# kindergarten

### Learning Story for Kindergarten

For kindergarten, students bring their understanding of numbers from their toddler and preschool years to a formal school environment. Opportunities for learning about numbers through play, movement, stories, songs and with materials is important in kindergarten.

In kindergarten, many students may be familiar with oral counting to ten or beyond as they begin the school year. During kindergarten, regular counting experiences help students connect the oral name of the number to a quantity of items and a symbol that represents that quantity. One-to-one correspondence when counting collections to ten is practiced. Students can make reasonable estimates of quantities to ten, using phrasing such as “about five” or “more or less than” to explain their estimate. Subitizing (instantly recognizing a small quantity without having to count) is a key indicator of mathematical understanding and further achievement in math and is a skill that can be practiced through dot cards and with materials. Kindergarten students use materials to build (compose) and break into parts (decompose) quantities within ten. Through these experiences and use of tools such as ten frames, students develop a sense of five and ten. Along with counting, being able to make five and ten and compose decompose quantities within 10 are important foundational concepts and skills for developing addition and subtraction concepts in grade one.

### Key Concepts

#### Counting to 10

Students are able to count to and from 10 using stable order counting orally, using one-to-one correspondence when counting objects or images, and demonstrate an understanding of cardinality (knowing that last number said when counting represents the total quantity counted). Students are able to compare magnitude within ten, knowing that 8 is more than 2 or 4 is one less than 5. Students will engage in counting collections using a variety of counting materials and strategies, including estimation.

#### Subitizing

Students are able to instantly recognize and name small quantities of objects or images/dots without counting. Kindergarten students generally can subitize 1-5 and flexible subitizing with different types of dot patterns is developed.

#### Composing and Decomposing Numbers to 10

Students learn to build and to see numbers in terms of their parts-whole relationships. Students compose and decompose quantities (how many ways can you make 5?) using materials and pictures. Students will develop a sense of five and ten and use five and ten as benchmarks to think about other numbers (7 is five and two, 9 is one less than 10).

#### Key Number Concept 1: Counting to 10

##### Overview

Kindergarten students bring many informal counting experiences from home into the classroom. This is an opportunity to honour children’s home languages and have students share how they count to 10 in their home language. Many kindergarten students will know how to orally count to ten as a chant, but need support in counting items with one-to-one correspondence. Counting skills are practiced with materials, movement games, songs and other experiences that connect concrete, pictorial and symbolic forms.

##### Number Sense Foundations:

The following concepts and competencies are foundational in developing understanding of counting in Kindergarten and are based on informal counting experiences at home and in pre-school learning environments.

• a sense that numbers are used to describe “how many?”
• number sequence to 10
• Counting orally by ones to and from 10
• oral number names to 10
• one-to-one correspondence may be developing (each object in a collection is counted once)
##### Progression:
• Counting begins with understanding that number names describe “how many?”
• Young children may learn the counting “chant” and count along with number names (often in random order) as they walk up the steps or “count” their collection of toy dinosaurs.
• Children develop a stable number order sequence when counting.
• Children develop how to count a collection of items.
• At first, children may touch the items and count but not keep track of which items they have counted and may not use a stable sequence of numbers when counting.
• Children with one-to-one correspondence may move each item to a new pile and name it as they count it. With growing counting confidence, they may do the counting sequence silently.
• They may take an unorganized pile of counters and put them in a line to count, touching each one as they count.
• Children may count with their eyes, often including a bit of a head nod as they count each item.
• Children demonstrate cardinality. Once they have counted a collection of items, and are asked, how many are there? they know to reply with the last number they named and that this number represents the whole quantity counted.
• Children can count a specific amount from a collection of materials. “Can you count 8 of those for me??
• Children develop an ability to count on, once cardinality is established. If there is a collection of six the student has counted and then three more objects are added, they may be able to count by saying 6…7, 8, 9.
##### Sample Week at a Glance:

Before this week of lessons, Kindergarten students will have participated in whole class oral counting tasks including counting the number of students in the class, how many pencils in each table group’s tub, and have done the routine of counting collections a few times. This week is focusing on counting quantities to five so is appropriate for earlier in the school year.

