Child recognizes and develops the ability to explain how material objects change and how they remain stable.
What educators might observe
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May be anxious about death
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Discusses the physical changes that accompany age
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Can imagine their adult family members growing old
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Compares the life cycles of different organisms (e.g., says that people live longer than dogs)
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Becomes conscious of time, but is not yet able to tell time on the clock (“Is it three o’clock? My grandma is coming to get me.”)
Ways educators might support the child's development
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Include books in the learning environment that help children understand death
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And So It Goes , by Paloma Valdivia
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Goodbye Mog , by Judith Kerr
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The Goodbye Book , by Todd Parr
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Ida Always , by Caron Levis and Charles Santoso;
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The Dead Bird , by Margaret Wise Brown
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Read non-fiction books about the life cycles of familiar animals (such as cats, dogs, and other animals that children see in their communities); explore rituals and routines for having pets and for pet deaths
What educators might observe
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Discusses what happens to the body after death
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Understands the patterns of the days of the week and the months of the year
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Asks questions about the properties of materials (e.g.,”What is the air made out of?”)
Ways educators might support the child's development
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Talk to family members about their beliefs about death and how they would like to explain death to the child
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Talk to children about the inevitability of the life cycle, and how it applies to everything that is alive
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Observe food as it turns to compost; discuss how it changes
What educators might observe
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Start to understand how ecosystems can change quickly (a storm) or slowly (a pond becoming a meadow)
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Combines and separates mixtures in sophisticated ways (e.g., uses a series of strainers to separate out the pebbles and silt in river water)
Ways educators might support the child's development
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Create opportunities for children to explore stability and change in local contexts
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Visit a local watershed to study water quality
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Look at photos of the local area in years past in comparison to today
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Ask about characters in chapter books (“How do they change over the course of the story? Why do they change? What is the same about them throughout?”)
Child uses symbolic thought to represent.
What educators might observe
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Assigns roles and acts out scenes from the economy (e.g., child dramatizes a farmer’s market and has peers work at different stalls and be customers)
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Uses art to reflect on their experiences (e.g., uses musical instruments to make a song about an experience they had)
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Shares stories and symbols from their own families and cultures
Ways educators might support the child's development
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Ask families about cultural or religious prohibitions to representation; create a welcoming and inclusive learning environment
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Invite children to use collage materials to make dollhouses out of cardboard boxes and make characters to inhabit the dollhouses
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Sing songs with space for children’s contributions and allow them to write new verses
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Create visual art while listening to different types of music
What educators might observe
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Represents specific details from architecture in their constructions
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Plans artistic representation with peers (e.g., child writes a story with friends and then makes puppets and scenery to dramatize the story)
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Experiments with different forms of representation they have learned about through media and trips to cultural institutions (e.g., child attends a field trip to see Balinese shadow puppets and then experiments with creating shadow puppets themselves)
Ways educators might support the child's development
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Invite families to share modes of artistic expression from their family, community, or culture
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Make paper dolls of historical figures; use cloth and scissors to clothe the dolls in historical costumes
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Act out stories that the children write
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Sing songs, such as:
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“I Had a Rooster”
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“The Cat Came Back”
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“The Foolish Frog”
What educators might observe
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Uses research to add realistic details to their representations (e.g., researches costumes from the past to create a dramatization of the life of a historical figure)
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Describes systems for symbolic thinking from the past, such as hieroglyphs
Ways educators might support the child's development
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Notice the particular forms of representation that are motivating for different children
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Encourage children to use art to represent their feelings
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Invite families to join children in creating
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Welcome families to celebrate children’s creations
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Challenge children to create models of villages, replicating complicated architectural details
Child develops the ability to store, retrieve, and share information about past experiences.
What educators might observe
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Begins to understand that history describes the collective memories of people and events from other times and places
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Asks questions of elders about how life was different in the past
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Shares significant events from their own family history with peers
Ways educators might support the child's development
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Include books in the learning environment that tell stories from history
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Histories of the children’s national and cultural groups (e.g., history of Taíno people)
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Biographies (e.g., Obama, Lincoln)
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Stories of historical events (e.g., The March on Washington)
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Descriptions of life at different periods of history (e.g., prehistoric man)
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Invite elders to the classroom to talk about their memories
What educators might observe
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Groups items they have to remember into easy-to-remember categories (e.g., animals, foods, shapes)
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Begins to identify which events happened long ago and which happened in the more recent past
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Starts to make connections between how history has shaped our present experience (e.g., “My friends and I can swim at the same pool because of Martin Luther King, Jr.”)
