Unit 1 Counting and Cardinality: Numbers 1 to 5

Transcription

1 Unit 1 Counting and Cardinality: Numbers 1 to 5 Introduction Students will begin by learning to say the count sequence from 1 to 10 in standard counting order. They will learn the count sequence and develop some fluency with it so that later they can focus on counting objects instead of dividing their attention between counting and recalling the count sequence. Counting is a complex process. It requires knowing the standard count sequence and understanding that, when counting, a given number is associated with exactly one object, that all objects must be counted exactly once, that objects can be counted in any order, and that the number of objects in a group does not depend on how they are arranged. Use students knowledge of their world (e.g., people have two arms, two legs, one nose, one mouth, etc.) as an anchor to which you can attach spoken and written numbers. Students will begin to build internalized connections between one and two objects, the spoken numbers one and two, the written numbers 1 and 2, and pictures of one and two objects. Extend these deepening connections incrementally to the numbers 3, 4, and 5. By the time students begin to learn about quantities for which they have less internal knowledge than they do for 1 and 2, the connection between quantities, spoken numbers, and written numbers will have become more solid. Signaling. In these lesson plans, we often suggest that all students signal their answers simultaneously (e.g., by flashing thumbs up or thumbs down for yes or no, or by holding up the number of fingers that corresponds to their answer). For a complete description of signaling, see p. A-20. Materials. Number cards and picture cards are used extensively throughout this unit. Use BLM Number Cards (1) to (5) (pp. I-8 12) whenever number cards are used and BLM Picture Cards (1) to (5) (pp. I-19 23) whenever picture cards are used. In addition to the BLMs provided at the end of this unit, the following Generic BLMs, found in section I, are used in Unit 1: BLM Finding the Mistakes (1) to (4) (pp. I-29 32) BLM Counting Out From a Larger Group (1) (p. I-36) Recurring activities. The following activities recur several times in the unit, with variations. I Start, You Finish Type: Whole class, pairs Objective: To complete a count sequence to a specified number Instructions: Explain that you will start counting to 5 and that students will finish counting, but they must stop when they get to 5. Have students close their eyes to help them develop listening skills. ELL students can keep their eyes open if they need to see you as you count. Maintain a steady, unrushed counting pace. Tell students to listen carefully to the numbers you Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-1

2 say. SAY: 1, 2, 3, 4. Students finish by saying 5. (You may have to prompt them the first few times you do this activity.) SAY: 1, 2, 3. Students finish by saying 4, 5. SAY: 1, 2. Students finish by saying 3, 4, 5. SAY: 1. Students finish by saying 2, 3, 4, 5. Repeat for counting from 1 to 10, with students counting silently with you. Repeat or do it in smaller chunks as needed throughout the unit. Variation: Students play in pairs. Player 1 starts the count and Player 2 finishes. Making Matches Type: Individual Objective: To match pictures of objects with the corresponding numerals Preparation: Provide each group of three to five students with two bins, one containing number cards for 1 and 2 and the other containing picture cards for one and two objects. Provide each student with glue and BLM Making Matches (1) to (2). Instructions: Divide students into groups of three to five. Show students Question 1. ASK: How many is this? (1) Hold up a number card for 1 and a number card for 2 and ASK: What number goes with the picture? Have students point to the correct card. Glue the number 1 inside the box above the circle and SAY: I put the number 1 here to show one circle. The number and picture match because they both show one. Repeat with Question 2. Then show students Question 7. Ask for the number, then show students picture cards with one and two objects. ASK: What picture goes with the number? Have students point to the correct card. (one object) Repeat with Question 8. Have students complete the remaining questions individually. Matching Pictures and Numbers Type: Pairs Objective: To match pictures of objects with the corresponding numerals Preparation: Provide two bins to each pair of students, one for discarded cards and the other containing a mix of number cards for 1 and 2 and picture cards for one and two objects. Instructions: Pair up students. Student 1 randomly picks a card from the bin and puts it face up on the desk. Student 2 draws cards one at a time from the bin until a card with either the matching picture card or the matching number card is found, and puts it with the first card. Either student can put the pair in the discard bin. Have students switch roles and repeat. Collecting Objects Type: Individual, active Objective: To associate numerals with groups of similar objects Preparation: Designate an area on the floor for each student and use tape and a marker to mark a total of six 1s and 2s in random order on the floor. Example: Instructions: Have students collect objects to put with each number, starting from the left. The example below uses shapes, but you can use any objects that students are familiar with Each number should have its own type of object (e.g., one book, two pencils, two objects that are red, one object that is soft). C-2 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

3 Finding the Mistakes Type: Individual Objective: To identify pictures of objects that are correctly or incorrectly matched with the corresponding numerals Preparation: Give each student BLM Finding the Mistakes (1). Instructions: Explain that there are mistakes in some of the pictures. Tell students they need to decide if the picture goes with the number. If the picture and number match, they color the happy face. If the picture and number do not match, they color the sad face. Show students Question 1. ASK: How many boxes is this? (1) What number is this? (1) Do the picture and the number match? (yes) SAY: Since they match, we color the happy face. Repeat with Question 2. Have students complete the remaining questions individually. The Counting Game Type: Whole class Objective: To count objects or people in the classroom Instructions: As you touch or point out objects or people in the classroom, have students count them together, at first aloud and eventually in their heads. Early in the year, specify how many objects you will count and count only similar objects. Later on, don t specify the number in advance; instead, have students stop counting when you stop touching objects, then ask how many objects you touched. Variations: 1. Students specify the kinds of objects and how many to count. 2. Students lead the counting. 3. As students become more adept, count dissimilar objects. Explain that you are counting touches, not objects. Counting Objects and Answering How Many? Type: Pairs Objective: To complete a template, count objects, and show how many objects there are Preparation: Provide students with glue and four bins: one containing number cards for 1 to 3, and the others containing paper squares in three different colors. Using construction paper, make a simple template for each student by drawing several groups of one to three boxes in a straight line. Leave enough space below each group of boxes for students to glue a number card. Lines should be clearly distinguishable from one another. Example: Instructions: Students glue one, two, or three of the same color square to each group of boxes. They exchange pictures with their partners, count the squares in each group (making marks as needed), and glue a number card below the group of boxes to show how many there are. Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-3

4 Counting Pictures of Objects and Answering How Many? Type: Individual Objective: To answer how many? about pictures of objects by recording the result with a number Preparation: Provide each student with a blank sheet of paper, glue, and two bins, one containing number cards for 1 to 3 and the other containing picture cards for one to three objects. Instructions: Have students randomly pick a picture card for one, two, or three objects, count the objects, and glue the picture and the number that shows how many there are onto their paper. Collecting and Counting Objects and Answering How Many? Type: Individual, active Objective: To group similar objects as shown by each group of boxes, count the objects, and answer how many there are in each group Preparation: Designate an area in the room for each student. Provide each student with glue and a bin containing numbers cards for 1 to 3. Using construction paper, make a simple template for each student by drawing one, two, or three boxes in a straight line. Example: Instructions: Have students gather a different kind of similar objects (e.g., blocks or erasers) for each group of boxes on the template. For each group of boxes, students place one object in each box, count the objects, and glue a corresponding number card beside the boxes to show how many there are. Counting Out Objects Type: Pairs Objective: To count out a specified number of objects Preparation: Provide each pair of students with two bins, one containing counters and the other containing numbers cards for 1 to 3. Instructions: Student 1 takes one number card randomly from the bin. The number on the card determines how many counters students need to count out. Student 2 takes counters out one at a time and both students count aloud. They return the number and counters to their respective bins, switch roles, and play again. Feeling Numbers with Fingers Type: Individual, pairs Objective: To gain tactile knowledge of numerals and improve fine motor skills Preparation: Make two types of tactile numbers using cardboard about 1/4 inch thick and measuring about 1 foot by 1 foot. For the first type, the number can be formed by a ridge about 1/4 inch above the surface of a piece of cardboard. Make the ridge by gluing rope, thick yarn, or modeling clay to a piece of cardboard in the shape of the number. For the second type, the number should form a groove about 1/4 inch below the surface of a piece of cardboard. Make the groove by drawing a number, such as 2, on one of the pieces of cardboard and cutting it out. C-4 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

5 Glue the left (L) and right (R) sides (but not the number) to another piece of cardboard, as shown below: L R Step 1: Draw a number on a piece of cardboard. Step 2: Cut around the number. Step 3: Glue the left and right sides to another piece of cardboard. Make tactile numbers of both types for 1, 2, and 3, and for the parts of 2 and 3 (e.g., the curved top of 2 and the curved top or bottom of 3). Instructions: Have students practice identifying the tactile numbers by touch. Students should run a finger along the sides of the ridge or the groove. They can also feel the top of the number, but this will be more difficult. After students have had opportunities to practice, pair up students. Student 1 closes their eyes. Student 2 selects a tactile number and Student 1 must identify the number by touch. Then partners switch roles. Remind students not to peek. Painting Numbers with a Sponge Type: Individual Objective: To practice painting numerals and parts of numerals Preparation: Write the numbers 1, 2, and 3 and the curved parts of 2 and 3 on separate pieces of paper. Make the whole numbers about 5 inches tall and the parts of numbers of a size to match. Put each number in a clear plastic sleeve. Give each student paint and a small sponge. Instructions: Students use a sponge to paint over the numbers and parts of numbers. Variation: Students use the index finger of their dominant hand instead of a sponge. Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-5

6 CCK-1 The 1 to 10 Count Sequence Pages 1 3 Standards: K.CC.A.1 Goals: Students are exposed to and begin to say the count sequence from 1 to 10 in standard counting order. Prior Knowledge Required: none Vocabulary: number, spoken numbers 1 to 10 Materials: egg carton with two sections cut off on one end 10 hardboiled eggs or objects about the same size picture of a parrot and picture of a numbered list of things to do blocks, alphabet letters, connecting cubes, and base ten blocks (see Activity Center) bins (see Activity Center) blocks of two colors (see Extension) alphabet letters (see Extension) Counting warm-up. SAY: Repeat after me. One. (students repeat) One, two. (students repeat) Continue in this way for each number from 3 to 10, reciting at a pace of about one number per second, so that students can follow along. SAY: One is a number. So is two. ASK: What other numbers do you know? Have volunteers offer a few answers. SAY: You are really good at this, so let s start from some bigger numbers. Have students repeat nine, then nine, ten. Continue in this way for eight ( eight, eight, nine, eight, nine, ten ), then seven ( seven, seven, eight, and so on). SAY: Now I will say the numbers from 1 to 5: one, two, three, four, five. Now I will say the numbers from 1 to 10: one, two, three, four, five, six, seven, eight, nine, ten. NOTE: Students can, but are not expected to, repeat the sequences from 1 to 5 and from 1 to 10. Use the following songs, chants, poems, and stories to help students listen for and learn the numbers 1 to 10, and learn to say the count sequence from 1 to 10. The activities are designed to be participatory; prompt students to chime in and say as many of the numbers as they can along with you, and eventually, instead of you. Do at least the first two activities and repeat as needed the activities are ordered from easiest to more challenging. You might use some or all of these songs, chants, poems, and stories at the beginning of each lesson in this unit. Activities Learning to say the numbers 1 to 10. Practice counting with students using an adapted version of If You re Happy and You Know It. SAY: We are going to learn a song about C-6 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

