Mathematics

Releases one item to reach for another.

Says or signs at least one number.

Imitates counting.

Says or signs number words, both in the correct sequence and out of sequence by memory.

Shows interest in counting or number-oriented play.

Says or signs numbers correctly up to 10, with or without objects.

Notices numbers or numerals in the environment.

Recognizes when others make errors while saying or signing a number sequence.

Begins to make number-like forms, such as a line or circle.

Says or signs numbers forward up to at least 20, with some mistakes.

Says or signs numbers backwards from 10.

Names the next number for numbers up to 10 (e.g., using a number line, can answer the question, "What number comes after 4?").

Reads some numbers from 0 to 10, saying number words in the correct order, with some mistakes possible.

Names or says some numbers from 0 to 10, saying number words in the correct order, with some mistakes possible.

Count forward, with and without objects, to at least 31. Count backward from 20. (MP6)

Count collections of objects up to 31 by grouping in 10s using ten-frames, cups, or other tools. (MP6, MP7)

Uses any number to signify "how many" while clearly not knowing what that number word means (e.g., when asked, "How many?" child replies "five" without counting, looking at, or knowing how to count to five).

Demonstrates and uses one-to-one counting to count up to four items (e.g., a child is asked to answer how many blocks are in the pile, and then touches each item once while counting).

Demonstrates and uses one-to-one counting to count with sets up to 10 items.

Read, write, compare, order, and represent whole numbers from 0 to at least 31 (with 0 representing the count of no objects) to answer the question, "how many?" Representations may include numerals, pictures, real objects, picture graphs, spoken words and manipulatives, such as connecting cubes. The numbers from 11 to 19 are composed of a 10 and one, two, three, four, five, six, seven, eight or nine ones. (MP4, MP8)

Responds to requests to give a small quantity of items (e.g., one, two) with some mistakes.

Gives one to two and only one to two items upon request.

Identifies a correct quantity (e.g., three or four objects) with a number word (e.g., "three" or "four") up to four items.

Gives the correct number of items consistently, when asked, up to four.

Identifies a correct quantity (between four and 10 items) with a number word (e.g., "four" or "six").

Gives the correct number of items consistently when asked, for between four and 10 items.

Identifies that the final number word used when counting out an item set represents the exact number of items in the set.

Understands the number of objects in a set does not change and is the same regardless of the arrangement or order in which they were counted (e.g., when there are five different animals in a group, the quantity is the same whether they are in a circle or a line).

Recognize that a number can be used to represent how many objects are in a set or to represent the position of an object in a sequence. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number with one and only one object. Understand that the last number said tells the number of objects counted. Understand that each successive number refers to a quantity that is one more. Name the position of an object in a sequence (ordinal count). (MP1, MP6)

Understands that a number word identifies, "How many?"

Understands that a number word refers to a specific quantity without knowing the exact quantity.

Associates a small quantity (e.g., one or two objects) with a number word or number (e.g., "one" or "two") up to two.

Associates a quantity (e.g., two or three objects) with a number word or number (e.g., "two" or "three") up to four.

Names small sets quickly and accurately, labeling groups as "two" or "three," up to three. This skill is often referred to as "subitizing."

Associates numerals (e.g., 3 or 4) with the correct number word or number (e.g., "three" or "four") up to 10.

Names small sets quickly and accurately, labeling groups as "four" or "five" (e.g., when a child sees five dots on a die, they know without counting that it is "five"). This skill is often referred to as "subitizing."

Recognize that a number can be used to represent how many objects are in a set. (MP1, MP6)

Grasps one object and reaches for another.

Groups a few items into categories (e.g., color, size, shape).

Compares two sets of up to four objects accurately using terms like "more" and "less" or "a little" and "a lot."

Uses terms like "more" and "less," "bigger" and "smaller," and "a little bit" and "a lot" to refer to approximate quantities.

Estimates quantities verbally without counting, although inconsistently and sometimes with mistakes.

