like circles, squares, and triangles when they see them on paper or in the classroom.
Identify circles, squares, rectangles

PK.GM.1.1

Students point to circles, squares, rectangles, and triangles when a teacher calls out the name. It's the first step in learning to recognize basic shapes by sight.
Describe and compare measurable attributes

PK.GM.2

Students notice that objects can be measured in different ways, like how tall, how heavy, or how long something is. They also compare two objects and say which one is bigger, longer, or heavier.
Identify measurable attributes of objects

PK.GM.2.1

Students look at everyday objects and describe what they notice about size or weight. They use words like big, little, long, short, tall, heavy, and light.
Directly compare two objects with a common measurable attribute using…

PK.GM.2.2

Students pick up two objects and compare them side by side, then say which one is longer or shorter, heavier or lighter, taller or shorter.
Sort objects into sets by one or more attributes

PK.GM.2.3

Students sort everyday objects into groups based on what they have in common, like color, shape, or size. It's an early step in learning to notice what makes things alike or different.
Collect and organize categorical data

PK.D.1

Students sort real objects into groups that belong together, like crayons by color or buttons by size, and count how many are in each group.
Collect and organize information about objects and events in the environment

PK.D.1.1

Students gather simple information about everyday things, like sorting blocks by color or counting how many kids chose each snack. They arrange what they find so it's easier to see and talk about.
Use categorical data to create real-object graphs, with guidance and support

PK.D.1.2

Students sort real objects into groups and line them up to make a simple graph. They might group toy animals by color or snacks by type to answer a question like "which group has more?"

Standard	Definition	Code
Know number names and count in sequence	Students learn the names of numbers and practice saying them in order: 1, 2, 3. This is the foundation for counting real objects later.	PK.N.1
Count aloud forward in sequence by 1s to 20	Students count out loud from 1 to 20, in order, without skipping a number.	PK.N.1.1
Recognize and name written numerals 0-10	Students look at a written number (like a 3, a 7, or a 0) and say its name out loud. This covers every numeral from zero to ten.	PK.N.1.2
Recognize that 0 (zero) represents the count of no objects	Zero means "none." Students learn that the number 0 stands for an empty group, like a plate with no cookies or a box with nothing inside.	PK.N.1.3
Count to tell the number of objects	Students count a small group of objects, like blocks or crayons, and say how many there are. The last number they say is the total.	PK.N.2
Identify the number of objects, up to 10, in a row or column	Students count a row or line of objects and say how many there are, up to ten. This is the first step toward understanding what numbers actually mean.	PK.N.2.1
Use one-to-one correspondence in counting objects and matching groups of…	Students count up to 10 objects by touching each one and saying one number at a time. They also match two groups to show the groups have the same amount.	PK.N.2.2
Understand the last numeral spoken when counting aloud tells how many total…	When students count a small group of objects out loud, the last number they say tells them how many are in the whole group. This is called the counting principle, and students practice it with groups of up to 10 objects.	PK.N.2.3
Count up to 5 items in a scattered configuration, not in a row or column	Students count up to 5 objects even when those objects are spread out randomly, not lined up. This builds the habit of counting what's there, not just what's neat.	PK.N.2.4
Compare sets using numbers	Students look at two groups of objects and say which group has more, which has fewer, or whether both groups have the same amount.	PK.N.3
Compare two sets of 0-5 objects using comparative language such as "same,"…	Students look at two small groups of objects and decide which group has more, which has fewer, or whether both groups are the same size.	PK.N.3.1
Recognize, duplicate	Students spot a repeating pattern (like red, blue, red, blue) and copy it or keep it going. This is the first step toward understanding how math rules work.	PK.A.1
Sort and group up to 5 objects into a set based upon characteristics such as…	Students sort small groups of objects by color, size, or shape, then say out loud what makes them alike.	PK.A.1.1
Recognize, duplicate	Students spot a repeating pattern, like red-blue-red-blue, then copy it and keep it going. They practice with objects, claps, or movements.	PK.A.1.2
Identify common shapes	Students name everyday shapes like circles, squares, and triangles when they see them on paper or in the classroom.	PK.GM.1
Identify circles, squares, rectangles	Students point to circles, squares, rectangles, and triangles when a teacher calls out the name. It's the first step in learning to recognize basic shapes by sight.	PK.GM.1.1
Describe and compare measurable attributes	Students notice that objects can be measured in different ways, like how tall, how heavy, or how long something is. They also compare two objects and say which one is bigger, longer, or heavier.	PK.GM.2
Identify measurable attributes of objects	Students look at everyday objects and describe what they notice about size or weight. They use words like big, little, long, short, tall, heavy, and light.	PK.GM.2.1
Directly compare two objects with a common measurable attribute using…	Students pick up two objects and compare them side by side, then say which one is longer or shorter, heavier or lighter, taller or shorter.	PK.GM.2.2
Sort objects into sets by one or more attributes	Students sort everyday objects into groups based on what they have in common, like color, shape, or size. It's an early step in learning to notice what makes things alike or different.	PK.GM.2.3
Collect and organize categorical data	Students sort real objects into groups that belong together, like crayons by color or buttons by size, and count how many are in each group.	PK.D.1
Collect and organize information about objects and events in the environment	Students gather simple information about everyday things, like sorting blocks by color or counting how many kids chose each snack. They arrange what they find so it's easier to see and talk about.	PK.D.1.1
Use categorical data to create real-object graphs, with guidance and support	Students sort real objects into groups and line them up to make a simple graph. They might group toy animals by color or snacks by type to answer a question like "which group has more?"	PK.D.1.2

