# 1 Mathematics Curriculum

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2 NYS COMMON CORE MATHEMATICS CURRICULUM Topic F 1 1 Lesson 22 focuses on having students look for common addends and discuss how those addends affect the total in systematic ways. For example, I see 3+2=5, 4+2=6, 5+2=7 and 6+2=8! Even though we re adding 2 each time and that stays the same, the totals are increasing by 1, because we re adding a number that s 1 more each time! Building upon this, Lesson 23 has students using the facts they know, such as those from Topic B s decomposition posters to explore patterns in problems where the totals are the same. The topic closes with Lesson 24 s addition fact practice where students actually get to practice their facts in an engaging, supportive environment with their peers (1.OA.6). A Teaching Sequence Towards Mastery of Development of Addition Fluency Within 10 Objective 1: Visualize and solve doubles and doubles plus 1 with 5-group cards. (Lesson 21) Objective 2: Look for and make use of repeated reasoning on the addition chart by solving and analyzing problems with common addends. (Lesson 22) Objective 3: Look for and make use of structure on the addition chart by looking for and coloring problems with the same total. (Lesson 23) Objective 4: Practice to build fluency with facts to 10. (Lesson 24) Topic F: Development of Addition Fluency Within 10 Date: 5/9/13 1.F.2

3 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 21 1 Lesson 21 Objective: Visualize and solve doubles and doubles plus 1 with 5-group cards. Suggested Lesson Structure Fluency Practice Application Problem Concept Development Student Debrief Total Time (12 minutes) (5 minutes) (28 minutes) (15 minutes) (60 minutes) Fluency Practice (12 minutes) Stand on Even Numbers 1.OA.5 Target Practice: 8 1.OA.6 (3 minutes) (9 minutes) Stand on Even Numbers (3 minutes) Note: Counting on allows students to maintain fluency with this strategy as they solve addition problems. Students sit in a circle and count by ones, each student saying one number to count up. When a student says an even number, she stands, 1, 2 (student stands), 3 4 (student stands).go around the circle until all students are standing. Students who are standing do not continue counting. Then, continuing in the same direction around the circle, students count backwards, beginning with the last number said and sitting on even numbers. Play the game a second time, instructing students who stay still to whisper their numbers and students who stand or sit to use a normal voice. Target Practice: 8 (9 minutes) Materials: (S) Each set of partners needs one Target Practice board (in a plastic sleeve), a dry erase marker, an eraser, 8 counters and a die Note: This activity addresses the core fluency objective for Grade 1 of adding and subtracting within 10. Use the Target Practice board you saved from G1-M1-Lesson 10 and follow the directions on the board. Use 8 as the target number. Lesson 21: Visualize and solve doubles and doubles plus 1 with 5-group cards. Date: 5/9/13 1.F.3

4 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 21 1 Application Problem (5 minutes) Jordan is holding a container with 3 pencils. His teacher gives him 4 more pencils for the container. How many pencils will be in the container? Write a number bond, number sentence, and statement to show the solution. Note: This problem is an application of the commutative property to count on from the larger addend from Lesson 20. It is also relevant to the concept development of the current lesson as a doubles plus one problem. Concept Development (28 minutes) Materials: (T) 5-group cards (1 through 6 only), addition chart, yellow and orange colored pencil for debrief (S) Personal board Have students sit next to their math partners on the carpet or at their tables. T: Let s count by 2s using our fingers. Watch me first. T/S: 2, 4, 6, 8, 10, 10, 8, 6, 4, 2. (Shows fingers.) T: Show me 1 and 1 with your pinkies like me. How many fingers are you holding up? S: 2. T: What is the number sentence? S: = 2. NOTE ON MULTIPLE MEANS OF REPRESENTATION: Some students may not be able to count by 2s without numerical visual cues at this point in the year. Use a tool such as a number line or the hundreds chart. Students can color the pattern counting by 2s on the number line or hundreds chart so they have a visual representation as they are counting with the class. T: Show me 2 and 2 fingers, your pinkies and ring fingers. Say the number sentence to tell how many fingers you re holding up. S: = 4. (Continue with 3 + 3, 4 + 4, 5 + 5, and back down to ) T: What did you notice about the numbers we added each time? S: We added the same number two times. T: We call those doubles. Lesson 21: Visualize and solve doubles and doubles plus 1 with 5-group cards. Date: 5/9/13 1.F.4