Count collections of objects up to 31 by grouping in 10s using ten-frames, cups, or other tools. (MP6, MP7)

Find a number that is 1 more or 1 less than a given number. (MP7, MP8)

Solve and represent a variety of addition and subtraction contextual situation types using objects, drawings, mental images or equations within 10. (MP4, MP5)

Uses signs like "more" to reference quantity.

Uses signs or words like "more" to reference quantity.

Notices when the quantity of a set of up to four objects has increased or decreased.

Combines or separates items (or sets of objects) to make another number.

States the number that comes before or after (up to the number five).

States the number that comes before or after (up to the number 10).

Understands that a quantity changes (increases or decreases) when a set of objects (more than four and up to 10) are combined or separated.

Names the next number in a set of up to 10 items without recounting, even when the set isn't visible.

Produces different sets that equal a specific sum of up to 10 (e.g., both "two and three" and "one and four" equal five).

Compose and decompose numbers less than or equal to 10 into pairs in more than one way with objects and pictures. Record each decomposition with a drawing or equation. (MP7)

Fluently add and subtract within 5. (MP2)

Orders a few objects by size with assistance.

Identifies the first or second item in a sequence upon request.

Uses ordinal position sequencing terms (e.g., "first," "most," "last," "before").

Orders a few objects by size without assistance.

Recognizes that a number word can be used to represent a position in a sequence (e.g., puts a specific object first or second when making a pattern).

Recognize that a number can be used to represent how many objects are in a set or to represent the position of an object in a sequence. When counting objects, say the number names in the standard order, pairing each object with one and only one number name and each number with one and only one object. Understand that the last number said tells the number of objects counted. Understand that each successive number refers to a quantity that is one more. Name the position of an object in a sequence (ordinal count). (MP1, MP6)

Adjusts reaching behavior to distance of object.

Experiments with "full" and "empty" (e.g., filling and emptying buckets/cups).

Orders a few objects by size with support.

Brings objects closer together to compare them.

Imitates using an object to measure another object.

Uses language or gestures to describe "full" and "empty."

Begins to understand the need to use standardized units, common and unconventional, to measure.

Demonstrates understanding of measurement terms (e.g., "longer" and "shorter" or "farthest" and "closest") by saying or pointing.

Uses standardized units, common and unconventional, to measure.

Compares and orders more than two items in some way (e.g., shortest to longest, smallest to biggest).

Uses comparison vocabulary (e.g., "longer" and "shorter," "taller" and "shorter," and "farthest" and "closest") with both discrete sets (e.g., blocks, books) and continuous properties (e.g., water, sand, height).

Compare objects with a measurable attribute in common, to see which object has "more of," "less of" or the "same as" the attribute and explain the reasoning. (MP3, MP5)

Describe several measurable attributes of objects such as length and weight. (MP4, MP6)

Anticipates familiar routines.

Notices changes in patterns (e.g., emotional reaction when preparation for feeding takes longer than usual).

Carries out steps of familiar routines (e.g., mealtime, handwashing).

Participates in familiar simple patterns (e.g., sound, body movement sequence with familiar songs).

Participates in a new simple pattern that is modeled (e.g., sound, body, color, size, movement).

Recognizes repeating patterns.

Copies simple existing patterns.

Extends a simple pattern.

Uses words or pictures to describe a simple pattern.

Applies a simple pattern rule to different materials or modes (sound, body, color, size, movement).

Copies an example of a complex pattern.

Recognize, create, complete, and extend simple patterns using shape, color, size, number, sounds, and movements. Patterns may be repeating, growing or shrinking. (MP1, MP7)

Recognize patterns in counting. Skip count by 10s starting at zero up to 100. (MP7)

Notices high contrast patterns, shapes, or lines (e.g., pays attention to black and white patterns or images on objects).

Shows interest in shapes and spatial relationships (e.g., rolling a ball, stacking small objects, attempting to fit pieces in puzzles).

Begins to recognize 2D and 3D shapes (e.g., circles, spheres, squares, and cubes) by naming or sorting objects.