Before

Read the picture book: Pete the Cat and His Four Groovy Buttons. As you are reading, stop and pause and have students count the number of buttons with you, as you point to the illustrations. You may also choose to introduce another language for counting as well. French, ASL,  a local Indigenous language or one of the student’s home languages.

(or choose a book that has illustrations that students can count with you)

During

Provide a collection of buttons or counters to each table group. Invite students to each choose a small handful of buttons and count them by 1s in different ways such as putting them in a row, moving them from a pile, or counting as you place each one in a cup. Invite each table/group of students to count out and leave collections of four buttons or counters on their table. Invite students to count the buttons in different languages and practice one-to-one correspondence.

After

Bring students together and refer back to the illustration in the book of Pete’s four buttons. Invite students to look at their own clothing or shoes and count something. Invite some students to share what and how they counted.

Before

Math Routine: Number Talk Images/Dot Images

Hold up a dot card with a quantity of 4 or 5 dots. Ask students: “How many dots and how do you know?” Invite students to share the different ways they counted or “saw” the dots. Repeat with another dot card or projected slide of dots.

During:

Math Workshop

-number arrangement cards with counters for students to place on top and count

-small sets of counting collections for students to count in partners

-number cards from 0-5 for students to put in order

-teacher led small group instruction: practice counting small sets of items focusing on one-to-one correspondence and cardinality

After

Closing circle: Invite students to share what they did, what they learned and what they think they need to practice next.

Before

Share a video such as Let’s Count the Moons and discuss how in many Indigenous languages the words we use to count with depend on what it is we are counting. Practice saying the first three or four number names in hən̓q̓əmin̓əm̓ or other local Indigenous language.

During

Go outside for a counting walk (or within your school). What can we count? Encourage students to find different groups of items to count (ie. trees, leaves, homes, rocks, street signs, etc) and practice counting in both English and hən̓q̓əmin̓əm̓ or other local Indigenous language

After

Closing circle: Invite students to share what they counted and how they counted them. Were some items more difficult to count than others? For example, birds flying or something far away. What counting strategies did you use if you couldn’t touch the items?

Before

Math Routine: Number Talk Images

Choose a photograph with a quantity of five. Ask students: “How many and how do you know?” Invite students to share the different ways they counted or “saw” the items. Repeat with another number talk image.

During

Math Workshop

-number arrangement cards with counters for students to place on top and count

-counters/materials and an iPad or camera for students to take photographs of their own number talk images

-dice, counters and five frames (roll dice, build number on five frame)

-teacher led small group instruction: felt board story of five speckled frogs, practice counting to five and then backwards from five as frogs jump into pond

After

Closing circle: Invite students to share what they did, what they learned and what they think they need to practice next.

Before

Five Speckled Frogs story or song using magnets or frog images or puppets to act out story. Practice counting to and from 5.

During

Math Workshop

-number arrangement cards with counters for students to place on top and count

-counting collections to 10-12 with ten frames as a tool to support counting

-dice, counters and five frames (roll dice, build number on five frame)

-teacher led small group instruction: assessment interview with each student, counting a collection of five objects (check for number sequence, one-to-one correspondence and cardinality)

After

Closing circle: Invite students to reflect on what they practiced today and what their counting goals are. Invite them to share what counting strategies they are using.

Based on formative assessment information from this week, next week’s planning would include developing number concepts, including counting with quantities of 6 and 7, connecting to the benchmark number of 5.

