1. Comparing and Categorizing

Child recognizes some similarities and differences between familiar and unfamiliar people, objects, or experiences.

0–9 months – See this age across all domains Infants

What educators might observe

• Distinguishes between objects they suck and those they do not
• Smiles when they see or hear familiar caregiver
• Gazes at unfamiliar object or person for longer period of time
• Shows preferences for particular activities, such as being carried rather than pushed in the stroller
• Explores how various toys feel and touches different objects in different ways

Ways educators might support the child's development

• Narrate when familiar individuals enter the room (“Here comes Ms. Kimball. You know Ms. Kimball. Hello, Ms. Kimball.”)
• Notice when a child is wondering about a new object (“You are looking at our new mobile. We hung it up in the window.”)
• Use descriptive vocabulary, such as rough, smooth, furry, bumpy, long, short, wet, and dry as children touch and explore their environment

8–16 months – See this age across all domains Infants

What educators might observe

• Shows preference for particular items such as toys, cups, or clothing
• Knows trash can is something you place items in, but may put objects other than trash in it
• Selects a duck when educator asks, “Where’s the duck?”
• When unfamiliar adult enters the room, may cry or move toward familiar person
• Begins to understand the similarities and differences in speech sounds and distinguishes and imitates patterns of speech
• Chooses to play with the red car even though there is a blue one just like it
• Knows some objects that go together (e.g., puts the doll in a toy stroller)

Ways educators might support the child's development

• Describe objects by their size, color, and shape (“You are rolling the big, red ball.”)
• Talk about which objects go together during caregiving routines (“I am getting ready to change your diaper. I need a clean diaper, wipes, and gloves.”)
• Play language games that emphasize speech sounds; for example, repeat the consonant sounds that the baby makes

15–24 months – See this age across all domains Toddlers

What educators might observe

• Helps clean up environment by putting materials in their places; puts books in basket, for example, or blanket in cubby
• Arranges objects in lines (e.g., makes a row of blocks)
• Points to a duck in a book when the educator asks, “Which one says, ‘quack?’”
• Identifies two identical toys by putting them together (or in response to the question, “Can you find one like this?”)
• Calls all the four-legged animals on a farm “cows,” although some are sheep and some are horses
• Connects objects and ideas, such as using a broom for sweeping or a shovel or cup to scoop sand or water

Ways educators might support the child's development

• Provide intentional collections of toys
  • An animal family with a male, a female, and a young animal
  • A variety of trucks, trains, and cars
  • A doll with a bottle, a brush, and clothes
  • A toy broom, mop, and dustpan
  • A collection of objects that are all the same color
  • A collection of heavy objects
  • A collection of pieces of fabric such as velvet and burlap
• Store and display collections of items in separate, accessible, attractively presented bins

24–36 months – See this age across all domains Toddlers

What educators might observe

• Collects a single type of object (e.g., picks up pinecones on a walk in the park)
• Calls a big animal “Papi” (“Daddy”) and a small animal “Bebe” (“Baby”)
• Begins to sort similar items into categories such as color or shape (e.g., retrieves blue ball when asked, “Could you please get the blue one?”)
• Identifies small, medium, and big objects when arranged in a series
• Uses one-to-one correspondence with objects(e.g., puts one straw in each cup.) objects (e.g., puts one straw in each cup)

Ways educators might support the child's development

• Provide puzzles and toys that encourage matching, such as shape sorters
• Incorporate categorization into games with children; for example, make up a story together in the block area about a family of goats and a family of sheep
• Label the same objects in a group in different ways (“mommy, child, baby” and then “big, small, tiny.”)
• Encourage child to group toys and compare similarities and differences between them (e.g., “Let’s find all the toys with wheels.”)