Begins to recognize 2D and 3D shapes (circles, spheres, squares, and cubes) by fitting objects into spaces (e.g., puzzles).

Recognizes 2D and 3D shapes in the environment.

Points to or names familiar 2D and 3D shapes (circles, spheres, squares, cubes, triangles) accurately when asked.

Begins to describe the attributes (round, straight, curved, etc.) that define 2D and 3D shapes, including sides and corners regardless of the shape's size or position (e.g., notices that "this block won't roll because it's not round").

Puts together (composes) and takes apart (decomposes) shapes.

Identify and compare two- and three- dimensional shapes such as squares, circles, triangles, rectangles, trapezoids, hexagons, cubes, cones, cylinders, and spheres using informal language to describe their similarities, differences, parts and other attributes. (MP2)

Compose, decompose and name simple shapes. Recognize shapes regardless of their overall size and orientation. (MP1, MP2)

Attends and responds to moving objects and sounds in their environment.

Develops an increasing ability to change positions and move their body from place to place.

Demonstrates awareness of differences between over and under, up and down, in and out.

Rotates, flips, or turns an object when they realize the object doesn't fit in a defined space.

Adjusts position and movement of own body relative to objects (e.g., moves around objects).

Explores how objects fit together in their environment.

Rotates objects to accurately fit through holes and spaces.

Puts together (composes) and takes apart (decomposes) shapes to create new shapes.

Recognizes and creates shapes that have symmetry.

Recognizes that complex shapes need to be rotated, flipped, or turned around before objects fit together (e.g., puzzle pieces).

Describe objects in the environment using names of shapes. Describe the relative positions of these objects using terms such as above, below, beside, in front of, behind and next to. (MP1, MP6)

Shows preference for familiar or novel toys, objects, and people.

Recognizes familiar objects from different perspectives.

Begins to understand personal location relative to landmarks or another person's location.

Uses terms to explain distances and lengths (e.g., "near" and "far," "above," and "front" and "back").

Uses a simple map of a visible area to locate placement, with verbal cues.

Recognizes and describes the position of objects in their environment.

Produces a simple map.

Describe objects in the environment using names of shapes. Describe the relative positions of these objects using terms such as above, below, beside, in front of, behind and next to. (MP1, MP6)

Uses senses to interact with objects in their environment (e.g., mouthing a toy or object).

Recognizes differences between familiar and unfamiliar (e.g., faces).

Begins to recognize similarities or differences of novel objects.

Matches items based on attributes meaningful to the child (e.g., sorting based on favorite color).

Imitates sorting.

Sorts objects based on an observable attribute, with or without assistance (e.g., shape, color, texture, size).

Demonstrates understanding that attributes are measurable (e.g., counting small objects of same color).

Says or shows the attribute used for sorting or comparing objects.

Sorts objects by using flexible rules (e.g., sort first by color, then sort the same objects by size).

Sorts objects using characteristics such as shape, size, color and thickness. (MP1, MP6)

Participates in simple data collection with support from a caregiver (e.g., watches caregiver chart answers to question of the day).

Collects information about one or more attributes (e.g., how many children like one food versus another).

Helps to chart or graph information as part of group activity (e.g., writes X on chart to indicate choice between two items).

Sorts information by one or more attributes with assistance from a caregiver (e.g., creates a chart of animals that are awake at night versus day).

Collects and shares data independently (e.g., asks peers about preferences for group chart activity).

Organize objects, draw pictures, or use tally marks to represent data and communicate observations. (MP3, MP6)

Identifies patterns, differences, or similarities of information displayed (e.g., on a chart).

Uses language words, pictures, or signs to describe those patterns, differences, or similarities of data.

Describes differences in data (e.g., more children like apples than bananas).

Uses data to answer questions and solve problems (e.g., "If there are 10 name cards on the name chart, we need 10 chairs at the table").

Notice and describe patterns in data-rich situations. (MP1, MP7)

Organize objects, draw pictures, or use tally marks to represent data and communicate observations. (MP3, MP6)