Lesson Name: Counting, Comparing, and Representing Numbers to 20 Estimated timeframe: January 5-22 (13 Days) Grading Period/Unit: CRM 10 (3 rd Nine Weeks) Lesson Objectives: Lesson Components Grade level/course: Kindergarten 1. The students will be able to count, generate, compare, and represent quantities up to 20 using objects, pictures, and numbers. Language Objectives: 1. The students will use language (e.g., as many as, more than, less than, etc.) to describe and compare quantities to 20. Prior Learning: The child should be able to count and represent amounts of up to 15 with pictures and objects and read, write, and label those quantities with corresponding numerals. Standards(Texas Essential Knowledge and Skills): K.2A count forward and backward to at least 20 with and without objects; K.2B read, write, and represent whole numbers from 0 to at least 20 with and without objects or pictures; K.2C count a set of objects up to at least 20 and demonstrate that the last number said tells the number of objects in the set regardless of their arrangement or order; K.2E generate a set using concrete objects and pictorial models that represents a number that is more than, less, than, and equal to a given number up to 20; K.2F generate a number that is one more than or one less than another number up to at least 20; K.2H use comparative language to describe two numbers up to 20 presented as numerals. Essential Questions: 1. In what situation would having 20 of something be too many, too few, or just enough? 2. What is the difference between a small number and a big number? 3. How do you know when you have counted exactly 20 objects? Vocabulary Counting words to 20, teens, tensframe, benchmark, count, set, quantity, few, more, eyeball estimate, greater than, less than, as many as Lesson Preparation Numeral cards 1-20 Connecting cubes Chart paper Markers Four 0-5 dot cubes (for 4 individual players) Caps for Sale by Esphyr Slobodkina Index cards Number line 1-20 Black Line: Quadruple Roll Recording Sheet Black Line: Animal Counting Cube Puzzle Cards (11-20) Black Line: Ten and Some More Number Cards (11-20) AISD Early Childhood Department, 2015 Page 1
Lesson Cycle Engage Tell the children to stand and form a circle. Have the class count off as they go clockwise round the circle taking attendance. Arrange a set of numeral cards (10-15) face down in the center of the circle area. Invite the last child to count off during the attendance routine to select one of the cards in the center and identify the numeral. Direct the class to proceed clockwise around the circle, starting from the child with the selected numeral card, and count on from that number e.g., if the child selected the numeral 11, he/ she would say that number, and the count would continue going clockwise from where he/she is located in the circle. When the count stops, the child who said the last counting word (20) will select another card from the center, and the class will continue the counting on game from that number. The counting circle stops when all of the cards in the in the middle have been selected. Numeral cards 10-15 are turned face down in the middle of the circle area. Invite a volunteer to grab a handful of connecting cubes out of a tub of about 100. Inform the class that you want to have exactly 20 cubes. Challenge the children to make a rough estimate as to about how many cubes there might be in that one handful. o Ask: Do you think [volunteer s name] might have grabbed exactly 20 cubes? What could we do to be sure how many there are? Count the cubes to verify how many you have collected so far. Call on a second volunteer to grab another handful of cubes. Remind the children how many cubes there were from the first handful and model how to count on from that number. Continue to select additional volunteers to grab one handful of cubes until you have reached the target number 20. If the last handful goes over, stop at 20 and return the remaining cubes to the bin. Count all of the cubes in the collection to verify that you have reached your goal of 20. Gather suggestions from the class about how to arrange the cubes so that trying to keep track of how many were counted/ not counted would be an easier task. If no one suggests, try out each of the following arrangements a straight line, a circle, and various rectangular arrays, including a 5-by-4 and 2-by-10 configuration. After making each arrangement, count the cubes so as to emphasize that the number has not changed. Make a pictorial representation of each arrangement on chart paper. Dismiss children to centers by allowing them to vote on which arrangement of 20 is easier to count. AISD Early Childhood Department, 2015 Page 2