7 numbers. Have students follow along as you say the counting sequence for each blank in the song at a steady, even pace do not rush the numbers to fit the rhythm of the song in its original form. Progress to the next counting number only when all students are comfortable with the current number. If you want to count to one, say If you want to count to one, say If you want to count to one, If you want to count to one, If you want to count to one, say If you want to count to two, say If you want to count to two, say If you want to count to two, If you want to count to two, If you want to count to two, say If you want to count to ten, say (everyone says one) (everyone says one) (everyone says one) (everyone says one, two) (everyone says one, two) (everyone says one, two) (everyone says one, two, three, four, five, six, seven, eight, nine, ten) 2. Listening for and repeating number words. SAY: I will read a poem. Listen for each number word I say, then say the number word again with me. The number words are at the beginning. I Know a Lot of Numbers I know a lot of numbers, I know them all by name. I sometimes name them forward, When I play the forward game. One s name is, Two s name is, Three s name is, Four s name is, Five s name is, Six s name is, Seven s name is, Eight s name is, Nine s name is, Ten s name is. I know a lot of numbers, I know them all by name. I sometimes name them backward, When I play the backward game. Ten s name is, Nine s name is, Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-7

8 Eight s name is, Seven s name is, Six s name is, Five s name is, Four s name is, Three s name is, Two s name is, One s name is. 3. Listening for and answering questions about a sequence of number words. The following story involves counting to 10, but you can lower the number and adjust the story and props to suit your class. Use an egg carton with two sections cut off one end, and ten hard-boiled eggs (or other objects of that size) to illustrate the story. As the story proceeds, fill one whole side of the carton before filling up the other side. Make sure students say each count sequence aloud together. It is important to reinforce the count sequence to avoid students saying, for example, that Two and One are on the bus. SAY: Let s pretend that the egg carton is a school bus. These ten eggs are ten friends. The friends want to take the bus to the pool. Let s begin the story. SAY: Ten friends want to ride the bus. They are going to the pool. Their names are One, Two, Three, Four, Five, Six, Seven, Eight, Nine, and Ten. One drives the bus. Put one egg in the carton. SAY: He picks up Two. Put a second egg in the carton on the same side. ASK: Which friends are on the bus? (One and Two) SAY: Next, One and Two pick up Three. ASK: Which friends are on the bus now? (One, Two, and Three) Continue adding one friend at a time, until all ten friends are on the bus. If you want to extend the story, SAY: One gets off the bus. ASK: Which friend is off the bus now? (One) SAY: One is off the bus. Next, Two gets off the bus. ASK: Which friends are off the bus now? (One and Two) Pointing to the two eggs, SAY: One and Two are off the bus. Repeat until the egg carton is empty. 4. Listening for words that sound like number words. In advance, prepare a picture of a parrot and a picture of a numbered list of things to do. Holding up the picture of a parrot, SAY: I am going to read a poem about a parrot that loves numbers. As I read, listen for words that sound like number words. Read the first two lines aloud and ASK: What number sounds like the word do? (2) PROMPT: Does one sound like do? (no) Does two sound like do? (yes) As you proceed, act out the dialogue by holding up the picture of the parrot in one hand and the picture of the list in the other hand. A Parrot and a List Parrot s List called Things to Do Said, Count the numbers one and two. Then Parrot said, I ll count some more, I ll count the numbers three and four. The List said, Now you mustn t mix C-8 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

9 The next two numbers five and six. Or surely it will be too late After counting seven, eight If you plan to start again To count the numbers nine and ten. Then Parrot said, I m sure you see, The next we count are one, two, three. The List said, Watch that you don t mix, The numbers four and five and six. Or surely there will be no time, After seven, eight, and nine Before we count them all again For us to count the number ten. Parrot said, I ll count some more, The numbers one, two, three, and four. And hopefully it s not too late To count the five, six, seven, eight. But before we count them all again, We can t forget the nine and ten. The List said, One, two, three, four, five. The Parrot said, Six, seven, eight, nine, ten. They both said, One, two, three, four, five, six, seven, eight, nine, ten. 5. Starting to count. NOTE: This is more difficult because there are many non-number words between the number words. Encourage students to chime in with the number that goes in the blank. After lots of practice, some students may enjoy performing the entire chant on their own. Starting to Count I start to count my numbers By saying one and. I try to think of what comes next, I m not sure what to do. I suddenly remember The next are three and. But now I m getting worried Since I can t remember more. Then somehow out of nowhere I remember five and. But my brain feels kind of funny, It might be playing tricks. But really what it s doing Is finding seven and. I wish that it would hurry up Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-9

10 I m in a muddled state. Well now I m feeling clever Since it found the nine and. I ll know the numbers better When I count them all again. 6. Play I Start, You Finish (see unit introduction, p. C-1). (end of activities) NOTE: You can find more traditional counting songs and rhymes by doing an online search for traditional counting songs and rhymes. Preparing for the AP pages. Students can complete AP Book K.1, Unit 1, pp. 1 3 at any time during the lesson and practice their fine motor skills by coloring the shapes. You might use the AP pages as a teacher-directed activity. For example, direct students to Question 1, and SAY: This is one circle. Color one circle. Have students color the shape. Repeat for the remaining questions. For students who do the Bonus questions, PROMPT: What does this show? (3 circles, 3 squares) Activity Center For guidance on selecting and using the activity centers, see Introduction, p. A-13. (MP.7) Sorting Objects Type: Pairs, individual Objective: To explore mathematical concepts, like quantity, size, patterns, and classification Preparation: Provide blocks, alphabet letters, connecting cubes, and base ten blocks each kind of object should be placed in its own bin. Instructions: SAY: These bins hold different objects. You can take out objects and put them any way you want. Have student pairs show and compare how they sorted the types, colors, and sizes of the objects they chose. Extension (MP.2, MP.3, MP.7) Give each student six blocks in two colors (three of each color) and three copies of four different alphabet letters. Show students a repeated pattern that uses a mixture of blocks and letters. For example, SAY: I have some blocks and letters in a row. I have a red block, the letter A, a red block, the letter A, a red block, the letter A. You can make your own pattern. Have students make three different repeating patterns. Pair up students and have them share and talk about their patterns with their partner. C-10 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

11 CCK-2 The Numbers 1 and 2 Pages 4 6 Standards: K.CC.A.1, K.CC.A.3 Goals: Students associate the spoken numbers one and two with one and two objects, pictures of one and two objects, and the written numbers 1 and 2. Prior Knowledge Required: Can say parts of the count sequence from 1 to 10 Can use pictures of objects to represent real objects Vocabulary: match, number, spoken numbers 1 and 2 Materials: 4 shoes all different, no pairs, some large and some small box or opaque bag 4 socks 4 blocks two should be identical BLM Number Cards (1) to (2) (pp. I-8 9) BLM Picture Cards (1) to (2) (pp. I-19 20) bins glue BLM Making Matches (1) to (2) (pp. C-58 59) tape (see Activity Center 2) BLM Finding the Mistakes (1) (p. I-29, see Activity Center 3) markers, colored pencils, or crayons of two different colors (see Extensions 1, 6) BLM Making the Same Shape (p. C-66, see Extension 1) BLM What Is Different? (1) to (2) (pp. C-67 68, see Extension 2) BLM Coloring to Make 2 (p. C-73, see Extension 6) Counting practice. Practice counting to 10 (see Introduction, p. A-9). Start by singing If You Want to Count to, Say. Continue with any of the other poems, chants, and stories from Lesson CCK-1. (MP.4, MP.7) Associating one or two objects with spoken numbers. Put four different shoes in a box or an opaque bag. Have students close their eyes, then hold up one shoe. Have students open their eyes and you SAY: This is one shoe. Repeat with two shoes. Hold up two shoes and ASK: How many shoes, one shoe or two shoes? (2) SAY: Two tells us the number of shoes. Repeat as needed, varying the order (for example, 1, 2, 2, 1, 2). When you show two shoes, use a variety of pairings. Instead of asking How many shoes, one shoe or two shoes?, ASK: How many shoes is this? Repeat as needed. Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-11

12 Repeat as needed with socks and then with blocks using a variety of pairings when showing two socks or two blocks. Using fingers to show numbers. SAY: I can show numbers with my fingers. Hold up your thumb as shown below and SAY: This is one. Hold up your thumb and your index finger as shown below and SAY: This is two. SAY: I will hold up one or two fingers. I want you to say how many fingers I am holding up. Repeat several times in any order. SAY: This time, I will say a number. You show me the number on your fingers. Students can use any finger or combination of fingers, including one on each hand, but you should use the signals shown above. Repeat several times. (MP.4, MP.7) Associating written numbers 1 and 2 with spoken numbers. Make a small deck of cards using number cards for 1 and 2. Hold up a number card for 1 and SAY: This is the number one. Repeat with a number card for 2. Holding the deck face down, show students the top card and ASK: What number is this, one or two? After students answer return the card to the bottom of the deck. Repeat as needed, eventually changing the question to: What number is this? Matching written numbers 1 and 2 with spoken numbers. Hold up a number card for 2 and SAY: Two. ASK: Are they the same? Do the numbers match? (yes) SAY: Two goes with this number 2. Let s all do a thumbs up because the numbers match. (students signal thumbs up) Hold up a number card for 2 and SAY: One. ASK: Do the numbers match? (no) SAY: Let s all do a thumbs down because the numbers do not match. (students signal thumbs down) Repeat as needed. (MP.4, MP.7) Associating pictures of objects with written and spoken numbers. Give each student a number card for 1 and 2. Ask students to show you the number 1, and then the number 2. Hold up a number card for 1 and SAY: Show me this number. (students hold up 1) Repeat for 2. SAY: Now I will show you a picture of one or two objects. You tell me how many. Show students a picture card for one or two objects. Ask students to say the number of objects and then hold up the card for that number (for example, students say one and then hold up a number card for 1). Repeat as needed. (MP.4, MP.7) Associating written numbers 1 and 2 with spoken numbers and objects. Give each student a picture card for one and two objects. SAY: Hold up the picture that shows one object. Ask several students to identify the object in their picture and say how many there are. Explain that even though the objects in the pictures are different, they all show one object. Repeat for 2. Prompt students to come to the same conclusion: the pictures on the cards may C-12 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

