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Cypher IV Math Leadership Project K-3 - Session 2 - Developing Early Number Concepts and Number Sense

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(Re) Introductions / Paula / Kim / Cathy / Shari / Tammy / Tina / Paula / Kim / Cathy / Shari / Tammy / Tina / Bernadette / Kathleen / Kathryn / Jenna / Nita / Dana

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Homework Review (Small Group) / Discuss in a small group / What have you tried in your classroom as a result of the last session? / What role did you play in the teaching and learning of math? / What role did the students play in their learning? / Discuss in a small group / What have you tried in your classroom as a result of the last session? / What role did you play in the teaching and learning of math? / What role did the students play in their learning? / What discoveries did you and your students make? / What misconceptions, if any, surfaced about the topic? How did you redirect the students? / What suggestions do you have for others when they try this?

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Objectives / Focus on the Big Ideas of early number concepts / Examine counting on and counting back / Discover the four key number relationships for numbers from 1 to 10 / Discuss relationships for numbers up to 100 / Focus on the Big Ideas of early number concepts / Examine counting on and counting back / Discover the four key number relationships for numbers from 1 to 10 / Discuss relationships for numbers up to 100

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Number Sense (Partner) / Discuss with a partner / What does it mean for a student to have a good sense of intuition of numbers? / What implications does teaching to encourage number sense have on how we work with students and what we emphasize in our classrooms? / Rejoin the large group in 10 minutes. If time permits, you may be asked to share. / Discuss with a partner / What does it mean for a student to have a good sense of intuition of numbers? / What implications does teaching to encourage number sense have on how we work with students and what we emphasize in our classrooms? / Rejoin the large group in 10 minutes. If time permits, you may be asked to share.

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Big Ideas (Small Group) / Read the Big Ideas for this chapter (p. 37). / Share an example from your teaching that illustrates the Big Ideas with your small group. / I will ask each small group to share one of their examples with the whole group. / Rejoin the large group in 5 minutes. / Read the Big Ideas for this chapter (p. 37). / Share an example from your teaching that illustrates the Big Ideas with your small group. / I will ask each small group to share one of their examples with the whole group. / Rejoin the large group in 5 minutes.

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Counting On & Counting Back (Large Group) / A number card from my pile of 20 is chosen. Beginning with the next player in the list, players count backwards down the list until one of the players says zero. / The player who says zero takes a counter and puts it near their name on the whiteboard. / I will choose another number card. / Play continues until someone has three counters. (The score board is on the next slide.) / As a large group, we will discuss our findings. / A number card from my pile of 20 is chosen. Beginning with the next player in the list, players count backwards down the list until one of the players says zero. / The player who says zero takes a counter and puts it near their name on the whiteboard. / I will choose another number card. / Play continues until someone has three counters. (The score board is on the next slide.) / As a large group, we will discuss our findings.

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Points / Paula / Kim / Cathy / Shari / Tammy / Tina / Paula / Kim / Cathy / Shari / Tammy / Tina / Bernadette / Kathleen / Kathryn / Jenna / Nita / Dana

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Counting On & Counting Back / A different way to play the game is to count on. Instead of counting back from the number, players count up too the highest number in the number cards. (In this case, it is 20. For younger students, teachers may choose to have the cards go up to 10.) The player who reaches that number takes a counter and play continues until someone has three counters. / Any further comments? / A different way to play the game is to count on. Instead of counting back from the number, players count up too the highest number in the number cards. (In this case, it is 20. For younger students, teachers may choose to have the cards go up to 10.) The player who reaches that number takes a counter and play continues until someone has three counters. / Any further comments?

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Spatial Relationships / Teaching Student-Centered Mathematics states, Children can learn to recognize sets of objects in patterned arrangements and tell how many without counting (p. 42). / I am going to quickly flash a ten-frame on the screen for about half a second. / Say the number that you saw out loud. / Teaching Student-Centered Mathematics states, Children can learn to recognize sets of objects in patterned arrangements and tell how many without counting (p. 42). / I am going to quickly flash a ten-frame on the screen for about half a second. / Say the number that you saw out loud.

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Spatial Relationships (contd) / Say the number you saw out loud.

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Spatial Relationships (contd) / Say the number you saw out loud.

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Spatial Relationships (contd) / 10-frames are useful for meeting the needs of visual learners who need to see the mathematics.

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One & Two More, One & Two Less / These relationships involve more than just the ability to count on 2 or back 2. Children should know that 7, for example, is 1 more than 6 and also 2 less than 9. Such relationships are essential for working with the early numbers, and later, for relating to numbers from 10 to 20. To explore this relationship, we will try an activity similar to Activity 2.11, Make a Two- More-Than Set (p. 45).

