4.5 Demonstrating literacy and mathematics behaviours
For more information about this frame, see Chapter 2.3, "Thinking about demonstrating literacy and mathematics behaviours".
For a complete list of the overall expectations in the Kindergarten program with their related specific expectations, see the appendix to this document.
Children's play is representational and provides the foundation for literacy and numeracy. (Council of Ministers of Education, Canada, Statement on Play-Based Learning, 2012, p. 14)
Play is how children learn. What we want to do in our play-based approach to learning is fire a child's imagination. Fire a child's curiosity.... Children learn by becoming fascinated, and the more fascinated they are, ... [the] more they will be driven to learn how to read... Their reading will be driven by their desire to learn about what they are captivated by. (Dr. Stuart Shanker, speaking in the video "Self-Regulation")
Young children engage in significant mathematical thinking and reasoning in their play... Combining free play with intentional teaching, and promoting play with mathematical objects and mathematical ideas, is pedagogically powerful. (D.H. Clements & J. Sarama, "The Importance of the Early Years", in R.E. Slavin [Ed.], Science, technology & mathematics [STEM], 2014, p. 5)
Overall expectations
As children progress through the Kindergarten program, they:
1. communicate with others in a variety of ways, for a variety of purposes, and in a variety of contexts
9. demonstrate literacy behaviours that enable beginning readers to make sense of a variety of texts
10. demonstrate literacy behaviours that enable beginning writers to communicate with others
11. demonstrate an understanding and critical awareness of a variety of written materials that are read by and with their educators
12. demonstrate an understanding and critical awareness of media texts
14. demonstrate an awareness of the natural and built environment through hands-on investigations, observations, questions, and representations of their findings
15. demonstrate an understanding of numbers, using concrete materials to explore and investigate counting, quantity, and number relationships
16. measure, using non-standard units of the same size, and compare objects, materials, and spaces in terms of their length, mass, capacity, area, and temperature, and explore ways of measuring the passage of time, through inquiry and play-based learning
17. describe, sort, classify, build, and compare two-dimensional shapes and three-dimensional figures, and describe the location and movement of objects through investigation
18. recognize, explore, describe, and compare patterns, and extend, translate, and create them, using the core of a pattern and predicting what comes next
19. collect, organize, display, and interpret data to solve problems and to communicate information, and explore the concept of probability in everyday contexts
20. apply the mathematical processes to support the development of mathematical thinking, to demonstrate understanding, and to communicate thinking and learning in mathematics, while engaged in play-based learning and in other contexts
21. express their responses to a variety of forms of drama, dance, music, and visual arts from various cultures
22. communicate their thoughts and feelings, and their theories and ideas, through various art forms
All children are viewed as competent, curious, capable of complex thinking, and rich in potential and experience.
Expectation charts
OE1
As children progress through the Kindergarten program, they:
communicate with others in a variety of ways, for a variety of purposes, and in a variety of contexts
Conceptual understandings
- Communication has the power to influence and encourage change.
- We learn about the world, others, and ourselves through listening.
- The ways in which people communicate are diverse and are influenced by their background experiences.
- Communication includes non-verbal behaviours and gesturing. We can experiment with words to achieve intended effects.
- Knowledge is socially constructed – created by people learning, working, and investigating together – and can be shared.
- Oral language is the basis for literacy, thinking, and relating in all languages.
See the Professional Learning Conversation following the chart.
Inside the classroom: Reflections on practice
Example 1: The Old Lady Who Swallowed a Fly
Setting the context: The children were gathered with the educators, who were reading aloud the big book I Know an Old Lady Who Swallowed a Fly. During the course of the reading, one of the children (A), referring to the old lady, said:
Child A: "She is really smart."
Educator's thoughts in the moment: I wonder what he means. That doesn't make sense.
Child B: "No, she is not smart, she is dumb; she is eating animals."
Educator's thoughts in the moment: A is younger and looks up to B. In fact B often corrects me. So now what? I want to rescue A and say something like, "A, why don't you ask a friend for help?" I feel worried for A because I don't want his feelings to get hurt. Should I say something about using the word "dumb"?
Rethink
"I decided to do something different. I waited a very brief moment and then said, 'Why are you thinking the old lady in the story is smart?'"
Child A: "Because she knows exactly which animal to eat and the order. She knows which animal will eat the one from before."
Child B: "Hey, yeah, she is smart."
Educator's thoughts upon reflection: This was so interesting. I was so concerned about protecting child A, but when I paused and gave child A a chance to explain his thinking, even though I was perplexed by what he said, it became clear that he'd been able to infer an important meaning from the text. Also he took a risk by disagreeing with child B, whom he looks up to. I am not critical about the fact that my instinct was to rescue child A, but I learned that sometimes waiting and probing a child's thinking leads to such rich learning. Waiting and asking a prompting question helped us all to learn from child A.
Strategies for supporting communication
Educators can:
- acknowledge what children are doing as a way to sustain their interest (e.g., "I see that you lined up your cars in a row");
- support children as they work through a process (e.g., "I see you found a way to get the car all the way down the ramp");
- reaffirm vocabulary that children use (e.g., "You're right. The blue car is faster than the red car");
- introduce new vocabulary informally (e.g., "Look at how far the blue car travelled");
- ask for clarification, elaboration, or justification (e.g., "What do you think will happen if you change the ramp?");
- challenge children's thinking by posing questions (e.g., "How did you know?" "Why did you decide...?");
- prompt children to retell in different ways, such as by labelling, identifying, describing, and/or summarizing (e.g., "Tell me how you made the ramp higher"; "Tell me why you...");
- guide children to make connections by comparing, contrasting, and/or applying (e.g., "That's the same as..."; "What does this make you think of?");
- lead children to reflect on experiences and encourage questioning, inferring, and further wonderings (e.g., "I wonder what would happen if...?"; "I wonder why...?"; "I wonder what you could try next").
Example 2: Ice fishing
Educators may need to re-examine their assumptions about how specific strategies promote intended learning.
Setting the context: A small group of children were discussing their expertise with ice fishing. The educators wanted to establish a space in the classroom where the children could retell and dramatize their ice-fishing experiences, so they provided materials for the children at the water table.
Educator's thoughts in the moment: How can we work some literacy into the children's play at the water table? ... Let's add letters. The children can fish for letters.
The children's experience: When asked what they thought they were learning, the children said they were learning how to fish.
Consolidating and considering: There was a disconnect between what the children thought they were learning and what the educators thought the children were learning. When learning is buried in an activity – in this case, using print out of context by fishing for letters – it may confuse the children.
Questions for reflection: What are the children learning?
- What do we think the children are learning when we introduce this new game?
- What might the children think they are learning?
- What other literacy opportunities might have been possible in the scenario of Example 2?
Video title: "Literacy Through the Day" – see the clips "Literacy as a whole class community – Creating a community of thinkers and readers: What strategies are the children thinking about and demonstrating?" and "Strategies to support oral language development".
| Specific expectations As children progress through the Kindergarten program, they: |
Ways in which children might demonstrate their learning | The educators' intentional interactions |
|---|---|---|
| 1.1 explore sounds, rhythms, and language structures, with guidance and on their own |
Saying "That rhymes with my name." "That is the word 'sat'. I know because I know the word 'cat'." "My name has three [syllables]." "That word starts just like my name." Doing A small group of children make their names with magnetic letters. Representing A small group of children chant nonsense words to rhyme with their names. A small group of children draw lines and representations of musical notes to show the sounds of their names. (The examples also show: literacy behaviours – awareness of concepts of print, the alphabetic principle, the fact that letters make sounds and the sounds have meaning [phonological and phonemic awareness]; reading and writing behaviours – matching letters and sounds and using that knowledge to write.) |
Responding The educators create a learning area using a filing cabinet and a table where children can work with magnetic letters. They place two sets of the children's name cards at the table so that they can observe the children's thinking about matching their names and what the children notice about the letters in their names and the names of their friends. The educators then document what the children are saying and doing so they can support the children's writing. Challenging An educator observes two children working with the name cards and magnetic letters. She places a class list on the table so that the children can work with the names of other children in the class. Extending At the sand table/bin, an educator works with a small group of children who are making signs for the city they have created. The educator models how to stretch out the words when saying them aloud, to enable the children to hear the sounds and match them to the letters that make the sounds. The educator then engages the children in interactive writing, as appropriate to the level of support they need. |
| 1.2 listen and respond to others, both verbally and non-verbally (e.g., using the arts, using signs, using gestures and body language), for a variety of purposes (e.g., to exchange ideas, express feelings, offer opinions) and in a variety of contexts (e.g., after read-alouds and shared reading or writing experiences; while solving a class math problem; in imaginary or exploratory play; in the learning areas; while engaged in games and outdoor play; while making scientific observations of plants and animals outdoors) |
Saying (At the sand table): "What are you doing?" "I'm building a road for my city." "It's too curvy. You should make it straighter." (After a class read-aloud): "That was a pretend story. Cats can't fly!" (In the gym or outside in the playground): "Can you do this?" (The child hops on one foot.) Doing (A small group of children are measuring their bean plants): "I think mine grew the most. It used to be four cubes tall and now it is seven cubes tall. Did yours grow?" "Mine hardly grew at all – it is only three cubes." (The examples also show: mathematics behaviours – recognizing quantities, including differences in quantities, and understanding the concept that objects can be measured.) Representing |
Responding The educators plan to observe children, giving them more time to communicate their thinking, both verbally and non-verbally. They use strategies such as waiting for the child to speak first while silently counting to a certain number before saying anything (wait time). They communicate to the children that they are trying to listen more and "listen differently", and to give the children more time to communicate their thinking. Challenging The educators begin to observe children in all contexts, with a focus on watching their non-verbal communication. They document the multiple ways that children communicate. Extending The evidence from their documentation about how children communicate is the educators' assessment for learning, which informs how they respond. The documentation is shared with the children as a form of assessment as learning to support the children's metacognition. |
| 1.3 use and interpret gestures, tone of voice, and other non-verbal means to communicate and respond (e.g., respond to non-verbal cues from the educator; vary tone of voice when dramatizing; name feelings and recognize how someone else might be feeling) 1.4 sustain interactions in different contexts (e.g., with materials, with other children, with adults) |
Saying "He was really BIG." (The child uses a loud voice when reading the word "big".) "She looks really angry in the picture. Look at her eyes." "First I put on my snow pants, and then I put on my boots." Doing Several children use non-verbal communication to support their thinking or to represent their thinking – for example, using their hands to outline the structure of an item they are building, counting or making a numeral in the air, putting their head down on a table to get a closer look. See "Kindergarten Matters: Re-imagining Literacy and Mathematics Throughout the Day" –the clip "Making Connections to Build Working Theories". A child shows another child how to do the tree pose in yoga, explaining how to place her legs and arms. Representing A child draws a picture of herself with a big smile on her face to show her feelings when her family gets a new kitten for a pet. Other children begin to draw, write, and talk about their pets or pets they would like to own. The educators talk with the children about how authors influence and inspire others to write in a particular writing form. Over time, the children and educators think about and document different purposes for writing. |
Responding The educators observe and create written records of the non-verbal communication used by the children.