13 be different, but all cards show two objects. SAY: This time I will show you a 1 or a 2. You tell me the number, then show me the picture that goes with it. Repeat as needed. (MP.4, MP.7) Associating spoken numbers one and two with written numbers and objects. SAY: I will say one or two. You show me the number card and the picture card for that number. Repeat as needed. (MP.4, MP.7) Associating spoken numbers, written numbers, and objects. Mix the three types of associations one at a time, present a picture card, a number card, or a spoken number, and ask students to respond with the corresponding associations. Activities 1 3 (MP.2, MP.7) 1. Making Matches (see unit introduction, p. C-2) NOTE: Have weaker students do Activity 2. Have stronger students with a good understanding of the numbers one and two move directly to Activity 3. (MP.2, MP.7) 2. Have students complete Questions 1 12 on AP Book K.1, Unit 1, pp Provide glue, number cards from BLM Number Cards (1) and (2), and picture cards from BLM Picture Cards (1) and (2). (MP.2, MP.7) 3. Have students complete Questions on AP Book K.1, Unit 1, p. 6. Tell students they need to decide if the picture goes with the number. If the picture and number match, they color the happy face. If the picture and number do not match, they color the sad face. You might demonstrate the first two questions on the page. (end of activities) Activity Centers (MP.2, MP.7) 1. Matching Pictures and Numbers (see unit introduction, p. C-2) (MP.2, MP.7) 2. Collecting Objects (see unit introduction, p. C-2) NOTE: Activity Center 3 is a bonus activity suitable for stronger students with a good understanding of the numbers one and two, and should only be assigned to students who completed Activity 3. (MP.2, MP.3, MP.7) 3. Finding the Mistakes (see unit introduction, p. C-3) Extensions 1. Give each student two different colors of markers, pencils, or crayons, and BLM Making the Same Shape. Have students color the unshaded shape so it looks the same as the shaded shape. Students can color over grid lines when necessary. Model how to make the first shape. Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-13

14 2. Have students color to show what is different between each set of two pictures on BLM What is Different? (1) to (2). Model how to do the first question by coloring the extra spot on the first dog. Answers: 1. extra spot on the first dog, 2. extra finger is up on the second hand, 3. extra pocket on the first boy, 4. extra crayon in the second box, 5. extra star on the first mug, 6. extra car on the first train (MP.2) 3. Students search the classroom to find 1s and 2s. These can include any digit in multidigit numbers (for example: 27, 61, 132). Students can look on book covers, calendars, posters, and other displays on classroom walls. (MP.2, MP.7) 4. Students work in pairs. Provide each student with a number card for 1 and 2, five picture cards of one object, and five picture cards of two objects. All cards are face up. Student 1 holds up a number or a picture and Student 2 holds up a corresponding picture or number. They switch roles and repeat. (MP.2, MP.7) 5. Repeat Extension 4, but have students work in larger groups. One student holds up a number or picture card and all of the other students hold up a corresponding picture or number card. Students take turns holding up the initial card. NOTE: Extension 6 is best suited for very advanced students. (MP.1, MP.2, MP.8) 6. Give each student two different colors of markers and BLM Coloring to Make 2. Students will color the squares in each box so that it has two parts, one in one color and one in a different color. Show students the example that is given on the BLM. Tell students that all the answers must be different. SAY: Any two squares of the same color that touch only at one corner do not count as a part. Draw on the board: SAY: This is not correct because the box has four parts, not two parts. Answers: NOTE: These are all the possible correct answers for this puzzle. C-14 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

15 CCK-3 The Number 3 Pages 7 9 Standards: K.CC.A.1, K.CC.A.3 Goals: Students associate the spoken number three with three objects, pictures of three objects, and the written number 3. Prior Knowledge Required: Can use pictures of objects to represent real objects Can associate the spoken numbers one and two with objects, pictures, and the written numbers 1 and 2 Can signal using thumbs up and thumbs down Vocabulary: correct, match, not correct, number, spoken numbers 1 to 3 Materials: 4 shoes all different, no pairs, some large and some small box or opaque bag 3 blocks of different colors and/or sizes groups of three similar objects (e.g., crayons, craft sticks, erasers) BLM Number Cards (1) to (3) (pp. I-8 10) 3 pieces of paper each with a 10-inch tall number for 1, 2, and 3 BLM Picture Cards (1) to (3) (pp. I-19 21) bins glue BLM Making Matches (3) to (4) (pp. C-60 61) tape (see Activity Center 3) BLM Finding the Mistakes (1) to (2) (pp. I-29 30, see Activity Center 4) BLM What Is Different? (3) to (4) (pp. C-69 70, see Extension 1) markers of three different colors (see Extension 5) BLM Coloring to Make 3 (p. C-74, see Extension 5) Counting practice. Practice counting to 10. Start by singing If You Want to Count to, Say. Continue with any of the other poems, chants, and stories from Lesson CCK-1. (MP.2, MP.7) Using fingers to show numbers. Tell a story using your fingers and familiar objects. SAY: I will tell a story about ladybugs. Raise your thumb and SAY: This is one ladybug. Raise your index finger and SAY: This is two ladybugs. Raise your middle finger, as shown below, and SAY: This is three ladybugs. Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-15

16 Continue with the story by saying that one, two, or three ladybugs climbed up a wall, using your fingers as you go. Repeat a few times, varying the number of ladybugs and have students say how many fingers you are holding up. Then say a number and have students show it with their fingers. They can use any finger or combination of fingers, including fingers from both hands. (MP.4, MP.7) Associating up to three objects with spoken numbers. Put four different shoes in a box or an opaque bag. Have students close their eyes, then hold up three shoes. Have students open their eyes. SAY: This is three shoes. Repeat with one shoe, and ASK: How many shoes, one shoe or three shoes? (1) Repeat with two shoes and ASK: How many shoes, two shoes or three shoes? (2) Repeat as needed: hold up one to three shoes and ASK: How many shoes: one, two, or three shoes? When students are comfortable with this, repeat using three different blocks, but instead ASK: How many blocks is this? Repeat as needed using a variety of groups of three similar objects. (MP.4, MP.7) Associating written numbers 1, 2, and 3 with spoken numbers. Make a small deck of cards using numbers cards for 1 to 3. Hold up a number card for 3 and SAY: This is the number three. Repeat for the number 2. Holding the deck face down, show students the top card and ASK: What number is this, one, two, or three? After students answer return the card to the bottom of the deck. Repeat as needed, eventually changing the question to: What number is this? (MP.4, MP.7) Associating spoken numbers one, two, and three with written numbers. Tape 10-inch tall numbers 1, 2, and 3 around your classroom so students can clearly see them. Since students will be answering by pointing at the numbers, put them far enough apart in order to easily see where they are pointing, as shown in the diagram below. NOTE: You will add numbers 4 and 5 in later lessons. The numbers can be left on the walls, as they will be used throughout Unit front classroom 1 5 SAY: I will say a number. You will point to that number on the wall. Repeat as needed. Matching written numbers 1, 2, and 3 with spoken numbers. Show students a thumbs up and SAY: This means correct. Show students a thumbs down and SAY: This means not correct. Show me not correct with your thumb. (thumbs down) Show me correct. (thumbs up) I will hold up a number 1, 2, or 3. Then I will say a number. If the number I say is the same as the number I hold up, it is correct, so show me thumbs up. If the number I say is not the same as the number I hold up, it is not correct, so show me thumbs down. For a non-match, have students say the number on the card. Repeat as needed. C-16 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

17 (MP.4, MP.7) Associating pictures of objects with spoken and written numbers. Explain that you will hold up a picture and students will point to the correct number of objects in the picture on the classroom wall. Hold up a picture card for one, two, or three objects. ASK: What number matches this picture, 1, 2, or 3? (students point to correct number) Pointing to the correct number on the wall, SAY: This number shows how many are in the picture. Repeat as needed. Activities 1 3 (MP.2, MP.7) 1. Making Matches (see unit introduction, p. C-2) Variation: Provide number cards for 1 to 3 and picture cards for one to three objects. Give each student glue and BLM Making Matches (3) to (4). You may need to show an example of each kind of match. NOTE: Have weaker students do Activity 2. Have stronger students with a good understanding of the numbers from 1 to 3 move directly to Activity 3. (MP.2, MP.7) 2. Have students complete Questions 1 12 on AP Book K.1, Unit 1, pp Provide glue, number cards for 1 to 3, and picture cards for one to three objects. 3. Have students complete Questions on AP Book K.1, Unit 1, p. 9. Remind them that if the picture and the number match, they color the happy face. If the picture and number do not match, they color the sad face. You might need to demonstrate with the first question. (end of activities) Activity Centers (MP.2, MP.7) 1. Matching Pictures and Numbers (see unit introduction, p. C-2) Variation: Instead of providing cards in a bin, have students place cards face up in an organized array. Provide six cards per student: a number card for each of 1 to 3, and a picture card for each of one to three objects. Students take turns to match one pair at a time. You might demonstrate making the first match. (MP.2, MP.7) 2. Matching Pictures and Numbers (see unit introduction, p. C-2) Variation: Use number cards for 1 to 3, and picture cards for one to three objects. (MP.2, MP.7) 3. Collecting Objects (see unit introduction, p. C-2) Variation: Use numbers from 1 to 3. Example: NOTE: Activity Center 4 is a bonus activity suitable for stronger students with a good understanding of the numbers 1 to 3, and should only be assigned to students who completed Activity 3. (MP.2, MP.3, MP.7) 4. Finding the Mistakes (see unit introduction, p. C-3) Bonus: Provide students with BLM Finding the Mistakes (2). Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-17