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Make a Two-More-Than Set / Construct a set of counters that is two more than: / / Construct a set of counters that is two more than: / / / / /

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Make a Two-Less-Than Set / Construct a set of counters that is two less than the card shown: / / Construct a set of counters that is two less than the card shown: / / / / /

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Anchoring Numbers to 5 & 10 / The numbers 5 & 10 can be used as anchors. They are especially useful when thinking about combinations of numbers. A key model to use with students to illustrate these relationships is the 10-frame.

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Anchoring #s to 5 & 10 (contd) / Here is a ten frame. To build the 7-frame: / Always fill the top row first, starting on the left - the same way that you read. / When the top row is full, counters can be placed in the bottom row, also starting on the left. / Here is a ten frame. To build the 7-frame: / Always fill the top row first, starting on the left - the same way that you read. / When the top row is full, counters can be placed in the bottom row, also starting on the left.

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Anchoring #s to 5 & 10 (contd) / Build 8 / Share what you know about the number 8 from looking at the ten-frame. / How could you use ten-frames to help students develop 5 & 10 benchmark relationships? / Build 8 / Share what you know about the number 8 from looking at the ten-frame. / How could you use ten-frames to help students develop 5 & 10 benchmark relationships?

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Part-Part-Whole Relationships (Small Groups) / Think about the number 8 divided into two different amounts. By using manipulatives or drawing a picture, show how eight things can be shown as two parts. Invent a story to go with your picture or display. / With your group, share how you arranged your materials into different parts. / Rejoin the large group in 10 minutes. / Think about the number 8 divided into two different amounts. By using manipulatives or drawing a picture, show how eight things can be shown as two parts. Invent a story to go with your picture or display. / With your group, share how you arranged your materials into different parts. / Rejoin the large group in 10 minutes.

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Dot Cards / There are many activities that will help students develop their number sense. Activities can involve more than 1 of the relationships discussed in this chapter. Dot cards can be used for activities. Dot cards display: / instantly recognizable patterns, / patterns that require counting, / combinations of 2 & 3 simple patterns, / 10-frames with standard placements of dots, & / 10-frames with unusual placements of dots. / There are many activities that will help students develop their number sense. Activities can involve more than 1 of the relationships discussed in this chapter. Dot cards can be used for activities. Dot cards display: / instantly recognizable patterns, / patterns that require counting, / combinations of 2 & 3 simple patterns, / 10-frames with standard placements of dots, & / 10-frames with unusual placements of dots.

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Dot Cards (4 Small Groups) / Divide yourselves into four small groups. Group 1: Activity 2.22, Double War (p. 53), Group 2: Activity 2.23, Dot-Card Trains (p. 53), Group 3: Activity 2.24, Difference War (p. 53), Group 4: Activity 2.25, Number Sandwiches (p. 53) / What number relationships are being addressed? What extensions could be made in the classroom? Other ideas for using the dot cards? Prepared to share, rejoin the large group in 10 min. / Divide yourselves into four small groups. Group 1: Activity 2.22, Double War (p. 53), Group 2: Activity 2.23, Dot-Card Trains (p. 53), Group 3: Activity 2.24, Difference War (p. 53), Group 4: Activity 2.25, Number Sandwiches (p. 53) / What number relationships are being addressed? What extensions could be made in the classroom? Other ideas for using the dot cards? Prepared to share, rejoin the large group in 10 min.

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Numbers to 100 / Look for patterns in the hundreds chart. / Lets share the patterns with the large group to emphasize the wide variety of patterns that can be found. / Look for patterns in the hundreds chart. / Lets share the patterns with the large group to emphasize the wide variety of patterns that can be found.

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After / What does it mean for a student to have a good sense or intuition of numbers? / What implications does teaching to encourage number sense have on how we work with students and what we emphasize in our classrooms? / Did anyone experience any Ah-ha moments? / Are there any points that need to be shared? / What does it mean for a student to have a good sense or intuition of numbers? / What implications does teaching to encourage number sense have on how we work with students and what we emphasize in our classrooms? / Did anyone experience any Ah-ha moments? / Are there any points that need to be shared?

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Homework / Try a variety of activities from the chapter with your students and be ready to share your experiences with the group at the next session. / Read Chapter 3, Developing Meaning for the Operations and Solving Story Problems (pp. 65-93). / Try a variety of activities from the chapter with your students and be ready to share your experiences with the group at the next session. / Read Chapter 3, Developing Meaning for the Operations and Solving Story Problems (pp. 65-93).

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