Challenging |
| 1.5 use language (verbal and non-verbal communication) in various contexts to connect new experiences with what they already know (e.g., contribute ideas during shared or interactive writing; contribute to conversations in learning areas; respond to educator prompts) |
Saying "I made a sandcastle like this at the beach." "I built a snowman with my sister like the one in the story." (The examples also show: literacy behaviour – making connections.) "I noticed that if I hold the tube up higher the water moves faster." (The example also shows: literacy behaviour – drawing conclusions.) Doing A child changes the height of the tube after several attempts to make the water move faster. Representing A child adds a letter to a familiar word during small-group interactive writing. A small group of children represent their experiences with the roads in their community and the role of the police officer, construction workers, and a local restaurant. Video title: "Play-Based Learning" – see the clip "The FDELK team members engage with children in different ways, prompting children to reveal their thinking in role". |
Responding "What do you notice when we add...?" "That is just like…." "You made a connection." The educators negotiate classroom materials with the children, discussing what is already available in different areas of the room and what else the children think they need to help them communicate and represent their thinking and learning. Video title: "Literacy Through the Day" – see the clip "Rethinking the learning environment to support literacy – Co-constructing the learning environment with the children". Challenging An educator works with a child on an interactive writing piece. From previous observations, he knows what letters the child knows, and uses prompts such as, "That starts like..." to help the child connect what he already knows to a new context. See "Kindergarten Matters: Re-imagining Literacy and Mathematics Throughout the Day" – the clips "Communicating Understanding Through Writing"; "Noticing and Naming the Learning"; and "Co-constructed Negotiated Learning". Extending The educators observe that the children are noticing and wondering about rain. They pose the following question: "What do you think we might see after the rain?" They record the children's ideas. The next day it is still raining. To help children connect their previous thinking to the new experience, the educators ask the children, "What do you think we will see today?" and extend the thinking by asking, "What makes you think that?" They record the children's ideas and work with the children to compare their current ideas to their previous responses. |
| 1.6 use language (verbal and non-verbal communication) to communicate their thinking, to reflect, and to solve problems |
Saying "I think we should try it like this." "I kept trying, and then I catched the ball." "I put the big block on the bottom, and then it was stable." "I used the picture, and then I knew the word." Doing A child decides to find all the children in the class who have the letter "S" in their name. He uses the word wall and tells another child his plan. This leads to more children joining the investigation. (The example also shows: literacy behaviour – using tools that writers use.) A child and an educator are co-constructing learning as the child is engaged in inquiry using a balance scale. The child is trying to figure out how to make the scale balance. Video title: "Numeracy Through the Day" – see the clip "Co-constructing learning". Representing During a class sharing time, a small group of children share their solution for joining their structures in the blocks area. |
Responding "I wonder how you knew that." "Were you thinking about...?" "How did you use the picture to figure out that word?" Challenging "How did you figure that out?" "What do you think would happen if...?" "What sound would we expect to hear at the beginning if the word is...?" Extending "What were you thinking about?" "I wonder if there is another way you could solve that problem." |
| 1.7 use specialized vocabulary for a variety of purposes (e.g., terms for things they are building or equipment they are using) |
Saying (In the blocks area): "We put a roof on our house." (At the water table): "I poured the water into a funnel." (In the gym): "Look at how I can balance on only my behind!" Doing After listening to a book about farming, a child creates a farm in the blocks area. "My silo doesn't have any grain in it yet." Representing A child puts together a collage in the visual arts area. "I used 'shiny' objects." A small group of children create a cave for frogs and spray water onto the rocks to demonstrate the waves crashing. Video title: "Play-Based Learning" – see the clip "How do educator teams co-construct learning through play and make learning visible?". |
Responding The educators reorganize the visual arts area. They remove most of the materials in order to have a more "controlled palette", and they add a variety of shiny papers and found objects to support the children's growing understanding of the properties of different materials. They talk with the children about what they notice. Using assessment for learning they document and notice and name how and why the children/artists use specialized vocabulary. The children use comparative language, and the educators notice and name the vocabulary. The children also begin to notice and name with each other. Challenging "I heard you say you put a roof on your house. I observed the 'angle' you used on the roof. (The educator points to the angle while using the word.) 'Angle' is a mathematical word." Extending The educators plan ways to support children's development of vocabulary. One strategy is to model new vocabulary in the context of the children's play in different areas. Video title: "Play-Based Learning" – see the clip "Following children's thinking to respond, extend and challenge". |
| 1.8 ask questions for a variety of purposes (e.g., for direction, for assistance, to innovate on an idea, to obtain information, for clarification, for help in understanding something, out of curiosity about something, to make meaning of a new situation) and in different contexts (e.g., during discussions and conversations with peers and adults; before, during, and after read-aloud and shared reading experiences; while exploring the schoolyard or local park; in small groups, in learning areas) |
Saying "Can you help me do this?" "Why does smoke go up when everything else seems to go down?" "What is the boy going to do now?" "What is this for?" "Can this go together?" "Why did you put that there?" Doing During small-group shared reading, the children ask questions about the book the educators have planned for their reading group. Representing The children are invited to write on sticky notes any questions they have about the empty bird's nest one of the children has brought to class. |
Responding The educators model different types of questions and use think-alouds to make the purpose for each type of question explicit for the children. They make their thinking visible with statements such as: "We use questions for different purposes." "I wonder – where are all the places we ask questions?" Challenging During small-group shared reading, an educator records the children's questions about the book and posts them for the children to revisit. Video title: "Literacy Throughout the Day" – see the clip "Literacy as a whole class community – Creating a community of thinkers and readers: What strategies are the children thinking about and demonstrating?". Extending The educators invite the children to use the names in the name pocket chart or the names on a class graph to think about questions such as: "How does knowing how many children came to class today help us figure out how many children are away?" The educators also document children's demonstration of mathematical behaviours/awareness such as interpreting data, comparing quantities, and thinking about more/less. |
| 1.9 describe personal experiences, using vocabulary and details appropriate to the situation
1.10 |
Saying "I went to visit my cousin on the weekend." "I had a bad cold and a fever, but I am feeling better now." Doing A small group of children describe and show the steps they took to roll a ball all the way down a ramp without the ball falling off the ramp. Representing At the sand table, the children retell the story of "The Gingerbread Man", based on a book they have just heard in a read-aloud. They use props that have been intentionally placed at the sand table by the educator to retell the events they remember from the story. Video title: "Literacy Through the Day" – see the clip "Literacy as a whole class community – Creating a community of thinkers and readers: What strategies are the children thinking about and demonstrating?". |
Responding During a whole-class discussion, the educators model the sequence for retelling. They think together with the children about the idea that audience and purpose are important when we plan to retell something. They also think together with the children about why we retell stories and events, both in school and outside of school. Challenging The educators take digital photographs of the children putting on their winter outdoor clothing. They invite the children to arrange the pictures in proper sequence and they record their observations of the children's sequencing. The educators work with a small group of children who would benefit from interactive writing to add text to the sequenced photos. Extending The educators meet with individual children or small groups of children to think about other things that happen in a particular sequence (e.g., making a cake). They invite the children to record the sequence in some way and to post it in an appropriate place in the classroom (e.g., the class bakery). (Note: The children are selected based on assessment information.) |
| 1.11 demonstrate an awareness that words can rhyme, can begin or end with the same sound, and are composed of phonemes that can be manipulated to create new words |
Saying "That word ends like my name." " 'Play' and 'day' end with the same sound." Doing A small group of children work with magnetic letters, making and breaking apart their names Representing A small group of children write a list of rhyming words on transparencies and project them on the wall. |
Responding An educator works with a small group of children who the team has determined (based on assessment information) need additional support with hearing sounds in words. In conversation with one child's family, the educators learn that the child has had several ear infections in the last couple of years. Together, the educators and the family talk about strategies to help the child both at home and at school. At school, the children use their name cards and sets of magnetic letters to make and break apart their names. The educators send home envelopes with letter tiles and name cards so the families can play the sound games at home. The educators also explain that hearing the sound is only one of the strategies readers use. For example, they can also use the pictures to support their reading. The educators also talk with the children about how hearing and thinking about the sounds is part of what writers/authors do. Challenging The educators work with a small group of children who have demonstrated that they can hear the first sound in a word. The educators support the children's focus on the last sounds in their names. Extending The educators generate rhymes and manipulate sounds (replacing or deleting initial sounds) and words in shared, guided, and independent activities such as singing songs or chants or participating in finger plays. |
Professional learning conversation
Re. OE1: A group of educators discuss the importance of maintaining the child's home language. Their focus is on the role that educators can play in helping families recognize the benefits of maintaining their home language as an integral part of their culture, values, social attitudes, and behaviour.
OE9
As children progress through the Kindergarten program, they:
demonstrate literacy behaviours that enable beginning readers to make sense of a variety of texts
Conceptual understandings
- Reading is an active process of interacting with and constructing meaning from text.
- Reading strategies help us to understand the meaning of different texts.
- Readers use a variety of strategies to think about and understand what they read.
See the Professional Learning Conversation following the chart.
| Specific Expectation As children progress through the Kindergarten program, they: |
Ways in which children might demonstrate their learning | The educators' intentional interactions |
|---|---|---|
| 9.1 use reading behaviours to make sense of familiar and unfamiliar texts in print (e.g., use pictures; use knowledge of oral language structures, of a few high-frequency words, and/or of sound-symbol relationships) |
Saying "I knew it said 'spider' 'cause I used the picture." "I know that says 'the'." "I made my voice loud here because it gets dark (pointing at the bold print)." Doing During independent reading, a child points to the words, looks at the pictures, and rereads after a miscue. A group of children are designing the letters for the class alphabet as a resource for children to use. The educators observe the children writing down the alphabet and then talking about which of the construction materials would work best for each letter. The educators ask themselves, "What reading strategies are the children using? What are we learning about the children's literacy behaviours and what they know about how letters and reading work?" Representing A group of children decide to make the dramatic play area into a bookstore. A group of children are using blocks to build a structure. The educators observe the children using the same underlying thinking and strategy they saw children using during the taking of a running record. (A child was cross-checking, trying something to see if it worked.) The educators name the strategy, saying, "That is just like when you were reading this morning." See "Kindergarten Matters: Re-imagining Literacy and Mathematics Throughout the Day" – the clip "Planning for Small Group Shared Reading". |
Responding The educators scaffold the children's application of reading strategies by thinking aloud and asking questions such as: "Let's do a picture walk of the book." "I noticed you looked at the pictures." "What makes you think that...?" The educators use the information they have gathered to support assessment for learning to decide on a text to read with a group of children. They ask themselves, "Why this learning, for these children, at this time?" Based on their assessment information, they determine that the level of support the children need is small-group shared reading, and then select an appropriate text. Challenging "If you think the word is 'jump', what letter will we see at the beginning when we lift the sticky note?" An educator notices and names to make the learning explicit as the children engage in a read-aloud. Video title: "Literacy Through the Day" – see the clip "Literacy as a whole class community – Creating a community of thinkers and readers: What strategies are the children thinking about and demonstrating?". Extending Assessment information reveals that a small group of children know a number of high-frequency words, have letter and sound knowledge, and are able to read simple patterned text. The educators determine that this group of children would benefit from a guided reading lesson using a non-fiction text. |
Professional learning conversation
Re. OE9: Following up on feedback from a meeting with families, an educator decides to send home a couple of the questions she uses when reading with children to help children comprehend the text. She asks some families to help by translating the following questions into the home language: "What do you think might happen in the book?" "How did you figure that out?" "What does this book remind you of?" The educator then also invites the families to share other questions that they ask when reading with their children.
OE10
As children progress through the Kindergarten program, they:
demonstrate literacy behaviours that enable beginning writers to communicate with others
Conceptual understandings
- Written communication enables us to make thoughts, ideas, and feelings visible to others.
- We write for a variety of reasons and purposes.
- It is important for others to understand what we are trying to say through writing.
- Writers think first about the purpose and the audience for their writing and then about what form of writing would best convey their desired meaning.
- Writers use different tools and resources to help them write.
