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This material is made freely available at www.njctl.org and is intended for the non-commercial use of students and teachers. These materials may not be used for any commercial purpose without the written permission of the owners. NJCTL maintains its website for the convenience of teachers who wish to make their work available to other teachers, participate in a virtual professional learning community, and/or provide access to course materials to parents, students and others. Click to go to website: www.njctl.org New Jersey Center for Teaching and Learning Progressive Mathematics Initiative
Kindergarten Counting and Cardinality www.njctl.org 2012-11-20
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Table of Contents Click on a topic to go to that section Count Sequence Numbers 0-6 Numbers 6-10 Number Writing 0-10 Comparing Numbers Hundredth Day of School
Count Sequence Click to return to the table of contents
The following activities are suggestions for you to work on as the year progresses. At this point students are not expected to be able to count to 100 or skip count. Teacher Instructions
Encourage children to count to 100 through daily routines. (ex. Let's see where 100 steps will take us down the hallway or around the playground.) Ask children to finish the sequence when you start counting with a random number such as 7. Use a stop sign or hand signal for interrupted counting. Children stop counting when sign is held up and then continue when sign is put down. Teacher Instructions Counting Sequence
Use bundles of tens (straws, sticks) to introduce counting by tens. As you add a day to calendar start adding one straw each day until you get to ten. Wrap bundle with rubber band and then start a new bundle... until you get to one hundred. Use hands (five fingers) to count by fives. Use shoes or socks to count by twos. Teacher Instructions Counting By Tens, Fives, and Twos
Count backward sometimes too. Count down to 0 like a rocket liftoff, a microwave, or a timer ticking. * Try counting down from a teen or higher number. * Ready for blast-off story. - Put on your astronaut suit. - Up the elevator to the top of the space ship. 1 2 3 4 5 6 7 8 9 10 (squat and begin to stand as the numbers go higher) - Buckle yourself in safely. - Count down for blast-off. (As they count down children go from standing to squat position.) - 10 9 8 7 6 5 4 3 2 1 Blast-off (Children jump ) Teacher Instructions
10, 9, 8, 7, ____ 7Counting backwards, what comes next? A 8 B 6 C 4
20, 19, 18, 17, 16, 15, 14, ____ 8Counting backwards, what comes next? A 13 B 15 C 10
13, 12, 11, 10, ____ 9Counting backwards, what comes next? A 14 B 9 C 0
Ordinal Numbers Ordinal numbers describe position. Ask children, questions such as: Who is first in line? Who is third from the end? What number is the person at the end of the line? Who is fifth in line? Identify children by their position in line. Then ask them to perform some sort of action. Teacher Instructions
X 16What position is the cow? A 6th B 7th C 8th D 9th E 10th
Hundredth Day of School Click to return to the table of contents
The following activities are suggestions for you to work on as you work towards the 100 th day of school. Refer back to these activities as you count the number of days to get to 100. Teacher Instructions
100th Day of School Activities for the 100th day of school... Have each child bring a collection of 100 objects. (such as... cereal, pennies, pasta, etc.) Read stories about the number 100. Count by 1s, 5s, and 10s to 100. Bundle sticks in 10 groups of ten and create one bundle of 100. Write numbers on a 100 grid. Mix 100 snack items and eat a fantastic treat. Place in a bag the number cards for counting by tens from 10 to 100. Invite ten students to each take a card, identify its number, and stand holding the card so the number faces outward. Then lead the seated students in putting the numbers in order from least to greatest. Teacher Instructions
Marshmallow numbers. Have the children make numerals 0 through 9 using toothpicks and miniature marshmallows. Have the children place pairs of toothpick numerals side by side to display two-digit numbers. Estimation Jars- Set up different size, clear jars filled with objects. Fill one of the jars with exactly 100 pieces. Ask students to guess which jar's contents are closet to 100 items. 100 -piece necklace. Give each student a piece of string, ten paper squares, and a plastic bag of beads or pasta. Ask the children to write the numerals 10, 20, 30... 100 on the separate paper squares. Ask students to string 100 beads and to place the appropriate number card on the necklace after every group of ten beads. 100 Headbands. Give each student a headband and have them write 100 in the center. Have the students decorate the strip with 100 stickers, stamps or drawings. Staple the headband to fit each child's head. More activities for the 100th day.
Have the students use cotton swabs and paint to create an apple tree with 100 apple dots. Or use the swab and paint to create their own design using 100 paint dots. Divide the class into 10 groups and have each group compile a list of ten words. Combine their lists to create a 100 word chart. 100 cents. Have the children collect 100 pennies, and then have them exchange the pennies for nickels and dimes. Make a snake that measure 100 inches long. Have the students decorate it with 100 designs. Make a banner that has 100 hand prints. Hang 100 balloons or streamers in the room. Ask the students to make a link with 10 chains. Combine the 10- link chains to make a 100 link chain. 100 Drops of Water. Have the students predict how full a bowl containing 100 spoonfuls of water will be. Use tape to mark where they predict it will go. Count as you pour 100 spoonfuls into bowl. More, more, more 100th day activities.