18 Extensions 1. Students color to show what is different between each set of two pictures on BLM What Is Different? (3) to (4). Answers: 7. extra pencil in the first pencil case, 8. extra finger is up on the first hand, 9. extra stripe on the second boy, 10. extra candle on the first cake, 11. extra leaf on the second flower, 12. extra dot on the first girl (MP.2) 2. Students search the classroom to find 1s, 2s, and 3s. These can include any digit in multi-digit numbers (for example: 38, 21, 562). Students can look on book covers, calendars, posters, and other displays on classroom walls. (MP.2, MP.7) 3. Repeat Activity Center 1, but have pairs work together to make a match. For example, Student 1 holds up a picture card for two objects and Student 2 holds up a corresponding number card for 2. They switch roles and repeat. (MP.2, MP.7) 4. Repeat Extension 3, but have students work in larger groups. One student holds up a number card or picture card and all the other students hold up a corresponding picture card or number card. Students take turns holding up the initial number card or picture card. NOTE: Extension 5 is best suited for very advanced students. (MP.1, MP.2, MP.8) 5. Give each student three different colors of markers and BLM Coloring to Make 3. Students will color the squares in each box so that it has three parts, each with a different color. Show students the example that is given on the BLM. Tell students that all the answers must be different. Draw on the board: SAY: This is not correct because it has four parts, not three. Selected answers: NOTE: There are many more correct answers to this puzzle than there are boxes on the BLM. If students want to do more, give them another copy of the BLM. C-18 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

19 CCK-4 Counting Pages Standards: K.CC.A.1 Goals: Students begin learning to count objects and then progress to counting actions and sounds. Prior Knowledge Required: Can associate the written numbers 1, 2, and 3 with spoken numbers, objects, and pictures of objects Can signal using thumbs up and thumbs down Vocabulary: correct, count, more than once, number, once, spoken numbers 1 to 4 Materials: pairs of similar objects (e.g., cups, cubes, dominoes) 4 crayons, each of a different color BLM Counting (p. C-75) 4 bins, each containing one kind of small object (e.g., counters, beans, pennies, ones blocks) (see Activity Center 1) BLM Counting Template (1) (p. C-76, see Activity Center 1) masking tape (see Activity Centers 2, 3) BLM Number Cards (1) to (3) (pp. I-8 10, see Activity Center 4) construction paper and glue (see Activity Center 4) BLM What Is Different? (5) to (6) (pp. C-71 72, see Extension 1) BLM Groups of 2, 3, and 4 (p. C-78, see Extension 5) Counting practice. Practice counting to 10. Start by singing If You Want to Count to, Say. Continue with any of the other poems, chants, and stories from Lesson CCK-1. NOTE: At this point, students are not expected to answer how many? questions after counting a group of objects students will do this in Lesson CCK-5. (MP.4) Counting one or two objects. SAY: I am going to count my ears. Touch one ear and SAY: One. Touch the other ear and SAY: Two. Ask students to help you count your knees by saying the numbers with you. Then, following your pace (about one number per second), have students count their own two feet, two thighs, one nose, and one chin. Repeat either with pairs of similar objects or with single objects. For example, put a cup at each end of a table far enough apart so when students point at them you can see where they are pointing. SAY: Let s count the cups. We will point at the cups as we count. Count the cups. Repeat with other objects until students can synchronize pointing and saying the number. Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-19

20 Tell students that they are going to play The Counting Game (see unit introduction, p. C-3). SAY: I will walk around and touch two objects. We will count them together. Choose pairs of similar objects. At first you choose the objects to count, then ask students for suggestions. (MP.3) Counting correctly. In this part of the lesson, you will teach the students three elements of counting objects correctly: touching each object once, saying one number for every object touched, and saying the counting numbers in the correct order. Affix two crayons, for example, red and blue, to the board side by side. Touch the red crayon once and SAY: I touched the red crayon once. Touch the red crayon more than once and SAY: I touched the red crayon more than once. Now I m going to touch the blue crayon. If I touch it once show me thumbs up, and if I touch it more than once show me thumbs down. Do this a few times. SAY: Now I m going to touch the red crayon and then the blue crayon. Have students signal thumbs up if you touch each crayon once, and thumbs down if you touch either (or both) crayons more than once. Repeat several times. Explain that to count objects correctly you touch each object once, not more than once. SAY: Now we re going to do something different. Touch the red crayon and SAY: One. I touched the red crayon and said one number. Touch it again and SAY: One, two, three, four. This time when I touched it I said more than one number. Repeat with the blue crayon, but have students signal thumbs up if you say one number, and thumbs down if you say more than one number. SAY: Now I m going to touch the red crayon and then the blue crayon. Do it, saying one for the red crayon and two for the blue crayon. SAY: Each time I touched a crayon I said one number when I do this show me thumbs up. Touch each crayon and say more than one number for either or both. SAY: When I do this show me thumbs down. Repeat several times, with students signaling thumbs up or down each time. Explain that to count objects correctly you say one number for each object. ASK: When we count, do we say 1, 2, 3 or 3, 1, 2? (1, 2, 3) SAY: I am going to count. Show me thumbs up if I say the numbers correctly. Show me thumbs down if I do not say them correctly. 1, 2, 3. (thumbs up) 3, 1, 2. (thumbs down) 2, 3, 1. (thumbs down) 1, 2, 3. (thumbs up) 1, 3, 2. (thumbs down) Affix a third crayon of a different color to the board. SAY: I m going to count the crayons. Show me thumbs up if I say the numbers correctly. Show me thumbs down if I do not say them correctly. Count the crayons a few times, sometimes in the correct order and sometimes not. (MP.4) Counting three or four objects. Practice the three elements of counting objects correctly for groups of three and then four crayons. Make sure the crayons you affix to the board are clearly different colors. (MP.4) Counting actions. SAY: I will clap three times and count the claps. Clap at about one clap per second as you count three claps. Repeat for one, two, and four claps and have students say the numbers with you. Once students are comfortable with counting like this, count other actions, such as taking steps or jumping. Have students perform each action and count at the same time. C-20 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

21 Activity (MP.2, MP.7) Counting pictures of objects. Draw on the board: SAY: Let s count these together. I will touch each happy face, and we will say the numbers together. Count from left to right at about one count per second. Give students BLM Counting. Show students Question 1 and SAY: Let s count the owls in the picture together. Count the owls together, then have students count on their own for the remaining questions. Remind students to count quietly. Provide more practice if needed by drawing similar pictures on the board, with the objects always arranged in a row as on the BLM. Have volunteers come up and lead the counting. (end of activity) Preparing for the AP pages. Remind students to practice counting quietly on their own to complete the questions on AP Book K.1, Unit 1, pp Circulate to observe each student s ability to count pictures of objects. Activity Centers (MP.2, MP.7) 1. Counting Objects Type: Individual Objective: To place objects on a template and then count them Preparation: Provide four bins, each containing one kind of small object (e.g., counters, beans, pennies, ones blocks). Provide students with BLM Counting Template (1). Instructions: Demonstrate how to fill in the first template on the BLM using, for example, counters: put one counter in each box as students do the same, then count the counters on the template. (3 counters) Have students repeat to fill in each template on the BLM. Tell students to use the same kind of object in a picture, and to choose different objects for different pictures. (MP.1, MP.2, MP.7) 2. Counting Actions Type: Groups of three, active Objective: To take one to four steps based on a set of instructions Preparation: Use masking tape to make a rectangle of 10 squares as shown below the squares should be approximately 1 foot by 1 foot: Instructions: Show students how to take a step by moving from one box to the next box in either direction, and say a number with each step. Play a demonstration round using three volunteers. Student 1 gives an instruction, such as Take two steps. Student 2, who is standing in a box, takes two steps. Student 3 counts the number of instructions. Once four instructions have been carried out, students change roles. Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-21

22 (MP.1, MP.2, MP.7) 3. Counting Boxes Type: Groups of three, active Objective: To count one to four adjacent boxes based on a set of four instructions Preparation: Use the same 10-square rectangle from Activity Center 2. Instructions: Students take turns giving four instructions, following them, and counting the number of instructions. For example, Student 1 says Count three boxes. Count one box. Count two boxes. Count four boxes. Student 2 follows each instruction. Student 3 keeps track of how many instructions have been carried out and says when it s time to switch. Students switch roles and repeat. 4. Making Designs with the Count Sequence Type: Small groups, creative Objective: To make pictures using the numbers 1, 2, and 3 Preparation: Provide each group with number cards for 1 to 3, separated by number. Draw a continuous path on a piece of construction paper. Example: Instructions: Students take turns gluing one number at a time to make the sequence 1, 2, 3, 1, 2, 3, on the path. Variation: Students make any part of the 1 to 3 sequence going up and down without skipping numbers (e.g., 1, 2, 3, 2, 1, 2, 3). Extensions 1. Students color to show what is different between each set of pictures on BLM What Is Different? (5) to (6). Answers: 13. the dog s head is raised in the second picture, 14. the roof on each house is different, 15. the girl in the first picture has pigtails, 16. the second picture shows only half a pizza, 17. the snowflakes in each picture are different, 18. the girl in the second picture has a scarf NOTE: Extensions 2 to 5 are best suited for advanced students. (MP.1, MP.2, MP.7, MP.8) 2. On a piece of paper, draw a 10-square rectangle like the one in Activity Center 2. Have students think about and then test combinations of one to four steps that start and finish on the same box (going either clockwise or counterclockwise). Demonstrate a combination of steps (e.g., four steps, four steps, two steps) going clockwise and then counterclockwise. Indicate each direction as you go by pointing and tell students that turning around is not allowed. Sample answers: 2 steps, 3 steps, 1 step, 4 steps; 4 steps, 2 steps, 2 steps, 2 steps (MP.1, MP.2, MP.7, MP.8) 3. Repeat Extension 2, but tell students that they need to stop one box past where they started. C-22 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

23 (MP.1, MP.2, MP.7, MP.8) 4. Repeat Extension 3, but tell students that they need to stop one box before where they started. (MP.1, MP.2, MP.3, MP.7) 5. Give each student six 2s, four 3s, and three 4s from BLM Groups of 2, 3, and 4. Show students a chain of four and a chain of two 2s placed end-to-end. SAY: These two chains line up. They start and end at the same place. Ask students to make chains of the same length using 2s, 3s, or 4s. Example: Place the 4s in a row, then place the 3s in a row below the 4s. Once the pieces are lined up, count the 4s (1, 2, 3) and the 3s (1, 2, 3, 4), as shown below: SAY: There are three 4s and four 3s. Have student pairs show and compare their work. NOTE: Students may notice patterns, such as four 2s is two 4s, or two 3s is three 2s. This indicates that they have recognized that 4 2 = 2 4 and 2 3 = 3 2, but do not use this language with students. Sample answers: one 4 and two 2s, two 4s and four 2s, two 3s and three 2s, four 3s and six 2s. Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-23