See the Professional Learning Conversation following the chart.
| Specific expectations As children progress through the Kindergarten program, they: |
Ways in which children might demonstrate their learning | The educators' intentional interactions |
|---|---|---|
| 10.1 demonstrate an interest in writing (e.g., choose a variety of writing materials, such as adhesive notes, labels, envelopes, coloured paper, markers, crayons, pencils) and choose to write in a variety of contexts (e.g., draw or record ideas in learning areas) 10.2 demonstrate an awareness that text can convey ideas or messages (e.g., ask the educator to write out new words for them) |
Saying "What does that say?" "What does it mean?" "I want to write a note to my friend." Doing A child notices the question "How many scoops?" posted at the sand table by the educators. The child begins to count the scoops. The children decide to take a survey to question their classmates about an event or a preference/opinion. See "Kindergarten Matters: Re-imagining Literacy and Mathematics Throughout the Day" – the clips "Provoking an Inquiry Stance in Mathematics" and "The Inquiry Process in Action". Representing A child writes a sign in the dramatic play area to show what movie is playing at the theatre. |
Responding The educators notice the children's growing interest in writing notes to each other. They talk with the children, saying, "We noticed that you were interested in communicating in writing with each other. Where do you think we could add writing materials to the classroom? What materials should we add?" Video title: "The Learning Environment" – see the clip "Thinking deeply about the learning environment – planning the materials and spaces to make learning visible". Challenging The educators notice the sign that has been made for the theatre. They ask the children what other information could be added to the sign that would be helpful to people coming to the movie. Extending The educators observe the children in the dramatic play area solving the problem of who will be the first to use some new materials that have been placed there by the educators. The educators ask the children to share their solution, including their list, with the rest of the class. |
| 10.3 write simple messages (e.g., a grocery list on unlined paper, a greeting card made on a computer, labels for a block or sand construction), using a combination of pictures, symbols, knowledge of the correspondence between letters and sounds (phonics), and familiar words |
Saying "This is a word in my language." "I used the word wall to help me write [the word]." "I wrote 'CLOSED' on the bookstore." "We used tallies to keep track of the number of ants in our ant farm." Doing Children write letters to one another and to family members, make signs in the blocks area, record their findings at the water table, make a list of classmates' names in the dramatic play area, and make greeting cards in the visual arts area. Representing A child who is reluctant to write in the writing area draws a labelled picture of his blocks structure in the blocks area. A child who is learning English writes labels for her picture in her home language. |
Responding To support children's use of written communication in many contexts, the educators post signs children have written in their home language(s).
Challenging |
| 10.4 use classroom resources to support their writing (e.g., a classroom word wall that is made up of children's names, words from simple patterned texts, and words used repeatedly in shared or interactive writing experiences; signs or charts in the classroom; picture dictionaries; alphabet cards; books) |
Saying "I know – I can use the word wall." "That is the same as a word from the book." "I know this is how you write it because I saw it on the card." Doing While playing with blocks, a group of children decide they need a secret password for their structure. To write the password, they use the word wall to help them figure out the letters for the words they want to write. Representing A small group of children make their own list of names, modelled after a class list. They use the list at the restaurant in the dramatic play area. |
Responding The educators place photographs of the children beside their names on the word wall. At the request of several of the children, they also place class lists in several areas as a resource for children's writing. The educators negotiate the placement of the materials with the children. This leads to more engagement for all children, and the educators gain insights into the children's thinking about what writers do. Video title: "Literacy Through the Day" – see the clip "Rethinking the learning environment to support literacy – Co-constructing the learning environment with the children" Challenging "What could you use to help you figure out how to write the word?" See "Kindergarten Matters: Re-imagining Literacy and Mathematics Throughout the Day" – the clips "Deepening Our Understanding: Supporting Children's Writing" and "Deepening Our Understanding: Supporting Children's Writing Using Technology". Extending The educators put words from the word wall on binder rings so they are portable and the children can use them at various places in the room. |
| 10.5 experiment with a variety of simple writing forms for different purposes and in a variety of contexts 10.6 communicate ideas about personal experiences and/or familiar stories, and experiment with personal voice in their writing (e.g., make a story map of "The Three Little Pigs" and retell the story individually to a member of the educator team during a writing conference) |
Saying "Let's make a list." "I am writing an invitation to my party." "I put these labels on my drawing of my structure." Doing A child in the dramatic play area decides to create an appointment book for the "doctor's office". The child also writes appointment cards for the "patients". Representing A child makes a drawing of a day at the park and retells her experiences to her classmates. |
Responding The educators observe that children in the dramatic play area are making an appointment book and writing appointments in it. An educator joins the play and prompts the children to include the sounds they hear in the words. Challenging A small group of children talk with an educator about a text feature they notice an author has used in a familiar read-aloud. The educator invites the children to try it in their own writing. A few days later, he notices that one of the children has tried the technique. He asks the child to share it with others. Video title: "Literacy Through the Day" – see the clip "Making Learning Visible - Observing, documenting, analysing, taking informed action. Rethinking Writing". Extending The children write their questions, ideas, and predictions, and the educators provide materials for the children to test out their theories. Video title: "Inquiry" – see the clip "What does it look like and sound like to co-construct inquiry with the children? Listening in on a classroom inquiry". |
Professional learning conversation
Re. OE10: The educators post the stages of picture making and the stages of writing in the writing area and on the Family Information Board. They post pedagogical documentation that shows the children's thinking and learning. Children have been drawing and writing to communicate a memory, retell an experience, describe a point of view, describe a structure, and/or gather data from their classmates. At subsequent family conferences, the educators ask the parent(s) to share the kinds of writing that children do at home, and discuss with the parent(s) how the samples of the children's work illustrate the stages of picture making and writing. Together, the educators and the parent(s) discuss the children's thinking, learning, and progress. At their drop-in coffee mornings, several parents comment that talking about the documentation has helped them understand their child's learning process.
OE11
As children progress through the Kindergarten program, they:
demonstrate an understanding and critical awareness of a variety of written materials that are read by and with their educators
Conceptual understandings
- Being literate enables people to think about and make sense of the world.
- We read for a variety of reasons and purposes.
- Reading makes us think and feel in different ways.
- There are different types of texts.
| Specific expectations As children progress through the Kindergarten program, they: |
Ways in which children might demonstrate their learning | The educators' intentional interactions |
|---|---|---|
| 11.1 demonstrate an interest in reading (e.g., expect to find meaning in pictures and text; choose to look at reading materials; respond to texts read by the educator team; reread familiar text; confidently make attempts at reading) 11.2 identify personal preferences in reading materials (e.g., choose fiction and non-fiction books, magazines, posters, or computerized interactive texts that they enjoy) in different contexts (e.g., educator team read-alouds, shared experiences in reading books, independent reading time) |
Saying "I like the bug books because I really like spiders." "I am making a maze. I read books about mazes all the time." "Read the book about Thomas again." Doing In the reading area, a group of children choose books from a basket. Previously, the educators have worked with the children to sort the books so the children can make informed choices. Representing In the dramatic play area, a group of children role-play characters from a book they have just heard in a read-aloud. |
Responding The educators document what books the children are choosing in order to gather more books they will be interested in reading. The educators rethink the environment to encourage literacy behaviours and awareness throughout the day and in different contexts, including the children’s reading and their documentation of their own learning. Video title: "The Learning Environment" – see the clips "Thinking about elements to repeat in the environment" and "Co-constructing and negotiating the learning environment – including the children's voices and ideas". Challenging An educator models sharing her individual reading preferences for the children. Extending The educators plan discussions focused on "how to choose a good book for yourself" (e.g., by looking at the front cover and the illustrations). |
| 11.3 demonstrate an awareness of basic book conventions and concepts of print when a text is read aloud or when they are beginning to read print (e.g., start at the beginning of the book; recognize that print uses letters, words, spaces between words, and sentences; understand that printed materials contain messages) |
Saying "That is the title of the book." "I know that letter." "Look, I remembered the finger space (between words)." Doing Children hold books the right way up, use a finger to demonstrate left to right directionality, and attempt to read the story. They begin to recognize the difference between letters and words. They may follow the print for the class, using a finger or a pointer, as a story is read aloud during shared reading. See "Kindergarten Matters: Re-imagining Literacy and Mathematics Throughout the Day" – the clips "Inviting the Children Into New Learning" and "Explicit Learning About Concepts of Print". Representing Children write random strings of letters and begin to leave a space between "words". |
Responding To help children develop basic concepts of print, the educators model print concepts during shared reading and modelled and interactive writing, asking questions such as: "Where do we start to read?" Challenging The educators create opportunities for the children to reread familiar text on their own, in small groups, and with the educators. The educators reflect and ask, "Why this learning, for these children, at this time?" They know that repeated reading, revisiting text, thinking about words and sentences, and making meaning from text are all foundational literacy behaviours. Extending An educator discusses with the children where to place co-constructed text for revisiting and rereading. |
| 11.4 respond to a variety of materials that have been read aloud to them (e.g., paint, draw, or construct models of characters or settings) |
Saying "My grandpa and I collected rocks, and we made an Inuksuk like the one in the painting." "I live in an apartment, too, just like the family in the book." Doing A small group of children decide to make an alphabet book using their names. They use digital photographs to make it look like a book in their classroom library. Representing After focusing on the comprehension strategy of visualization, the children share their images, using words, movement, and/or graphic representation. See "Kindergarten Matters: Re-imagining Literacy and Mathematics Throughout the Day" – the clip "Reading and Writing Connections". |
Responding After reading a book about a forest to the children, an educator asks questions such as: "How do you think the author feels about forests?" "How do you think the author wants us to feel about forests?" "Why do you think there are photographs instead of illustrations in the book?" The educators ask questions for similar purposes with other texts. The purpose is to elicit the children's thinking about the perspective of the author, and to think critically about the message and point of view. Challenging After reading a book about a social issue relevant to the class, an educator ask questions such as: "Who is this book written for?" "Who is telling the story?" "How would this story be different if another person or character told the story?" Extending Visualization is a comprehension strategy that is quite abstract for young children but is one way to support their understanding of text. For several days the educators focus on having children practise the strategy of visualizing or making pictures in their minds. In order to make this abstract strategy more concrete, the educators plan for the children to practise visualization on a rainy day. After guiding the children's observations of a rainy day, the educators then ask the children to close their eyes and "paint" a picture in their heads of what they have seen. The children share their "pictures" orally. Several days later, the educators read aloud a poem about the rain, building on the children's prior understanding. |
| 11.5 make predictions regarding an unfamiliar text that is read by and with the educator team, using prior experience, knowledge of familiar texts, and general knowledge of the world around them (e.g., use the cover pictures and/or title to determine the topic and/or text form) |
Saying "I think it is going to be about a party because there are balloons on the cover." "I think the baby is going to cry because babies cry when they are hungry." "I think this is non-fiction because there is a photograph on the cover." "I think this is going to be about two friends because there are two kids on the cover." (Another child states): "Maybe they could be brothers." "I thought that was the word 'sandcastle' because I looked at the picture and it starts with 'S'." Doing A child looks out of the window to see if it is still raining, in order to predict whether the class will be going outside to play. A child looks ahead in a book and then turns back, saying, "I thought that the girl wasn't going to let her sister play with her new game, but she did." Representing A small group of children record a written response to the questions of the day (posted by the educator team): "Do you think it will rain tomorrow? What makes you think that?" |
Responding "What do you think might happen in the book? How did you figure that out?" Challenging "What in the book makes you think that?" "What does the picture tell us about what might happen in the book?" "What clues did you use to try and figure that out?" Extending "What words do you think might be in this book?" "What do you know about birds that will help you read this book?" |