5 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 21 1 MP.8 Give 2 minutes for students to work with their partners and practice making doubles number sentences. Partner A flashes doubles fingers, Partner B says the number sentence. They switch roles after 1 minute. T: (Shows two 5-group cards showing 3 dots.) Without counting all, tell how many dots there are. S: 6. T: How did you know? S: I saw doubles. 3 and 3. That makes 6. Continue with 2 + 2, 4 + 4, and 5 + 5, ensuring the students use the term doubles to explain what they see and eventually naming it as a strategy. Congratulate them on getting better at mastering their doubles facts. T: (Shows 3 dots card and 4 dots card.) Without counting all, tell how many dots there are. S: 7. NOTE ON MULTIPLE MEANS OF REPRESENTATION: Help students connect calculations to body parts by counting with their fingers. When solving 3 + 3, students should hold up 3 and 3 fingers, and count by 2s. They wriggle their pinkies and say 2, wriggle pinkies and ring fingers and say 4, wriggle pinkies, ring and middle fingers and say 6. T: How did you know so quickly? Turn and talk to your partner. (Circulates and listens.) T: [Student 1] said she saw 3 and 3 plus another dot! Give a thumbs up if you see 3 dots hiding inside these 4 dots. S: (Show thumbs.) T: She used her doubles fact to help. 3 plus 3 (circles 3 dots and 3 dots), that s. S: 6. T: Plus another dot? S: 7. T: How is related to 3 + 3? S: It s making doubles and adding 1 more. T: This is called doubles plus 1. Let s see if we can find more doubles facts hiding inside another expression. (Continue with 1 + 2, 3+ 2, and ) T: (Projects the numerals 4 and 5.) How would you solve 4+5 using today s lesson? Turn and talk to your partner and solve on your white board. S: (Writes = 9.) Use our doubles facts = 8. Add 1 more and you get 9. T: (Projects 3 + = 6.) What number is missing here? Talk with your partner to decide. Tell each other how you know. S: (Discuss with partner.) T: What is the missing number in 3 + = 6? S: 3! T: How do you know? S: I know that = 6. I thought of the doubles. If I have 3 (holds up three fingers on one hand), I need 3 more to make 6. Lesson 21: Visualize and solve doubles and doubles plus 1 with 5-group cards. Date: 5/9/13 1.F.5

6 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 21 1 T: (Projects 3 + = 7.) What number is missing here? Discuss with your partner. Remember to use words or your personal white boards to explain your thinking. S: (Discuss with partner.) T: What is the missing number in 3 + = 7? S: 4! T: How could the last problem, = 6, help you with this one? S: If you know is 6, and now you need to have 7, then you know you need 1 more than last time, so now it s (Continue with 4+4 and 4+5.) Problem Set (10 minutes) Students should do their personal best to complete the problem set within the allotted 10 minutes. For some classes, it may be appropriate to modify the assignment by specifying which problems they work on first. Some problems do not specify a method for solving. Students solve these problems using the RDW approach used for Application Problems. On this Problem Set, we suggest all students begin with number 1, number 2, number 5, number 6 and possibly leave number 7 (d) and (e), number 8 and number 9 to the end if they still have time. Student Debrief (15 minutes) Lesson Objective: Visualize and solve doubles and doubles plus 1 with 5-group cards. The Student Debrief is intended to invite reflection and active processing of the total lesson experience. Invite students to review their solutions for the Problem Set. They should check work by comparing answers with a partner before going over answers as a class. Look for misconceptions or misunderstandings that can be addressed in the Debrief. Guide students in a conversation to debrief the Problem Set and process the lesson. You may choose to use any combination of the questions below to lead the discussion. (Post the addition chart.) Can you find all the Lesson 21: Visualize and solve doubles and doubles plus 1 with 5-group cards. Date: 5/9/13 1.F.6

