first 20 days of instruction kindergarten mathematics

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First 20 Days of Instruction

Kindergarten Mathematics

Table of Contents

Lesson/ Activity Resource Page(s)

1st Week of School 5E Lesson Model 1 - 5

1st Week of School Student/ Activity Pages 6

2nd Week of School 5E Lesson Model 7 - 12

2nd Week of School Student/ Activity Pages 13 - 18

3rd Week of School 5E Lesson Model 19 - 23

3rd Week of School Student/ Activity Pages 24 - 26

4th Week of School 5E Lesson Model 27 - 32

4th Week of School Student/ Activity Pages 33 - 49

Additional Resources

Multiple Representation Number Line Cards (Counting Jar) 50 - 55

Individual Student Number Lines (1-20) 56 - 57

Gumball Counting Game (Making Equal Sets 1-10) 58 - 60

0-10 Multiple Representation Number Wall Display 61 - 71


Lesson Name: Taking Inventory of Ourselves and Classroom Materials

Estimated timeframe: 1st Week of School

Lesson Components

Lesson Objectives: The student will practice counting by rote to 20, focusing on maintaining the correct counting sequence through the digits (1-9), the teens (10-19) and transitioning to 20.

Language Objectives: The student will learn to recite the counting word sequence 1-20.

Prior Learning: Students should have an informal understanding that counting is a process for telling how many. To engage in counting, the child should know the majority of the counting word sequence to 10, not necessarily in order.

Standards (Texas Essential Knowledge and Skills): K.2A count forward and backward to at least 20 with and without objects;

K.2C count a set of objects up to at least 20 and demonstrate that the last number said tells the number of objects in the set regardless of their arrangement or order;

K.5 recite numbers up to at least 100 by ones and tens beginning with any given number.

Essential Questions: 1. What do numbers tell you/ not tell you? 2. How do you determine how many things or people there are? 3. Why do the counting words we say always go in the same order?

Vocabulary Lesson Preparation Order, sequence, count, numbers, one-to-one, perseverance, effort, strategy, counting words 1-20, calendar, attendance

Snap cubes (20 per pair of students in the class)

vertical number line (1 to 20) displayed on chart paper—e.g., 1 on the bottom and 20 at the top

Itsy Bitsy Spider song displayed on chart paper

2’ string per pair of students

Classroom calendar

Individual Student Calendars (See Attachment)

Emily’s First 100 Days of School by Rosemary Wells

Lesson Cycle

Engage

Schedule of Sessions from Unit 1 “Who Is In School Today? Investigations (2nd Edition)

Monday Tuesday Wednesday Thursday Friday

(Engage/ Explore/ Explain sections.) Session 1.1 (p. 24) The Attendance Routine

Session 1.2 (p. 32) Attendance: Counting Around the Circle

Session 1.5 (p. 44) Comparing Materials

Session 1.6 (p. 47) Making an Attendance Stick

(Elaborate/ Evaluate sections.) Session 1.4 (p. 41) Calendar

Morning Opening (Attendance Routine): (15 minutes)

Introduce the “Attendance Routine: How Many Are We?” Session 1.1 (p. 24) from Unit 1 of the Investigations In Number, Data, and Space (2nd Edition) Teacher’s Manual. Continue to revisit this routine throughout the week, introducing various components and variations that can be used throughout the year. See the recommended timeline in the above table:

Math Time: (Monday)

Refer back to the attendance routine you introduced during the morning opening. Point out that this is a procedure that you conduct in order to welcome each child every morning and also as a way to keep track of all the children


who are present at school that day (e.g., if someone were to get lost, taking attendance allows you to count and compare the number of children returning from the playground or from lunch to the total you counted in the morning). Emphasize that the attendance procedure is a safety measure to make sure that all children are accounted for. When you introduce the attendance stick on Thursday, break off and distribute one cube at a time to each child upon returning from lunch or recess. Point out that if no cubes remain, everyone has returned safe and sound to the classroom. Store the stick in a “treasure box,” emphasizing that the children are your special treasure of whom you have the responsibility to keep safe.

Introduce the song, “The Itsy Bitsy Spider.” As the students sing, model the finger movements—e.g., go up the water spout by switching back and forth with the pointer finger on one hand touching the thumb on the opposite hand; join both hands to make an arch, raising it slowly to demonstrate the sun coming out of the clouds; cross hands back and forth to mimic the sun drying the rain.

The Itsy Bitsy Spider Went up the water spout; Down came the rain And washed the spider out; Out came the sun And dried up all the rain; And the Itsy Bitsy Spider Went up the spout again.

Emphasize the effort and persistence that the Itsy Bitsy Spider put forth to continue her trek up the water spout in spite of all the adversities—e.g., the rain.

Tell the children that when they are solving problems or attempting to do something new, they should also use effort and persistence to keep going, even when the task is difficult.

Inform the children that throughout the year, they will practice counting up to 100. Explain that for today, they will make a partial effort toward this goal, counting by ones up to 20 instead of all the way to 100.

Display a vertical number line illustrated on chart paper with the number 1 oriented at the bottom and 20 at the top. Relate the vertical progression of the number line to the upward ascent that the Itsy Bitsy Spider made as she climbed the water spout. Say: “When we count, we start at the bottom at one and move up.”

Explain to the children that you will show them how to make a water spout with 20 snap cubes. As you build a tower of 20 snap cubes, prompt the class to count with you as you join each cube together one by one—e.g., as you take one cube say a corresponding count word: “one (take one cube), two (snap on cube on top), three (snap another cube on top), etc.”

Exploration

Dual Language Activity 1: (This activity is also appropriate for all classrooms)

Distribute bags or bins of snap cubes to groups of students. Pair children with a partner.

Instruct each dyad to work together to count out 20 cubes and then build a tower. Distribute the work load evenly among each partner by having both children count out as many cubes as there are fingers on his/ her hand (10 all together). Then, direct both students to join their tower of 10 together and double check/ count to be sure there are 20 altogether.

Ask: How do you know you have 20? What strategy did you use to help you count and keep track of how many cubes

Attendance Routine

CChhiillddrreenn

““ccoouunnttiinngg ooffff””

NNoott HHeerree


you had altogether?

When each pair of children has completed their tower, encourage them to write their names on a Post-it Note and attach it to the tower.

Math Stations/ Centers (Monday-Friday):

Dismiss the children to a math station where they can continue to explore new materials—color tiles, pattern blocks, Geoblocks, snap cubes, buttons, etc.