| 11.6 use prior knowledge to make connections (e.g., to new experiences, to other books, to events in the world) to help them understand a diverse range of materials read by and with the educator team |
Saying "I live in an apartment, too." "That's just like the other book we read." "That book is just like the movie I saw." Doing During an outdoor inquiry, children use their prior knowledge gained from investigating shadows (e.g., the knowledge that shadows move when you move) to investigate what happens to shadows when they sit down. Representing The children use their prior knowledge (after having built a bridge in the blocks area) to build a "tunnel bridge". |
Responding An educator models the use of think-alouds to make explicit the reading strategy of using prior knowledge to make connections. The educators document their observations of children during play (to support assessment for learning). After analysing the pedagogical documentation, they learn that the children have been making connections to their prior experiences in their play. They plan to name and notice the strategy (making connections to prior knowledge) as one that readers use to help them understand what an author means. Video title: "Play-Based Learning" – see the clip "The FDELK team members engage with children in different ways, prompting children to reveal their thinking in role". Challenging "What does that remind you of?" "What in the book made you think that?" "You built the structure just like in the book." "I wonder if you could make other structures just like in the book." Extending The educators support the children as they take digital pictures of their shadows. They have been reading books about shadows. The children wonder why they don't have shadows indoors. The pictures will help them make connections when they revisit their inquiry indoors. |
| 11.7 use illustrations to support comprehension of texts that are read by and with the educator(s) |
Saying "It is in a park, because look at the swings." "I think they are going to play in the snow because they are wearing snowsuits." "I thought it said 'train', but the picture is a truck." "I put a picture of the dog so people would know it is the word 'dog'." "I saw the pictures here, and I think these are the enemies of the ants." (After breaking the word into parts, the child says): "Yes, the word is 'predators', so I was right. They are the enemies." Doing A small group of children, with support from an educator, reread familiar texts, including texts created in the classroom by the children (documentation, charts, stories), using the illustrations to help their comprehension. During a small-group shared reading experience the educator leads the children through a "picture walk" to anticipate what they will encounter when they read the book together. The educator makes a mental note of the children's thinking to document later. See "Kindergarten Matters: Re-imagining Literacy and Mathematics Throughout the Day" – the clip: "Inviting the Children into New Learning". Representing An educator takes a photo on a tablet of a construction a group of children have been making to accompany the writing the children are doing to make their own version of the book. |
Responding The educators model for the children how they can use the illustrations to help them understand what is happening in the text and figure out words they don't know. Challenging "What do you think the word will be under the sticky note? How can you use the picture to help you figure it out?" Extending The educators notice that several of the children are consulting non-fiction texts to find out more about ants. They work with the children to support them in applying what they already know (e.g., about using pictures and/or photographs), and also to draw their attention to other features of the texts that can help them find the information they are looking for. |
| 11.8 demonstrate knowledge of most letters of the alphabet in different contexts (e.g., use a variety of capital and lower-case manipulative letters in letter play; identify letters by name on signs and labels in chart stories, in poems, in big books, on traffic signs; identify the sound that is represented by a letter; identify a word that begins with the letter) See the Professional Learning Conversation following the chart. |
Saying "It is a 't'. It starts just like my name." "It makes a 'J' sound." "I know it is a 'd' because it has a ball and a stick." "I see a 'b' like the one in 'book'." Doing After shared reading of some alphabet books, an educator helps the children create an alphabet book, using the children's names and pictures of objects in the classroom to represent the letters. Representing Two children work at a whiteboard with magnetic letters. They sort and compare the letters. Video title: "Literacy Through the Day" – see the clip "Rethinking whole-class instruction and moving towards small-group, differentiated support. Reflections on the impact on children's learning. Children's Engagement". |
Responding The educators place a pocket chart holding the children's name cards beside the magnetic letters and whiteboard, so the children can use the names as a reference. Video title: "Play-Based Learning" – see the clip "How are educator teams rethinking their role in play-based learning?". Challenging "If the word is 'boy', what will the first letter be?" "If the word is 'snow', what is the first sound? What sound do you hear at the end of the word?" (Note: The educators pose the questions based on assessment information.) Video title: "Literacy Through the Day" – see the clip "Literacy as a whole class community – Creating a community of thinkers and readers. What strategies are the children thinking about and demonstrating?". "I wonder what will happen if I take away this letter and replace it with this one." "Look what happens when I put this letter beside this one. It makes a completely different sound. Isn't it interesting how letters work?" Extending The educators put the word wall words on Velcro so the children can sort the words by first letter. As the year progresses, they add some high-frequency words. |
| 11.9 retell, orally or with non-verbal communication, familiar experiences or stories in proper sequence (e.g., in new and creative ways, using drama, visual arts, non-verbal communication, and representations; in a conversation) 11.10 retell information from non-fiction materials that have been read by and with the educator team in a variety of contexts (e.g., read-alouds, shared reading experiences), using pictures and/or props |
Saying "First he ... then ..." "So they went around the corner and then ..." "She brushed her teeth and then went to bed." Doing Using digital photographs to show the life cycle of the class butterflies, a child orally retells the sequence: "First the butterfly is an egg, and then it turns into a caterpillar. The caterpillar spins a chrysalis, and then it's a beautiful butterfly." Representing A small group of children make videos to show the life cycle of the butterflies that they are caring for in their classroom, for future viewing and discussion. A small group of children and an educator use dramatic play props for opportunities for children to retell familiar stories and experiences. Video title: "Literacy Through the Day" – see the clip "Literacy as a whole class community – Creating a community of thinkers and readers. Examples of Gradual Release of Responsibility Making Connections between oral language, reading and writing". |
Responding During a whole-class discussion, the educators model the sequence for retelling. The educators think together with the children about the idea that audience and purpose are important when we think about retelling. They also think together about why we retell stories and events in school and outside of school. The educators model the use of pictures and words to retell a familiar experience such as brushing teeth, washing hands, or tidying up the sand. Challenging An educator models retelling a fiction text, using natural materials. The children use the materials to retell familiar stories. See "Kindergarten Matters: Re-imagining Literacy and Mathematics Throughout the Day" – the clip "Re-thinking Literacy Structures". Extending The educators model retelling a non-fiction text, using words and the photographs in the text. Video title: "Inquiry" – see the clip "Reflections on inquiry: the power of inquiry. Co-constructing and making learning visible". |
Professional learning conversation
Re. SE11.8: The educators from all the classes in the school discussed how they were rethinking letters. They had built a culture of collaboration based on many courageous conversations. They were comfortable with and open to reflection and to rethinking their practice based on evidence of the effects of various changes, which they had also studied together.
The educators reflected on all of the thinking that was evident in the shared documentation from their collaborative inquiry questions: "What do children know/notice about letters?" "How do they use that knowledge in their reading, writing, and conversations?" The following are excerpts from their professional conversations as they shared their pedagogical documentation:
"I used to think I needed a program to teach letters."
"Children already know a lot about letters."
"When we put out the letters and asked what children noticed about the letters, we got pages of documentation."
"Yes, we did, too, but I think what made me feel confident to let go of all the activities I used to do was that through the documentation and observation we were able to see with more certainty how to differentiate the learning. We also gained a better understanding of children we were puzzled by and a better idea of where we needed to support those children. For example, we showed one child our cell phone and she recognized the letters in that context. Then we were able to circle back and help the child identify the letters in another context [in print]."
"The children in our class sorted the letters. They began to see the different features of the letters."
"The children in our class did that, too."
"They started making comparisons and connections to their names, and to other words. We found out a lot more about what the children already knew to guide our practice [assessment for learning], especially when we were supporting them in their writing."
OE12
As children progress through the Kindergarten program, they:
demonstrate an understanding and critical awareness of media texts
Conceptual understandings
- Media texts are constructed to persuade and influence the reader or viewer.
- Media texts are everywhere.
- Media texts can influence our thoughts, ideas, feelings, beliefs, and wishes.
- We need to think about how media texts can affect us.
| Specific expectations As children progress through the Kindergarten program, they: |
Ways in which children might demonstrate their learning | The educators' intentional interactions |
|---|---|---|
| 12.1 respond critically to animated works (e.g., cartoons in which animals talk, movies in which animals go to school) 12.2 communicate their ideas, verbally and non-verbally, about a variety of media materials (e.g., describe their feelings in response to seeing a DVD or a video; dramatize messages from a safety video or poster; paint pictures in response to an advertisement or CD) |
Saying "I learned that they put toys in cereal boxes because they want kids to buy the cereal." Doing A small group of children use props to dramatize a story they have just heard about children being prejudiced. Representing A small group of children make signs about how to be safe on the school bus. |
Responding To help children develop strategies for reflecting on media texts, educators ask questions such as: "Why did people make this cartoon?" "Who likes to watch cartoons or animated works?" "What is it about this cartoon that makes you want to watch it?" In a think-aloud, the educators say, "Media texts are made to try to get the reader or viewer to do something or believe something." Challenging "Sometimes you buy cereal and there are toys in the box. Why do you think the people who made the cereal put the toys in there?" Extending "Someone made this poster. What thoughts do you have about why they chose to use a wolf on it rather than some other animal? What are you supposed to think about the wolf? What did they want us to see? Why?" |
OE14
As children progress through the Kindergarten program, they:
demonstrate an awareness of the natural and built environment through hands-on investigations, observations, questions, and representations of their findings
Conceptual understandings
- People have the capacity to feel a sense of wonder about the world.
- The natural and built worlds are connected and have an impact on one another.
- Human-built and natural systems interact with one another.
| Specific expectation As children progress through the Kindergarten program, they: |
Ways in which children might demonstrate their learning | The educators' intentional interactions |
|---|---|---|
| 14.1 ask questions about and describe some natural occurrences, using their own observations and representations (e.g., drawings, writing) |
Saying "The snow is melting." "The leaves are turning red." "Why did all the worms come out of the ground?" "Why is my banana all brown now?" Doing In the dramatic play area, a child is sorting the dress-up clothes. One pile has a simple drawing of a snowman on top. She tells one of the educators that she is putting away the winter clothes because it is summer now. Representing A child paints a picture with two panels, showing what the sky looks like both during the day when he is playing outside and at night before he goes to bed. |
Responding In response to a question from a child about why worms come out onto sidewalks and driveways when it rains, an educator invites a small group of interested children to work with an educator to find the answer to the question. The educators invite the children to share their theories about why this happens, and then they think together about how they could find out how well their theories explain what they have noticed. (Note: The focus of the learning is not facts about worms but ways children can explore their questions through inquiry.) Challenging "I wonder what we might see if we looked closely at the snow." "What did you observe when you picked up some snow and held it in your hands? What are your thoughts about why that happened?" "What tool can we use to see the snow better?" Extending The educators relate the children's natural curiosity to their own professional curiosity expressed in the conceptual understanding "People have the capacity to feel a sense of wonder about the world" (see above). The children observe and think about change. The children and the educators discuss and represent their thinking in multiple ways. See "Kindergarten Matters: Re-imagining Literacy and Mathematics Throughout the Day" – the clip "Provoking an Inquiry Stance". |
OE15
As children progress through the Kindergarten program, they:
demonstrate an understanding of numbers, using concrete materials to explore and investigate counting, quantity, and number relationships
Conceptual understandings
- Numbers represent a common organizational structure that we use in our lives and in our world to communicate/represent value.
- Numbers can be taken apart (decomposed) and put together (recomposed).
- The ability to decompose and recompose is a useful strategy in all aspects of mathematical thinking.
- We can use objects, pictures, symbols, and/or words to represent number and quantity.
- There are many ways to count. Each way to count has a proper sequence.
- Quantity can be represented in many ways.
- The same quantity can look different (concept of abstraction).