Ways educators might support the child's development
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Research the histories of the national and cultural groups of the children in the class, and be prepared to weave examples from these groups into discussions of history
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Invite each child to contribute to a timeline of a time period that includes now
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Sing songs that touch on history
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“If I Had a Hammer”
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“If You Meet Me at the Back of the Bus”
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“Fillimiooriay”
What educators might observe
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Intentionally selects and uses organizational strategies to remember information
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Uses language to describe chronology, such as “decade” and “century”
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Uses resources such as books and websites to organize information into a chronological sequence
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Connects their family history to broad historical events
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Identifies changes over time in their community
Ways educators might support the child's development
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Use self-talk to describe strategies for organizing information to make it easier to retrieve
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Ask children to write from perspectives of figures they have read and learned about (What was it like to be a knight’s horse, for example?)
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Welcome children to link their family histories to larger discussions of historical events
Child becomes a scientific thinker by manipulating objects, asking questions, making observations and predictions, and developing generalizations.
What educators might observe
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Uses non-fiction books to find answers to questions
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Develops hypotheses (e.g., If a hermit crab prefers a particular shell, the child says, “I think it’s because he has more room to grow in there.”)
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Describes a strategy for finding out if their hypothesis is true
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Uses prior knowledge to make generalizations about what might happen (e.g., The child says, “Fruits grow on trees, so I think if I plant this orange seed, a tree will grow.”)
Ways educators might support the child's development
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Use photography to gather observations over time; for example, observe a tree through several seasons or watch a pumpkin over the weeks around harvest, and ask children to come up with theories about why changes occur
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Ask children to do research by looking in books for answers to their questions
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Question the child’s reasoning to explore their thought process, but without concern for correctness (“What makes you think that? How did you figure that out?”)
What educators might observe
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Seeks scientific solutions that are rational and consistent and that work in similar situations
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Plans simple experiments (e.g., child builds spinning tops and hypothesizes that a wide top will spin for a longer period of time than a flat one)
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Observes changes in living organisms and the natural environment over time (e.g., independently checks corn plants every morning to see how they are growing)
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Works with peers to collaboratively plan experiments
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Compares their observations to those of their peers
Ways educators might support the child's development
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Provide sketchbooks to record natural phenomena, and make predictions; for example, ask children to draw a seed as they plant it, then when it has sprouted, and as a plant growing over time
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Invite children to document their observations in a variety of ways (charts, notes, or graphs, for example)
What educators might observe
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Compares their observations with observations in books and websites
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Poses specific questions and then seeks to answer them through research, experiments, and observations (e.g., child wonders how to make a brick and then reads about the topic and mixes various combinations of materials to see which make the best bricks)
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Identifies and interviews experts to find out the answers to their questions
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Reviews data recorded in tables over several days to draw conclusions
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Starts to understand observations as components of systems (e.g., solar system, digestive system) and identifies individual parts and how they work together
Ways educators might support the child's development
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Invite families to share areas of expertise with the class
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Support children in generating questions for research
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Provide graphic organizers so that children are able to successfully complete a multiday investigation
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Create role models for children
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Visit scientists at work
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Read about scientists who changed history
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Ensure representation of women and members of non-dominant racial, linguistic, and cultural groups
Child understands and explores the causes and effects of actions and events.
What educators might observe
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Believes their own theory about the cause of an event, regardless of the evidence
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Discusses how rules impact people and the environment (e.g., recycling)
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Reflects on how some actions can help others feel better (e.g., cheering up a sad friend by sharing their snack)
Ways educators might support the child's development
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Ask children why the water in a clear or open container left on the heater or windowsill diminishes over a few days
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Plant beans in a plastic bag lined with a wet paper towel; ask why some grow and some do not
What educators might observe
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Designs experiments that will prove their previously held beliefs about causes, rather than objective experiments
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Describes choices people make based on availability of resources (e.g., talks about how lack of food causes migration)
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Asks questions about how things change over time
Ways educators might support the child's development
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Engage in group conversation about children’s theories of causation
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Analyze choices people made in creating the built environment (e.g. ‘Why did engineers choose to build a vertical lift bridge here?”)
What educators might observe
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Demonstrates understanding of how humans have affected the environment and how actions and rules are adopted to protect the environment
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Discussing the purpose of tools (e.g., how windmills produce clean energy)
Ways educators might support the child's development
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Create opportunities for children to see how changing certain factors causes a predictable change in outcome
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Teach children about climate change and engage the class in analyzing and reducing the group’s use of carbon
Child plans and uses hands, tools, and technology to solve problems with materials.