24 CCK-5 Counting 1, 2, and 3 Pages Standards: K.CC.A.1, K.CC.A.3, K.CC.B.4a, K.CC.B.4b, K.CC.B.5 Goals: Students count to answer how many? questions about one, two, or three objects arranged in different ways. Prior Knowledge Required: Can associate the written numbers 1, 2, and 3 with the spoken numbers, objects, and pictures of objects Can signal using thumbs up and thumbs down Can count to 3 Vocabulary: count, how many, last number, number, spoken numbers 1 to 4 Materials: 4 shoes all different, no pairs, some large and some small 4 similar blocks 6 crayons groups of three similar objects (e.g., books, pens, chairs) 3 strips of paper one with two buttons glued or sewn to it and two with three buttons bins straw segments counters BLM How Many? (1) to (2) (pp. C-79 80) glue (see Activity Centers 1 4) BLM Number Cards (1) to (3) (pp. I-8 10, see Activity Centers 1 4) paper squares of three different colors (see Activity Centers 1, 2) construction paper (see Activity Centers 1, 4) BLM Counting Template (2) (p. C-77, see Activity Center 2) BLM Picture Cards (1) to (3) (pp. I-19 21, see Activity Center 3) BLM Joining the Black Dots (p. C-85, see Extension 4) Counting practice. Practice counting to 10. Start by singing If You Want to Count to, Say. Continue with any of the other poems, chants, and stories from Lesson CCK-1. Review associating one, two, or three objects with spoken numbers. Hold up two shoes and ASK: How many shoes is this? (2) Repeat for one shoe and then three shoes. Review counting. SAY: Let s practice counting. Demonstrate counting one, two, three, and four similar blocks. Then repeat with students counting together. Practice with other objects as needed. C-24 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

25 Remembering the last number said when counting. Affix three crayons to the board in a horizontal line. SAY: I am going to count these crayons. Try to remember the last number I say. Count the crayons, then ASK: What was the last number? (3) Write 3 to the right of the crayons on the board. Repeat with two crayons, then one crayon. Practice with other groups of one, two, and three similar objects, for example, books and chairs. Ask students to suggest items to count. As an added challenge, SAY: Let s do that with some bigger numbers. Gather six similar classroom objects, count them aloud, and ask for the last number. Repeat for seven, eight, nine, and ten objects. Play The Counting Game (see unit introduction, p. C-3) for groups of three similar objects. (MP.8) When counting objects, the last number said is the number of objects. Affix two similar objects, such as small blocks, to the board. ASK: How many blocks are there? (2) Write 2 to the left of the blocks. SAY: Now I will count the blocks. Try to remember the last number I say. Count the blocks, ask students for the last number, and write it to the right of the blocks. Point to the 2 on the left and SAY: This is how many blocks there are. Point to the 2 on the right and SAY: This is the last number I said when I counted. ASK: Are these numbers the same or different? (the same) Repeat for 3 and 1 using other small objects, as shown below: Pointing to the numbers in the examples on the board, SAY: These numbers are the same every time. The last number we say when we count tells how many blocks there are. (MP.8) Count to say how many. Show students three books. SAY: I will count these books. Count the books, then ASK: What was the last number I said? (3) SAY: That means there are three books. Repeat with numbers 1, 2, and 3 using a variety of similar objects. Show students two pens. SAY: Now I will count pens. Count the pens, then ASK: How many pens are there? (2) Repeat with numbers 1, 2, and 3 using a variety of similar objects. For one example, ask three volunteers to come to the front and count them. The number of objects does not depend on how they are arranged. Affix a strip of paper with two buttons to the board, as shown below: ASK: How many buttons are there? (2) SAY: Let s count to make sure. Point to each button as students count aloud together. ASK: How many are there? (2) Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-25

26 Rotate the strip of paper on the board, as shown below: ASK: How many buttons are there? (2) Did the number change when I turned them? (no) Repeat with a strip of paper with three buttons, first oriented horizontally and then vertically. SAY: Now I will cut this strip and put the pieces on the board. Cut the strip of paper in two, and affix the two pieces to the board, as shown below: ASK: How many buttons are there? (3) SAY: Let s count to make sure. Point to each button as students count aloud together. ASK: Did the number change when I cut the strip? (no) Repeat as needed with other groups of similarly assembled objects. The number of objects does not depend on counting order. Affix the strip of two buttons horizontally onto the board. ASK: If I count the big button first, will there be two? (yes) Count them aloud. ASK: If I count the small button first, will there be two? (yes) Count them aloud. ASK: Is the number of buttons the same no matter which one we count first? (yes) Repeat with the strip of two buttons turned vertically. Repeat with a strip of paper with three buttons. First affix it to the board horizontally, then vertically, and finally cut it into two pieces as before. Repeat as needed with other groups of similarly assembled objects. Arrangement and counting order does not affect how many there are. Divide the class into groups of three to five students. Give each group a bin of straw segments. SAY: Everyone take out one straw. ASK: How many straws do you have? (1) SAY: Put the straw in the other hand. ASK: How many straws do you have? (1) Did the number change when you put the straw in the other hand? (no) SAY: Pick up another straw. Hold both straws in one hand. ASK: How many straws do you have? (2) Have students move one straw to the other hand. ASK: How many straws do you have? (2) Have students move the second straw to the other hand and repeat the question. ASK: Does moving the straws change the number of straws? (no) Repeat with a third straw. Activity (MP.1, MP.7) Finding how many and keeping track of what has been counted. Divide the class into groups of three to five students. Give each group a bin of counters and provide each student with BLM How Many? (1) to (2). NOTE: Make sure students use counters that fit within the dashed outline circles on the BLM and in the AP pages for this lesson. C-26 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

27 Show students Question 1 and SAY: Put a counter on every circle. Then count your counters quietly. ASK: How many are there? (2) Have students find the number 2 and circle it. SAY: This shows there are two counters. Repeat for Question 2. SAY: It is easy to forget which ones I counted. Demonstrate how that might happen by counting the same counter twice. Then count each counter and make a mark near each counter as shown below. When you get to the first counter again, SAY: This has a mark on it. The mark shows I already counted it, so I will not count it again. Have students do the same and then circle 3 to show there are three counters. Question 2 should look like this: Have students complete Questions 3 8 individually. (end of activity) Activity Centers (MP.1, MP.2, MP.7) 1. Counting Objects and Answering How Many? (see unit introduction, p. C-3) (MP.1, MP.2, MP.7) 2. Counting Objects and Answering How Many? (see unit introduction, p. C-3) Variation: Use BLM Counting Template (2). (MP.2, MP.7) 3. Counting Pictures of Objects and Answering How Many? (see unit introduction, p. C-4) (MP.2, MP.7) 4. Collecting and Counting Objects and Answering How Many? (see unit introduction, p. C-4) Extensions (MP.1, MP.2) 1. Draw on the board: SAY: There are three groups: small boxes, big boxes, and very big boxes. ASK: What is the same about the three groups of boxes? What is different about the groups of boxes? Sample answers: Same: all groups have two objects, all objects within each group are the same; Different: each group has a different size of box Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-27

28 (MP.2, MP.3) 2. Draw on the board: SAY: There are three groups. ASK: What is the same about the groups? What is different about the groups? Sample answers: Same: all groups have two objects; Different: each group has a different kind of object (MP.2, MP.3) 3. Draw on the board: SAY: There are three groups. ASK: What is the same about the groups? What is different about the groups? Sample answers: Same: all groups have the same kind of object; Different: each group has a different number of objects NOTE: Extension 4 is best suited for advanced students. (MP.1, MP.2, MP.8) 4. Provide students with BLM Joining the Black Dots. For each picture, have students draw a different continuous path to join the two black dots. Paths are made by drawing a combination of vertical and horizontal lines and can have no gaps in them. Explain that students cannot backtrack, that lines cannot be diagonal, and that no part of a path can be retraced. Answers: C-28 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

29 CCK-6 Counting Out 1, 2, and 3 Pages Standards: K.CC.B.5 Goals: Given the number 1, 2, or 3, students count out that many objects from a larger group of objects. Prior Knowledge Required: Can associate the written numbers 1, 2, and 3 with spoken numbers, objects, and pictures of objects Can use pictures of objects to represent real objects Can signal using thumbs up and thumbs down Can count to 3 Can count and answer how many objects there are (up to three objects) Vocabulary: count, count out, how many, last number, number, spoken numbers 1 to 3 Materials: box containing at least 4 similar blocks bins counters BLM Counting Out From a Larger Group (1) (p. I-36) BLM Number Cards (1) to (3) (pp. I-8 10, see Activity Centers 1 3) BLM Coloring 1, 2, and 3 Fish (p. C-86, see Extension 1) 20 similar objects (see Extension 2) Counting practice. Practice counting to 10. Start by singing If You Want to Count to, Say. Continue with any of the other poems, chants, and stories from Lesson CCK-1. Review that the last number said when counting objects is the number of objects. Hold up three fingers on one hand and count as you touch each one, using a finger from your other hand. ASK: What was the last number I said? (3) SAY: The last number I said is how many fingers I have up. ASK: How many fingers do I have up? (3) Repeat as needed. Counting out objects from a larger group. SAY: There are a lot of students here. I would like two students to come to the front. Have two volunteers come to the front one at a time and count them as they approach. ASK: How many students are standing here? (2) PROMPT: What is the last number I said? SAY: Now I would like three more students to come up. Count them as they approach and ASK: How many students came? (3) Repeat for four more students. (4) Have all of the students sit down. If needed, repeat so all students in the class get to come to the front. Provide a box containing four similar blocks and ask for a volunteer. SAY: Please take out two blocks. Count each block as the student takes them out of the box, one at a time. Ask how many blocks the student took out. Repeat for four blocks, then three blocks. Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-29