3-year-olds – See this age across all domains Preschool

What educators might observe

• Shows understanding of the words “same” and “different”
• Remarks on physical differences that they notice among members of the community
• Recognizes and labels aspects of an experience (tall, long, fun)
• Identifies categories of objects, for example, knows that dogs, cats, and cows are all animals

Ways educators might support the child's development

• Openly discuss differences children remark on in their community (“Yes, Mr. Brown has no legs. He uses his electric wheelchair to move around.”)
• Extend this learning about differences (“In what other ways do people move around?”)
• Play simple sorting games with children; for example, dress a paper doll for different kinds of weather
• Read books, such as those by Ann Morris, that show types of shoes, hats, bread, or transportation around the world

4-year-olds – See this age across all domains Preschool

What educators might observe

• Sorts by a given attribute, forming categories
• Uses comparative words (e.g., faster, slower, louder)
• Identifies the measurable attributes of objects such as length or weight and describes them using the appropriate vocabulary (e.g., small, big, short, tall, empty, full, heavy, light)
• Lines up objects in order to determine which is longer
• Fills large containers with cups of water and counts how many cups fit in each container

Ways educators might support the child's development

• Make a simple Bingo game with 9 squares of colors, shapes, or animals; the cards from this game can also be used for a simple matching game
• If children are comparing objects, offer them a standard or non-standard tool for measurement
• Play “duck, duck, goose” using different categories, such as “train, train, car”

5-year-olds – See this age across all domains Preschool

What educators might observe

• Sorts by a single attribute and reclassifies according to another attribute (e.g., sorts writing implements by type and then re-sorts them by color)
• Arranges 5–10 objects shortest to longest, biggest to smallest, or heaviest to lightest
• Compares number of objects by counting, even when one of the objects is bigger, up to 10

Ways educators might support the child's development

• Compare characters in a story or subjects in a non-fiction text
• Create class charts and surveys with student information such as siblings, caretakers, or ways of getting to school; use these to compare aspects of the class
• Compare classroom materials, sorting different sizes or shapes of blocks, for example, and discussing how to use them

6-year-olds – See this age across all domains Early elementary

What educators might observe

• Compares several aspects of something (e.g., compares animals, identifying similarities and differences between the ways they move, eat, and defend themselves)
• Notices and compares changes over time (e.g., compares the length of the day at different times of the year, saying, “It used to be dark when I was picked up.”)
• U ses a repeating unit to measure length (e.g., uses a line of small blocks to measure a book)
• Identifies similarities and differences among the lives of people in different families and communities

Ways educators might support the child's development

• Offer objects for comparison and categorization
  • Photos of animals
  • Collections of rocks or leaves
  • Keys
  • Buttons
• Engage children in using categorization for social good; for example, categorize recycling materials
• Provide unit blocks and rulers for measurement
• Create activities to measure distance (e.g., hold a paper airplane contest, then chart the results in a graph)

7-year-olds – See this age across all domains Early elementary

What educators might observe

• Reverses mental actions (e.g., knows that a ball of clay rolled into a long snake contains the same amount of clay as the ball)
• Chooses a strategy for comparison (e.g., uses graphs to compare their observations of the natural world)
• Understands the need for a standard unit when measuring length

Ways educators might support the child's development

• Offer formats distinctly for comparison and categorization, such as Venn diagrams and three-column charts
• Offer vocabulary such as “traits,” “similar,” and “category”
• Use “greater than” and “less than” to compare quantity
• Compare standard and non-standard units of measure, some of which can be parts of the body; use inches, feet and meters, but also fingers, hands, and items like paper clips

8-year-olds – See this age across all domains Early elementary

What educators might observe

• Creates hierarchical categorizations (e.g., child categorizes plants based on the ecosystems in which they live, then divides the plants that live in the desert into cacti and succulents)
• Compares their home life to that of children who live in different places and to the lives of children who lived a long time ago

Ways educators might support the child's development

• Invite families to visit the classroom to talk about their childhoods; use Venn diagrams to compare and contrast
• Read books aloud about children who live in different kinds of families; ask the children questions about how the character’s lives are similar to and different from their own
• Visit a natural history museum or botanical garden and talk about the categories the curators use

2. Number Sense and Quantity

Child understands and explores numbers and quantity.

