Counting and recognizing numbers
Students count out loud to 100 and learn what numbers up to 10 actually mean when they look at a pile of objects. They start to recognize small groups by sight without counting one by one.
Kindergarten is the year numbers start to mean something. Students learn that the number five stands for five real things they can count, point to, or line up. They begin adding and taking away small groups with their fingers and with pictures, and they start spotting circles, squares, and triangles in the world around them. By spring, students can count to 100, write the numbers up to 20, and tell which group of objects has more.
Students count out loud to 100 and learn what numbers up to 10 actually mean when they look at a pile of objects. They start to recognize small groups by sight without counting one by one.
Students sort objects by color, size, and shape, and finish patterns that repeat or grow. They name circles, squares, triangles, and rectangles in the world around them.
Students line objects up to compare which is longer, heavier, or bigger, and use words like more than and less than to talk about groups. They start to notice time words like morning, afternoon, and tomorrow.
Students put small groups together and break them apart to see how numbers up to 10 are made. They find one more and one less, share objects into equal piles, and start to name pennies, nickels, dimes, and quarters.
Students collect information about things around them, like favorite snacks or kinds of weather, and arrange real objects or pictures into simple graphs. They talk about what the graph shows and which group has more.
Counting connects to quantity. Students match spoken numbers to real objects, learning that the last number counted tells how many things are in a group.
Students count out loud from 1 to 100, one number at a time, then practice again jumping by tens: 10, 20, 30, all the way to 100.
Counting a group of objects and writing or saying the number that matches. Students learn that the number 7, for example, always means exactly seven things, whether the objects are toys, apples, or fingers.
Students learn words like first, third, and tenth to describe where something sits in a line or sequence. Given a row of objects, they can say which one is fifth or last.
Students look at a small group of dots or objects and say how many there are without counting one by one. This works with tidy rows and scattered arrangements, up to 10 objects.
Starting from any number between 1 and 20, students count forward out loud, with or without physical objects in front of them.
Students read and write numbers from 0 to 20 and show what those numbers mean using drawings, objects, or words. The number 7 isn't just a symbol; it matches seven real things students can count and point to.
Given any number up to 10, students say what comes just before it and just after it. If the number is 6, one more is 7 and one less is 5.
Looking at two groups of objects or two numbers, students decide which is more, which is less, or whether they match. They practice saying it out loud using words like "more than," "less than," or "equal to."
Students use blocks, fingers, or drawings to figure out simple adding and subtracting with numbers up to 10. The focus is on understanding what happens when you combine groups or take some away, not just memorizing answers.
Students break a small number into two parts and put those parts back together, using blocks, drawings, or fingers. For example, 7 can be split into 4 and 3, then combined again.
Students split a shape or group of objects into equal parts so everyone gets the same amount. This is the first step toward understanding fractions.
Students split a group of objects into two equal piles. This is the first step toward understanding fractions, division, and fair sharing.
Students learn the names of everyday coins: penny, nickel, dime, and quarter. They can look at a coin and say what it is called.
Students learn to recognize a penny, nickel, dime, and quarter by sight and name each one correctly.
| Standard | Definition | Code |
|---|---|---|
| Understand the relationship between quantities and whole numbers | Counting connects to quantity. Students match spoken numbers to real objects, learning that the last number counted tells how many things are in a group. | K.N.1 |
| Count aloud forward in sequence to 100 by 1s and 10s | Students count out loud from 1 to 100, one number at a time, then practice again jumping by tens: 10, 20, 30, all the way to 100. | K.N.1.1 |
| Recognize that a number can be used to represent how many objects are in a set… | Counting a group of objects and writing or saying the number that matches. Students learn that the number 7, for example, always means exactly seven things, whether the objects are toys, apples, or fingers. | K.N.1.2 |
| Use ordinal numbers to represent the position of an object in a sequence up to… | Students learn words like first, third, and tenth to describe where something sits in a line or sequence. Given a row of objects, they can say which one is fifth or last. | K.N.1.3 |
| Recognize without counting | Students look at a small group of dots or objects and say how many there are without counting one by one. This works with tidy rows and scattered arrangements, up to 10 objects. | K.N.1.4 |
| Count forward, with and without objects, from any given number up to 20 | Starting from any number between 1 and 20, students count forward out loud, with or without physical objects in front of them. | K.N.1.5 |