Exploration Dual Language Activity 1: (This activity is also appropriate for all classrooms) As the rest of the class is working at centers /math stations, gather a group of 4 children. Demonstrate and then play a new game called Quadruple Roll: 1. All 4 players begin the game by counting out a set of 20 cubes. 2. Each player rolls a 0-5 dot cube and places that many cubes in the center. 3. One player counts how many cubes were collected all together as a group and represents that amount on the recording sheet using both pictures (e.g., hash marks) and numbers. The cubes from that roll are then bundled together in a stick and removed from the center. 4. The game continues until all 4 players have had an opportunity to count and represent the number of cubes in the center. Individual Student 1-20 Number Lines: Encourage children to arrange 0-20 train numeral cards in numerical order. Remind the children to check their arrangement with a 1-20 number line/ anchor chart posted somewhere in the classroom. Challenge those children who are able to quickly and accurately arrange the number line to use counters (e.g., cubes) to represent the numerical value indicated on the corresponding card. Explanation DAY 1 Debriefing Session (15 minutes maximum): Gather the children in a whole group session to debrief the strategies they used to count, combine, and represent the totals from the Quadruple Roll game. Ask the following questions to guide the children to think about the quantification strategies they used: When you rolled the dot cube, what strategy did you use (e.g., one-to-one correspondence, eyeballing/ estimating, etc.) to determine how many cubes to take? How did you count the total counting on/ counting all? How did you arrange the cubes so that they would be easy to record on the recording sheet? How did you know you had represented each cube in the collection? AISD Early Childhood Department, 2015 Page 3
DAY 2 Introduction: Read the book, Caps for Sale, by Esphyr Slobodkina. Gather suggestions from the children about what the vendor could do to remember how many caps he had on top of his head without having to draw a picture of each one. If no one suggests, propose that the vendor could write the numeral of the last counting word he says after he finishes counting the caps. Then, when he forgets, he can simply read the numeral, which will help him remember and see a mental picture of the number of caps he should have in his inventory. Call on a volunteer to write the numeral 16 (the number of caps on the vendor s head) on an index card. Discuss what the children could do if they did not know how to read the numeral but wanted to count out a set of caps that matches it. Display a horizontal number line (1-20) on the carpet. Ask another volunteer to find the numeral on the number line that is identical to the number the previous volunteer wrote on the index card. Model how to begin at the numeral 1 on the number line and move forward, assigning one cube per numeral until you reach 16. Count the cubes to confirm that there are 16. Explain that during math stations/ center time, the children will practice labeling sets of objects they count with a corresponding numeral. Elaboration Math Centers/ Stations (DAYS 2-8): Before dismissing the children to math stations/centers, begin to introduce various Choice Time activities (one per day of the week) as recommended in the Elaboration section as well as from Investigations (2 nd Edition, 2012) Unit 4, Investigation 3, Session 3.1, Racing Bears (p. 90); Session 3.3 One More, One Less (p. 100); Session 3.4, Double Compare (p. 104); Session 3.5, More or Less at the End (p. 109); Session 3.6, Build It/ Change It (p. 113); and Session 3.7, Who Has More? (p. 117).. Other suggestions for Choice Time stations include Activity 2.22, Double War (p. 53) and Activity 2.26, Ten and Some More (p. 55) from John A. Van de Walle s Teaching Student Centered Mathematics Grades K-3, Volume Two. Game: Compare (Numerals 0-20) 1. Pair children with a partner. Each player needs to shuffle his/ her deck of 1-20 numeral cards and place them face down. 2. Both players remove a card from the pile and compare. The child comparing the card with the highest/ greatest value takes both cards. IF the values are equivalent, each player keeps his/ her respective card. 3. The game continues until the children have played all cards. The child with the most cards wins the game. AISD Early Childhood Department, 2015 Page 4