Explanation

Debriefing Math Stations Centers (Monday):

Gather the group back together and distribute to each pair of children their respective tower of 20.

Lead each dyad in reciting the 1-20 sequence and counting one-by-one as a whole group. To do this, have one partner point to each cube as his/her friend recites the counting sequence to 20. Remind the children to start at the bottom and count up. Then, proceed to another round, allowing the partners to switch roles—e.g., as one child counts, the other points to each cube on the cube stick.

Complement the children on their persistence and effort. Lead the group in singing the following addition to the Itsy Bitsy Spider song:

The Itsy Bitsy Spider Climbed to the very top; Hesitated for the moment But she never stopped; When she reached her goal She waved to all her friends; And the Itsy Bitsy Spider Went up the spout again.

Math Time (Tuesday –Friday):

Begin to create a “What Good Counting Looks Like” chart with the group. Revisit this chart and make additions to it throughout the week (Tuesday – Friday) as you observe the children implementing appropriate counting strategies—e.g., double checking, using one-to-one correspondence. Make these observations during math stations/ center time as the children are exploring the classroom materials they will be using throughout the year.

Elaboration

Math Time (Friday/ End of the week):

Draw the students’ attention to the classroom calendar and ask for ideas about its purpose.

After the students have shared their ideas, introduce Emily’s First 100 Days of School by Rosemary Wells (This book is available in Spanish) or Pepper’s Journal by Stuart Murphy. Each of these books shows how calendars are used to mark and keep track of important events. Do not read Emily’s First 100 Days of School in its entirety. Instead, read only up the first 5 days of Emily’s school year and relate this to the first 5 days that your students have been in school.

What Good Counting Looks Like

1. Count slowly 2. Say the numbers in order—e.g. “1, 2, 3, 4, 5” not “2, 1, 4, 6, 3.” 3. Double Check 4. Point to each cube on the stick as you count. 5. Report the total when you are finished counting.


Point out how you will use the calendar to count and keep track of the number of days the children have been in school. Mention how you will also use the calendar as a tool to advertise and post important events, such as birthdays, field trips, assemblies, etc.

OPTIONAL: Make a classroom journal that you can display on the wall. Title it, “Our First One-Hundred Days of School.” At the close of the first day of classes, read only the section from Emily’s First 100 Days of School that describes and illustrates what she did her first day of school. Illustrate and write out on an index card about an important event that occurred in your classroom on the first day of school. Post the picture on the 100 Days of School Wall and label it with the numeral ‘1’. At the close of each day, invite one student to illustrate/ write one entry to include on the wall. Post the corresponding numeral beside the student’s illustration. Continue adding entries up to the 100th day of school.


Pass out blank calendars to each student so they can make their own August calendar to take home.

Encourage the students to copy the August calendar displayed in the room and to mark important days like the first day of school.

Allow the students to help each other write numerals or draw pictures. Many will not be able to write numerals. You might want to distribute a chart with numerals for the students to copy. Do not insist that the students write all of the numerals, as this might be too overwhelming.

As students finish, they may continue to select from the free exploration choice time activities.

Evaluation (check for understanding)

Formative: As the children are working in pairs to create their tower of 20, take anecdotal notes or create a checklist to indicate which group of children needs assistance to make a set of 10, which ones use the number of fingers on their hands to help them make an equivalent set of 10, and which ones have achieved a mastery level—e.g., those who count out a set of 10 cubes accurately without referring to a model (e.g., a number line or the fingers on their hand.) Summative: (One-on-one interview): During centers, show each child a pile of about 21 counters. Prompt the children to estimate how many cubes there might be. Then, instruct the child to count the set to verify the estimate. After the child counts, ask him/ her how many cubes were just counted.

Does the child count each object once and only once?

Does the child say a counting word for each object he/she counts? If so, up to what number?

Does the child recite the counting word sequence from one to twenty? If so, up to what number?

Does the child demonstrate the cardinal principal of number—that the last word in the count tells how many?

English Language Proficiency Standards

ELPS (c) 2.B Recognize elements of the English sound system in newly acquired vocabulary.

Anchors of Support

Make available a ‘1-20’ number line with a space underneath each numeral for children to be able to keep track of how many items they have counted (Refer to the individual number lines located on pp. 56-57). Place a happy face and a left-to-right arrow to show where to begin and how to proceed in the counting sequence.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

College and Career Readiness

I.D.1. Self-monitor learning needs and seek assistance when needed.

I.D.3. Strive for accuracy and precision.

21st Century Skills

Use systems Thinking – Analyze how parts of a whole interact with each other to produce overall outcomes in complex systems.


Differentiation strategies

Special Education: Encourage the children to match the snap cubes to each finger on their hand as they make a tower of 10 cubes. Then, pair children who have difficulty keeping track of large quantities with a more competent counter. Encourage partners to work together to check each other’s cube stick of 10.

English Language Learners: Point to each numeral on the vertical number line as you guide the class in the rote counting sequence. Although English Language Learners may not know the English counting word sequence, they perhaps will more readily recognize the numerical symbols (digits). This accommodation will allow ELLs to assign a visual representation to their newly acquired rote counting English word sequence. NOTE: Some cultures (e.g., Mandarin Chinese, Korean, etc.) have different number symbols. In addition, pair an emergent ELL with a more fluent English speaker as they practice the 1-20 counting sequence.

Extension for Learning: Encourage those children who have mastered to 1-20 sequence to continue the count up to 30. After they count, prompt them to share what they notice about the 20-29 sequence. Ask: Which numbers repeat? What comes after 29? If time permits, discuss the grouping of numbers by decades.


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Lesson Name: Getting to Know Our Classroom Materials: Describing Attributes and Sorting

Estimated timeframe: 2nd Week of School

Lesson Components

Lesson Objectives: The student will be able to sort and differentiate among manipulative materials by attending to likenesses and differences in relation to their mathematical attributes—size and shape.

Language Objectives: The student will be able to compare and justify sorting rules using language that describes

mathematical attributes related to size and shape.

Prior Learning: Students should have basic vocabulary for describing attributes such as color, texture, and appearance.

Standards (Texas Essential Knowledge and Skills):

K.2C count a set of objects up to at least 20 and demonstrate that the last number said tells the number of objects in the set regardless of their arrangement or order; K.8A collect, sort, and organize data into two or three categories;

Essential Questions:

1. How are you able to tell if an object is alike or different from another object? 2. What words do you use to help you describe an object’s shape and size? 3. How do you tell which objects go together?