30 Put all the blocks back in the box and ask for another volunteer. SAY: Please take out two blocks. This time have the volunteer count each block as they are taken out. Ask how many blocks the volunteer took out. Repeat for three and then four blocks. Activities 1 2 (MP.2) 1. Counting out objects from a larger group. Divide the class into groups of three to five students. Give each group a bin of counters. SAY: We are going to count out some counters. Tell students how many counters to count out of the bin. Set the pace for counting out at about one number per second. Have students take out counters from the bin at the same time as you and say the corresponding numbers at the same time. After each count out, have students return the counters to the bin. Repeat as needed, mixing the order (e.g., count out three, next count out one, then count out two). When students are comfortable, continue to set the pace for taking out counters from the bin, but this time have only the students count. When they are comfortable with this, ask the following questions after each count out. ASK: What was the last number you said? How many counters did you take out? Eventually, omit the first question and ASK: How many counters did you take out? (MP.1, MP.2, MP.7) 2. Counting out pictures of objects from a larger group. SAY: I will draw a picture of a bin with counters in it. Draw on the board: SAY: I want to count out two counters. ASK: Can I take counters out of the picture I drew? (no) Pretend to try to take counters out of the picture. SAY: I cannot take counters out of the picture. So instead, I will make a mark on the counters I want to take out. Explain that the marks should be simple. As you say one, draw a mark on a counter. As you say two, draw a mark on another counter. (see sample drawing below) Before making copies of BLM Counting Out From a Larger Group (1), write numbers on the BLM as shown below: Give students the BLM. Direct them to the first question. Tell students that the number shows how many to count out. ASK: What number is this? (2) Tell students that it doesn t matter which counters they mark, but they do have to mark two counters. SAY: Let s count out two counters C-30 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

31 together. Have students mark a counter on their BLM as you SAY: One. Have them mark another counter as you SAY: Two. Repeat for the second and third questions. Have students complete the rest of the BLM on their own. (end of activities) Activity Centers (MP.2, MP.7) 1. Counting Out Objects (see unit introduction, p. C-4) (MP.2, MP.7) 2. Counting Out Objects (see unit introduction, p. C-4) Variation: One partner takes out one number card but both partners count out the specified number of counters on their own. Then they compare to see if they have the same number of counters. Partners switch roles and repeat. (MP.1, MP.2, MP.7) 3. Counting Out Objects (see unit introduction, p. C-4) Variation: Students work on their own to collect several similar objects. Students use the objects they collected instead of counters. Extensions 1. Students complete BLM Coloring 1, 2, and 3 Fish. NOTE: Extensions 2 to 5 are best suited for advanced students. You might use prompts to help guide students thinking. (MP.1, MP.2, MP.3, MP.7, MP.8) 2. Students count out three objects from a group of 5, a group of 10, and a group of 20 similar objects. They decide if the number of objects in the whole group changes the number they count out. Have students share their thinking. Answer: The group can be any size but I always count out three objects. (MP.1, MP.2, MP.3, MP.7) 3. Give students two counters. ASK: Can you count out three counters? Why or why not? Have students share their thinking. Answer: No. There are not enough. I need one more. (MP.1, MP.3, MP.7) 4. ASK: How are counting 3 and counting out 3 from a bigger group the same? How are counting 3 and counting out 3 different? Have students share their thinking. Answers: Same: The number counted is the same. Different: With counting, I count everything but with counting out, I only count some. (MP.1, MP.2, MP.3, MP.7, MP.8) 5. Make counters available to students. Tell students to work with a partner and think of counting out 4 problems that cannot be done. Have them show why they cannot be done. Sample answers: Start with three objects and try to count out 4, start with two objects and try to count out 4, start with one object and try to count out 4, start with no objects and try to count out 4. Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-31

32 CCK-7 Writing 1, 2, and 3 Pages Standards: K.CC.A.3 Goals: Students begin to model, trace, and write the numbers 1, 2, and 3, progressing from using gross motor skills to fine motor skills. Prior Knowledge Required: none Vocabulary: count, number, numerals 1 to 3 Materials: cardboard, glue, and rope, thick yarn, or modeling clay (see Activity Center 1) paper, clear plastic sleeves, paint, and small sponges (see Activity Center 2) modeling clay (see Activity Center 3) transparencies of BLM Number Cards (1) to (3) (pp. I-8 10, see Extension 1) 6 straws per student (see Extension 2) scissors (see Extension 2) Counting practice. Practice counting to 10. Start by singing If You Want to Count to, Say. Continue with any of the other poems, chants, and stories from Lesson CCK-1. Play a few rounds of The Counting Game (see unit introduction, p. C-3). Activities Tracing numbers in the air. Draw on the board three large boxes about 2 feet tall and write the numbers 1 to 3 in them, as shown below: l 2 3 Explain that you will trace over the number 1 with your finger. SAY: Trace over the 1 in the air at the same time as I do. Say one as you use the point of your index finger to trace 1 slowly, with your arm extended. As you demonstrate, SAY: I want you to use one finger. Repeat to trace 2 and then 3. Repeat several times in counting order. SAY: Let s do this a few more times. This time I will not start with 1. Mix the order and repeat several times. C-32 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

33 2. Tracing parts of numbers and entire numbers in the air. Draw on the board the same picture as in Activity 1, but leave the first box empty. ASK: What number is missing? (1) Have students trace the number they have to imagine (1) and the numbers they can see (2 and 3) several times, first in counting order, then in mixed order. Revise the picture on the board, as shown below: l 2 3 Trace the parts that students can see (1, the top of 2, and 3) and the part they have to imagine (the bottom of 2) several times in counting order, then mix the order. Repeat with the second box only showing the bottom of 2, then with the 2 missing altogether. Repeat the sequence for 3. Revise the picture on the board so that only the 3 is shown. Lead students in tracing the numbers they have to imagine (1 and 2) and then the number they can see (3) in counting order, and then in mixed order. Repeat with just the 2, and then just the 1. (MP.1) 3. Tracing numbers 1, 2, and 3 and parts of numbers 2 and 3. Students who finish Activities 1 2 early can trace the parts of numbers and entire numbers on AP Book K.1, Unit 1, pp (end of activities) Activity Centers (MP.2, MP.7) 1. Feeling Numbers with Fingers (see unit introduction, p. C-4) 2. Painting Numbers with a Sponge (see unit introduction, p. C-5) 3. Painting Numbers with a Sponge (see unit introduction, p. C-5) Variation: Students use modeling clay instead of paint to make the number 1 and the curved parts of 2 and 3. Have students put the parts together to form the entire number. Then students make each of the numbers 2 and 3 in one piece. ASK: Is it easier to make 2 and 3 in parts or in one piece? (MP.1, MP.2, MP.7) 4. Tracing and Coloring Numbers Type: Individual Objective: To practice tracing numbers 1, 2, and 3 and parts of numbers 2 and 3. Instructions: Have students complete AP Book K.1, Unit 1, pp For Questions 5 7, students will trace the numbers and color the pictures. Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-33

34 Extensions 1. In advance, copy BLM Number Cards (1) to (3) on transparencies and cut out the cards. Give each student two of each number card. For each number, students turn one copy upside down, flip it over, or both, and compare it with the right-side-up version. Students explain which numbers look the same when turned upside down and/or flipped over, and which numbers look different. Answers: 1 and 3 look the same (students may have to rotate the flipped 3 to make it look the same), 2 looks different (MP.1, MP.2, MP.3, MP.7, MP.8) 2. Give each student six straws, each marked with a line at its midpoint. Challenge students to construct the numbers 1 to 3 (not at the same time) using some or all of the straws. Have student pairs discuss why it is harder to make 2 and 3 than 1. Have students cut the straws on the marked line and construct the numbers 1, 2, and 3 again. Have student pairs discuss if it is easier to make the numbers with smaller straws. If so, have them explain why they think so. Have students predict and discuss with a partner what would happen if they used even smaller pieces to construct the numbers. C-34 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

35 CCK-8 Counting 4 Pages Standards: K.CC.A.1, K.CC.A.3, K.CC.B.4a, K.CC.B.4b, K.CC.B.5 Goals: Students count to answer "how many?" questions about four objects arranged in different ways. Given the number 4, students count out four objects from a larger group of objects. Prior Knowledge Required: Can use pictures of objects to represent objects Can count to 3 Can count up to three objects in various arrangements Can count out up to three objects from a larger group Can signal using thumbs up and thumbs down Can count and say how many objects there are Vocabulary: count, count out, how many, number, numerals 1 to 3, numeral 4 Materials: counters 4 straws bins BLM How Many? (3) to (4) (pp. C-81 82) BLM Counting Out From a Larger Group (1) (p. I-36) glue (see Activity Centers 1 3) construction paper (see Activity Centers 1, 3, 4) paper squares of three different colors (see Activity Center 1) BLM Number Cards (1) to (4) (pp. I-8 11, see Activity Centers 2 4) BLM Picture Cards (1) to (4) (pp. I-19 22, see Activity Center 2) 2 mugs, 4 marbles, teaspoon, and water (see Extension 1) pictures of squares and pictures of circles (see Extension 2) Counting practice. Practice counting to 10. Start by singing If You Want to Count to, Say. Continue with any of the other poems, chants, and stories from Lesson CCK-1. Play a few rounds of The Counting Game (see unit introduction, p. C-3). Review that the last number said when counting objects is the number of objects. Hold up four fingers on one hand and count them. Have students point at your fingers and count with you. ASK: How many fingers do I have up? (4) Repeat with more examples as needed. The number of objects does not depend on how they are arranged. Affix four counters to the board in a horizontal line. SAY: Let s count these together. Have students point to the counters one at a time from left to right while counting. ASK: How many are there? (4) Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-35

36 Repeat counting from right to left. ASK: How many are there? (4) Repeat for the following arrangements: vertical (count top to bottom, then bottom to top), a 2 2 array (count clockwise starting from the top left corner, then counterclockwise), and scattered (count two different ways), as shown below: horizontal vertical 2 2 array scattered Arrangement and counting order does not affect how many there are. Pick up one straw and SAY: I have one straw. One at a time, pick up three more straws, and for each straw, ASK: How many do I have? Move one straw at a time to the other hand and each time, ASK: How many straws do I have? Did the number change when I moved straws from one hand to the other? (no) Activities 1 2 (MP.1, MP.2, MP.7) 1. Finding how many and keeping track of counting. Divide students into groups of three to five. Give each group a bin of counters and provide each student with BLM How Many? (3) to (4). NOTE: Make sure students use counters that fit within the dashed outline circles on the BLM and in the AP pages for this lesson. Show students Question 9 and SAY: Put a counter on each circle. Then count the counters quietly. ASK: How many are there? (4) Show students a number 4 on the BLM and SAY: This is the number 4. Have students find the number 4 and circle it on their BLM. Repeat for Question 10. Remind students that they can draw marks beside each counter if they need help remembering what they already counted. Have students complete Questions 11 to 16 on their own. (MP.2, MP.7) 2. Counting out pictures of objects from a larger group. Draw on the board: SAY: I want to count out three counters. ASK: Can I take counters out of a picture? (no) SAY: Since I cannot take counters out, I will mark counters. One at a time, mark and count out three counters. Before making copies of BLM Counting Out From a Larger Group (1), write numbers on the BLM as shown below: C-36 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