0–9 months – See this age across all domains Infants

What educators might observe

• Holds one object in each hand and then drops one when someone holds out a third object
• Explores one toy at a time by holding and mouthing it

Ways educators might support the child's development

• Sing number songs to the child
  • “Ten fingers, ten toes, two little eyes, one little nose…”
  • “Five little ducks went out to play...”
  • “Uno, dos, tres amigos...”
• Reference numbers and quantity as the educator interacts with the baby (“I see one little baby looking at me.”)
• As the child picks up, holds on to, and releases objects from their hands, name the quantity in each hand

8–16 months – See this age across all domains Infants

What educators might observe

• Tries to hold onto two large balls while reaching for third ball
• Fills a bucket with objects and dumps it out
• Holds a block in each hand and bangs them together
• Shakes head “no” when asked if they want more food
• Puts multiple blocks in each cup of a muffin tin

Ways educators might support the child's development

• Use comparative vocabulary as you interact with children (“Carla has more cars than Shante.”)
• Slowly count with children throughout the day. How many
  • Steps on the staircase?
  • Keys on a ring?
  • Wheels on a car?

15–24 months – See this age across all domains Toddlers

What educators might observe

• Puts three animals in a row when playing
• Understands and communicates the concepts of “more” and “all done” through words or gestures
• Identifies which group has “more” with collections in which one has much more than the other
• Names groups of one or two (e.g., when shown a pair of shoes, says “two shoes.”)

Ways educators might support the child's development

• Encourage counting out loud in multiple languages
• Read books about numbers that reinforce concepts of one-to-one correspondence, numerical order, and mathematical concepts of more, less, too many, and all gone
• Use number and quantity vocabulary during mealtimes (“two crackers, one apple, and one cup of milk), and count as you pour each cup of water (“one, two, three, and stop”)
• Name groups of two objects, and identify groups that do not include two items (“That’s not two, that’s three!”)

24–36 months – See this age across all domains Toddlers

What educators might observe

• Starts counting with “one”
• Says all the number words they know when counting objects, even when the quantity of objects is small
• Reuses the number words they know if the quantity of objects is greater than the number words they know
• Uses “a little” and “a lot” to describe quantity
• When told, “Give me one,” hands educator just one object
• When educator says, “Just take two,” takes only two slices of apple from the bowl
• Demonstrates one-to-one correspondence with objects (e.g., puts one block in each muffin tin)

Ways educators might support the child's development

• Encourage children to set the table for snack or lunch with one cup, one plate, and one napkin at each chair
• Use language to describe quantity throughout the day (“We have a lot of apples for snack! We have many more apples than we can eat.”)
• Incorporate counting into representational play with children (“There are three bears in the house. One, two, three.”)
• Provide egg cartons, ice cube trays, and muffin tins with small blocks so children can practice one-to-one correspondence

3-year-olds – See this age across all domains Preschool

What educators might observe

• Recognizes and names some numerals when pointing to them
• Recognizes that numerals can be written and pretends or attempts to write some
• Verbally counts to 10 with some correspondence, but skips some objects and counts others twice
• Produces sets of three (e.g., “Bring me three paint brushes from the art center”)
• When asked for five of something, counts out three and says, “One, two, five.”
• Changes word order or gives up on one-to-one correspondence to make the answer the one they had predicted or their favorite number (e.g., “one, two, three, four, 100!”)
• Matches small sets (one to four) of different items and shows they are the same quantity

Ways educators might support the child's development

• Use numbers and counting throughout the day, such as counting how many children are at the sand table
• Present sets of one to four objects and ask “How many?” questions; encourage children to name the sets before counting (“How many blocks do I have? That’s right I have two blocks.”)
• Point out quantities of items that the child possesses, such as two shoes, one hat, one jacket, or three stuffed animals; count each item out loud to correspond the number with the quantity of the items
• Model placing the objects that the child wants to count in a line
• Give child simple tasks that involve counting (“Give every child one cracker”)

4-year-olds – See this age across all domains Preschool

What educators might observe

• Attempts to count to 20 by ones
• Recognizes the number of objects in groups of four without counting
• Accurately counts five to 10 objects in a line and answers the “how many” question with the last number counted
• Can match a number of objects with a written numeral 0 to 5 (0 representing a count of no objects)
• When asked for five of something, counts out five objects
• Compares groups of one to six objects by matching (e.g., gives each child a bagel and says that there are the same number of bagels as children)
• Counts the number of objects in a group so they can compare and say which has more, up to five objects; however, if the objects in one group are larger, may say that group has more (e.g., says three large trucks are more than five small cars