Vocabulary Lesson Preparation

Attribute, shape, size, sort, alike, different, strategy,

part, whole, observe, circle, square, triangle

Seven Blind Mice by Ed Young

Corduroy by Don Freeman

Brown Bear, Brown Bear by Bill Martin Jr.

Chart paper

Classroom manipulatives (e.g., buttons, pattern blocks, color tiles, snap cubes, Geoblocks, ect.)

Individual baggies with 10 manipulatives materials (per pairs of students)

Floor Puzzle

Button Cards (See attachment)

Dice Game Attribute Cards (See attachment)

Which One Does Not Belong (See attachment)

Lesson Cycle

Engage

Schedule of Sessions from Unit 1 and 2 “Who Is In School Today? Investigations (2nd Edition)


LABOR DAY HOLIDAY

Session 1.4 (p. 41) Calendar: Adding Special Days Introduce the Exemplar Lesson outlined in the Engage/ Explore/ and Explain sections below

Introduce Session 2.2 (p. 64) Describing Buttons and Session 2.3 (p. 70) Button Match-Up. Encourage the children to use attribute vocabulary as they explore and sort the materials. Observe the children and debrief each session by adding good strategies for using and taking care of materials to the Proper Usage of Materials Chart.

Continue with the Exemplar Lesson outlined in the Elaborate/ and Evaluate section.

OOppttiioonnaall:: Session 2.4 (p. 76) Attribute Match-Up


Morning Opening (Calendar Routine): (15 minutes)

Revisit the calendar routine as outlined in Session 1.4 “Calendar: Adding Special Days” (p. 24) from Unit 1 of the Investigations In Number, Data, and Space (2nd Edition) Teacher’s Manual. Plan and plot out special occasions/days that will occur in the new month of September. Lead the class to help you to determine where each numeral will go, starting with the first day of the month. Count down 30 spaces to mark the last day of September. Emphasize the left-to-right progression and return sweep pattern you use to enumerate the squares.

Math Time: (Tuesday)

Show the students a box labeled with a question mark. Inform the students that you have hidden something from the classroom inside the box and that their job is to figure out what the mystery object is. Lead the class in a discussion on how to figure out what is inside the box:

How could we figure out what is inside this box without removing the mystery object?

Since we cannot see what is inside the box, which of our other five senses could we use?

If you felt what was inside the box, what words do you think you would use to describe the object’s texture (tell how it feels)?

Point out that the words we use to describe objects are attributes.

Explain the rationale for reading the book, Seven Blind Mice by Ed Young: o This book introduces us to a group of seven mice who cannot see. When animals or people cannot see, we say

that they are blind. Each of these seven mice has a different way of figuring out the identity of a strange something that shows up one day at a nearby pond. As I read the book, think about which of these seven blind mice has the best strategy for figuring out what the strange something is.

As you read the book, pause after each mouse investigates the strange something’s identity. Prompt the students to explain if they agree or disagree with each mouse’s observation.

After reading the book, ask the students to discuss why the white mouse was able to figure out the true identity of the strange something. If no one points out her strategy, explain that the white mouse was successful because she went around the whole something, investigating all of its parts instead of stopping at the first part she approached. Tell the students that the white mouse was using a “looking at all of the parts” strategy in order to figure out the whole.

Exploration

Illustrate why the other mice were not successful looking at only one part of the strange something. First, cut a 2-inch hole in the mystery box. Then, put the mystery object up against the hole in the box so that the students only see a small portion of the whole item. Ask the children to describe what they see and if they can figure out just by looking at this small part what is inside the box.

Remove the mystery item so that students can compare their predictions. Congratulate students for being good observers. Tell students that they always need to use an “observing all of the parts” strategy when they are looking at data (describing what something is like).

To illustrate the concept of how parts are related to a whole, point out how each student in the classroom is just one part of the class: o If a visitor only met the girls in our classroom, he would never know the whole class, which includes the boys and

the girls.

Explain that for the remainder of the day, the students will use their observation skills to describe classroom manipulatives. Inform the class that they will use words that describe the attributes—color, shape and size—of the manipulatives they explore.

Science Connection: Review color, shape, and size vocabulary, as well as words that describe what something is made of and how something smells, sounds, or feels.

Dual Language Activity 1: (This is a partner activity is also appropriate for all classrooms)

Distribute a baggie containing no more than 10 math manipulatives—e.g., pattern blocks, color tiles, buttons, teddy bear counters, snap cubes, Geoblocks, etc.—to pairs of children. NOTE: When making these making these baggies ahead of time, include one item that does not belong with the rest of the manipulatives—e.g., one color tile mixed in with an assortment of buttons.

Explain that the manipulatives inside the baggie are typically stored in bins available at the manipulative/ math


center, but you have misplaced one item inside the baggie that does not belong.

Instruct the partners to use their mathematical analysis/ observation skills to determine which item does not belong and place it inside the appropriate bin at the math manipulative center.

Remind the children that the purpose of this activity is for you to determine if they are capable of making sure that all items they use during the year to model their mathematical thinking are stored and taken care of properly.

Math Stations/ Centers:

Dismiss children to stations around the room set up with a bin of manipulatives, a set of magnifying lenses, paper, and writing utensils. Direct the children to explore the materials and encourage them use the magnifying lenses to observe the manipulatives closely. As they are exploring the manipulatives, ask questions that challenge the children to describe attributes: o What color/ shape/ size are these blocks/ buttons/ cubes? o Do they make a sound? If so, what do they sound like? o If someone could not see this block, how would you describe how it feels? o How do you think the toy manufacturer made this block/ button? What material did he/ she use?

When the children are finished exploring, instruct them to draw a picture of the manipulative they were using. Encourage the children to use attribute vocabulary to describe the manipulative they were using. Make the children aware that they will share these descriptions with the whole class after center time.

Small Group/ Teacher Directed Activity (Floor Puzzle): Before conducting this lesson, make a large picture on poster board of some object that is familiar to the students—i.e. a cat, a house, a bus, etc. Cut apart the poster into individual puzzle pieces. Distribute one piece of the puzzle to each child in the group. Ask the children if they can tell what the “mystery object” is. Then, instruct the group to work cooperatively, putting the pieces together so that they can see the whole.