- We are learning that as we move up or down the counting sequence, the quantity increases or decreases by the number we are counting by (concept of magnitude).
| Specific expectations As children progress through the Kindergarten program, they: |
Ways in which children might demonstrate their learning | The educators' intentional interactions |
|---|---|---|
| 15.1 investigate (e.g., using a number line, a hundreds carpet, a board game with numbered squares) the idea that a number's position in the counting sequence determines its magnitude (e.g., the quantity is greater when counting forward and less when counting backward) |
Saying "Every time I add a block, my building gets taller." "When I walk forward on the number line, the numbers get bigger. When I walk backward they get smaller." Doing Children use manipulatives to move forward and backward along a number line and use their bodies to move around on a hundreds carpet. Representing A child draws a number line based on the model used in the classroom and puts sticky notes on numbers that represent a quantity less than 4, greater than 8, and so on. |
Responding "What happens when we move up the number line? How do you know? What about when we move backward on the number line? How do you know?" Challenging An educator creates a large number line on the floor of the classroom and invites individual children to stand beside different numbers. The team member calls a new number and challenges children to predict whether they will have to move forward or backward from their current position to get to the new number – for example: "You are standing at nine, and you want to move to six. Which way will you have to move on the number line?" One at a time, the children test their predictions by moving up or down the line to the new number. The educator then asks, for example: "If you were standing at nine and then moved to six, what happened to the numbers?" Extending The educators ask the children to retell the math story they had read earlier, about a mother duck teaching her babies how to swim. To extend the children's learning, they say: "In our story, one more duck went into the pond. How many ducks are in the pond now? How do you know? Show me how you figured that out." |
| 15.2 investigate some concepts of quantity and equality through identifying and comparing sets with more, fewer, or the same number of objects (e.g., find out which of two cups contains more or fewer beans [i.e., the concept of one-to-one correspondence]; investigate the ideas of more, less, or the same, using concrete materials such as counters or five and ten frames; recognize that the last number counted represents the number of objects in the set [i.e., the concept of cardinality]) |
Saying "Let's count the cars. I have six and you have five. That means I have one more. Let's get another one so we can have the same." "You counted thirty-five buttons. I go even higher. I can count forty buttons." Doing In the dramatic play area, a child counts out placemats, one for each child seated at the table, and says "I counted five placemats. That means five children are here for lunch." Representing Pointing to the sorting tray, a child notices that she has "the same amount on both sides". Children notice that the towers in a block structure are uneven, and decide to even them up: "See, we had five here and six here. We had to add this one to make them the same." |
Responding "How many marbles have you got in your hand? Let's count." Challenging "How many marbles do you think will fit in my hand? Do you think it will be more or fewer than you have in your hand? How could we find out?" Extending "This stack of large blocks is bigger than that stack of small ones. Which stack has the most blocks? Show me how you figured that out." |
| 15.3 make use of one-to-one correspondence in counting objects and matching groups of objects 15.4 demonstrate an understanding of the counting concepts of stable order (i.e., the concept that the counting sequence is always the same – 1 is followed by 2, 2 by 3, and so on) and of order irrelevance (i.e., the concept that the number of objects in a set will be the same regardless of which object is used to begin the counting) |
Saying "I counted five children. I need five pieces of apple – one for each child." Doing In the dramatic play area, a child counts out placemats, one for each child seated at the table. An educator observes a child counting the number of people (made from building materials) for the imaginary house she has built. Each time she counts, the child gives one count to each object. Even though she counts accurately, she recounts starting with a different object. The educator notices and names what the child is doing. Representing A child points to the pieces of apple on a plate while counting. Although the child points to a piece of apple more than once, the numbers are still stated in the proper sequence (i.e., 1, 2, 3, 4...). (The example illustrates the concept of stable order.) A group of children play with the number line that the class and educators have co-constructed. The educators observe the children moving an object along the number line and counting. They supply a basket of cubes and add the correct number of cubes to match the numeral. (The example establishes a foundation for the concept of magnitude.) |
Responding An educator models order irrelevance by counting a set of cars several times, each time starting the count at a different point in the set. "What do you notice about how I am counting the cars? I am going to count them again. What do you notice this time?" The educator places apple slices on a plate. "I noticed that you helped to line up the placemats so that there was one placemat for each child at the table. Now, how many apple slices will you need so that everyone has a piece? How did you figure that out?" Challenging "There are three children in our group now. Three more children want to join. I wonder how many more chairs we will need." On the class number line, the educators model starting a count at a different point on the number line. "When do we have to start at one?" Extending The children collect and record data that represent their personal opinions about the question "Would you rather ... or...?" The educators want to observe the children's thinking about quantity relationships (to support assessment for learning), and they decide that the data about the children's opinions can provide a context for doing this. The educators ask the children to use linking cubes, lined up in rows according to which opinion they hold, to create a concrete graph. The educators discuss the graph with the children (e.g., "Which opinion has the most children [concept of quantity]? How do you know that [concept of magnitude]? Which opinion has the fewest children [concept of quantity]? How do you know that [concept of magnitude]? Why do you think more people would rather... than...?"). The educators document which children counted the cubes to determine quantity, and which children used the length of the stacked cubes ("This one is taller so it has more"), thus demonstrating an understanding of the concept of magnitude. They then place a small mat and a larger mat on the floor. Children from the "most" line are asked to stand on the smaller mat, while children from the "fewest" line are asked to stand on the larger mat. The educators ask "What do you notice?" and the children respond with questions such as: "Why does the side with fewer people look like there are more? Why is the side with more all squished on the mat [concept of abstraction]?" (See connections to SE15.3 above.) The educators intentionally present provocations that will help children develop the concepts of:
|
| 15.5 subitize quantities to 5 without having to count, using a variety of materials (e.g., dominoes, dot plates, dice, number of fingers) and strategies (e.g., composing or decomposing numbers) 15.6 use information to estimate the number in a small set (e.g., apply knowledge of quantity; use a common reference such as a five frame; subitize) |
Saying "I know there are five buttons here because they look like the five on the dice in my game." "It's five. I saw four red and one blue." "I think it will take three scoops to fill the pail." Doing A child works with a five frame, filling the frame with different objects. He tells another child that he knows he has four buttons because one of the spaces in the frame is empty. Representing Some children use sticky notes to record their estimate of how many small scoops it would take to fill a container at the sand table. They use tallies, saying that doing so makes it easier to count: "See, here it is five. After you get to four you make a line like this that shows it is five." They ask the educators for a bigger scoop to compare the number of scoops. The educators ask the children about their thinking. Two of the children think that they will need fewer scoops, but two others are not convinced, so they test their theories. One of the children makes a separate tally chart to keep track of the number of scoops. The educators take photographs and post them on the blog to share with the families that what the children have been doing is much more than counting. It is evidence of children's thinking about quantity and the importance of knowing that each count represents a quantity that increases when they add more and decreases when they go down the number line. |
Responding "How did you know there were five buttons?" "How many sticks do you think there are? How do you know that?" Challenging "Why do you think there are more than five buttons in this set? How can you show that using a five frame?" Over time, the educators show the children different arrangements of the number "5" using cubes with one variable (e.g., all pink but on two different plates), two different colours in many compositions, and then two different objects (e.g., small cubes and big cubes [concept of abstraction]). They think aloud: "We can make five in many ways. Quantity can be represented in many ways". Extending After analysing their pedagogical documentation (to support assessment for learning), the educators add a die into the children's play with glass beads at a light table. Until now, the children have been creating various patterns with the beads. The educators add the die into the play to help children use the same materials to think about number sense and quantity relationships. That is, with the addition of the die, the children's play changes from making patterns with the beads to the creation of a game that includes a number concept. (The game involves rolling the die, counting out the number of beads indicated by the die from the pile, and then sliding them through the remaining lines of beads on the table. The number of beads that are knocked out of the line is the player's score for that round.) Video title: "Numeracy Through the Day" – see the clips "Children learning from and with each other" and "Reflections on making numeracy visible and intentional based on observations". |
| 15.7 explore and communicate the function/purpose of numbers in a variety of contexts (e.g., use magnetic and sandpaper numerals to represent the number of objects in a set [to indicate quantity]; line up toys and manipulatives, and identify the first, second, and so on [to indicate ordinality]; use footsteps to discover the distance between the door and the sink [to measure]; identify a favourite sports player: "My favourite player is number twenty-four" [to label or name]) 15.8 explore different Canadian coins, using coin manipulatives (e.g., role-play the purchasing of items at the store in the dramatic play area; determine which coin will purchase more – a loonie or a quarter) |
Saying "There are five placemats in the house area. I put a 'five' card on top so we don't forget how many we have." "I am fourth in line." "It is thirty-eight steps from our classroom door to the door of the washroom." (In the class bakery): "You make a sign that says "Three for $1.00. I'll put three on each plate." "My lucky number is five." Doing A group of children create an ordinal numbers game. Using sticky notes, they place different numbers, from 1 to 10, on the back of each child in the group and then form a line. One child then organizes the children, placing them in order based on the numbers on their backs. Representing In the dramatic play area, a group of children set up a grocery store, pricing the items by writing numerals on them. Other children shop for items and then use coin manipulatives to purchase them. A group of children put numbers on the parking garage. Another group of children use numbers to describe the floor they live on in their building and add them to the large box that the educators brought in for the children to use to create an elevator. See "Kindergarten Matters: Re-imagining Literacy and Mathematics Throughout the Day" – the clip: "Small-Group Learning About Numbers". |
Responding "Who was the third person to come to school today? How do you know?" Video title: "Numeracy Through the Day" – see the clips "Engaging in Children's Play to Make Mathematics Learning Visible" and "Mathematics in Inquiry – Responding to Children's Ideas". Challenging An educator joins the play in the dramatic play area. "This detergent costs four dollars. I'm looking for something less expensive." The educators and children explore cardinal and ordinal numbers and the interesting use of numbers in our world. For example, the educators use a "rekenrek" with the children to communicate their thinking in multiple ways: "Which one is the fourth one in the group? How do you know?" "Show me a four. How do you know?" (The educators think aloud): "Isn't it interesting to think of all the different purposes for numbers? What else do we use numbers for? See "Kindergarten Matters: Re-imagining Literacy and Mathematics Throughout the Day" – the clip "Small-Group Learning About Numbers". Extending The educators create number cards to fit into a pocket chart that contains cards with the children's names on them. They invite the children to determine their place in the chart (e.g., by counting, by comparing their spot with a neighbour's) and then to select the number card that corresponds to the pocket that contains their name and put the card in the correct pocket. The children are then asked to discuss who is third, who is seventh, and so on. The educators intentionally present provocations that will help children:
|
| 15.9 compose and decompose quantities to 10 (e.g., make multiple representations of numbers using two or more colours of linking cubes, blocks, dot strips, and other manipulatives; play "shake and spill" games) 15.10 investigate addition and subtraction in everyday experiences and routines through the use of modelling strategies and manipulatives (e.g., join two sets of objects, one containing a greater number than the other, and count all the objects; separate out the smaller number of objects and determine how many remain) and counting strategies (e.g., use a counting sequence to determine how many objects there are altogether; count backward from the largest number to determine how many objects remain) |
Saying "I only have three wheels for my car. I need one more to make four." "There are five people at the snow table but we only have three scoops. We need two more scoops." "We used to have eight placemats in our class café. But three got ripped. Now we only have five." Doing Some children represent the quantity of 8 by counting 1 through 8 using their fingers. Other children put up one hand, count from 1 to 5 using each finger, pause, and then continue to count to 8 using three more fingers. Still others put up all five fingers of one hand at once and say "Five" then count on, using three more fingers and saying "Six, seven, eight. There are eight." Representing Children represent the quantity of 7 using 4 cubes on one plate and 3 on another or 7 tally marks, or by putting up all five fingers of one hand and saying "Five", and then counting two more fingers on the other hand. |
Responding The educators model different strategies for composing and decomposing numbers using manipulatives, five frames, ten frames, and story problems, asking questions such as, "If the five frame is full, and you remove three buttons, how many buttons are left?" Challenging "How else could we show that?" "How did you figure that out?" "How many more do you think we need?" "How many do we have now?" Extending One of the educators puts out 10 counters so that children can use them to re-enact a number song they have been learning: "How many ducks are in the pond now? How do you know?" "How many people had an apple for lunch? How do you know?" |
, 
).See also OE20: SE20.1 and SE20.2
OE16
As children progress through the Kindergarten program, they:
measure, using non-standard units of the same size, and compare objects, materials, and spaces in terms of their length, mass, capacity, area, and temperature, and explore ways of measuring the passage of time, through inquiry and play-based learning
Conceptual understandings
- We are thinking and learning about how measurement helps us to describe, compare, and communicate.
- Objects and shapes have measurable attributes that can be compared and communicated in different ways.
- We use different tools to measure different things.
- The attribute we are measuring determines the tool we will use and therefore the unit of measurement.
- The unit used to measure makes a difference.
- Any space in between units counts as a measure.
- We use comparative and descriptive language when communicating about measurement attributes.
- The ability to decompose and recompose is a useful strategy in all aspects of mathematical thinking.
- The strategy of decomposing and recomposing shapes in geometry helps us think about measurement.