Ways educators might support the child's development

• Observe children’s use of counting, oneto-one correspondence, estimating, and simple arithmetic in their play; connect to and extend this learning
• Offer games that ask children to match a numeral to a number of things
  • String six beads on a pipe cleaner
  • P ick a card and fill the basket with that number of objects
  • Roll a dice and do a movement that many times
  • Jump, clap, or stomp one to five times and ask the children to hold up the number of fingers that matches the number of movements
• Include books related to number and quantity in the learning environment
  • The Doorbell Rang , by Pat Hutchins
  • Anno’s Counting Book , by Mitsumasa Ann
  • Ten Black Dots , by Donald Crews
  • City by Numbers , by Stephen Johnson
  • Fish Eyes , by Lois Ehlert

5-year-olds – See this age across all domains Preschool

What educators might observe

• Quickly names the number of objects in groups of five without counting
• Tells what number comes after any number between one and 20
• Explains that numbers tell “how many” of something
• Recognizes and writes numerals 1 through 10
• Divides up to 20 objects between four or five people by dealing out an object to each person
• Uses the words “first,” “second,” “third,” up to and including “tenth” (e.g., says, “I came in fourth” when describing a race with classmates
• Counts on their fingers
• Keeps track of objects that have and have not been counted (e.g., slides objects they have already counted to the side)
• Counts backward from 10 by taking away objects

Ways educators might support the child's development

• Provide bags of objects to count (10 acorns, 14 keys, 19 cubes) and ask children to count and draw the objects in them
• Allow children to freely play with math manipulatives before using them to solve problems
• S et up the dramatic play area as a store, and invite children to use number cards to “purchase” objects
• Analyze the mathematical thinking in children’s errors
• Provide games with dice and dominoes so that children can practice recognizing the number of items in a small set without counting
• Find math in the body, and play finger math; for example, hold up three fingers on one hand and ask children how many fingers are folded down

6-year-olds – See this age across all domains Early elementary

What educators might observe

• Understands that 10 is always 10, whether it is made by adding 6+4 or 7+3
• Starts counting with numbers other than one (e.g., asked to count from four to seven, counts four, five, six, seven)
• Answers questions about quantity such as, “How many more?” “How many fewer?” by counting up or down (e.g., when asked how many is three more than six? The child responds, “Six, seven [puts up a finger], eight [puts up another finger], nine [puts up a third finger])
• Understands place value; understands value of a digit according to the place of the digit within a number
• Makes whole objects from parts when counting (Given three whole plastic eggs and four plastic egg halves, knows they have five whole eggs)

Ways educators might support the child's development

• Create a number line adding one number each day for the whole year, and use it to practice counting by ones, twos, fives, and tens
• Offer structures like a 100’s chart or number line sections for organizing number systems
• Play games in which children roll a dice or spin a spinner and move a piece along a path
• Provide strong context for solving problems with numbers (With 23 children in the class, does everyone have a snack if you have 18 snacks? How many more we need or how many extra do we have?)

7-year-olds – See this age across all domains Early elementary

What educators might observe

• Realizes that the number is unchanged, even when the arrangement looks different (e.g., when counters are spread out, says that there are the same number of counters as when they were together)
• Understands the reversibility of operations (e.g., subtraction is the reverse of addition)
• Uses groups, skip counting, and place value to quickly identify sets shown quickly (“I saw three sets of ten and three sets of two, so the answer is 36.”)
• Uses a mental number line to compare numbers
• Counts forward and backward by ones and using skip counting
• Solves all types of single digit addition and subtraction problems, with flexible strategies and known combinations

Ways educators might support the child's development

• Play more games on a number line (If you start at 12, how many to get to 15? How do you get to 100 from 64?)
• Keep locating math in the body; ask questions like how many fingers in the class?
• Provide base 10 materials to model numbers
• Play “I’m Thinking of a Number” in which children seek clues of what numbers are smaller or larger than the one in mind