8 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 21 Template 1 Addition Chart Lesson 21: Visualize and solve doubles and doubles plus 1 with 5-group cards. Date: 5/9/13 1.F.8

9 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 21 Problem Set 1 Name Date Add the numbers on the pairs of cards. Write the number sentences. Color doubles red. Color doubles plus 1 blue Solve. Use your doubles to help. Draw and write the double that helped = = Lesson 21: Visualize and solve doubles and doubles plus 1 with 5-group cards. Date: 5/9/13 1.F.9

10 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 21 Problem Set 1 7. Solve the doubles and the doubles plus one number sentences. (a) = (a) = (b) = (c) = (d) = (b) = (c) = (d) = (e) 3 + = 6 (e) 3 + = 7 (f) 5 + = 10 (f) 4 + = 9 8. Show how this strategy can help you solve: = 9. Write a set of 4 related addition facts for letter (d). Lesson 21: Visualize and solve doubles and doubles plus 1 with 5-group cards. Date: 5/9/13 1.F.10

11 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 21 Exit Ticket 1 Name Date Write the double and double plus one number sentence for the 5- group card. 4 5 Lesson 21: Visualize and solve doubles and doubles plus 1 with 5-group cards. Date: 5/9/13 1.F.11

12 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 21 Homework 1 Name Date 2 Draw the 5- group card to show a double. Write the number sentence to match the cards Fill in the 5- group cards in order from least to greatest, double the number, and write the number sentences. 1 Lesson 21: Visualize and solve doubles and doubles plus 1 with 5-group cards. Date: 5/9/13 1.F.12

13 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 21 Homework 1 Solve the number sentences = 5 + = = 2 4 = = 4 + Match the top cards to the bottom cards to show doubles plus Solve the number sentences. Write the double fact that helped you solve the double plus one = 3 + = = 9 Lesson 21: Visualize and solve doubles and doubles plus 1 with 5-group cards. Date: 5/9/13 1.F.13

18 NYS COMMON CORE MATHEMATICS CURRICULUMNYS COMMON Lesson 22 Problem Set 1 Name Date Use RED to color boxes with 0 as an addend. Find the total for each. Use ORANGE to color boxes with 1 as an addend. Find the total for each. Use YELLOW to color boxes with 2 as an addend. Find the total for each. Use GREEN to color boxes with 3 as an addend. Find the total for each. Use BLUE to color the boxes that are left. Find the total for each. red Lesson 22: Look for and make use of repeated reasoning on the addition chart by solving and analyzing problems with common addends. Date: 5/9/13 1.F.18

19 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 22 Exit Ticket 1 Name Date Some of the addends in this chart are missing! Fill in the missing numbers Lesson 22: Look for and make use of repeated reasoning on the addition chart by solving and analyzing problems with common addends. Date: 5/9/13 1.F.19

20 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 22 Homework 1 Name 4 Date Solve the problems without counting all. Color the boxes using the key. Step 1: Color problems with + 1 or 1 + blue. Step 2: Color remaining problems with + 2 or 2 + green. Step 3: Color remaining problems with + 3 or 3 + yellow = 8 + = = = 5 + = = = 8 + = = 1 + = = = 3 + = = = = = 4 + = = = 2 + = = = 1 + = 3 Lesson 22: Look for and make use of repeated reasoning on the addition chart by solving and analyzing problems with common addends. Date: 5/9/13 1.F.20