Self-Directed Learning Activity (Which Button Does Not Belong): Children use clothespins to select a button displayed on each task card that does not belong with the other buttons. Remind the children to look at all the buttons as a whole and then determine a rule that applies to all but one of the buttons. The button that does not fit that rule is eliminated—marked off with a clothespin

Explanation

Transition Read and chant Brown Bear, Brown Bear together as a class. Begin to compose a class chart titled, “Proper Usage of Math Materials”. On chart paper, list the appropriate/ good behaviors you observed the children use during center time.

Call on individual student volunteers who each worked with a different set of manipulatives to share and describe their “mystery manipulative drawing” with the rest of the class. Remind the children not to tell what the manipulative is.

The red triangle with 3

holes does not belong.


Tell the rest of the class to be good listeners in order to figure out which of the three sets of manipulatives—the buttons, pattern blocks, or cubes—the student volunteer is describing.

Bring attention to the attribute vocabulary the student volunteer uses to describe the manipulative.

Elaboration

Math Time (Friday/ End of the week):

Remind the children about the work they did yesterday describing the attributes of manipulative materials in the classroom: o Yesterday, we used words called attributes to describe the color, shape, size, and texture of manipulitives in the

classroom. Today, we are going to continue to use our observation skills to listen and look for a mystery object. Let’s practice. I am going to describe someone in our classroom. Listen and look carefully.

Describe one child in the classroom, pointing out his/ her clothing, hair and eye color, the length of his/ her hair, and the child’s gender. Congratulate the children on their good listening and observation skills.

Introduce Corduroy by Don Freeman. Explain that the book is about a bear that loses lost a button on his overalls, but he thinks about its attributes in order to find it: o I want you to pay attention to how Corduroy describes his lost button and how he tries to find his button by

thinking about its attributes.

After reading the story, ask the children to describe Corduroy’s lost button. Highlight how it is white and round. Ask the children to describe other attributes that the button might have so that Corduroy could not confuse it with a button on a mattress. ***NOTE: You might want to show the children a picture of a mattress with buttons so that they can see that most mattress buttons do not have visible holes like the buttons on a shirt.

Distribute Baggies with an assortment of buttons to pairs of children. Direct the s children to find a button within the assortment that matches Corduroy’s white and round button.

Ask the children to explain how they know they have found a matching button. Point out that each child was using a problem-solving strategy called “process-of-elimination:” o When you eliminate something from a group, you are removing it because it does not match an attribute. For

example, when you were looking for Corduroy’s button, you eliminated all of the buttons in the group that were not white or round.

Tell the students that during center time, they will play a game with a group of classmates in which they must eliminate buttons that do not match an attribute.


Game (Roll an Attribute): Demonstrate how to play the game. Choose student volunteers to take turns rolling an attribute die and finding all of the corresponding button cards.

Begin the game by demonstrating how to lay the 27 button cards on the floor so that each card is facing up and can be clearly seen. Point out the 3 separate attribute dice: the color die, the shape die, and the number die. 1. Instruct one student volunteer to roll any of the 3 attribute dice. 2. Elect a student volunteer to eliminate all of the button cards that do not adhere to the attribute on the die. For

example, if the child rolls the color die, and it lands on red, then the other volunteer must locate all of the red buttons and remove the other buttons that are NOT red from the carpet. Only 9 red button cards should remain.

3. Call on another volunteer to roll a different die—e.g. shape—and remove all buttons that do not have that attribute. After the second roll, there should only be 3 cards remaining.

4. After the final roll (the number of holes die), only one card will remain. This card will be the “winning” button card.

Cut apart the Attribute

Button Game Cards


Instruct the class to describe the winning card, using all of the attributes that were rolled—e.g. “The winning button is red, shaped like a triangle, and has 3 holes.”

Math Stations/ Centers: Dismiss children to stations set up around the room with bins of buttons and trays for free exploration. As the children are exploring the buttons, do not insist that they sort them into groups, but be aware that some will begin to sort and classify without any teacher direction. If children are simply exploring the buttons, ask questions that elicit descriptions about the attributes of each button: o What types of colors, shapes, and sizes of buttons do you see? o Do you have a favorite button? How would you describe it?

Small Group/ Teacher Directed Activity: Set up a place in the room, preferably on a carpeted area, for a group of 3 children to play the “Roll an Attribute” game. Remind the children that they need to take turns rolling the attribute dice and eliminating all the buttons that do not fit the attribute shown on the top face of the die. If necessary, play one more demonstration game. When the children eliminate the “winning” button, instruct them to describe and draw a picture of it so that other classmates can locate it without looking at their drawing. Remind the children to include all of the clues that would describe the button—its color, shape, and number of holes. Play at least 3 rounds so that each of the children in the group will have a chance to provide clues describing a button.


Formative: Make anecdotal records, documenting which attribute vocabulary words—color, shape, size, positional, texture, etc.—that the child knows. In the anecdotal notes, record direct quotes that show how the child uses this vocabulary to describe concrete data: o To which attributes does the child attend—color, shape, size, position, texture? o Does the child use the correct words to describe these attributes? o How does the child explore manipulatives with less distinguishable and obvious characteristics, such as objects that

are all of the same color or shape? Summative:

Work Samples: Collect the drawings and dictations of the clues the students use to describe the “winning” button for the “Roll an Attribute” game.


1.E internalize new basic and academic language by using and reusing it in meaningful ways in speaking and writing activities that build concept and language attainment;

Anchors of Support

Make sure the child is exploring manipulatives with easily

distinguishable characteristics, such as color, shape, or size. Also

provide the child with a chart displaying these recognizable

attributes. Then, point to one of the attributes on the chart and

ask the child to identify a manipulative with that characteristic—

e.g. “Show me a button with this color, red.” (As you say the

color word, point to its matching shade on the chart.)


VI.B.1 Describe Data: Determine types of data.

VIII. A.1 Mathematical Problem Solving: Analyze given information

21st Century Skills

Manage the flow of information from a wide variety of sources.



Special Education: If the child is distracted or overwhelmed with trying to analyze 27 buttons for the “Roll An Attribute” game, reduce the number of cards—i.e. 9—and the number of attribute dice from 3 to only 2, or 1 if necessary—color and shape. (Use the attribute that the child is most successful naming and identifying.)

English Language Learners: When the child has eliminated the “winning” button, encourage him/ her to describe the button, using all of the 3 attributes—color, shape, and the number of holes. If the child fails to provide the clues for the button coherently, restate his/ her description to model speaking in complete sentences—e.g. “The button is red, shaped like a square, and has 2 holes.”