8-year-olds – See this age across all domains Early elementary

What educators might observe

• Uses groups, multiplication, and place value to visually recognize sets shown briefly (“I saw groups of 10s and twos, so I thought six tens is 60 and four twos is eight, so 68.”)
• Rounds numbers to the nearest 10 or
• Builds skills to multiply and divide up to 10 × 10 accurately
• Solves word (story) problems using addition, subtraction, multiplication and division

Ways educators might support the child's development

• Engage children in a cooking activity that calls for ingredients in ½, ¼, ¾, or ¹∕₃ measures
• Ask children to write word problems that fit number sentences for their classmates to solve
• Practice addition, subtraction, multiplication, and division skills using Jeopardy-type games

3. Patterning

Child develops the ability to identify, describe, extend, and create patterns.

0–9 months – See this age across all domains Infants

What educators might observe

• Associates objects and actions with their daily rhythm (e.g., reaches for favorite blanket when tired)
• Begins to show understanding of what comes next (e.g., burping after bottle, holding legs up for diapering)

Ways educators might support the child's development

• Create and maintain predictable routines for the child’s day, including feeding, resting, bathing, and playing
• Rock and sway the child in rhythmic movements
• Use song to draw the child’s attention to the rhythm of the day (e.g. songs that include such phrases as “good morning,” “time for rest,” “time to say goodbye, see you tomorrow”)
• Rock, sway, swaddle, sing, and talk to the child with a flow and inflection that is repetitive and predictable

8–16 months – See this age across all domains Infants

What educators might observe

• Hands object back and forth to educator
• Demonstrates understanding of what comes next in their daily routines (e.g., goes to get shoes after breakfast because the group always goes outside at this time)

Ways educators might support the child's development

• Talk to families about the rhythms of their caregiving routines, in order to reaffirm children’s sense of what comes next
• Play back-and-forth games with children
  • Rolling balls
  • Swinging
  • Handing objects back and forth
• Use vocabulary related to patterns: “my turn” and “your turn”

15–24 months – See this age across all domains Toddlers

What educators might observe

• Anticipates and follows familiar sequences of events (e.g., washes hands, sits at the lunch table)

Ways educators might support the child's development

• Read books that involve a simple sequence of events encompassing breakfast, lunch, dinner, or morning, noon and night, such as The Big Red Barn , by Margaret Wise Brown
• Sing repetitive songs, read repetitive stories, and recite nursery rhymes with child
  • I Went Walking , by Sue Williams
  • “The Wheels on the Bus”
  • “Where is Thumbkin?”
  • “Los Pollitos Dicen”

24–36 months – See this age across all domains Toddlers

What educators might observe

• Calls a striped shirt with no repeating unit a “pattern”
• Copies simple repeating patterns (e.g., if the educator squats then stands repeatedly, the child continues this motion)

Ways educators might support the child's development

• Look for patterns in the natural and built environment with the child
• Encourage the child to help set the table at mealtimes
• Engage children in cooking activities where patterns are reinforced (e.g., when taking turns mixing, chant, “Stir, stir, stir, pass! Stir, stir, stir, pass!)

3-year-olds – See this age across all domains Preschool

What educators might observe

• Recognizes patterns in their environment (e.g., looks at a striped scarf and says, “It’s a pattern.”)
• Plays with patterns in language (e.g., sings, “La di dee, la dee da, la dee di.”)

Ways educators might support the child's development

• Create simple patterns with music; play the drums and dance with children
• Encourage children to point out patterns in the environment
• Engage children in patterns of movement

4-year-olds – See this age across all domains Preschool

What educators might observe

• Describes simple AB patterns (e.g., when the teacher claps then stomps, child names whether to clap or stomp next)
• Extends visual patterns; continues building a line of blocks that an older child has begun (e.g., triangle, triangle, square, triangle, triangle, square)
• Identifies repeating patterns in numbers ( “10, 20, and 30 all end in 0.”)