21 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 23 1 Lesson 23 Objective: Look for and make use of structure on the addition chart by looking for and coloring problems with the same total. Suggested Lesson Structure Fluency Practice Application Problem Concept Development Student Debrief Total Time (12 minutes) (8 minutes) (30 minutes) (10 minutes) (60 minutes) Fluency Practice (12 minutes) Happy Counting: by 2s 1.OA.5 Missing Part: 8 1.OA.6 Number Bond Dash: 8 Day 2 1.OA.6 (2 minutes) (5 minutes) (5 minutes) Happy Counting: by 2s (2 minutes) Note: This activity supports the connection of counting on by 2 and adding 2. Do the Happy Counting activity from G1-M1-Lesson 3, counting by 2s from 0-20 and back. Missing Part: 8 (5 minutes) Materials: (S) 5-group cards (0-8 only) Note: This activity addresses the core fluency objective for Grade 1 of mastery of sums to 10. Students work with a partner, using 5-group cards. Each student puts a card on his or her forehead. The partner tells how many more to make 8. Students must guess the cards on their foreheads. Partners can play simultaneously. Number Bond Dash: 8 Day 2 (5 minutes) Materials: (T) Stopwatch or timer (S) Number Bond Dash: 8 Problem Set, marker to correct work Note: This activity addresses the core fluency objective for Grade 1 of mastery of sums to 10. Follow procedure for Number Bond Dash remembering today is the second day with making 8. Students Lesson 23: Look for and make use of structure on the addition chart by looking for and coloring problems with the same total. Date: 5/9/13 1.F.21

24 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 23 1 Which totals are the easiest for you to solve? Why? Which totals do you think you need the most practice? What can you do to get better at these expressions? (Point to the Addition Chart from yesterday s work.) How is today s work similar to what we did yesterday? How is it different? Exit Ticket (3 minutes) After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help you assess the students understanding of the concepts that were presented in the lesson today and plan more effectively for future lessons. You may read the questions aloud to the students. Lesson 23: Look for and make use of structure on the addition chart by looking for and coloring problems with the same total. Date: 5/9/13 1.F.24

25 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 23 Problem Set 1 Name Date Use your chart to write a list of number sentences in the spaces below. Totals of 10 Totals of 9 Totals of 8 Totals of 7 Lesson 23: Look for and make use of structure on the addition chart by looking for and coloring problems with the same total. Date: 5/9/13 1.F.25

26 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 23 Exit Ticket 1 Name Date Circle all the boxes that total 10. Make a straight line through all the boxes that total Lesson 23: Look for and make use of structure on the addition chart by looking for and coloring problems with the same total. Date: 5/9/13 1.F.26

27 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 23 Homework 1 Name Date Fill in the missing box and find the totals for all expressions. Use your completed addition chart to help you Lesson 23: Look for and make use of structure on the addition chart by looking for and coloring problems with the same total. Date: 5/9/13 1.F.27

32 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 24 Fluency Template 1 Friendly Fact Go Around: Addition Strategies Review = = = = = = = = = = = = = = = = = = = = = = = = Lesson 24: Practice to build fluency with facts to 10. Date: 5/9/13 1.F.32

33 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 24 Fluency Template 1 Lesson 24: Practice to build fluency with facts to 10. Date: 5/9/13 1.F.33

34 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 24 Template 1 Expression Cards Lesson 24: Practice to build fluency with facts to 10. Date: 5/9/13 1.F.34

35 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 24 Template Lesson 24: Practice to build fluency with facts to 10. Date: 5/9/13 1.F.35

36 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 24 Template Lesson 24: Practice to build fluency with facts to 10. Date: 5/9/13 1.F.36

37 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 24 Problem Set 1 Name Related Fact Ladders Date = = = = = = 10 Lesson 24: Practice to build fluency with facts to 10. Date: 5/9/13 1.F.37

38 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 24 Exit Ticket 1 Name Date Solve the number sentences. Use the key to color. Once the box is colored, you do not need to color it again = = = = 7 = = 1 + = = = = = = 5 + Color doubles - Red. Color +1 - Blue Color +2 - Green Color doubles +1 - Brown CHALLENGE: List the number sentences that can be colored more than 1 way. Lesson 24: Practice to build fluency with facts to 10. Date: 5/9/13 1.F.38

39 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 24 Homework 1 Name Date Solve and sort the number sentences. One number sentence can go in more than one place when you sort = = = = = = = = = = = 1 + = Doubles Doubles Mentally visualized 5-groups Write your own number sentences and add them to the chart. Lesson 24: Practice to build fluency with facts to 10. Date: 5/9/13 1.F.39

40 NYS COMMON CORE MATHEMATICS CURRICULUM Lesson 24 Homework 1 Solve and practice the math facts Lesson 24: Practice to build fluency with facts to 10. Date: 5/9/13 1.F.40

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