What educators might observe
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Investigates the motion and movement of objects when solving problems with materials (e.g., notices and compares how different balls bounce higher than others)
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Identifies and describes tools made for different purposes
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Uses sophisticated strategies to make their block buildings more stable
Ways educators might support the child's development
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Include tools in the learning environment that children can access for a variety of purposes
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scissors
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staplers
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hole punches
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hammers
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measuring tapes
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hand drills
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Invite children to systematically test the stability of their block buildings by rolling balls at them
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Offer encouragement and guidance (“These problems can be solved! You can figure this out. What if you…?”)
What educators might observe
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Uses a second problem-solving strategy if the first one is unsuccessful
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Pays attention to the relevant part of solving a problem (e.g., examines the attachment of the axles and wheels when the toy car won’t roll)
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Uses logic and reasoning to solve problems with materials (e.g., uses their knowledge of how the physical properties of objects affect their behavior and motion)
Ways educators might support the child's development
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Observe and reflect on children’s processes as they solve problems with materials
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Consider which children are most engaged in engineering: Are girls as engaged as boys? Why or why not?
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Invite children to make complex marble runs, taking into account both the angle and length of the ramps
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Offer objects in the environment as models for children’s problem-solving; for example, show them a hinge on a door, or point out how bricks are stacked in a building
What educators might observe
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Takes more than one variable into account when solving problems with materials (e.g., considers both weight and distance when setting up a balance)
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Plans their actions when encountering a difficult problem with materials
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Systematically builds things and reverses their actions to take things apart
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Identifies tools and simple machines made to solve problems by people long ago or in a different place, and compares those tools and machines to the ones we use today
Ways educators might support the child's development
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Invite families to visit the classroom and share a tool from their culture, nation of origin, or childhood
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Provide opportunities for children to learn problem-solving strategies from one another
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Challenge children to invent objects to solve common classroom or household problems (e.g., a magnetic paper-clip picker-upper)
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Look for texts that show different ways a problem has been solved throughout history (e.g., irrigation)
Child recognizes some similarities and differences between familiar and unfamiliar people, objects, or experiences.
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)
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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.”)
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U ses a repeating unit to measure length (e.g., uses a line of small blocks to measure a book)
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Identifies similarities and differences among the lives of people in different families and communities
Ways educators might support the child's development
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Offer objects for comparison and categorization
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Photos of animals
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Collections of rocks or leaves
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Keys
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Buttons
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Engage children in using categorization for social good; for example, categorize recycling materials
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Provide unit blocks and rulers for measurement
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Create activities to measure distance (e.g., hold a paper airplane contest, then chart the results in a graph)
What educators might observe
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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)
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Chooses a strategy for comparison (e.g., uses graphs to compare their observations of the natural world)
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Understands the need for a standard unit when measuring length
Ways educators might support the child's development
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Offer formats distinctly for comparison and categorization, such as Venn diagrams and three-column charts
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Offer vocabulary such as “traits,” “similar,” and “category”
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Use “greater than” and “less than” to compare quantity
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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
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)
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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
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Invite families to visit the classroom to talk about their childhoods; use Venn diagrams to compare and contrast
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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
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Visit a natural history museum or botanical garden and talk about the categories the curators use
Child understands and explores numbers and quantity.
What educators might observe
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Understands that 10 is always 10, whether it is made by adding 6+4 or 7+3
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Starts counting with numbers other than one (e.g., asked to count from four to seven, counts four, five, six, seven)
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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])
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Understands place value; understands value of a digit according to the place of the digit within a number
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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
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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
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Offer structures like a 100’s chart or number line sections for organizing number systems
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Play games in which children roll a dice or spin a spinner and move a piece along a path
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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?)
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)
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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
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Counts forward and backward by ones and using skip counting
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Solves all types of single digit addition and subtraction problems, with flexible strategies and known combinations
Ways educators might support the child's development
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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?)
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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
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
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Builds skills to multiply and divide up to 10 × 10 accurately
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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
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Ask children to write word problems that fit number sentences for their classmates to solve
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Practice addition, subtraction, multiplication, and division skills using Jeopardy-type games
Child develops the ability to identify, describe, extend, and create patterns.
What educators might observe
-
Identifies the smallest unit of a pattern
-
Skip counts by tens, fives, and twos
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Explains the rule for a number pattern. For example, 5, 10, 15, 20 is the “plus five” number pattern
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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
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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
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
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.)
Child understands how objects, points, lines, and shapes fit in space.
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?
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Distance—how far?
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Location—where?
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Identification—what objects?
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Coordinates—what are they?
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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
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
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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
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Construct the tallest tower
-
Attempt to build buildings observed in the neighborhood
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
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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