Ways educators might support the child's development

• Invite children to join you in creating a pattern of music using simple instruments such as a tambourine and a triangle
• Ask children to notice patterns in the world, such as in seasons or daily schedules
• Provide materials such as pattern blocks and color tiles that suggest creating AB patterns
• Use songs and games to teach patterns:
  • Red Light, Green Light
  • Duck, Duck, Goose
  • Head, Shoulders, Knees, and Toes

5-year-olds – See this age across all domains Preschool

What educators might observe

• Creates and identifies simple repeating patterns (e.g., draws a pattern of hearts and stars around the edge of their picture)
• Creates and extends simple growing patterns (e.g., stacks one, then two, then three blocks to make a staircase)
• Explains growing patterns such as the pattern of “plus one” in addition (“If I add one, I get the next number.”)
• Describes a “jump, jump, clap” movement as two of something then one of something
• Pays attention to the linguistic patterns in the names of numbers, “Four, forty, and four hundred all sound like four!”

Ways educators might support the child's development

• Provide materials such as wooden cubes to build a staircase to model a “plus one” pattern
• Create ABC patterns together using clapping, tapping, and patting on the body; ask children to follow your pattern and then allow them to lead, with you following their pattern
• Sing songs with patterns, such as “Everyone Comes from a Different Place”

6-year-olds – See this age across all domains Early elementary

What educators might observe

• Identifies the smallest unit of a pattern
• Skip counts by tens, fives, and twos
• Explains the rule for a number pattern. For example, 5, 10, 15, 20 is the “plus five” number pattern
• Looks for and explains patterns in a number chart
• Understands the commutative principle of addition (2+3 = 5, 3+2 = 5)

Ways educators might support the child's development

• Continue to notice patterns in the world on numbered streets and avenues or windows on buildings
• Model addition with materials to ground math ideas in concrete experience; use two colors of tiles to show the commutative property of addition (two green and three red is five tiles; three green and two red is still five tiles)
• Invite children to make patterns while stringing with small beads or weaving

7-year-olds – See this age across all domains Early elementary

What educators might observe

• Skip counts by hundreds, tens, fives, twos
• Identifies the rule needed to extend a pattern or identify a missing number in a pattern (2, 5, 8, 11, 14, 17)
• Tells time to the nearest five minutes on different types of clocks

Ways educators might support the child's development

• Use materials such as pattern blocks to build growth patterns and describe them (“One hexagon has six sides. How many sides on two hexagons? On three hexagons?”)
• Invite children to observe, copy, and create patterns that grow; for example, make a square out of four cubes, make the square grow to nine cubes, then 16, and describe the pattern with numbers

8-year-olds – See this age across all domains Early elementary

What educators might observe

• Skip counts by hundreds, tens, sixes, fives, fours, and twos
• Is able to detect an error in a number pattern
• Explains mathematical patterns using the properties of operations
• Generalizes the properties of multiplication: (a X 1 = a) (a X b = bXa)

Ways educators might support the child's development

• Create AABBA patterns for classmates to complete and/or find the errors
• Practice looking at an analog clock, describing the number correspondences
• Give children a sense of time (Time sitting in silence for a minute, then do something repetitive such as snapping fingers or drawing stars for a minute, two minutes, or five minutes.)

4. Spatial Sense and Geometry

Child understands how objects, points, lines, and shapes fit in space.

0–9 months – See this age across all domains Infants

What educators might observe

• Looks at own hands and feet as they move through space
• Watches a ball rolling away after accidently knocking it
• Observes a ball bounce up and down
• Uses vision and hearing to track the path of someone walking by

Ways educators might support the child's development

• Provide comfortable, safe space for the child to move freely on the floor
• Provide materials of various sizes and shapes for the child to explore, such as different types of fabrics, silicone muffin tins, ice trays, or metal jar rims
• Present collections of balls
• Use vocabulary related to spatial awareness (e.g, “in,” “on,” “under,” “up,” “down,” and “to”)