Pre-Kindergarten

Know number names and count in sequence

PK.N.1

Students learn the names of numbers and practice saying them in order: 1, 2, 3. This is the foundation for counting real objects later.
Count aloud forward in sequence by 1s to 20

PK.N.1.1

Students count out loud from 1 to 20, in order, without skipping a number.
Recognize and name written numerals 0-10

PK.N.1.2

Students look at a written number (like a 3, a 7, or a 0) and say its name out loud. This covers every numeral from zero to ten.
Recognize that 0 (zero) represents the count of no objects

PK.N.1.3

Zero means "none." Students learn that the number 0 stands for an empty group, like a plate with no cookies or a box with nothing inside.
Count to tell the number of objects

PK.N.2

Students count a small group of objects, like blocks or crayons, and say how many there are. The last number they say is the total.
Identify the number of objects, up to 10, in a row or column

PK.N.2.1

Students count a row or line of objects and say how many there are, up to ten. This is the first step toward understanding what numbers actually mean.
Use one-to-one correspondence in counting objects and matching groups of…

PK.N.2.2

Students count up to 10 objects by touching each one and saying one number at a time. They also match two groups to show the groups have the same amount.
Understand the last numeral spoken when counting aloud tells how many total…

PK.N.2.3

When students count a small group of objects out loud, the last number they say tells them how many are in the whole group. This is called the counting principle, and students practice it with groups of up to 10 objects.
Count up to 5 items in a scattered configuration, not in a row or column

PK.N.2.4

Students count up to 5 objects even when those objects are spread out randomly, not lined up. This builds the habit of counting what's there, not just what's neat.
Compare sets using numbers

PK.N.3

Students look at two groups of objects and say which group has more, which has fewer, or whether both groups have the same amount.
Compare two sets of 0-5 objects using comparative language such as "same,"…

PK.N.3.1

Students look at two small groups of objects and decide which group has more, which has fewer, or whether both groups are the same size.
Recognize, duplicate

PK.A.1

Students spot a repeating pattern (like red, blue, red, blue) and copy it or keep it going. This is the first step toward understanding how math rules work.
Sort and group up to 5 objects into a set based upon characteristics such as…

PK.A.1.1

Students sort small groups of objects by color, size, or shape, then say out loud what makes them alike.
Recognize, duplicate