##### Suggestions for Assessment

By the end of Kindergarten, students will be able to count to and from 10 fluently both orally and by counting small sets of items to 10. Performance task-based math conferencing or interviews can be done throughout the school year to monitor progress with counting.  This could look like asking each child to count to 10 orally and then also providing them with a collection of 10 objects and asking them to count them for you – noting correct use of number names, number sequence, one-to-one correspondence and cardinality. Instructional practices such as reading counting stories, singing counting songs and doing counting finger plays are a form of formative assessment as you notice students’ ability to follow along with the embedded counting experience. Routines such as choral counting, counting collections and clothesline help students to make connections between different representations of numbers, see patterns and practice symbolic notation of numbers and can be a rich source of observational assessment information – watch and listen as students engage in whole class or small group discussions using these routines.

Ten Black Dots by Donald Crews (picture book)

Five Speckled Frogs (picture book)

Let’s Count the Moons (video)

Choral Counting and Counting Collections: https://www.stenhouse.com/content/choral-counting-counting-collections

Number Arrangement Cards from Kathy Richardson

Number Talk Images

#### Key Number Concept 2: Subitizing

##### Overview

Subitizing is an important number concept in the early years and is a key indicator of overall success in mathematics. It involves both number and spatial relationships and competencies such as visualizing. Subitizing is knowing how many of something there are without having to count. There are two types of subitizing: perceptual (instant recognition, usually for numbers 1-3) and conceptual (students may mentally decompose the quantity into parts such as seeing 5 as 2 and 3).

##### Number Sense Foundations:

Children may bring experience with card and dice games that have begun their development of subitizing during their early years at home or in preschool learning environments. The following concepts and competencies are foundational in supporting understanding of subitizing:

• Number names for 1-6
• Recognizing familiar dot patterns such as found on dice and dominoes
• Visualizing and holding mental images
##### Progression:
• Young children develop an understanding that “how many?” of something can be described with a number name
• Children learn the number names and can assign them to small quantities such as 1-5
• Children are able to instantly recognize small quantities or items (either objects or images) such as 1, 2 or 3 without having to count them (perceptual subitizing).
• Students begin to be able to subitize quantities such as 4, 5 and 6 especially with experience using the regular dot patterns found on dice and dominoes. They may be mentally seeing a quantity in parts to help them subitize.
• Students are able to subitize irregular or unfamiliar dot patterns.
##### Sample Week at a Glance

Before this week of lessons, Kindergarten students will have done some initial subitizing tasks such as quick image dot cards. These lessons are suitable for the first half of the school year in Kindergarten

Before

Read Ten Black Dots by Donald Crews, stopping to  have students discuss the different ways the dots are arranged. Share the word “subitizing” and explain that some amounts we know right away, without having to count.

During

Provide students with black circles or counters and have them choose a quantity between 3-7. Have them arrange the materials in different ways, thinking about how the arrangements help them know how many there are. Invite students to draw their own dot pictures with their arrangements.

After

Have students share and compare the ways they created their dot pictures.

Before

Math Routine: Quick Images with dot cards (hold up dot card for 1-2 seconds and then put down, ask students how many dots they saw and how they saw them, focus on subitizing and explaining how they see the amount)

During

Math Workshop: Students choose learning experiences focused on the concept of subitizing.

-Dot Cards with a partner

-Number Arrangement cards and materials (to place on)

-TouchCounts app

-Teacher led small group instruction: roll regular dice and have students call out quantity (subitizing) or count, share different ways to see the quantity of dots; on a mini-whiteboard, create a tally graph for the number of rolls for each number 1-6

After

Closing circle: Invite students to share what they did, what they learned and what they want to practice next.

Before

Math Routine: Same But Different

Use an image from the early numeracy section of Same But Different  or two Tiny Polka Dot Cards or something similar (different organizations of dots) and ask students to think about how they are the same and how they are different.

During

Play Dot Memory with partners of students. Using dot cards, ten frame cards, playing cards or Tiny Polka Dot cards, have partners turn over the cards face down in an array. Partners take turns turning over two cards, subitizing or counting the quantity and if they match, they remove those two cards. If they don’t match, the student puts them back face down and it is the other student’s turn. Play until all cards have been matched and removed from the array.