8–16 months – See this age across all domains Infants

What educators might observe

• Attempts to roll body over
• Puts smaller object inside larger one, such as placing small toy in a bucket
• Uses trial and error to play with objects that can fit inside openings (e.g., tries to put different sized balls into the top of a large jug)
• Repeatedly puts things in and takes them out (e.g., sticks a peg in a hole and pulls it out again)
• Takes rings off a stacking ring and then puts one or two back on
• Stacks blocks on each other, but may put bigger block on smaller one or try to balance a square on a triangle
• Gets in and out of things (e.g., climbs into a large laundry basket and then climbs back out)

Ways educators might support the child's development

• Encourage pointing at objects, and verbally acknowledge the item that is being pointed to
• Provide materials in the learning environment that support the development of spatial sense
  • Shape sorter
  • Nesting cups
  • Ring stackers
  • Simple knob puzzles
• Provide collections of objects that are the same shape
  • A collection of cubes, including boxes and blocks
  • A collection of circles, including rings, lids, and round pieces of paper

15–24 months – See this age across all domains Toddlers

What educators might observe

• Rolls ball back and forth with educator
• Puts together a knob puzzle with two or three separate pieces
• Uses trial and error to place a group of nesting objects, such as boxes of different sizes, inside one another
• Makes a line of blocks next to one another
• Turns a book right side up after looking at the pictures and realizing it is upside down

Ways educators might support the child's development

• Encourage whole body movement
  • Roll in the grass or on the rug
  • Crawling, walking, and running over distance
  • Kicking, throwing, and rolling balls
  • Crawling through tunnels
• Name shapes in the environment
• Take children on community walks along different routes and discuss the landmarks you see; ask children to point to different landmarks at various points along the path
• Provide various size and shaped containers that children can fill with water, sand, or play dough

24–36 months – See this age across all domains Toddlers

What educators might observe

• Matches shapes with similar sizes and orientations
• Completes three or four piece puzzles
• Stacks rings on a post with the biggest on the bottom and the smallest on the top
• Understands words related to position (e.g., “Please put the basket on the table” or “Please get under the covers.”)
• Understands the words “longer,” “shorter,” “big,” and “little”
• Places blocks on one another to make a stack, lining up the edges

Ways educators might support the child's development

• Outline shapes on the floor using string or tape, and encourage the children to go inside
• Provide different sized boxes, wagons, and wheelbarrows that the children can climb in and out of and can use to move objects or other children
• Talk about the shapes of blocks with children; compare the blocks with one another
• Emphasize words describing where objects are in relation to one another (“beside” and “between”)
• Help the child to find themselves in space (“Where is your pinky finger? Where is your elbow?”)

3-year-olds – See this age across all domains Preschool

What educators might observe

• Uses words to indicate direction and position, but not always accurately
• Builds vertical and horizontal components within a block building
• Identifies and names circles and squares
• Calls two shapes the same, if they have similar parts but are not identical (e.g., when both shapes have pointy parts)
• Plays with combining shapes and pulling them apart

Ways educators might support the child's development

• Set up simple obstacle courses with children such as hopscotch, hopping over a hoop, jumping up and down, or twirling with a ribbon, use positional words such as “over,” “under” and “through” as children move through the obstacle course
• Tape shapes on the ground, and ask children to do movements as they go around them
• Name and identify shapes children make while drawing and writing
• Invite children to reach into “feely boxes” and pull out a shape that matches the one the educator is holding
• Identify shapes and angles in everyday life, such as a circles on the tops of cup, rectangular pieces of paper, the angle made when the scissors open, or the angle at the edge of the table

4-year-olds – See this age across all domains Preschool

What educators might observe

• Uses blocks to build in multiple directions, with multiple points of contact between components
• Builds arches, enclosures, corners, and crosses
• Follows a model to create simple shapes out of lines (e.g., organizes sticks to make a triangle or rectangle)
• Slides and turns pieces to make them fit in a simple puzzle
• Calls a shape a rectangle because it “looks like a door,” rather than naming sides and angles
• Calls a variety of open or closed pointy shapes “triangles”
• Experiments with combining shapes to make a new shape (e.g., in the block area, accidently puts two triangles together to make a square, and then repeats this action intentionally)

Ways educators might support the child's development

• Include materials in the classroom environment that develop geometric concepts
  • Blocks
  • Jigsaw puzzles
  • Magnetic shapes
  • Shape puzzles
  • Pattern blocks
  • Unit blocks
  • Legos
• Go on community walks along different routes and discuss which route was longer or shorter and why
• Describe the location of objects the child is trying to find, rather than pointing to them (e.g., “The tape is beside the construction paper.”)
• Present many examples of squares and rectangles, varying orientation and size; include squares as examples of rectangles (If children say, “That’s a square,” reply, “It is a square, which is a special type of rectangle.”