PK.A.1.2

Students spot a repeating pattern, like red-blue-red-blue, then copy it and keep it going. They practice with objects, claps, or movements.
Identify common shapes

PK.GM.1

Students name everyday shapes like circles, squares, and triangles when they see them on paper or in the classroom.
Identify circles, squares, rectangles

PK.GM.1.1

Students point to circles, squares, rectangles, and triangles when a teacher calls out the name. It's the first step in learning to recognize basic shapes by sight.
Describe and compare measurable attributes

PK.GM.2

Students notice that objects can be measured in different ways, like how tall, how heavy, or how long something is. They also compare two objects and say which one is bigger, longer, or heavier.
Identify measurable attributes of objects

PK.GM.2.1

Students look at everyday objects and describe what they notice about size or weight. They use words like big, little, long, short, tall, heavy, and light.
Directly compare two objects with a common measurable attribute using…

PK.GM.2.2

Students pick up two objects and compare them side by side, then say which one is longer or shorter, heavier or lighter, taller or shorter.
Sort objects into sets by one or more attributes

PK.GM.2.3

Students sort everyday objects into groups based on what they have in common, like color, shape, or size. It's an early step in learning to notice what makes things alike or different.
Collect and organize categorical data

PK.D.1

Students sort real objects into groups that belong together, like crayons by color or buttons by size, and count how many are in each group.
Collect and organize information about objects and events in the environment

PK.D.1.1

Students gather simple information about everyday things, like sorting blocks by color or counting how many kids chose each snack. They arrange what they find so it's easier to see and talk about.
Use categorical data to create real-object graphs, with guidance and support

PK.D.1.2

Students sort real objects into groups and line them up to make a simple graph. They might group toy animals by color or snacks by type to answer a question like "which group has more?"

Standard	Definition	Code
Know number names and count in sequence	Students learn the names of numbers and practice saying them in order: 1, 2, 3. This is the foundation for counting real objects later.	PK.N.1
Count aloud forward in sequence by 1s to 20	Students count out loud from 1 to 20, in order, without skipping a number.	PK.N.1.1
Recognize and name written numerals 0-10	Students look at a written number (like a 3, a 7, or a 0) and say its name out loud. This covers every numeral from zero to ten.	PK.N.1.2
Recognize that 0 (zero) represents the count of no objects	Zero means "none." Students learn that the number 0 stands for an empty group, like a plate with no cookies or a box with nothing inside.	PK.N.1.3
Count to tell the number of objects	Students count a small group of objects, like blocks or crayons, and say how many there are. The last number they say is the total.	PK.N.2
Identify the number of objects, up to 10, in a row or column	Students count a row or line of objects and say how many there are, up to ten. This is the first step toward understanding what numbers actually mean.	PK.N.2.1
Use one-to-one correspondence in counting objects and matching groups of…	Students count up to 10 objects by touching each one and saying one number at a time. They also match two groups to show the groups have the same amount.	PK.N.2.2
Understand the last numeral spoken when counting aloud tells how many total…	When students count a small group of objects out loud, the last number they say tells them how many are in the whole group. This is called the counting principle, and students practice it with groups of up to 10 objects.	PK.N.2.3
Count up to 5 items in a scattered configuration, not in a row or column	Students count up to 5 objects even when those objects are spread out randomly, not lined up. This builds the habit of counting what's there, not just what's neat.	PK.N.2.4
Compare sets using numbers	Students look at two groups of objects and say which group has more, which has fewer, or whether both groups have the same amount.	PK.N.3
Compare two sets of 0-5 objects using comparative language such as "same,"…	Students look at two small groups of objects and decide which group has more, which has fewer, or whether both groups are the same size.	PK.N.3.1
Recognize, duplicate	Students spot a repeating pattern (like red, blue, red, blue) and copy it or keep it going. This is the first step toward understanding how math rules work.	PK.A.1
Sort and group up to 5 objects into a set based upon characteristics such as…	Students sort small groups of objects by color, size, or shape, then say out loud what makes them alike.	PK.A.1.1
Recognize, duplicate	Students spot a repeating pattern, like red-blue-red-blue, then copy it and keep it going. They practice with objects, claps, or movements.	PK.A.1.2
Identify common shapes	Students name everyday shapes like circles, squares, and triangles when they see them on paper or in the classroom.	PK.GM.1
Identify circles, squares, rectangles	Students point to circles, squares, rectangles, and triangles when a teacher calls out the name. It's the first step in learning to recognize basic shapes by sight.	PK.GM.1.1
Describe and compare measurable attributes	Students notice that objects can be measured in different ways, like how tall, how heavy, or how long something is. They also compare two objects and say which one is bigger, longer, or heavier.	PK.GM.2
Identify measurable attributes of objects	Students look at everyday objects and describe what they notice about size or weight. They use words like big, little, long, short, tall, heavy, and light.	PK.GM.2.1
Directly compare two objects with a common measurable attribute using…	Students pick up two objects and compare them side by side, then say which one is longer or shorter, heavier or lighter, taller or shorter.	PK.GM.2.2
Sort objects into sets by one or more attributes	Students sort everyday objects into groups based on what they have in common, like color, shape, or size. It's an early step in learning to notice what makes things alike or different.	PK.GM.2.3
Collect and organize categorical data	Students sort real objects into groups that belong together, like crayons by color or buttons by size, and count how many are in each group.	PK.D.1
Collect and organize information about objects and events in the environment	Students gather simple information about everyday things, like sorting blocks by color or counting how many kids chose each snack. They arrange what they find so it's easier to see and talk about.	PK.D.1.1
Use categorical data to create real-object graphs, with guidance and support	Students sort real objects into groups and line them up to make a simple graph. They might group toy animals by color or snacks by type to answer a question like "which group has more?"	PK.D.1.2