100 Balloons and Cheers for the 100th day of School. On the next page count by 5s and cheer for the 100th day of school.
Numbers 0-6 Click to return to the table of contents
Numbers 0-6 Encourage children to count the number of items in total. Count squirrels outside, blocks at center time, cookies at snack time). They may also count children who are present or objects at discovery center. When counting objects, say the number names in standard order, pairing each object with one and only one name. The children should understand that the last number said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. The children should understand that each successive number name refers to a quantity that is one larger. Teacher Instructions
As you introduce each number in this unit the following activities might be used. Drop objects in a container and have the children count how many drops they hear. Read a favorite counting book to reinforce counting and cardinality. Finger "Digits"... Display a certain number of fingers. Have the children select number card that matches number of digits. Show a number card and have the children hold up the correct number of fingers. Number Search The children will search for specific number of objects in the classroom. (ex. 3 pencils) Play "Simon Says". Teacher Instructions
Individual Number Poster Each child can make a number poster for each number. 1. Write number at top of paper. 2. Draw, use stickers, or glue objects that represent number. 3. When finished with unit compile number book. Teacher Instructions
This is the number one. Count the object and trace the number 1.
This is the number 2. Count the objects and trace the number 2. 2
Count the objects. Circle the correct number 1 2
Play "I Have One, You Have Two" Children take turns making number statements. The first child might say, "I have one mouth." The next child then replies, "I have two eyes". The children keep taking turns adding one each time until they get to six. Then start over again with one. Teacher Instructions
Numbers 6-10 Click to return to the table of contents
Numeral Definition: A word, symbol or figure that represents a number. For example, seven, VII, llll ll, and 7 are all numerals that represent the same number. Counting Objects When counting objects, say the number names in the standard order, pairing each object with one and only one number name. Understand that the last number said tells the number of objects counted. The number of objects is the same regardless of their arrangement or the order in which they were counted. Understand that each successive number name refers to quantity that is one larger.
Number Clap- Each student has number cards labeled 0-10. The teacher claps her/his hands. The students count silently. The children find the number card that corresponds to claps and hold up the card. They then find the correct number of objects from pile in center of table. Number Sequence- Use number cards and place in correct sequence against timer. Number Trace- Trace number cards with finger. The cards should have raised numbers or sand paper. Next page - match number of objects to numeral. Working with Numbers 0-10
Tally Marks Tally marks are another way to represent a number of objects. You might want to introduce tally marks with this story or another of your own. Once there were five caterpillars. They decided to take a nap on a beautiful green leaf. Each caterpillar crawled onto the leaf. 1...2...3...4... When it was number 5's turn there was no room for him. So he decided to lay across the other four.
5 6 78 9 8 6 7 To sequence numbers we must put them in the correct order, each time adding the number that represents one more. 1 234 5 6 78 9 1 0
Numbers follow a sequence. In this sequence the next number represents one more. What number should come next? What number came first? 5 6 ____ 8 9 ____ ____ 5 6 ____ 8 9 6 7 _____ 7 8 ____ ___ 7 8 ____ 9 10
5 6 7 8 9 10 35Are these numbers in correct sequence? A Yes B No
6 7 _____ 36What number comes next? A 7 B 8 C 9 D 10
_____ 8 9 37What number comes first? A 1 B 6 C 7 D 10
4 6 5 7 8 9 10 38Are these numbers in correct sequence? A Yes B No
Number Writing 0-10 Click to return to the table of contents
The following stroke- formations will lay the groundwork for number writing. Circular O O O Horizontal - - - - - Curved Diagonal / / / / / Vertical l l l Figure 8's 8 8 8 l l l
Let's go to the circus and practice our strokes. Use your straight arm to write in the sky. Then practice on your smart board, dry erase board, or paper. Strokes start on the next page.
Comparing Numbers Click to return to the table of contents
Give the students opportunities to determine which group is larger, smaller or the same as another group. The children should identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group by using matching and counting strategies. Extend this skill by having the students create groups with one more or one less object.
Exploring Same Number Draw the same number of buttons as button holes.
Exploring Same Number Place one dog on each stool. We need the same number of dogs as stools.
Comparing Written Numerals Ask children to distinguish the quantity of a written numeral compared to another written numeral. Display written numerals from 1 to 10 and have the children compare the two numbers. Use the terms more and less as you compare the numbers.
You have five green buttons and I have seven. Which number is more?
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