After

Closing circle: Invite students to reflect on how different organizations of dots make subitizing more or less difficult for them. Have students share what visualizing strategies they use.

Before

Math Routine: Quick Images with ten frames (visualizing different ways to see quantities)

During

Math Workshop: Students choose learning experiences focused on the concept of subitizing.

-Dot Cards with a partner

-Ten frames with a partner

-Roll and Graph math game (roll a dice, subitize or count quantity and record on a tally graph)

-Teacher led small group instruction: math story with counters (fish) under a paper lily pad, lift lily pad and ask students to subitize quantity (use quantity from 1-5)

After

Closing circle: Invite students to share what they did, what they learned and what they want to practice.

Before

Teach students how to count to 5 in ASL.  Share signs for different numbers and have students match with their fingers/hands.

During

Math Workshop:

-Dot Cards or Ten Frames with a partner

-Dice (1-6) Games

-Number Arrangement cards

-TouchCounts app

-ASL cards – copy signs with hands and order cards from 1-10

-Teacher – assessment check-in with each student;  dot cards and subitizing 2, 3, 4 and 5

After

Closing circle: Reflection and self-assessment of where students are in their ability to subitize. Hold up dot cards from 1-6 and ask students to use the ASL sign for that number if they are able to subitize that amount.

Based on formative assessment information from this week, next week’s planning would include extending ways to use subitizing to compose and decompose numbers and practice counting on. Note whether students need more practice with subitizing unfamiliar dot organizations.

##### Suggestions for Assessment

By the end of Kindergarten, students will be able to subitize quantities to five (some may subitize beyond but are likely counting on or composing two parts mentally) and explain their thinking and visualizing strategies. Over the school year, teachers can have a collection of dot cards (both regular and unfamiliar dot patterns with quantities from 1-6) and do short math interviews/conferences with each student.

#### Key Number Concept 3: Decomposing

##### Overview

In Kindergarten, build and take apart quantities of materials to 10. They may use math manipulatives like Unifix Cubes, rocks or leaves outside, or loose parts such as glass gems or bottle caps. Kindergarten students begin the year think about ways to make five and may use a five frame to support their thinking. As the year continues, students are composing and decomposing quantities to ten and use a ten frame as one tool to support their thinking. It is important for Kindergarten students to use five as a benchmark number when thinking about other numbers. For instance, a student might compose seven by thinking about five and two more. Students are expected to decompose quantities flexibly and fluently and are often asked: How many different ways can you make (or decompose) 10? Students can make ten using two parts (6 and 4) or with multiple parts (4 and 2 and 3 and 1). Being able to “play” with numbers in many ways supports students’ thinking with addition and subtraction in grade one.

##### Number Sense Foundations:

Young children bring their understanding of number with them to Kindergarten. Many children will be able to hold up their fingers to show how old they are or give you three of something if you ask them to. The following concepts and competencies are foundational in supporting understanding of decomposing in Kindergarten:

• A general sense that number words or symbols represent a quantity
• A sense of five-ness developed through understanding their age and how many fingers they have
• Counting and matching number names or symbols to quantities
##### Progression:
• Students understand that a number name or symbol represents a quantity.
• Students understand that a quantity is made up of parts, either individual units or combinations of units.
• Students understand that a quantity can be broken into parts and put back together again and retain the same quantity.
• Students understand that composing and decomposing quantities of objects can be represented with pictures, symbols and numbers and with tools such as ten frames.
• Students are flexible in their thinking and realize that quantities can be decomposed and composed in many different ways, sometimes with two parts (4 and 6 make 10) and sometimes in multiple parts (3 and 3 and 2 and 1 and 1 make 10).
##### Sample Week at a Glance

Before this week of lessons, students have had many experiences with ways to make five and using five and ten frames. This series of lessons is suitable for the second half of the school year.