Dual Language Activity 2 (DAYS 2-5) 11-20 Animal Puzzle Cards : (This activity is also appropriate for all classrooms) 4. Gather a group of small children as the rest of the class works at other math stations set up around the room. 5. Distribute a tower of 10 connecting cubes to each child. Ask: How many of each color are there? Count to confirm that each tower has exactly 10. 6. Introduce the Animal Counting Cube Puzzles and 11-20 Number Cards. Display the giraffe puzzle and model how to fill it by arranging connecting cubes face up inside the outline. 7. After using up one tower of 10, point to the one empty square space remaining inside the outline. Ask: How many more cubes do I need to complete the puzzle? 8. Borrow one cube from another tower of 10 and emphasize how 11 is one more than 10. 9. Assign pairs of children a puzzle that will contain a maximum of 15 cubes e.g., the lizard (12), the alligator (13), the tiger (14), and the fish (15). Allow the children to work with their partner filling their assigned puzzle. Make sure each pair choses whose cube tower they will use first, and whose tower they will use to borrow extra cubes. 10. When the children use up one tower of 10 connecting cubes, challenge them to look at the remaining empty squares inside the outline to determine how many extra cubes they will need to complete the puzzle. 11. Display the 11-15 Numeral Cards and guide each pair to figure out which card shows how many cubes they used to fill their outline. Lead the children to see that the numeral corresponds to the language used to describe how many e.g., one ten (point to the representative numeral the 1 in 14) and four more (point to the 4) is called fourteen. 12. Introduce the remaining Animal Counting Cube Puzzle Cards for numbers 16-20 for the children to fill in and label during center time. alligator How many cubes? AISD Early Childhood Department, 2015 Page 5
Evaluation (check for understanding) Formative: Make 4 copies of each groups Quadruple Roll recording sheet so that you can have a work sample collected for every child in the class. Highlight which roll the child recorded on the representative copy and make notes on the sheet describing any relevant observations about the strategies he/ she used to count and represent the combined total. Summative (DAYS 8-9): Consult the Benchmark 2 Assessment Task on p. 157 of the Investigations 2 nd Edition (2012) Unit 6. In this performance task, the students are given a set of 20 loose cubes and are asked to determine how many there are. Note whether students: o Count each object once and only once (which involves a system for keeping track of what has been counted and what remains to be counted. o Double check their counting When the children are finished counting, ask them how many cubes there are. o Can the students tell you the number, or do they recount the set to answer the question? English Language Proficiency Standards 1(E) internalize new basic and academic language by using and reusing it in meaningful ways in speaking and writing activities that build concept and language attainment; 3(E) share information in cooperative learning interactions. Anchors of Support Take pictures of children in the classroom carrying out the following strategies (in addition to any additional ones you have generated as a group) for counting and representing quantities to 15: Count each object once. No double counting. Keep track of your count. Remember that the last word you say when you count tells you how many objects you counted. Affix these pictures next to their representative strategy generated with the help of the class and written down on an anchor chart, which should be posted somewhere where the children can refer to and use it. College and Career Readiness V.A.1 (Probabilistic Reasoning/ Counting Principles) Determine the nature and the number of elements in a finite sample space. IX.A.1 (Communication and Representation/ Interpretation of mathematical work) Model and interpret mathematical ideas and concepts using multiple representations. 