37 Give students the BLM. Direct students to the first question. Remind students that the numbers show how many to count out. SAY: Let s count out two counters. Have students mark a counter on their BLM as you SAY: One. Repeat for a second counter. Repeat for the next two questions. Then have students complete the rest of the BLM on their own. (end of activities) Activity Centers (MP.1, MP.2, MP.7) 1. Counting Objects and Answering How Many? (see unit introduction, p. C-3) Variation: Use the numbers 1 to 4 and the template shown below: (MP.2, MP.7) 2. Counting Pictures of Objects and Answering How Many? (see unit introduction, p. C-4) Variation: Use the numbers 1 to 4. (MP.1, MP.2, MP.7) 3. Collecting and Counting Objects and Answering How Many? (see unit introduction, p. C-4) Variation: Use the numbers 1 to 4 and the template shown below: MP.2, MP.7) 4. Counting Out Objects (see unit introduction, p. C-4) Variation: Use the numbers 1 to 4. (MP.2, MP.7) 5. Counting Out Objects (see unit introduction, p. C-4) Variation: Use the numbers 1 to 4. Students work on their own to collect several similar objects. Students use the objects they collected instead of counters. Extensions (MP.1, MP.2, MP.3, MP.7) 1. Drop four marbles into an opaque mug, and then drop 4 teaspoons of water into an identical mug. Have students predict what they will see when they look into the mugs. Have them talk about why they can see four marbles but not 4 teaspoons of water. Ask them to think of things that might behave the same way as the water. Ask what they could do to the water so that they could see the 4 teaspoons of water. (freeze each teaspoon of water or put each of the teaspoons of water into separate sealable bags) Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-37

38 NOTE: Extensions 2 and 3 are best suited for advanced students. 2. a) Put six pictures of squares and six pictures of circles in a bin. Have students count out four squares (they take out a picture and keep it if it is a square or put it back if it is a circle). Then they put the squares back. Repeat for counting out four circles. Ask why it might be confusing if they were asked to count out 4. b) Put eight squares and four circles in the bin and have students count out four squares and then four circles as in part a). ASK: Is it faster to count out squares or circles? Why do you think so? c) Put seven squares and five circles in the bin and have students count out four squares and then four circles. ASK: Is it faster to count out squares or circles? Why do you think so? d) Put nine squares and three circles in the bin and have students count out four squares and then four circles. ASK: Can you do it? Why or why not? Answers: a) Because students do not know what four objects to count out, only squares, only circles, or some of both. b) It is definitely faster to count out squares because there are a lot more squares than circles. c) It might be faster to count out squares since there are more squares than circles. d) No, there are not enough circles to count out 4. (MP.1, MP.2, MP.7) 3. Put 12 counters in a bin. Have students find how many times (without putting any counters back) they can a) count out 3 b) count out 4 Answers: a) 4 times, b) 3 times C-38 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

39 CCK-9 The Number 4 Pages Standards: K.CC.A.1, K.CC.A.3 Goals: Students associate the spoken number four with four objects, pictures of four objects, and the written number 4. Prior Knowledge Required: Can use pictures of objects to represent real objects Can associate the written numbers 1, 2, and 3 with spoken numbers, objects, and pictures of objects Can signal using thumbs up and thumbs down Can say how many objects there are when the objects have been counted correctly Vocabulary: correct, count, how many, match, not correct, number, numerals 1 to 4 Materials: groups of similar objects, (e.g., crayons, colored craft sticks, buttons, erasers) box or opaque bag BLM Number Cards (1) to (4) (pp. I-8 11) piece of paper with a 10-inch tall number 4 BLM Picture Cards (1) to (4) (pp. I-19 22) bins glue BLM Making Matches (5) to (6) (pp. C-62 63) tape (see Activity Center 3) BLM Finding the Mistakes (2) to (3) (pp. I-30 31, see Activity Center 4) Counting practice. Practice counting to 10. Start by singing If You Want to Count to, Say. Continue with any of the other poems, chants, and stories from Lesson CCK-1. Play a few rounds of The Counting Game. Using fingers to show numbers. Show 1, 2, and 3 with your fingers. Then hold up four fingers as shown below and SAY: This is 4. Show one to four fingers a few times in any order and have the class say the number. Then say a number and have students show it with their fingers. They can use any finger or combinations of fingers, including fingers from both hands. Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-39

40 (MP.4, MP.7) Associating up to four objects with a spoken number. Put a group of six similar objects, such as crayons, in a box or opaque bag. Have students close their eyes, then you hold up four crayons. Ask students to open their eyes, then SAY: This is four crayons. Repeat with one crayon, but instead ASK: Is this one crayon or four crayons? (1) Repeat with two crayons and ASK: Is this two crayons or four crayons? (2) Repeat with three crayons and ASK: Is this three crayons or four crayons? (3) Repeat with one to four crayons and ASK: Is this 1, 2, 3, or 4 crayons? When students are comfortable with this, use different objects and change the question to: How many [objects] is this? Repeat as needed. (MP.4, MP.7) Associating written numbers 1, 2, 3, and 4 with spoken numbers. Make a small deck of cards using number cards for 1 to 4. Hold up a number card for 4 and SAY: We learned that this is the number 4. Hold up any of the numbers from 1 to 4 and have all students say the number. Holding the deck face down, show students the top card and ASK: What number is this, 1, 2, 3, or 4? After students answer return the card to the bottom of the deck. Repeat as needed, eventually changing the question to: What number is this? (MP.4, MP.7) Associating spoken numbers one, two, three, and four with written numbers. Tape a 10-inch tall number 4 on the classroom wall, as shown below: 3 2 front classroom 1 5 SAY: I will say 1, 2, 3, or 4. You point to the number on the wall. Repeat as needed. Matching written numbers 1, 2, 3, and 4 with spoken numbers. Remind students that thumbs up and thumbs down mean correct and not correct, respectively. SAY: I will hold up a number card, then I will say a number. Show me thumbs up if the number I say is correct. Show me thumbs down if the number I say is not correct. Hold up a number card for 1, 2, 3, or 4 and say either the correct number or an incorrect number. Students signal thumbs up or down accordingly. For non-matches, have students say the correct number on the card. Repeat as needed. Activities 1 4 (MP.1, MP.2, MP.7) 1. Associating pictures of up to four objects with spoken and written numbers. Hold up a picture card of one to four similar objects. Have students say the number together and then point to the correct number on the classroom wall. Repeat as needed. (MP.1, MP.2, MP.7) 2. Making Matches (see unit introduction, p. C-2) Variation: Provide number cards for 1 to 4, picture cards for one to four objects, glue, and BLM Making Matches (5) to (6). C-40 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

41 NOTE: Have weaker students do Activity 3. Have stronger students with a good understanding of the numbers 1 to 4 move directly to Activity 4. (MP.1, MP.2, MP.7) 3. Have students complete Questions 1 18 on AP Book K.1, Unit 1, pp Provide glue, number cards for 1 to 4, and picture cards for one to four objects. (MP.1, MP.2, MP.7) 4. Have students complete Questions on AP Book K.1, Unit 1, p. 25. Remind students that if the picture and the number match, they color the happy face. If the picture and the number do not match, they color the sad face. You might demonstrate the first question. (end of activities) Activity Centers (MP.2, MP.7) 1. Matching Pictures and Numbers (see unit introduction, p. C-2) Variation: Instead of providing cards in a bin, have students place cards face up in an organized array. Provide eight cards per student: a number card for each number 1 to 4, and a picture card for each of one to four objects. Students take turns to match one pair at a time. You might demonstrate the first match. (MP.2, MP.7) 2. Matching Pictures and Numbers (see unit introduction, p. C-2) Variation: Use number cards for 1 to 4, and picture cards for one to four objects. (MP.2, MP.7) 3. Collecting Objects (see unit introduction, p. C-2) Variation: Use the numbers 1 to 4. (see example below) NOTE: Activity Center 4 is a bonus activity suitable for stronger students with a good understanding of the numbers 1 to 4. (MP.2, MP.3, MP.7) 4. Finding the Mistakes (see unit introduction, p. C-3) Variation: Provide students with BLM Finding the Mistakes (2). Bonus: Provide students with BLM Finding the Mistakes (3). Extensions (MP.2) 1. Students search the classroom to find 1s, 2s, 3s, and 4s. These can include any digit in multi-digit numbers (for example: 74, 32, 561). Students can look on book covers, calendars, posters, and other displays on classroom walls. Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-41

42 (MP.2, MP.7) 2. Repeat Activity Center 1, but have pairs work together to make a match. For example, Student 1 holds up a number card for 3 and Student 2 holds up a corresponding picture card of three objects. They switch roles and repeat. (MP.2, MP.7) 3. Repeat Extension 2, but have students work in groups. One student holds up any card and all of the other students hold up a corresponding card. Students take turns holding up the initial card. NOTE: Extensions 4 and 5 are best suited for advanced students. (MP.1, MP.2, MP.3, MP.7) 4. a) Provide students with two groups of similar objects, one with three objects, the other with four objects. SAY: Try to make two groups of four objects. ASK: Can you do it? SAY: Show me. b) Provide students with a group of four objects and one of five objects. SAY: Try to make two groups of four objects. ASK: Can you do it? SAY: Show me. Have students share their thinking with a partner. Sample answers: a) No, I can make one group of four but I need one more to make another group of four. b) Yes, I can make two groups of four, but there is one object left. (MP.1, MP.2, MP.3, MP.7) 5. Provide students with four groups of similar objects. Each group should be its own kind of object and contain one to four objects (e.g., one crayon, two markers, three stamps, four erasers). a) ASK: Can you arrange the groups to make two groups of four with some left over? SAY: Show me. b) ASK: Can you make two groups of four with none left over? SAY: Show me. Have students share their thinking with a partner. Sample answers: a) Yes. I put one and three together to make four and the group of four is already four. There are two left over. b) No. No matter how I arrange the groups to make two groups of four, there are always two left over. C-42 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