| Read, write, discuss | Students read and write numbers from 0 to 20 and show what those numbers mean using drawings, objects, or words. The number 7 isn't just a symbol; it matches seven real things students can count and point to. | K.N.1.6 |
| Find a number that is 1 more or 1 less than a given number up to 10 | Given any number up to 10, students say what comes just before it and just after it. If the number is 6, one more is 7 and one less is 5. | K.N.1.7 |
| Compare and order whole numbers from 0 to 10 with and without objects, using… | Looking at two groups of objects or two numbers, students decide which is more, which is less, or whether they match. They practice saying it out loud using words like "more than," "less than," or "equal to." | K.N.1.8 |
| Develop conceptual understanding with addition and subtraction | Students use blocks, fingers, or drawings to figure out simple adding and subtracting with numbers up to 10. The focus is on understanding what happens when you combine groups or take some away, not just memorizing answers. | K.N.2 |
| Compose and decompose numbers up to 10 using objects and pictures | Students break a small number into two parts and put those parts back together, using blocks, drawings, or fingers. For example, 7 can be split into 4 and 3, then combined again. | K.N.2.1 |
| Understand the relationship between whole numbers and fractions through fair… | Students split a shape or group of objects into equal parts so everyone gets the same amount. This is the first step toward understanding fractions. | K.N.3 |
| Distribute a set of objects into at least two smaller equal sets | Students split a group of objects into two equal piles. This is the first step toward understanding fractions, division, and fair sharing. | K.N.3.1 |
| Identify coins by name | Students learn the names of everyday coins: penny, nickel, dime, and quarter. They can look at a coin and say what it is called. | K.N.4 |
| Identify pennies, nickels, dimes | Students learn to recognize a penny, nickel, dime, and quarter by sight and name each one correctly. | K.N.4.1 |
Students copy a repeating pattern, like red-blue-red-blue, using blocks, sounds, or movements. They show the same pattern in a new way without changing the order.
Students sort up to 10 objects into groups by color, size, or shape, then say out loud what makes each group the same.
Students spot a repeating or growing pattern, then copy it, finish it, or keep it going. The pattern might use shapes, colors, sizes, or sounds.
| Standard | Definition | Code |
|---|---|---|
| Duplicate patterns in a variety of contexts | Students copy a repeating pattern, like red-blue-red-blue, using blocks, sounds, or movements. They show the same pattern in a new way without changing the order. | K.A.1 |
| Sort and group up to 10 objects into a set based upon characteristics such as… | Students sort up to 10 objects into groups by color, size, or shape, then say out loud what makes each group the same. | K.A.1.1 |
| Recognize, duplicate, complete | Students spot a repeating or growing pattern, then copy it, finish it, or keep it going. The pattern might use shapes, colors, sizes, or sounds. | K.A.1.2 |
Students sort circles, squares, triangles, and rectangles by shape, then connect those shapes to real objects like wheels, boxes, and doors.
Students sort and name squares, circles, triangles, and rectangles by looking at their sides and corners. This is the start of geometry.
Students sort flat shapes, like circles, squares, and triangles, into groups by what they look like or how big they are.
Students count the sides and corners of flat shapes like squares, triangles, and circles, and learn to use everyday words alongside math words to describe what they notice.
Students fit small shapes together like puzzle pieces to fill the outline of a bigger shape, with no gaps and no overlapping.
Students stack and combine blocks, boxes, and other solid objects to build bigger structures. They explore how three-dimensional shapes fit together to make something new.
Students look at everyday objects and match them to shapes they know, like noticing a window is a rectangle or a ball is a circle. They use those shapes to draw or build simple models of things around them.
Students sort and line up objects by where they are or how they measure up, such as which block is tallest or which crayon is shortest. They practice putting things in order from biggest to smallest or nearest to farthest.
Students practice describing how two objects differ using everyday words like longer, heavier, bigger, above, or beside. This is the language behind rulers, scales, and maps.
Students line up to 6 objects by size, from shortest to tallest or lightest to heaviest. They explain which comes first and why.
Students look at a group of objects, find two things they have in common (like color and shape), and sort them into groups based on those shared traits.
Students fill two containers with small objects and say which one holds more. It's an early lesson in comparing capacity before numbers like "cups" or "liters" come into the picture.
Students learn to connect times of day to daily routines, like knowing morning means breakfast or bedtime follows a bath. The focus is on understanding how time shapes the day, not yet reading a clock.
Students learn words like yesterday, today, tomorrow, morning, and night to describe when things happen in their day. It's the first step toward reading a clock and understanding how time is organized.