See the Professional Learning Conversation following the chart.
| Specific expectations As children progress through the Kindergarten program, they: |
Ways in which children might demonstrate their learning | The educators' intentional interactions |
|---|---|---|
| 16.1 select an attribute to measure (e.g., capacity), determine an appropriate non-standard unit of measure (e.g., a small margarine container), and measure and compare two or more objects (e.g., determine which of two other containers holds the most water) 16.2 investigate strategies and materials used when measuring with non-standard units of measure (e.g., why feet used to measure length must be placed end to end with no gaps and not overlapping, and must all be the same size; why scoops used to measure water must be the same size and be filled to the top) |
Saying "I lined the blocks up from shortest to tallest." "This cereal box has more capacity than that shoebox. I know because it holds more cubes." "We used five papers to cover the small table. It took us fifteen papers to cover the big table." "Ahmed used his shoes to measure how far it is from the front of the room to the door. We watched to make sure his heel touched his toe every time." Doing A group of children use footsteps to measure the classroom. Some measure the distance from the front to the back of the classroom, while others measure the distance from one side of the classroom to the other. The children then get together to compare their results. Two children are playing in the blocks area with the floor blocks. One of the girls lies down on the floor and says, "See if you can measure me." They try lining up different blocks. At first they use different sizes and have spaces between them. Then one child says, "Wait, you have to put them together like this" (moving them close together). Another child lies down and says, "My turn this time. Try and measure all around me." The educators make a video of the interaction to study it with each other and with the children. They want to notice, name, and talk with the children about their thinking about the concept of using a uniform non-standard unit to measure. Representing A principal is working in the classroom and having a conversation with a child at the snack table. She says to the child, "Where would I find you if you were not at the snack table?" The child says, "The blocks. I built a big boat there before." The principal replies, "I wonder if you and I have the same idea of big in our minds." The child goes over to a measuring tool that the class created for comparing the children's heights over time and measuring growth. The tool is made up of uniform paper squares. The child says, "It was about sixteen floors", then counts the squares to a total of sixteen. He says to the principal as he places his hand parallel to the sixteenth square, "It was about this big." The principal says, "Thanks for showing me how high your boat was." She shows the child what she thought "big" meant, and they compare their thinking and talk about the differences. A child uses a spoon to fill a container with sand and records the results. She then uses a cup to fill the same container and records the results. She shares her learning with an educator: "It took more spoons than cups to fill the container. It took longer with the spoon than the cup." |
Responding To help children recognize that objects have measurable properties, the educators ask questions such as: "What else is as tall as this block?" "Does this water feel warmer or colder than your hand?" "How much does this book weigh? Do you think it weighs more than two wooden blocks?" "Why was it important for Ahmed's heel and toe to touch when he was measuring?" "How would your results have been different if you had filled the cup all the way to the top?" Challenging "Which do you think is bigger, the height or the width of your building? How can you find out?" (Thinking aloud, the educators say): "'Big' can mean different things – for example, it can mean tall, or wide." After watching the video of the children measuring each other, the educators invite the children to watch with them. They ask the children to think about the material they used to measure (blocks), and about other materials they could have used. They also ask the children what they would need to think about the next time they measure something. Extending "The scales say that the large block is heavier than two small blocks. I wonder what you could do to make the scales balance." The educators place two boxes of different sizes on the table with some linking cubes. They ask a small group of children to tell them which box is bigger, and then ask them how they could use the materials on the table to prove their predictions. Some of the children put the cubes in the boxes randomly. Others methodically connect the cubes till the boxes are filled. The educators ask the children, "Which of the ways of filling the boxes with cubes is more accurate? Why do you think that?" Video title: "Numeracy Through the Day" – see the clip "Co-constructing Learning". |
Professional learning conversation
Re. OE16: A group of educators talked about the calendar routine. Four of the educators from two of the classes had removed their daily calendar routine. Two of the educators were sceptical about doing so. Their four colleagues shared that their observations and research showed that the children were not learning about time but were "rote learning" the routine. They said, "We still keep a real calendar in the dramatic play area and use five frames to count down days – such as, 'Four days until we have library time'. We talk about the big idea – that we measure time – but now we use pictures for the flow of the day."
For more perspectives, see the clip: "Why Remove the Calendar Routine? One Educator Team's thinking and connections to the FDELK document".
OE17
As children progress through the Kindergarten program, they:
describe, sort, classify, build, and compare two-dimensional shapes and three-dimensional figures, and describe the location and movement of objects through investigation
Conceptual understandings
- Our world is composed of shapes and figures that are put together in particular ways for particular purposes.
- Shapes and figures have different properties and attributes.
- We can understand and describe our world by looking at how shapes and figures work together.
- When an object changes its position in space, or when we change our perspective on an object, it may look different but it is still the same object.
- We can use positional language to describe an object's location.
- Many of the properties in two-dimensional shapes can also be found in three-dimensional figures.
- The strategy of decomposing and recomposing is useful in all aspects of mathematical thinking.
- The strategy of decomposing and recomposing shapes in geometry helps us think about measurement.
See the Professional Learning Conversation following the chart.
| Specific expectations As children progress through the Kindergarten program, they: |
Ways in which children might demonstrate their learning | The educators' intentional interactions |
|---|---|---|
| 17.1 explore, sort, and compare the attributes (e.g., reflective symmetry) and the properties (e.g., number of faces) of traditional and non-traditional two-dimensional shapes and three-dimensional figures (e.g., when sorting and comparing a variety of triangles: notice similarities in number of sides, differences in side lengths, sizes of angles, sizes of the triangles themselves; see smaller triangles in a larger triangle) |
Saying "We sorted all the triangles. These are all triangles because they all have three sides. Then I put these here because they are all small triangles, and these over here are all big ones. But I made another pile of shapes that look like triangles, but they aren't because their sides are all curvy." "This is a weird, long shape, but it has three sides. It looks like a triangle all stretched out." "That shape is like the roof on my house." "That looks like all the windows in my building." "All of these things are rectangular prisms. I thought this one was, too, but then Erin showed me that the sides aren't straight up and down. So it can't be." "I need some more long blocks so I can make my tower look the same on both sides." See "Kindergarten Matters: Re-imagining Literacy and Mathematics Throughout the Day" – the clip "Re-thinking Mathematics Structures". Doing A group of children sort some found materials using sorting hoops. The children sort according to different attributes. Two children create a game with tangrams. Using a "pretend" line as the divider, one child places a tile on one side. The other child has to put the same tile down on the other side. This continues until they decide their design is complete. They invite other children to play the game, explaining that the rule is that both sides have to look the same. Representing During gym time, the children use their bodies to represent different shapes. The children say to the educators, "We built a triangle." |
Responding "What do you notice about the shape of this card? How would you describe it? Can you think of something that's the same shape?" "Do you see any other shapes that remind you of this shape?" "What did you notice when you moved the shapes around?" Challenging "Use three strips of paper to show me a triangle." "Use your strips to show me something that is not a triangle." When the children say, "We built a triangle," the educators reply, "We were watching you and thought we would come over." The children repeat, "See, we wrote 'The triangle house' and we used a triangle shape for the word." An educator, wondering about the children's working theories, says, "I am looking and I see so many squares." All the children say together, "No, see, they are two triangles and when you put them together they make a square. See, that means there are more triangles." In reflecting on their interactions with the children (to support assessment for learning) the educators note that they also saw and heard evidence of the children's reasoning about quantity relationships, counting strategies, proportional reasoning, connecting, and reflecting. Extending "Look at the objects in the sorting circle. What do you notice about all of these things? Can you tell what rule I was using to sort them? What else could we add to this group?" The educators decide to observe and document the language children use to describe, compare, and sort materials. They talk with the children about their observations. After observing the children making symmetrical designs with the tangrams, an educator decides to further explore the concept of symmetry with the children. She shows the children a series of shapes (e.g., squares, rectangles, kites, rhombi, different kinds of triangles, trapezoids, parallelograms) and asks them to visualize how the shapes would look if they were folded in half. As the children check their predictions, the educator asks questions such as: "What did you notice about the shapes when they were folded?" "What do all the shapes in this pile have in common?" "What do you think would happen if we used a mirror with the shapes that did not fold neatly into themselves?" |
| 17.2 communicate an understanding of basic spatial relationships (e.g., use terms such as "above/below", "in/out", "forward/backward"; use visualization, perspective, and movements [flips/reflections, slides/translations, and turns/rotations]) in their conversations and play, in their predictions and visualizations, and during transitions and routines |
Saying "I am sitting beside my friend." "This book looks different when I stand it up and look at it from above rather than in front of it." (The example illustrates the concept of perspective.) (When working on a picture puzzle): "First we need to flip all of the pieces over so we can see the pictures. Then we just keep turning the puzzle pieces till we find the ways they will fit." "When I close my eyes I can see that the beebot needs to go three steps forward [slide], and then turn right [turn] and go one step forward to get to the flower." Doing Two children work together to build a structure with floor blocks. One child uses spatial terms such as "on top", "beside", and "behind" to describe to the other where to place the blocks. The other child follows these directions accurately. Using tangrams and pattern blocks, children create designs using spatial reasoning: "I can make the designs the same on both sides." "These look different, but they are the same." Two children work to create a design and use non-verbal communication to look at their design on different levels and from different sides. Representing After drawing a map of the classroom, a group of children add directional arrows and labels. They take turns being the "programmer" who provides directions to the "robot" to move from one place in the classroom to another, using language such as "Take five steps forward; turn to the right; take nine steps forward." |
Responding An educator supports the children's exploration of spatial relationships by saying: "Who is in front of you in line?" "Stand near Rosa." "In what ways will the block look different if you slide it forward?" "How did you remember where Saran's snack was?" Challenging The educators lead the children in a game in the schoolyard. The children have to move in the space according to the directions and then describe what they see. As the children's positions change, the educators challenge the children to describe how their perspective on the schoolyard changes. "Move far away from the door." "In what ways do the houses look different now from how they looked before you moved?" Extending The educators create a cube made of linking cubes. The bottom row is red, the middle row is blue, and the top row is yellow. They ask the children: "What do you think this cube will look like if I slide it straight across the table? Get a picture in your head (visualize) of how it might look the same and how it might look different." After sliding the cube, the educators ask the children to check their predictions. They then repeat the sequence, flipping and turning the cube, each time asking the children to visualize how the cube will look the same and different and then giving them time to check and talk about their predictions. One of the educators works with a small group of children who have been exploring flips, slides, and turns with a variety of objects in the classroom. He prints the children's names on individual cards, and then asks them to visualize what they might see when they reflect their names in a mirror, when they rotate them, and when they slide them into different positions on the table. After the children check their predictions, the educator asks questions such as: "Could you still recognize your name? Why?" (Note: Most children will respond that they can still recognize their name because the letters are the same even though in the mirror they appear backwards and in reverse order.) The educator then asks the children to visualize what will happen when they reflect individual letters such as "b", "d", or "p" in the mirror, rotate them, and slide them into different positions on the table. He again asks them to check their predictions, using magnetic or sandpaper letters. (Note: Some children may say that the letters have "turned into" different letters when they are reflected and rotated.) Together they discuss the concept that their names and the letters are like the other objects in the room – they may look different, but they are still the same, no matter how they are moved. |
| 17.3 investigate and explain the relationship between two-dimensional shapes and three-dimensional figures in objects they have made (e.g., explain that the flat surface of a cube is a square) |
Saying "The side of the house I built looks like a square." "I put a triangle inside the square on the geoboard." "There is a circle on the bottom of the cone." "I built a rocket ship. Look at the cone on top. The front is a big rectangle." Doing A child works in the visual arts area, using a stamp to paint each side of the cube, and states, "I have six sides." Representing The children take a photograph of their structure and post it in the blocks area to help them describe to the rest of the class how they built their structure: "We put a row of big blocks on the bottom. On top of them we put smaller cubes." |
Responding "What do you notice about the sides of a cube?" "What do you notice about the bottom of a cone? The bottom of a pyramid?" Challenging While observing a child in the blocks area, an educator says, "I noticed you have used a lot of rectangular blocks. Can you tell me why you chose that shape?" Extending "What do you notice about the blocks on the top (pointing) compared to the blocks on the bottom?" "How did you figure out how to make the structure stable when you changed the blocks on the top?" |
See also OE20: SE20.3 and SE20.4
Professional learning conversation
Re. OE17: A group of educators discussed their evolving thinking about geometry. They reflected that they had previously thought that geometry with young children was about learning terms and vocabulary. After their experience with observing children and documenting their observations, they determined that children compose and decompose shapes constantly in their play. They decided to investigate a professional focus question: "How do children think about the attributes and properties of shapes? " They also read about and discussed how knowing the attributes of shapes (those characteristics that apply to only some of the shapes in a group) and their properties (those characteristics that apply to all of the shapes in a group) is foundational and connected with children's current and later thinking about measurement. Children's knowledge about how shapes are composed informs their later learning about measurement.