5-year-olds – See this age across all domains Preschool

What educators might observe

• Correctly uses position words such as “beside,” “under,” and “inside” to describe objects
• Slides, flips and turns pieces to make them fit in a puzzle, but does not always move them in the right direction at first
• Recognizes that there are other shapes that are not common (e.g., rhombus and hexagon)
• Spontaneously creates symmetrical buildings in the block area
• Builds complex bridges with multiple arches, ramps, and stairs at the ends
• Intentionally puts pattern block shapes together to make another shape for a picture

Ways educators might support the child's development

• Invite children to draw maps of routes, illustrating what landmarks will be passed or seen on different routes
• Draw maps of the playground and use them to go on a scavenger hunt
• Challenge the child to cover hexagon pattern blocks with other pattern blocks and see what works
• Introduce vocabulary such as “sides,” “angles,” and “parallel lines”
• Identify and describe the symmetry children spontaneously create in their art work
• Hunt for shapes outside and around the school; take photographs of them and print them out as shape books for the classroom

6-year-olds – See this age across all domains Early elementary

What educators might observe

• Uses maps with picture clues to determine paths and find objects
• Discriminates and names most common shapes, including rhombuses, without making mistakes such as calling ovals circles
• Moves one shape on top of another to check if it fits exactly
• Divides circles and rectangles into halves or fourths to develop understanding of part/whole
• Uses blocks to make complex towers or other structures involving multiple levels with ceilings

Ways educators might support the child's development

• Look at maps with children and encourages them to describe
  • Direction—which way?
  • Distance—how far?
  • Location—where?
  • Identification—what objects?
  • Coordinates—what are they?
• Encourage children to make representations out of pattern blocks (for example, a ship with a smoke stack and rhombus-shaped smoke); they may trace their pattern block images to create pattern block puzzles for one another
• Read books by Rebecca Emberly and others that show how to represent objects with different shapes

7-year-olds – See this age across all domains Early elementary

What educators might observe

• Pays attention to the spatial relationships of all the parts of complex figures
• Folds paper squares to make two triangles, folds them again to make more triangles, and describes the process
• Uses simple coordinates to locate a place on a map or a move on a chessboard
• Systematically checks that two shapes are the same by comparing all attributes
• Recognizes and describes situations in which angle knowledge is relevant (e.g., “I need to change the angle to make the car go faster down this ramp.”)

Ways educators might support the child's development

• Invite children to use materials such as clay, straw, and pipe cleaners to construct shapes
• Encourage children to describe why a figure belongs or does not belong to a shape category
• Show children how to “test” right angles on rectangles with a “right-angle checker,” (thumb and index finger held apart at 90°, or the corner of a piece of paper)
• Solve construction problems with blocks
  • Build a bridge from point A to point B
  • Construct the tallest tower
  • Attempt to build buildings observed in the neighborhood

8-year-olds – See this age across all domains Early elementary

What educators might observe

• Uses maps to follow routes, even when they don’t have pictures or the distances are not accurate
• Mentally moves shapes and says what they need to do to make them fit into a puzzle
• Names the class of shapes explicitly based on properties, including angle measure
• Sorts shapes hierarchically, based on properties

Ways educators might support the child's development

• Create realistic and abstract art using shapes, lines, and understanding of orientation of those things on paper
• Observe the use of shapes in artwork from different cultures, drawing attention to the cultures of the children in the class
• Describe the properties of a shape and invite the children to name that shape
• Place shapes in a category, and ask children to name the reason for the classification