Extension for Learning: Select a student volunteer who played the “Roll An Attribute” game during center time. Tell the child to provide clues about the attributes of the “winning” button so that the rest of the class can locate it. When the volunteer finishes giving clues, and the class is sure which of the 27 button cards the child is describing, allow him to show the rest of the class his drawing of the button to verify the classmates’ guess.


Which one does not belong?





Roll an

Attribute

Button Game


Cut apart and attach to the back of a foam

die. Makes 3 different dice.


Attribute Word Chart RRReeeddd Square

BBBllluuueee Circle

YYYeeellllllooowww Triangle

GGGrrreeeeeennn Rectangle

OOOrrraaannngggeee Trapezoid

PPPuuurrrpppllleee Rhombus

BBBrrrooowwwnnn Hexagon

BBBlllaaaccckkk Oval

WWWhhhiiittteee 2 w PPPiiinnnkkk 3 e GGGrrreeeyyy 4 r


Lesson Name: Counting, Creating, and Representing Numbers 0-5

Estimated timeframe: 3rd Week of School

Lesson Components

Lesson Objectives: The student will use objects, numbers, symbols, and pictures to count, generate, and represent sets up to 5.

Language Objectives: The student will use language to explain and communicate their mathematical ideas and

strategies for quantifying sets to 5

Prior Learning: Students should have an informal understanding that counting is a process for telling how many and be able to instantly recognize small quantities to 3. To engage in counting, the child should know the majority of the counting word sequence to 5 (not necessarily in order) and apply one-to-one correspondence in order to determine how many.


K.2B read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures; K.2D recognize instantly the quantity of a small group of objects in organized and random arrangements;


1. When in 5 too many/ too few? 2. Is it always necessary to count to figure out how many? 3. Up to which number is it easy to just see how many without counting each item—why?


Counting words to 5, benchmark, five-frame, count, set, quantity, few, more, eyeball estimate

Any version of the story, The Three Bears.

Craft materials (toothpicks, pompom balls, etc.) and manipulatives for making and representing sets up to 5

Jars or baggies labeled A, B, and C—each with a different color combination (1-5) of teddy bear counters.

See-through Counting Jar with 5 items (e.g., toothbrushes)

Numeral cards and Number line (See attachment)

Chart paper and writing materials (paper, pencil, journal)

Lesson Cycle

Engage

Schedule of lessons from available resources—e.g., Texas Go Math, Investigations (2nd Edition) etc.


Exemplar Lesson: (Engage/ Explore/ Explain sections.)

Exemplar Lesson: (Elaborate section) Hands-On Standards (PK-K), Lesson 2, (p. 16) Texas Go Math, Lesson 1.2

Texas Go Math, Lesson 1.2


Exemplar Lesson: (Evaluate section); Investigations, Session 2.1 (p. 58) The Counting Jar; Texas Go Math, Lesson 1.4

Morning Opening (Attendance/ Calendar Routine): (15 minutes)

Revisit the attendance stick and calendar routines that were introduced during the first and second weeks of school. Make reference to the good counting behaviors that were recorded on the class chart.

NNOOTTEE:: The children will begin

Math Journals this week during

small groups, Tuesday-Friday.


Math Time:

If the children are unfamiliar with Goldilocks and the Three Bears, begin this session by reading the book in its entirety. (NOTE: Any version of this story will suffice—e.g., Goldilocks and the Three Bears by James Marshall.) Otherwise, simply pause and highlight the pages of the book where Goldilocks comes across the chairs, bowls, and beds to the occupants of the house. Draw the children’s attention to the quantity of each of these possessions: o If Goldilocks were to look at the number of chairs in this house, how many people would she think might live

there? How many chairs/ bowls/ beds do you see? How did you figure out how many?

Lead the children to understand that some quantities are small enough that it is not necessary to count each item one-by-one. Emphasize this idea by showing the children a baggie with 2 cubes and asking them to determine how many they see. Comment on how easy it was to just tell how many without counting each cube one by one. Call this strategy eyeballing. (NOTE: Math educators call this skill ‘subitizing’—instant recognition of small quantities—but this term is not necessary for children to know.)

Now show the children a baggie with 10 cubes, prompting them once again to tell how many: o Did you have to count? Why/Why not?

Guide the children to compare the two different strategies they used to figure out both quantities—the set of 2 versus the set of 10.

Explain that some quantities, such as 10, are too large to eyeball, thus requiring people to count in order to determine how many.

Exploration


Display a jar with 5 items (something a person would use) inside.

Inform the children that Goldilocks came upon a new house and found this jar of toothbrushes inside the bathroom. She needs their help to figure out how many toothbrushes there are inside so that she will know how many bears live in this house.

Instruct the children to select among any of the manipulative materials at the math center they have been exploring during the past two weeks to show how many items there are in the counting jar: o Your job is to count out as many of the manipulatives you select as there are items in the jar.

Allow the children to display their representation inside a see-through baggie or a paper plate.

Make sure the children write and post their name on the baggie/ paper plate and display their representation near the counting jar.

Math Stations/ Centers (5 Collage):

Set out bins of various craft materials (toothpicks, buttons, stickers, pompoms, etc.) at the art center.

Direct the children to trace around their hand (which has 5 fingers) on a piece of construction paper. They will make a number collage by gluing sets of different craft materials (in groups of 5) around their handprint.

Remind the children that there should be enough of the materials in every set for each finger on their hand. (NOTE: If the children are unable to count one-by-one, encourage them to match one item to each finger on their hand in order to make an equivalent set of five).

Encourage the children to write and label the picture with the numeral 5.


Explanation

Debrief Centers/ Math Stations:

Transition the children from math centers/ stations to the class meeting area. Facilitate this transition with a counting song—e.g., “5 Little Ducks” http://www.youtube.com/watch?v=HOWt5un1-Ts.

Refer to the display of manipulative representations that the children created to show how many items were in the counting jar.

Select 3 to 5 volunteers to share and explain how they figured out how many items were inside the counting jar. Begin to create a “Strategies for Counting” chart that documents the methods—e.g., eyeballing, counting with their fingers/ eyes, etc.—the children share or which you observed them use as they were completing the counting jar activity.

Emphasize the strategy of one-to-one correspondence, being sure to encourage the volunteers who share to check their work by matching each manipulative in their representation to one corresponding item in the counting jar.