OE18
As children progress through the Kindergarten program, they:
recognize, explore, describe, and compare patterns, and extend, translate, and create them, using the core of a pattern and predicting what comes next
Conceptual understandings
- Patterns are predictable.
- There are specific ways we can describe patterns.
- Patterns always have an element of repetition.
- The core of a pattern helps us to think about and name what comes next in the pattern.
- The ability to recognize and understand patterns is helpful in all aspects of everyday life.
- I am learning to communicate why something is a pattern and what comes next.
- If we do something to the front of a pattern, it affects what we do in other parts.
- Algebra can be used to think about mathematical relationships, to communicate, and to analyse change.
See the Professional Learning Conversation following the chart.
Professional learning conversation
Re. OE18: After consulting some professional sources, an educator gives a presentation on the importance of offering children opportunities to explore patterns. Exploration that enables children to develop the ability to notice patterns and generalize from them provides a foundation for algebraic reasoning. (Algebra is the language that allows us to express generalizations in a mathematical way.) The educator understands that children need to extend their ability beyond simply identifying a pattern. They need practice in predicting what will happen, talking about relationships, and seeing connections. The educator decides to use a strategy of covering up the middle of the pattern to require children to engage in more deductive reasoning. She also plans ways to model for children the use of the statement, "I know it is a pattern because...". During professional learning conversations with colleagues, the educators begin to understand how they can further prompt algebraic thinking in children's explorations, translations, and creations of patterns. They see the connections to other aspects of mathematics, such as number and quantity relationships.
OE19
As children progress through the Kindergarten program, they:
collect, organize, display, and interpret data to solve problems and to communicate information, and explore the concept of probability in everyday contexts
Conceptual understandings
- We collect data to learn about and understand the world.
- We pose questions to help us collect data.
- We can collect and organize data in different ways for different purposes. We can represent data in different ways (e.g., using graphs, charts, tables, and other tools). The way we represent data (our choice of tools) is based on the features of the data we want to share to answer our question(s).
- Graphs, charts, tables, and other tools help us see the patterns in the data collected.
- We can make inferences and predictions and draw conclusions based on the patterns we see in the data we have collected and graphed.
See the Professional Learning Conversation following the chart.
| Specific expectations As children progress through the Kindergarten program, they: |
Ways in which children might demonstrate their learning | The educators' intentional interactions |
|---|---|---|
| 19.1 ask questions that can be answered through data collection (e.g., "What is your favourite...?"; "How many pets do our classmates have?"; "Which month had the most snowy days – January or February?"), collect data, and make representations of their observations, using graphs (e.g., concrete graphs such as people graphs or graphs using representational objects; picture graphs) 19.2 interpret data presented in graphs (e.g., "There are more children in the pizza line than in the hot dog line – that means more children like pizza"; "The blue bar is twice as long as the yellow bar"; "There were twice as many snowy days in January as snowy days in February") and draw conclusions (e.g., "There are more blue cubes than yellow cubes"; "January was more snowy than February") |
Saying "Which is your favourite ...?" "How many different ways are there to do up our shoes?" "More people like to eat rice than broccoli. I know because there are more names in this row. I counted them." (Note: It is important, when children are comparing quantities, for the columns and/or bars/rows to be lined up.) Doing A group of children are planning to make soup for the class restaurant. One child starts to write the recipe on chart paper. Another child remembers that, in the survey, more children liked rice than liked broccoli, so the group decide to put four scoops of rice in the soup and only one scoop of broccoli. Two children notice that some creature has dug up the flowers in their garden at home. They wonder if that has ever happened to others. The educators invite them to take a survey to find out. Representing After conducting a survey on pet ownership among their classmates, a group of children create a graph with separate columns showing the number of children who have cats, dogs, birds, hamsters, and fish. They also have a column for "no pets". (Note: It is important, when children are comparing quantities, for the columns and/or bars/rows to be lined up.) |
Responding "How are you going to keep track of the answers to your question?" "How can we decide which way is best to show the data we have collected?" Challenging The educators challenge the children to think about the results of their survey, asking questions such as: "What did you find out?" "How did you find this out?" "How many people did you ask?" "What makes you think that?" "How can we use the data that we gathered?" Extending The educator team plan an inquiry after a child poses the question "How many pockets are on our clothing today?" A team member asks, "What makes something a pocket?" and then asks, "How will we show how many pockets we have?" The team document the children's learning on video. The team then analyse the video with the children to examine the learning and further the children's thinking. |
| 19.3 respond to and pose questions about data collection and graphs |
Saying "I wonder what would have happened if we had added hot dogs to our survey?" "There are five people standing in the laces row and fifteen people standing in the Velcro row. Where are the leftover children standing?" "More people like to eat rice than broccoli. I know because there are more names in this row. I counted them." "There are only two people left on the graph that are four [years old]." "More people picked indoor gym than outdoor gym. See, the line goes higher." (The child points to the bar on the bar graph.) (Note: It is important, when children are comparing quantities, for the columns and/or bars/rows to be lined up.) Doing Children add their thinking to an ongoing class graph in a designated area of the classroom. Both educators and children contribute questions related to things they are curious about in the graph. Representing A group of children use clipboards to take surveys with their friends. The educators take photos of the surveys and project them, to give the children opportunities to communicate their thinking and observations about the data collected. |
Responding The educators have the children line up in two rows to create a concrete graph to respond to a child's question: "Who likes to play in the blocks and who likes to play in the sand?" The educators ask, "What do you notice? Did it surprise you who likes to play in the blocks?" See "Kindergarten Matters: Re-imagining Literacy and Mathematics Throughout the Day" – the clips "Provoking an Inquiry Stance in Mathematics" and "The Inquiry Process in Action". Challenging The educators discuss with the children ways in which they can represent their "people graph" using other materials in the classroom. Extending The educators extend the children's learning about graphs by exploring ideas such as the following:
|
See also OE20: SE20.5 and SE20.6
Professional learning conversation
Re. OE19: An educator suggests an idea to help familiarize children with data and graphs while involving them in planning a field trip. After brainstorming field-trip destinations with children, the educator creates a graph with pictures showing possible destinations and invites children to put a mark on the graph (e.g., their name, their picture, a sticker) indicating their choice. To extend their thinking, the children examine the graph to determine the most popular and least popular destinations. The educators discuss with the children the importance of thinking about the visual message of the graph – in other words, how to read a graph (visual literacy). They ask: "How does presenting the information in a graph help us to think about our trip?"
OE20
As children progress through the Kindergarten program, they:
apply the mathematical processes to support the development of mathematical thinking, to demonstrate understanding, and to communicate thinking and learning in mathematics, while engaged in play-based learning and in other contexts
Conceptual understandings
- We use the mathematical processes embedded in many different contexts to make sense of our experiences and communicate our thinking.
- Problem solving: Problems can be solved collaboratively. There are many ways to solve a problem. Solving problems helps us learn how to think like mathematicians.
- Reasoning and proving: Observing mathematical strategies and talking about them help make us aware of our mathematical thinking. When we explain our thinking and reasoning, we all learn more.
- Reflecting: Reflective statements and questions deepen our understanding by helping us think critically about our answers/solutions.
- Selecting tools and strategies: The processes of thinking about and choosing tools and strategies help us to understand ideas and solve problems.
- Connecting: Connections can be made between the mathematics in play-based learning and questions related to our interests and daily experiences.
- Representing: There are many ways to represent our ideas and thinking. We can show our thinking by using concrete materials, pictures, numbers, and gestures, or by using physical actions, such as hopping, tapping, or clapping, or in various other ways.
- Communicating: Mathematical thinking can be communicated in many ways, including oral, visual, and concrete means.
Note: The specific expectations in the following chart are used as examples to illustrate that the mathematical processes are relevant to and embedded in all expectations that relate to demonstrating mathematics behaviours, regardless of their particular focus (e.g., on number sense and numeration or measurement or geometry and spatial sense).
In the following chart, the mathematical processes that are most relevant in the examples provided are identified in square brackets. (Other mathematical processes may also be involved, but are not stated.)