| Standard | Definition | Code |
|---|---|---|
| Recognize and sort basic two-dimensional shapes | Students sort circles, squares, triangles, and rectangles by shape, then connect those shapes to real objects like wheels, boxes, and doors. | K.GM.1 |
| Recognize squares, circles, triangles | Students sort and name squares, circles, triangles, and rectangles by looking at their sides and corners. This is the start of geometry. | K.GM.1.1 |
| Sort two-dimensional objects using characteristics such as shape and size | Students sort flat shapes, like circles, squares, and triangles, into groups by what they look like or how big they are. | K.GM.1.2 |
| Identify attributes of two-dimensional shapes using informal and formal… | Students count the sides and corners of flat shapes like squares, triangles, and circles, and learn to use everyday words alongside math words to describe what they notice. | K.GM.1.3 |
| Use smaller two-dimensional shapes to fill in the outline of a larger… | Students fit small shapes together like puzzle pieces to fill the outline of a bigger shape, with no gaps and no overlapping. | K.GM.1.4 |
| Compose larger, undefined shapes and structures using three-dimensional objects | Students stack and combine blocks, boxes, and other solid objects to build bigger structures. They explore how three-dimensional shapes fit together to make something new. | K.GM.1.5 |
| Use basic shapes and spatial reasoning to represent objects in the real world | Students look at everyday objects and match them to shapes they know, like noticing a window is a rectangle or a ball is a circle. They use those shapes to draw or build simple models of things around them. | K.GM.1.6 |
| Compare and order objects according to location and measurable attributes | Students sort and line up objects by where they are or how they measure up, such as which block is tallest or which crayon is shortest. They practice putting things in order from biggest to smallest or nearest to farthest. | K.GM.2 |
| Use words to compare objects according to length, size, weight, position | Students practice describing how two objects differ using everyday words like longer, heavier, bigger, above, or beside. This is the language behind rulers, scales, and maps. | K.GM.2.1 |
| Order up to 6 objects using measurable attributes, such as length and weight | Students line up to 6 objects by size, from shortest to tallest or lightest to heaviest. They explain which comes first and why. | K.GM.2.2 |
| Identify more than one shared attribute between objects | Students look at a group of objects, find two things they have in common (like color and shape), and sort them into groups based on those shared traits. | K.GM.2.3 |
| Compare the number of objects needed to fill two different containers | Students fill two containers with small objects and say which one holds more. It's an early lesson in comparing capacity before numbers like "cups" or "liters" come into the picture. | K.GM.2.4 |
| Tell time as it relates to daily life | Students learn to connect times of day to daily routines, like knowing morning means breakfast or bedtime follows a bath. The focus is on understanding how time shapes the day, not yet reading a clock. | K.GM.3 |
| Develop an awareness of simple time concepts within daily life, using… | Students learn words like yesterday, today, tomorrow, morning, and night to describe when things happen in their day. It's the first step toward reading a clock and understanding how time is organized. | K.GM.3.1 |
Students sort objects or pictures into groups, count each group, and answer questions about what the data shows (like which group has more).
Students gather information about everyday objects or events, like counting how many red and blue crayons are in the box, and sort what they find into groups that make it easy to compare.
Students sort real items or draw pictures to build a simple graph that shows how many things belong in each group.
Students look at a simple picture graph or a row of real objects and answer questions about what the data shows, like which group has more or which has the fewest.
| Standard | Definition | Code |
|---|---|---|
| Collect, organize, and interpret categorical data | Students sort objects or pictures into groups, count each group, and answer questions about what the data shows (like which group has more). | K.D.1 |
| Collect and organize information about objects and events in the environment | Students gather information about everyday objects or events, like counting how many red and blue crayons are in the box, and sort what they find into groups that make it easy to compare. | K.D.1.1 |
| Use categorical data to create real-object graphs and pictographs | Students sort real items or draw pictures to build a simple graph that shows how many things belong in each group. | K.D.1.2 |
| Draw conclusions from real-object graphs and pictographs | Students look at a simple picture graph or a row of real objects and answer questions about what the data shows, like which group has more or which has the fewest. | K.D.1.3 |
Students should count to 100 by ones and tens, read and write numbers up to 20, and add and subtract small amounts up to 10 using objects or pictures. They should also name basic shapes, sort objects, and recognize a penny, nickel, dime, and quarter.
Count everything. Count steps up the stairs, count grapes on a plate, count toy cars lined up on the floor. After a while, start counting from a number other than one, like starting at seven and going to twenty.
Start with counting to 20 and matching numbers to small sets of objects. Build subitizing and one more or one less through the middle of the year. Save composing and decomposing numbers up to 10 for later, once students are steady with quantities.
Students do not write equations yet. They put two small groups of objects together to find how many, or take some away to see what is left. Snacks, blocks, and buttons work well at home.
Counting from a number other than one trips up many students, and so does writing numbers like 12 through 19 without reversing the digits. Subitizing also needs steady practice with dot cards and dice patterns.
Point out circles, squares, triangles, and rectangles on signs, food, and toys. Make simple patterns with socks, spoons, or crayons and ask students what comes next. Sorting laundry by color or size is good practice too.
Students can count to 100, count on from any number to 20, and compare two small groups using more than, less than, or equal to. They can break apart numbers up to 10, name common shapes, and read a simple picture graph.
Five to ten minutes a day is plenty. Short bursts during snack time, bath time, or a walk work better than a long sit-down session. The goal is steady practice, not drills.