Lead the children to make sense of the differences in the size/ proportion appearances of the different representations on display. That is, although each display should have 5 items, those representations that were created with objects that are notably larger in size will appear to have more than those that were created with smaller items. Count the objects in each set to help the children recognize that the numerical value of the collection (rather than its size appearance) is what matters when comparing quantity. Emphasize that the last number you say during every count always stops at five, meaning that there are 5 items altogether.

Elaboration

Math Time (Tuesday through Thursday) Small Groups/ Math Stations (Introducing the Math Journal):

This activity is best suited for small groups as it will be necessary to monitor the students as they begin to learn routines for using and maintaining a math journal.

Instruct the children to record their counting jar representations on paper (in a math journal).

In addition to using numbers and pictures, encourage them to write down and explain the strategy they used to figure out the number of items in the jar. Post the “Strategies for Counting” chart you created in the Explanation section of this lesson (see above) for the children to reference as they are explaining and writing. (NOTE: Accept scribbles for children who cannot write. Do not encourage copying. You want to honor the children as authentic writers. Remind them that they will learn to use letters, words, and sentences this year to help them communicate their ideas so that they can remember and reflect on their thinking.)

SSttrraatteeggiieess ffoorr CCoouunnttiinngg

http://www.youtube.com/watch?v=HOWt5un1-Ts



Display 3 mini counting jars/ baggies, each labeled A, B, and C respectively. Make sure that each jar/baggie has a different color combination of teddy bear counters—e.g., whereas one jar would have 5 blue, 4 red, 3 green, 2 yellow, 1 orange, 0 purple; another jar might contain 5 red, 4 purple, 3 orange, 2 green, 1 yellow, and 0 blue.

Instruct the children to work with a partner and select one of the labeled jars to inventory. Explain that their task is to sort and count the teddy bear counters inside the jars/ baggies and use numeral cards (0-5) to label how many there are of each color—red, blue, yellow, orange, green, purple, etc.

Allow the children to record their data on grid/ graphing paper (see attachment) and write the numerals that correspond to each set—e.g., 5 blue, 3 green, 4 yellow, 2 purple, 1 orange, 0 green.


Formative: Observe the children as they engage in the counting activities outlined in this lesson. Make anecdotal records of the strategies you see the children use to count and generate sets up to 5. Look for the following behaviors: o Is the child’s rote counting synchronous with their one-to-one tagging of each object they enumerate? o Does the child understand that the last number he/she says as she counts the set tells how many items there are

altogether? When you ask, “How many;” does the child state the value of the set he/she counted or does she/ he recount the set, starting over at one?

o Does the child have to count each object one-by-one, or can she/he instantly recognize the quantity (e.g., subitize) without counting?

Summative:

Work sample: Refer to pp. 58-60 from Session 2.1, The Counting Jar, in the Investigations In Number, Data, and Space (2nd Edition) Unit 1 teacher guide. Place 5 counters inside a see-though container and encourage the children to estimate how many items they think they think there might be. After they record their estimate, encourage them to open the container and count each item inside in order to confirm their estimate. Make sure that each child makes a pictorial and numerical representation of the number of items that were actually inside the jar.

Checklist: Document the children’s progress with counting using the Assessment Checklist: Counting, which is referenced in the Investigations Resource Masters as M5. Begin a checklist that documents the numerals the child can identify, name, and write.


ELPS 2.E use visual, contextual, and linguistic support to enhance and confirm understanding of increasingly complex

and elaborated spoken language;

Anchors of Support

Make a 1-5 number line available to children who need this tool in order to complete the Mini-Counting Jar/ Numeral Labeling activity described in the Dual Language Activity 2 under the Elaborate section. Instruct the children to start at the happy face and arrow near the numeral one and go left to right from 1 as they arrange each teddy bear under a corresponding numeral. Explain that the last number the line of teddy bears reaches indicates how many there are altogether. A number line black line master is attached to this lesson (see attachment).


I.A.1 Number representation: Define and give examples of complex numbers.

I.C.1 Number sense and number concepts: Use estimation to check for errors and reasonableness of solutions.


21st Century Skills

Identify and ask significant questions that clarify various points of view and lead to better solutions.


Special Education: If a child struggles to count and represent the 5 objects displayed in the Counting Jar, reduce the number of items in the jar to 4 or 3.

English Language Learners: Encourage children to use their home language to count the number of items in the counting jar. Then, recount the set in English to model and emphasize the applicability/ transferability of the one-to-one matching method used in both languages.

Extension for Learning: Instruct the children to make a snap cube tower that shows how many people are in their immediate family (those that live in their house). Allow the children to refer to a family photo in order to check their counting. Then, have the children complete a pictorial representation


One-Inch Grid Paper


0-5 Numeral Cards

0 1 2

3 4 5

0 1 2

3 4 5


1-5 Number Line

1 2 3 4 5

1-5 Number Line

1 2 3 4 5


Lesson Name: Just Enough: Introduction to Problem Solving (Making Equal Sets to 5)

Estimated timeframe: 4th Week of School

Lesson Components

Lesson Objectives: The student will explore and use strategies for making equal sets to 5.

Language Objectives: The student will begin to justify and explain their problem solving strategy for making an

equivalent set

Prior Learning: Students should know the majority of the counting word sequence to 5 (not necessarily in order) and apply one-to-one correspondence in order to determine how many.


K.2B read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures; K.2D recognize instantly the quantity of a small group of objects in organized and random arrangements; K.1B Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution;


1. When in 5 too many/ too few? 2. Is it always necessary to count to figure out how many? 3. What do you do to figure out if you have enough of something?


Counting words to 5, five-frame, count, set, quantity, few, more, eyeball estimate, strategy, one-to-one correspondence

See Attachments for Quick Image Dot Cards, 5-Frame Cards, and Concentration Game Cards

1 large dot foam cube (and smaller dot cubes)

Ice cube trays and grid boards

2-sided color counters, tongue depressors, snap cubes, pattern blocks

Chart paper

Journal and Writing Tools

Benny’s Pennies by Pat Brisson

Lesson Cycle

Engage

Schedule of lessons from available resources—e.g., Texas Go Math, Investigations (2nd Edition) etc.