| Specific expectations As children progress through the Kindergarten program, they: |
Ways in which children might demonstrate their learning | The educators' intentional interactions |
|---|---|---|
| 20.1 demonstrate an understanding of number relationships for numbers from 0 to 10, through investigation (e.g., show small quantities using fingers or manipulatives) 20.2 use, read, and represent whole numbers to 10 in a variety of meaningful contexts (e.g., use a hundreds chart to read whole numbers; use magnetic and sandpaper numerals to represent the number of objects in a set; put the house number on a house built in the blocks area; find and recognize numbers in the environment; write numerals on imaginary bills at the restaurant in the dramatic play area) See also OE15 |
Saying (Pointing to a book): "That is a six. There are six frogs on the log." [reasoning and proving; communicating] "I know there are seven counters because all of the five frame is full and there are two counters left." [reasoning and proving; reflecting; communicating] "I can make seven like this with five here and two here (using hands), and I can make seven like this, with four here and three here." [representing; communicating] "I have five big cubes and five small cubes. They are the same amount. I know because I counted them. But see, it looks like there are more big ones." [reasoning and proving; reflecting; communicating] (This example demonstrates understanding of the concept of abstraction. For a similar example, see OE15 and its related specific expectations.) Doing After hearing a story about children playing hopscotch, a group of children draw a hopscotch court on the tarmac in the playground. They use the picture in the storybook to determine how many spaces their hopscotch court needs. After drawing ten spaces on the tarmac with chalk, one child numbers the spaces from 1 to 10. As the children take turns playing, the educators hear them saying things like, "I'm on five and you're on three. You're two behind me." [connecting; selecting tools and strategies] Representing During a class community walk, a child points to her own house and states that she lives in house number two hundred and fifteen. Another child disagrees with her and says the number is two-one-five. The children collaboratively solve the problem about the house number. The child who lives in the house states that her parents have taught her that she lives in house number two hundred and fifteen, so she must be right. Another child adds that she, too, has heard of numbers in the hundreds. She says that she can even count to one hundred, so two hundred and fifteen must be right. The children continue to engage in discussion with each other and agree to keep walking to explore the other house numbers on the street. [problem solving; representing; reflecting] |
Responding "Which plate has three dots? Which plate has five dots? Which plate has two dots? How can we make the number of dots on the plates the same?" "Two more than five is seven. What is two less than five?" Challenging The educators and children are inquiring about numbers in their environment. The children discover numbers in their environment (in the classroom and around the school, both inside and outside). During this inquiry, the children are exposed to multiple opportunities to explore with numbers and learn how they are used. See "Kindergarten Matters: Re-imagining Literacy and Mathematics Throughout the Day" – the clip "Small-Group Learning About Numbers". Extending During their inquiry about numbers in the environment, the children have multiple opportunities to explore with numbers. Based on their observations, the educators decide to provide opportunities to extend the children's thinking/understanding about numbers by going on a community walk. During the community walk, the educators introduce new vocabulary – words such as "investigate" and "compare" – and challenge and respond to the children's' thinking about what they know about numbers. The children's thinking leads to the question "Why do we have numbers on houses and buildings?" |
| 20.3 compose pictures, designs, shapes, and patterns, using two-dimensional shapes; predict and explore reflective symmetry in two-dimensional shapes (e.g., visualize and predict what will happen when a square, a circle, or a rectangle is folded in half); and decompose two-dimensional shapes into smaller shapes and rearrange the pieces into other shapes, using various tools and materials (e.g., stickers, geoboards, pattern blocks, geometric puzzles, tangrams, a computer program) 20.4 build three-dimensional structures using a variety of materials and identify the three-dimensional figures their structure contains See also OE17 |
Saying "My house has four sides. See, I counted them. When you turn it around it still has the same sides, but two sides look like rectangles. The other two look like squares." [reasoning and proving; communicating] "I put these two triangles together and they make a square, but these two triangles don't. I think it is because they are a different size."[selecting tools and strategies; reflecting; communicating] Doing A small group of children use pattern blocks to compose new shapes (e.g., by using two squares to make a rectangle). [selecting tools and strategies] Using large letter cards and mirrors, children explore the reflective symmetry of letters of the alphabet. [selecting tools and strategies; connecting] After building a structure with wooden blocks, two of the children do a tally to see how many of each shape they have used. They post their findings beside their structure. [reasoning and proving, representing, reflecting] Representing Using found materials of various geometric shapes, some children work together to create a vehicle. [problem solving; representing] After reading aloud a story that is illustrated with tangram designs, an educator asks the children to make one of the designs in the story. The children place the tangram pieces on a design template and then re-create the design by placing the pieces in the same pattern beside the template. [connecting; representing] |
Responding The educators place some magnetic shapes on a cookie sheet for the children to use to compose pictures and designs. They ask: "What happens when you turn the shapes around? When you flip them or slide them? How many sides do you see?" Challenging "You used many different shapes to design your picture. How did you decide what shapes to use?" Extending The educators ask themselves: "How do children compose and decompose shapes when they are building with blocks?" They observe and document as the children work in the blocks area (to support assessment for learning). Later, they share the documentation with the children. The children clarify, add to, and communicate their thinking. The educators project the image of the structure on the whiteboard and flip it to prompt the children to engage in spatial reasoning. |
| 20.5 investigate and describe how objects can be collected, grouped, and organized according to similarities and differences (e.g., attributes like size, colour) 20.6 use mathematical language (e.g., "always/sometimes/never"; "likely/unlikely") in informal discussions to describe probability in familiar, everyday situations (e.g., "Sometimes Kindergarten children like pizza more than hot dogs"; "It is likely that January will be a snowy month") See also OE19 |
Saying "I sorted my animals by size." [communicating] "There are five people standing in the laces row and fifteen people standing in the Velcro row."[communicating] "More people like to eat rice than broccoli. I know because there are more names in this row. I counted them." [reasoning and proving; connecting; reflecting; communicating] "There are only two people left on the graph that are four [years old]." [connecting; communicating] "My brother always meets me at the bus stop after school." [connecting; communicating] "Maybe we will have spaghetti for dinner tonight." [connecting; communicating] "There is no way that a tiger would come to our classroom." [connecting; reflecting; communicating] Doing A small group of children sort books based on the types of pictures on the front cover and describe the reasoning behind their sorting [reasoning and proving; connecting; communicating] Representing After conducting a survey on pet ownership among their classmates, a group of children create a graph with separate columns showing the number of children who have cats, dogs, birds, hamsters, and fish. They select clipboards and decide how to represent the choices on the graph. They use pictures they find online and then ask their classmates to sign their name beside the pet that they have. Midway through the survey they have to add another column that says "No pets". [representing; problem solving; reflecting] |
Responding An educator notices the children sorting the book covers. She joins the group and asks them to talk about their categories for sorting. The children pose a problem for the class to figure out: "Is there one book that can go into two categories?" The educators offer the children some sorting circles (hula hoops) so the children can begin to explore categories visually using Venn diagrams. Challenging The educators challenge the children to think about the results of their survey: "How many children and how many adults were part of your survey?" "What did you find out?" "Were you surprised by what you found out? What did you think would be the most popular pet? What made you think that?" Extending The educators ask the children who conducted the survey to think about the following question: "If you were to ask five more people to tell you what kind of pet they own, what do you predict their answer would be? Why do you think that?" The educators document the children's thinking and how they use their prior experience with the data to think about their predictions, as well as the children's reasoning, communication, reflections, and the connections they make. |
OE21
As children progress through the Kindergarten program, they:
express their responses to a variety of forms of drama, dance, music, and visual arts from various cultures and communities
Conceptual understandings
- The arts are a vehicle for understanding different cultures and communities and expressing our own ideas about them.
- Through interacting with various works of dance, drama, music, and visual arts, including multimedia art works, we deepen our awareness and appreciation of diverse perspectives.
- The arts have symbols that are rooted in a particular social, historical, and cultural context and therefore may have meanings that are different from what we know from our own culture and time.
- The arts provide a natural vehicle through which we can explore and express ourselves.
| Specific expectations As children progress through the Kindergarten program, they: |
Ways in which children might demonstrate their learning | The educators' intentional interactions |
|---|---|---|
| 21.1 express their responses to drama and dance (e.g., by moving, by making connections to their experiences with drama and dance, by talking about drama and dance) 21.2 dramatize rhymes, stories, legends, and folk tales from various cultures and communities (e.g., use actions, pictures, words, or puppets to tell a story in the dramatic play area or in the blocks area) |
Saying "He was wondering what was going to happen when they wouldn't let the new kid play." "I would let them play with me." "That puppet show we saw was just like the story we read." Doing After seeing a production of a familiar story they have previously heard read aloud, several of the children talk about how the costumes and movements remind them of what happened in the book they read. Representing A child uses pictures of faces that express a range of different emotions to identify how she feels at different points in a dramatic presentation. |
Responding "How was the puppet show the same as the story? How was it different? What else did it remind you of?" "What else about the troll was scary?" Challenging One of the children has a family member who is a dancer. The educators invite the dancer to share his dance style with the class. Extending The educators use the children's reflections on the choices made by some of the characters in a favourite read-aloud book as the basis for discussing with the class a social issue that has been happening in the classroom and asking them to suggest ways to resolve the issue. |
| 21.3 express their responses to music by moving, by making connections to their own experiences, or by talking about the musical form 21.4 respond to music from various cultures and communities (e.g., folk songs, Indigenous chants, songs in different languages, Inuit throat singing) |
Saying "I heard that song at a wedding. It makes me want to dance." "I can sing a song in my language." "That music sounds very soft. It makes me feel calm, just like when we do yoga. We should use that music during yoga." "I like using the tablet and headphones to listen to music and stories." "Can we add some music into the background of our story, like in the movies?" Doing The educators have introduced background music in the visual arts area. Children move their paintbrushes to the rhythm and flow of different selections of music. The children spontaneously sing a song from a familiar movie while playing with playdough. Representing A small group of children describe their personal responses to a piece of music. The educators record their responses in an interactive writing experience. |
Responding "What does this song remind you of or make you think of?" "How did you feel when you heard the music?" The educators talk with the children about some of their thinking: "We were thinking about trying to play soft, relaxing music and we want to know how everyone will feel about it." "We can try playing different music at different times to see how it makes us feel and think." Challenging "I noticed that you used the paints to show how the background music made you feel. How could you move your body to show the same thing?" Extending The educators play music from sites they have researched online. Some of the songs have been shared by the families in the community and some are known around the world. Families send in some of their favourite music and tell stories about why it is special. In some cases, families share in their home language, and older siblings in the school support communication. |
| 21.5 express their responses to visual art forms by making connections to their own experiences or by talking about the form 21.6 respond to a variety of visual art forms (e.g., paintings, fabrics, sculptures, illustrations) from various cultures and communities |
Saying "That boy looks scared in the picture. I don't like being in the dark either." "All the wavy lines make the picture look like it is moving." "The sculpture of the soldier in the park looks sad. His head is down, and his eyes are closed." Doing After seeing the fabrics brought in by a classmate's family, a child brings in a kilt made from his family's tartan. Representing After viewing a painting with wavy lines, a child tells an educator that the lines make her think of water. She creates her own art work using the same element: "This is me swimming. The wavy lines mean that the water is moving." A small group of children notice the patterns on the carpet in the blocks area. They find the core of the pattern and explain how that helped them know it was a pattern because they could see (predict) what would come next. They bring their observations to the whole class to discuss: "Are the shapes the same even though this one is facing the other way? How do we know?" "What if I look at the pattern from this side?" |
Responding "When someone's head is down and her eyes are closed, what else might she be feeling (e.g., tired, thoughtful)?" "What does Tia's picture make you think of?" "I wonder why the painter used so many dark lines." Challenging A small group of parents bring in patterned fabrics from their countries of origin and share the stories behind the patterns in the fabrics with the children. Afterwards, an educator discusses the patterns with the children and then invites them to create their own fabric patterns. Extending The educators ask the children and their families to look for examples of art at home and in the places where they work, play, and shop. The children share their feelings about the art that they have viewed: "I saw my uncle's carvings. They looked really heavy." "The store where we shop had photographs for sale. They were pictures of buildings in our neighbourhood. I found lots of shapes in the buildings." |
OE22
As children progress through the Kindergarten program, they:
communicate their thoughts and feelings, and their theories and ideas, through various art forms
Conceptual understandings
- There are many ways to communicate thinking, theories, ideas, and feelings.
- We can discover and interpret the world around us through the arts.
- Through the arts, we can become critically literate and creative citizens of the world.
- The arts provide a natural vehicle through which we can explore and express ourselves in a variety of creative ways.
See the Professional Learning Conversation following the chart.
| Specific Expectation As children progress through the Kindergarten program, they: |
Ways in which children might demonstrate their learning | The educators' intentional interactions |
|---|---|---|
| 22.1 communicate their ideas about something (e.g., a book, the meaning of a word, an event or an experience, a mathematical pattern, a motion or movement) through music, drama, dance, and/or the visual arts |
Saying "That poem has a pattern in it. I can clap the pattern while you say the words." "I don't know what this letter is, but you write it like this (motions in the air to show the letter shape)." Doing When trying to show the motion of a kite flying, the child stands up, throws her hands in the air, and says, "Whoooosh." The educators invite the children to show "five". Over time, the children show "five" in a variety of ways by: - showing various combinations on their fingers; - grouping themselves together; - writing the numeral; - using five of various materials in their structures. Representing A group of children demonstrate spatial reasoning as they create a large floor model from smaller models of various types of spirals seen in the environment. |
Responding The educators show the children a series of paintings and sculptures and keep the art works on display for a period of time. They listen to and record the children's conversations about the art works. The children learn about an artist who uses hearts in his paintings and sculptures and make an immediate connection to their own art works. The educators show examples of work by a Canadian artist who uses dark outlines in all of his paintings and offer the children fine black pens as an invitation to try out the technique. Challenging The children have been creating simple patterns with a variety of materials in the classroom. The educators challenge a small group of children to represent the patterns they have made in music or dance. (Note: This connects to OE18, which deals with patterns.) The educators document and analyse, with the children, a video of children using gestures and the positions (rotating, sliding) of shapes to explore the attributes of shapes. They use the experience to discuss and explore the element of perspective with the children. Extending The educators work with a small group of children to further explore the element of colour in visual art. The children create art works that use one particular colour and also incorporate natural materials, then ask other children to tell them how the art works make them feel. |
Professional learning conversation
Re. OE22: After reading about music education for young children, the educators discuss how music supports the development of reading skills, reasoning skills, math skills, and science concepts, and how it enhances self-esteem. The educators decide to focus first on exploring different rhythms in music, to support the development of reading skills. They decide to use music from the various cultures of children in the classroom in order to help them to make connections to their prior knowledge and experiences. Families volunteer to share recorded music associated with their culture. Children mark the rhythms in different ways and compare them to poems, chants, and songs that have been heard, read, and/or sung in class. The educators observe, record their observations, and discuss how to use their observations in future planning.
Updated: December 15, 2023
Published: August 03, 2016