43 CCK-10 Writing 4 Pages Standards: K.CC.A.3 Goals: Students begin to model, trace, and write the number 4, progressing from using gross motor skills to fine motor skills. Prior Knowledge Required: none Vocabulary: count, number, numerals 1 to 4 Materials: cardboard, glue, and rope, thick yarn, or modeling clay (see Activity Center 1) paper, clear plastic sleeves, paint, and small sponges (see Activity Center 2) modeling clay (see Activity Center 3) transparencies of BLM Number Cards (1) to (4) (pp. I-8 11, see Extension 1) 6 straws per student (see Extension 2) scissors (see Extension 2) finger paints or crayons (see Extension 3) BLM Finding the Hidden Number 4 (p. C-87, see Extension 3) Counting practice. Practice counting to 10. Start by singing If You Want to Count to, Say. Continue with any of the other poems, chants, and stories from Lesson CCK-1. Play a few rounds of The Counting Game (see unit introduction, p. C-3). Review tracing 1, 2, and 3 in the air. Draw on the board three large boxes about 2 feet tall and write the numbers 1 to 3 in them, as shown below: l 2 3 ASK: What numbers did I write? (1, 2, 3) SAY: Let s practice tracing them in the air. Say one as you use the point of your index finger to trace 1 slowly, with your arm extended. Repeat to trace 2 and then 3. Repeat a few times in counting order and then in mixed order. Always say the number aloud before tracing it. Activities Tracing numbers in the air. Draw on the board a large box about 2 feet tall and write the number 4 in it, as shown below: Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-43

44 Explain that you will trace over the number 4 with your finger. SAY: Trace over the 4 in the air at the same time as I do. Say four as you use the point of your index finger to trace 4 slowly, with your arm extended. Have students trace the 4 with you several times. 2. Tracing parts of a number in the air. Draw on the board: SAY: This is part of a number. ASK: What is the number? (4) Have students trace the angled part with you in the air several times, and then trace both parts of the number 4 in the air the part they can see followed by the part they need to imagine several times. Draw on the board: SAY: I want to ask you a tricky question. This is part of a number. Put up your hand if you know the number. ASK: What is the number? (4) What other number could this be part of? (1) Have students trace the vertical part with you in the air several times, then trace both parts of the number 4 in the air the part they need to imagine followed by the part they can see several times. (MP.1) 3. Tracing 4. Students who finish early can complete AP Book K.1, Unit 1, p. 26. (end of activities) Activity Centers (MP.2, MP.7) 1. Feeling Numbers with Fingers (see unit introduction, p. C-4) Variation: Use 1, 2, 3, and Painting Numbers with a Sponge (see unit introduction, p. C-5) Variation: Use 4 and the parts of Painting Numbers with a Sponge (see unit introduction, p. C-5) Variation: Students use modeling clay instead of paint to make the number 4 and the parts of 4. They put the parts together to form the entire number. Then have students make the number 4 in one piece. ASK: Is it easier to make 4 in parts or in one piece? (MP.1, MP.2, MP.7) 4. Tracing and Coloring Numbers Type: Individual Objective: To practice tracing the numbers 1 to 4 and parts of the number 4 Instructions: Have students complete AP Book K.1, Unit 1, pp For Questions 3 6, students will trace the numbers and color the pictures. C-44 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

45 Extensions 1. In advance, copy BLM Number Cards (1) to (4) on transparencies and cut out the cards. Give each student two of each number card. For each number, students turn one copy upsidedown, flip it over, or both, and compare it with the right-side up version. Students explain which numbers look the same when turned upside-down and/or flipped over, and which numbers look different. Sample answers: 1 and 3 look the same (students may have to rotate the flipped 3 to make it look the same), 2 and 4 look different (MP.1, MP.2, MP.3, MP.7, MP.8) 2. Give each student six straws, each marked with a line at its midpoint. Challenge students to construct the numbers 1 to 4 (not at the same time) using some or all of the straws. Have student pairs discuss why it is harder to make 2 and 3 than 1, and if 4 is easier to make than 2 and 3. Have students cut the straws on the marked line and construct the numbers 1 to 4 again. Have student pairs discuss if it is easier to make the numbers with smaller straws. If so, have them explain why they think so. Have students predict and discuss what would happen if they used even smaller pieces to construct the numbers. 3. Provide BLM Finding the Hidden Number 4. Tell students to look for the 4 that is hiding in each picture. Have students trace the 4s using a tool of their choice (e.g., finger paints, crayons). Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-45

46 CCK-11 Counting 5 Pages Standards: K.CC.A.1, K.CC.A.3, K.CC.B.4a, K.CC.B.4b, K.CC.B.5 Goals: Students count to answer "how many?" questions about five objects arranged in different ways. Given the number 5, students count out five objects from a larger group of objects. Prior Knowledge Required: Can use pictures of objects to represent objects Can count to 4 Can count up to four objects in various arrangements Can count out up to four objects from a larger group Can signal using thumbs up and thumbs down Can count and answer how many objects there are for up to four objects arranged in different ways Vocabulary: count, count out, how many, number, numerals 1 to 4, numeral 5 Materials: counters bins BLM How Many? (5) to (6) (pp. C-83 84) BLM Number Cards (1) to (5) (pp. I-8 12, see Activity Centers 1 5) glue (see Activity Centers 1 3) construction paper (see Activity Centers 1, 3) paper squares of three different colors (see Activity Center 1) BLM Picture Cards (1) to (5) (pp. I-19 23, see Activity Center 2) 9 blocks per student (see Extension 3) Counting practice. Practice counting to 10. Start by singing If You Want to Count to, Say. Continue with any of the other poems, chants, and stories from Lesson CCK-1. Play a few rounds of The Counting Game (see unit introduction, p. C-3). Review that the last number said when counting objects is the number of objects. Hold up five fingers on one hand and count them. ASK: How many fingers am I holding up? (5) Repeat with other examples of five objects as needed. The number of objects does not depend on how they are arranged. Affix five counters to the board in a horizontal line. SAY: Let s count these together. Point to the counters one at a time from left to right and have students count together. ASK: How many are there? (5) Repeat counting from right to left. ASK: How many counters are there? (5) Repeat for the following arrangements: vertical (count top to bottom and bottom to top), one row of 3 C-46 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

47 and one row of 2 (count clockwise, then counterclockwise from the top left corner), and scattered (count two different ways), as shown below: horizontal vertical 3 and 2 scattered Activities 1 2 (MP.2, MP.7) 1. Keeping track of counting when finding how many. Divide students into groups of three to five. Give each group a bin of counters and provide each student with BLM How Many? (5) to (6). NOTE: Make sure students use counters that fit within the dashed outline circles on the BLM and in the AP pages for this lesson. Show students Question 17 on the BLM. One at a time, point to each number and ask what it is. When you get to 5, SAY: This is the number five. Put a counter on each circle. Then quietly count the counters from one end to the other. ASK: How many are there? (3) Have students circle the number 3. Repeat for the second question. Remind students that they can draw marks beside each counter if they need help remembering what they already counted. Have students do the remaining questions on their own. (MP.2, MP.7) 2. Counting out objects from a larger group. Divide students into groups of three to five. Give each group a bin of counters. SAY: Let s count out four counters. You set the pace and everyone counts aloud. Then students put the counters back. Repeat as needed for 2, 3, and 4, in any order. When students are comfortable, you set the pace but only students count. When they are comfortable with this, ask how many counters they took out. (end of activities) Activity Centers (MP.1, MP.2, MP.7) 1. Counting Objects and Answering How Many? (see unit introduction, p. C-3) Variation: Use the numbers 1 to 5 and the template shown below: (MP.2, MP.7) 2. Counting Pictures of Objects and Answering How Many? (see unit introduction, p. C-4) Variation: Use the numbers 1 to 5. Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-47

48 (MP.1, MP.2, MP.7) 3. Collecting and Counting Objects and Answering How Many? (see unit introduction, p. C-4) Variation: Use the numbers 1 to 5 and the template shown below: (MP.2, MP.7) 4. Counting Out Objects (see unit introduction, p. C-4) Variation: Use the numbers 1 to 5. (MP.2, MP.7) 5. Counting Out Objects (see unit introduction, p. C-4) Variation: Use the numbers 1 to 5. Students work on their own to collect several similar objects. Students use the objects they collected instead of counters. Extensions NOTE: Extensions 1 to 3 are best suited for advanced students. (MP.1, MP.7, MP.8) 1. Students start with 15 counters in a bin. Challenge them to find out how many times (without replacing any counters) they can count out a) 5 b) 3 Answers: a) 3, b) 5 (MP.1, MP.2, MP.3, MP.8) 2. Give each student a bin containing 20 counters. Have students assemble a group of counters from which... a) five counters can be counted out exactly twice with none left over. b) five counters can be counted out exactly three times with none left over. Answers: a) a group of 10 counters, b) a group of 15 counters NOTE: For part b), students can, but are not required to, count all 15 counters as long as they can demonstrate that five can be counted out exactly three times. (MP.1, MP.2, MP.3, MP.7, MP.8) 3. Give each student a bin containing nine blocks. ASK: How many times can you count out five blocks? (1 time) How many more blocks will you need to count out 5 exactly two times? (1 more block) What if you start with eight blocks? How many more will you need to count out 5 exactly two times? (2 more blocks) What if you start with seven blocks? How many more will you need to count out 5 exactly two times? (3 more blocks) What if you start with six blocks? How many more will you need to count out 5 exactly two times? (4 more blocks) Have students talk about questions of their choice with a partner. C-48 Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality

49 CCK-12 The Number 5 Pages Standards: K.CC.A.1, K.CC.A.3 Goals: Students associate the spoken number five with five objects, pictures of five objects, and the written number 5. Prior Knowledge Required: Can use pictures of objects to represent real objects Can associate the written numbers 1, 2, 3, and 4 with the spoken numbers, objects, and pictures of objects Can signal using thumbs up and thumbs down Can count and answer how many for up to five objects arranged in different ways Vocabulary: correct, count, how many, match, not correct, number, numerals 1 to 5 Materials: groups of similar objects (e.g., crayons, colored craft sticks, buttons, erasers) box or opaque bag BLM Number Cards (1) to (5) (pp. I-8 12) piece of paper with a 10-inch tall number 5 BLM Picture Cards (1) to (5) (pp. I-19 23) bins glue BLM Making Matches (7) to (8) (pp. C-64 65) tape (see Activity Center 3) BLM Finding the Mistakes (2) to (4) (pp. I-30 32, see Activity Center 4) Counting practice. Practice counting to 10. Start by singing If You Want to Count to, Say. Continue with any of the other poems, chants, and stories from Lesson CCK-1. Play a few rounds of The Counting Game (see unit introduction, p. C-3). Using fingers to show numbers. Show 1, 2, 3, and 4 with your fingers. Then hold up five fingers as shown below and SAY: This is 5: Show one, two, three, four, or five fingers a few times in any order and have the class say the number. Then say a number and have students show it with their fingers. Students can use any finger or combination of fingers, including fingers from both hands. Teacher s Guide for Kindergarten Unit 1 Counting and Cardinality C-49