Common Questions

What math should students know by the end of the year?
Students count out loud to 20, recognize written numbers 0 through 10, and count up to 10 objects one at a time. They also name circles, squares, rectangles, and triangles, and compare small groups using words like more and fewer.
How can families practice counting at home?
Count real things together: stairs going up, grapes on a plate, socks coming out of the dryer. Point to each item as students say the number. Five minutes a day builds the habit of matching one number to one object.
My child can say numbers to 20 but miscounts objects. Is that normal?
Yes. Saying the number words and actually counting objects are two different skills. Slow down and touch each item while saying the number. The last number said is the total, and that idea takes a lot of practice to click.
How should counting be sequenced across the year?
Start with counting aloud to 10 and matching one number to one object in a neat row. Move to counting up to 10 in rows or columns, then to scattered groups of up to 5. Saving scattered counting for later in the year prevents a lot of frustration.
What does zero mean at this age?
Students learn that zero is the number for none. Show an empty plate, an empty cup, or a bowl after the crackers are gone, and ask how many are left. Naming zero as a real count helps later when students compare groups.
How can shapes and patterns be practiced at home?
Go on a shape hunt around the kitchen: the clock is a circle, a window is a rectangle, a slice of pizza is a triangle. For patterns, clap-stomp-clap-stomp, or line up red-blue-red-blue blocks and ask what comes next.
Which skills usually need the most reteaching?
One-to-one correspondence and the idea that the last number said is the total. Many students recite numbers without connecting them to objects. Plan short, daily counting routines with real objects rather than worksheets.
How is data introduced at this age?
Students sort real objects into groups and line them up to compare. A simple example: have students place their shoe under a velcro or laces label, then count which row is longer. That is a real-object graph, and it builds the base for bar graphs later.
How do I know students are ready for Kindergarten math?
Students count to 20, recognize numbers 0 through 10, count up to 10 objects accurately, and compare two small groups using more, fewer, or same. They can also name the four basic shapes and copy a simple repeating pattern.