21 st Century Skills Communication and Collaboration (Collaborate with Others): Assume shared responsibility for collaborative work, and value the individual contributions made by each team member. Differentiation strategies Special Education: Break down the number of steps the child must follow as he/she represents the number of cubes his/her group collected during the round he/she is the recorder for the Quadruple Roll game. (See the Practice section of the lesson below.) First, have the child arrange the cubes in a straight line. Then, tell the child to remove one cube at a time from the linear arrangement as he/she makes a corresponding hash mark on the recording sheet. English Language Learners: Remind ELLs that the counting words for numbers 11-19 are spoken opposite AISD Early Childhood Department, 2015 Page 6
from the way that they are written. Otherwise, the children may write the numerals backwards e.g., writing down 61 for the word sixteen. Point to each numeral on a numeral card as you say the counting word so that the children can visualize the backwards sequence e.g., when saying the word sixteen, show the numeral 16, pointing to the 6 first and the 1 second. Extension for Learning: During center time, allow the children to roll a dot cube and move that number of spaces on a number line representing the sequence of numbers 1-20. Encourage the children to count on from the last number they rolled e.g., if they landed on 12 and then roll a 3, they should count forward, thirteen, fourteen, and fifteen. CRM Planning Schedule Monday Tuesday Wednesday Thursday Friday Engage & Explore sections of the Exemplar Lesson Explore section of the Exemplar Lesson Go Math: Lesson 8.1 Explain & Elaborate section of the Exemplar Lesson Go Math: Lesson 8.2 Elaborate section of the Exemplar Lesson Go Math: Lesson 8.3 Elaborate section of the Exemplar Lesson Elaborate section of the Exemplar Lesson Investigations: Unit 4, Session 3.1 Elaborate section of the Exemplar Lesson Investigations: Unit 4, Session 3.3 Elaborate section of the Exemplar Lesson Investigations: Unit 4, Session 3.4 Elaborate section of the Exemplar Lesson Go Math: Lesson 8.4 Go Math: Lesson 8.5 Go Math: Lesson 8.6 Go Math: Lesson 8.7 Go Math: Lesson 8.8 Investigations: Unit 4, Session 3.5 Investigations: Unit 4, Session 3.6 Elaborate section of the Exemplar Lesson Investigations: Unit 4, Session 3.7 Elaborate section of the Exemplar Lesson Evaluation section of the Exemplar Lesson Evaluation section of the Exemplar Lesson Go Math: Lesson 8.7 Go Math: Lesson 8.8 Other resources include Teaching Student-Centered Mathematics: Grades K-3; REMEMBER, if you cannot get to every activity suggested, that is okay. Choose and pick wisely. AISD Early Childhood Department, 2015 Page 7
Train Numeral Cards 1 2 3 AISD Early Childhood Department, 2015 Page 8
Train Numeral Cards 4 5 6 7 AISD Early Childhood Department, 2015 Page 9
Train Numeral Cards 8 9 10 11 AISD Early Childhood Department, 2015 Page 10
Train Numeral Cards 12 13 14 15 AISD Early Childhood Department, 2015 Page 11
Train Numeral Cards 16 17 18 19 AISD Early Childhood Department, 2015 Page 12
Train Numeral Cards 20 AISD Early Childhood Department, 2015 Page 13
Roll 1 Quadruple Roll Recording Sheet picture number Roll 2 picture number Roll 3 picture number Roll 4 picture number AISD Early Childhood Department, 2015 Page 14
fish How many cubes? AISD Early Childhood Department, 2015 Page 15
turtle How many cubes? AISD Early Childhood Department, 2015 Page 16
bear How many cubes? AISD Early Childhood Department, 2015 Page 17
giraffe How many cubes? AISD Early Childhood Department, 2015 Page 18
alligator How many cubes? AISD Early Childhood Department, 2015 Page 19
elephant How many cubes? AISD Early Childhood Department, 2015 Page 20
\ Lesson Template antelope How many cubes? AISD Early Childhood Department, 2015 Page 21
tiger How many cubes? AISD Early Childhood Department, 2015 Page 22
snake How many cubes? AISD Early Childhood Department, 2015 Page 23
lizard How many cubes? AISD Early Childhood Department, 2015 Page 24
Tens and Ones Number Cards 10 1 10 2 11 12 10 3 10 4 13 14 AISD Early Childhood Department, 2015 Page 25
10 5 10 6 15 16 10 7 10 8 17 18 AISD Early Childhood Department, 2015 Page 26
10 9 10 10 19 20 AISD Early Childhood Department, 2015 Page 27
1-20 Number Line 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 AISD Early Childhood Department, 2015 Page 28