Exemplar Lesson: (Engage/ Explore/ Explain sections.) Texas Go Math, Lesson 2.1

Exemplar Lesson: (Elaborate section) Hands-On Standards (PK-K), Lesson 1, (p. 16) Texas Go Math, Lesson 2.2



Exemplar Lesson: (Evaluate section); Texas Go Math, Lesson 2.5

Morning Opening (Attendance Routine): (15 minutes)

Continue staggering and varying the math routines (the attendance stick, calendar, number/ question of the week/day, etc.) you have introduced up to this point. In the lesson outlined below, you will introduce an additional routine (Quick Images) that you can insert at least once weekly into your daily schedule.

NNOOTTEE:: The children will begin the Problem

of the Day routine Wednesday –Friday in

small groups.


Math Time: (Monday)

Show the children a large foam dot cube and allow them to share where they have used or might have seen something like it. Explain that some people use the cube to play board games: o First you roll it. When it lands and stops rolling, look at the arrangement of dots on the face of the cube that is

showing at the very top. The number of dots that is showing face up tells you how many spaces to move on a game board or how many points you have scored.

Roll the dot cube with the children gathered around it in a circle so that everyone can see on what face it lands. Make enough rolls so that the children can see that each face has a different number of dots. For each roll, instruct the children to use their fingers to show the number of dots they see.

Incorporate movement by allowing the children to make as many stomps, claps, or jumps as there are dots on the face that is showing.

Transition to a different activity, instructing the children to sit quietly so that they can be ready to play a new game in which they must concentrate and focus closely.

Select and display one of the dot images of 3 or 4 from the attachments section appended to this lesson. Instruct the children to look carefully at the configuration of dots so that they can explain how they remember seeing it. Explain that you will only show the image for 5 quick seconds.

Cover or remove the dot image and invite the children to use words and numbers to describe what they saw: o How many dots did you see altogether? Explain how the dots were grouped? How would you describe the image

so that someone could draw what you saw on paper?

As the children share, use numbers, pictures, and words to record their descriptions on chart paper.

If time permits, repeat this process with another dot image—this time increasing the number to 5.

Exploration

Math Stations/ Centers (Monday through Friday): Before dismissing children to math stations/ centers, select volunteers to help you demonstrate the following activities to the rest of the group: (NOTE: Add the games listed below to the activities that were introduced the previous week—e.g., Number Collages, Counting Jar Inventories, etc.

Path Games: Children roll a 0-5 dot cube to determine how many spaces to proceed down a given path or to decide how many counters (e.g., pompoms) to place inside the individual compartments of an ice cube tray, moving from left to right and top to bottom (return sweep). Variation: The children can build a snap cube tower, rolling a dot cube and adding that many cubes.

Copy My Roll: Children work with a partner. One player starts by rolling a 0-5 dot cube. The partner must use his/her fingers to represent the number of dots on the part of the cube facing up. The children then switch roles. Encourage the children to check each other’s finger representation.

“I see 4 dots at the top and 1 dot

at the bottom. 1+4=5”

“I see a row of 2, another row of

2, and then another dot by itself

at the bottom. 2+2+1=5”


Make a Tally Collection of 5: Model the process for making tally marks. Introduce the following chant to facilitate the process, lifting a finger for each count: “One, two, three, and four, add five; now shut the door “(lay your thumb across the palm of your hand to signal the fifth and final diagonal mark). Pair the children with a partner. The children take turns rolling a 0-5 dot cube and making a tally mark configuration with that many tongue depressors. Encourage the children to count how many groups of 5 they were able to make. NOTE: Allow the children to refer to the pictorial representation of tally marks (0-5) located in the attachments section appended to this lesson.

Matching Sets Concentration Game: Children work with a partner or in groups of 4 (pairs of 2 playing opposite of each other). Assign each partner or pair one of two types of playing cards—the finger cards or the 5-frame cards. The children shuffle and arrange their respective cards face down in a 2-by-3 matrix. Differentiate among the two sets of cards by placing an assigned color dot sticker on the back of each card—e.g., red dots for the finger cards and blue dots for the 5-frame cards. One partner or team begins by turning over a card from one of the sets and then another card from the opposite set. If the two cards match by number—e.g., 4 fingers and 4 dots—the player/team keep that pair of cards. If the two cards that were played do not match, the player/team must turn the cards over face down in the same position inside the matrix where they were before. The players continue by taking turns comparing cards. The partner/team who collects the most pairs of cards wins the game.

NOTE: Be sure not to devote yourself to one particular group. Circulate among the various stations, asking questions and monitoring/ looking for good work behaviors. Make note of interesting strategies and helpful working behaviors that you observe so that you can share them with the children during the debriefing session that follows the math center/ station time. Dual Language Activity 1: (This is a partner activity is also appropriate for all classrooms)

Pair the children with a partner. Distribute a set of 5 double-sided color counters and one Copy My Dot Image game board to each player.

Instruct both children to count their respective set of counters (dots) to be sure that there each has exactly 5.

Direct both players to turn around with their backs to each other so that neither one can see the other’s board. The children then construct a dot image by arranging each of their counters in a special configuration within the 3-by-3 matrix board.

When both players finish, they turn back around and compare each other’s image.

Encourage both partners to use words and numbers to describe his/her dot image: o How would you describe your dot image? How many dots are on the bottom/ top/ middle row? o What would you have to do to your image to make it look like (partner’s name)?

“Mine looks like a

lowercase t with 1 dot

on top, 3 in the middle,

and 1 on the bottom

“Mine looks like an x

with 2, 1, and 2.


Explanation

Debriefing Time: (Monday and Tuesday)

Transition the children from math centers/ stations to the class meeting area. Facilitate this transition with a counting song—e.g., “Joannie (or Johnny) Works With 5 Hammers” (Link to the following YouTube video: http://www.youtube.com/watch?v=_tItt6n7rIw)

Allow the children to briefly share what they did during math stations/ centers. Make note of various strategies (e.g., eyeball estimation, counting, one-to-one matching) related to making equal sets. (Refer to the Good Counting Chart you began the first week of school): o What strategy did you use to count the dots on the cube? o How did you know how many spaces to move/ counters to add?

Use chart paper to create a “What Good Work Looks Like During Math Stations” chart. Write down appropriate behaviors you observed during this work time, explaining how these actions and strategies were helpful and useful for accomplishing mathematical thinking.

Post the chart and continue to add to it when necessary. Spend at least one additional day monitoring and rotating among these stations so as to be sure the children are capable of working independently when you begin to pull small groups.

Elaboration

Math Time (Wednesday through Friday)

Continue the Quick Images routine you introduced in the Engage section above, selecting among and displaying additional images from the attachment section.