Before

Read Twelve Ways to Get to Eleven by Eve Merriam. Playfully engage with the illustrations in the book.

During

Invite students to choose a number between 5-10 and use concrete materials, pictures and symbols to make that number in many different ways. They may be encouraged to annotate their representations with words and numbers. Take a photograph of each student’s collection of ways to make their number.

After

Closing Circle: Choose two or three of the students’ photographs and project them so everyone can see them. Invite the students to share their thinking and strategies for representing their number.

Before

Math Routine: Number Talk Image

Choose a photograph with a quantity between 8-10 and project for all students to see. Ask students to turn and talk to share different ways they see the quantity. Record some of their “ways” and discuss/compare.

During

Math Workshop: Students choose learning experiences focused on the concepts of decomposing.

-Students choose a number card and represent that number using multiple materials (glass gems, dot cards, number cards, tallies, ten frames, etc)

-Make Ten math game – roll dice and place that number of counters on a ten frame and then call out what the other part is to make ten, partner checks student’s thinking and then takes their turn

-TouchCounts math app

-Teacher led small group instruction: Using the number 9 (or adapt for students) invite students to show you three or more ways to make 9 using a set of counters, checking for fluency and flexible thinking

After

Closing circle with students share what they did, what they learned and what they want to practice next.

Before

Math Routine: Splat!

Choose a Splat! with a total quantity between 8-10 and focus on having students share their strategies for figuring out how many dots are under the Splat! (parts-whole thinking).

During:

Math Stories – Model a short math story using Splat! as an inspiration (frogs under a lily pad, penguins under an ice floe, etc). Invite students to create their own math stories focusing on a missing part. Have partners share and solve each others’ math stories. Provide ten frames as tools to support student thinking.

After

Closing circle: Choose one of the students’ stories to discuss and solve as a class. Consider how to decompose the quantity into more than two parts and how the story would have to change for this. Invite students to brainstorm new math story ideas for Math Workshop tomorrow.

Before

Math Routine: Ways to Make 9

Invite students to share different ways to make 9 (ie 5 and 4, 3 and 5 and 1) recording their ways with numbers and words or using number bond notation).

During

Math Workshop:

-Ways to Make 10 (or choose a different number) – record on whiteboards or represent with materials

-Math Stories, continue math stories creation from yesterday

-Make Ten math game – roll dice and place that number of counters on a ten frame and then call out what the other part is to make ten, partner checks student’s thinking and then takes their turn

-Teacher led small group instruction: Using the number 9 (or adapt for students) invite students to show you three or more ways to make 9 using a set of counters, checking for fluency and flexible thinking

Closing circle with students share what they did, what they learned and what they want to practice next

Before

Math Routine: Quick Images

Using number arrangement cards, and hold up an image for 2-3 seconds and ask students to hold the image in their mind. Have students share how many items they think there are. Hold up the image again and have students describe how they saw the quantity.

During

Using number arrangement cards for 9 and 10, invite students to choose counters in three colours and cover the number arrangement cards with quantities, thinking about parts-whole relationship. Students could record their combinations for that number on a whiteboard or paper.

After

Closing circle: Invite students to reflect on what they have learning about numbers this week and set a goal for their own learning for next week.

##### Suggestions for Assessment

By the end of Kindergarten, students are expected to fluently and flexibly compose and decompose quantities to ten using both five and ten as benchmark numbers. They are able to think about parts-whole relationships concretely, pictorially and symbolically. An assessment task for the end of the year would be to ask students to make 10 in many different ways with materials, tallies or pictures, using two-part relationships as well as multi-part relationships. At the end of Kindergarten, most students will be able to make ten in at least three different ways.

Twelve Ways to Get to Eleven by Eve Merriam (picture book)

Number Talks (link to info on site)

Number Talk Images http://ntimages.weebly.com/

Number Arrangement Cards to 10 (Kathy Richardson)

Splat! Math Routine