For Wednesday’s session, introduce the 5-Frame with 3 dots spaced together on the left-hand side, leaving 2 empty squares next to each other on the right. Flash the image for 5 seconds and then prompt the children to use numbers and words to describe the arrangement: o How many dots did you see? How many empty spaces?

Display the image one again so that the children can confirm and verify the mental image they saw: o How many dots do you think would fit altogether inside the entire frame?

Introduce an additional 5-frame—the frame with 1 dot on the left, 2 empty spaces in the middle, and 2 dots together on the right (3 dots total).

Repeat the process outlined in the above for sharing out and verifying how the children visualized the image. Model how to show mathematical thinking by recording on chart paper the ideas children share.

Dual Language Activity 2: Modeling a process for the problem-solving (This activity is also appropriate for all classrooms since it is a way to introduce your campus’s recommended problem-solving template)

Introduce Benny’s Pennies. Do not read the book in its entirety. Stop at the page where each of Benny’s 5 family members requests a particular gift—the mother wants something beautiful, the brother something good to eat, the sister something nice to wear, the dog something uttered in barks, and the cat (also unable to use words) something uttered in a loud meow.

Explain that Benny has 5 pennies to spend, each of which he will use to buy a gift for each family member. o How many gifts will Benny need to buy? How do you know?

http://www.youtube.com/watch?v=_tItt6n7rIw


Continue reading up to the part where he purchases a paper hat for his sister. Close the book and inform the group that they will be able to use objects, pictures, numbers and words to show how many gifts Benny has purchased so far, and how many more he has to buy.

Guide the children in small groups as they record how they solved the problem you posed in the above. Use questions to help the children visualize what the problem is asking and what they need to figure out and show on paper: o How could you use cubes to show the number of people in Benny’s Family? How many cubes would you need?

How will you keep track of what you which family members you have drawn/need to draw? Which numeral would you write to show that amount?

o How could you use another manipulative—pattern blocks, pennies, etc.—to show the number of gifts Benny has purchased so far? Which numeral would you write to show that amount?

o How could you group the two manipulatives you used so that you could see how many more gifts he needs to purchase? What does your grouping strategy show? What is it you are trying to show?

NOTE: Pull no more than 2 small groups a day (Wednesday through Friday) during math stations/ centers so that you can closely monitor and guide the children through the problem-solving process. In order to minimize disruptions, do not start this process until Wednesday or on another day when at some point the class has satisfactorily shown that they can work independently as you pull small groups.


Formative: Observe the children as they engage in the quick image and dot cube activities outlined in this lesson. Make anecdotal records of the strategies you see the children use to count and generate sets up to 5. Look for the following behaviors: o Is the child’s rote counting synchronous with their one-to-one tagging of each object they enumerate? o Does the child understand that the last number he/she says as she counts the set tells how many items there are

altogether? When you ask, “How many;” does the child state the value of the set he/she counted or does she/ he recount the set, starting over at one?

o Does the child have to count each object one-by-one, or can she/he instantly recognize the quantity (e.g., subitize) without counting?

Summative:

Work sample: Make a photocopy of the child’s Benny’s Pennies story response/ math journal entry. Place the entry in the child’s portfolio. Consult the Teacher Note, “Story Problems in Kindergarten” (p. 174), from Unit 4, “Measuring and Counting, ” in the Investigations in Number, Data, and Space (2nd Edition) teacher guide. This article provides more information on what to anticipate as children solve problems involving number and the various strategies kindergarteners will typically use.

Checklist: Document the children’s progress with counting using the Assessment Checklist: Counting, which is referenced in the Investigations Resource Masters CD as M5. Begin a checklist that documents the numerals the child can identify, name, and write.


ELPS 1.H develop and expand repertoire of learning strategies such as reasoning inductively or deductively, looking for

patterns in language, and analyzing sayings and expressions commensurate with grade-level learning expectations.


Anchors of Support

Allow the children to refer to the anchor charts you create with the group. These charts would be richer and more meaningful to the children if they contained photographs of specific students in the class modeling/ exemplifying the desired, appropriate behaviors.

Children who are unfamiliar with numerals and how to use them to label quantities need access to a number line. Use a happy face or arrow to indicate a starting place next to the numeral 1. Instruct the children to start there, placing one object from the set they are counting under each subsequent numeral as they move left to right down the number line. Inform the children that the last numeral they reach with the line of objects indicates the total number of items there are in the set.


Cross Disciplinary Standard I.A.1a Identify what is known, not known, and what one wants to know in a problem.

21st Century Skills

Learning and Innovation Skills: Elaborate, refine, analyze and evaluate their own ideas in order to improve and maximize creative efforts.


Special Education: Use your hand to guide the child’s touching or moving of objects if she/he has difficulty synchronizing her/his rote counting with objects. This adaptation will help the child to focus on accomplishing just one mathematical task rather than expend all their attention and effort on coordinating two processes simultaneously.

English Language Learners: When introducing a word problem or multi-step number story, go beyond verbal cues by encouraging the children to act out all the steps involved in the sequence of events and changes to the initial quantity. They should be allowed to experience and visualize the steps before transferring the experience and structure of the changing number scenario to a fixed mental image.

Extension for Learning: Allow the children to use numbers, pictures, and words to create their own Benny’s Pennies story.


Subitizing Concentration Cards

© 2014 AISD Early Childhood Department Page 34

Quick Images for 5


Quick Images for 5


Quick Images for 4


Quick Images for 3


5-Frame Image Cards


“““CCCooopppyyy MMMyyy DDDooottt IIImmmaaagggeee””” BBBoooaaarrrddd


555


444


333


222


111


000


111000 999

aaa sss


888 777

ddd fff


666 555

ggg hhh


444 333

jjj kkk


222 111

lll ;;;


000

000---111000 MMMuuullltttiiipppllleee

RRReeeppprrreeessseeennntttaaatttiiiooonnn CCCooouuunnntttiiinnnggg CCCaaarrrdddsss

;;;


Individual Student Number Line (1-20)

1 2 3 4 5

6 7 8 9 10

11 12 13 14 15

16 17 18 19 20


1 2 3 4 5 6 7 8 9 10

NNuummbbeerr LLiinnee


111000 ten


999 nine


888 eight


777 seven


666 six


555 five


444 four


333 three


222 two


111 one


000 zero

first 20 days of instruction kindergarten mathematics

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