1. N UMBER S ENSE K-2 Math & Science Collaborative at the Allegheny Intermediate Unit

2. R EFLECTING ON N UMBER S ENSE Go to mscsummercourses2013.wikispaces. com and then to the number sense page. Respond to the discussion prompt “Visual Representations”. Math & Science Collaborative at the Allegheny Intermediate Unit

3. A GENDA Response to wiki prompt Sharing of Number Sense Visual Activity Do these children have number sense? – videos Games to Develop Number Sense Mental Math Videos Article discussion Planning Math & Science Collaborative at the Allegheny Intermediate Unit

4. C OMMUNITY OF L EARNERS Building a strong and supportive community of learners is essential in making number sense routines beneficial and productive for everyone. Students share out thinking Work through misunderstandings in front of peers Have time to think for themselves Math & Science Collaborative at the Allegheny Intermediate Unit

5. S HARING : N UMBER SENSE VISUAL ACTIVITY With your group, share the activity you used. How did the students respond to the activity? What challenges, if any, did you encounter? What role did the visual play in the success or challenge of the activity? Math & Science Collaborative at the Allegheny Intermediate Unit

6. L EARNING P ROGRESSION : K-5 O PERATIONS AND A LGEBRAIC T HINKING Read the learning progression for the grade level assigned to you. Make note of how it is connected to number sense. Math & Science Collaborative at the Allegheny Intermediate Unit

7. K1 – dot cards and ten frames Which students are able to subitize and unitize five and which ones are not? What evidence do you have? How do the visual representations support students’ in developing number sense? How does the ten-frame with seven dots provide opportunities for students to use five as a unit? How does the teacher elicit and support students’ uses of different strategies? What evidence did you find of the students engaging in the Standards for Mathematical Practice? How does what you saw in the video connect to what you read about in the progression? D O THESE STUDENTS HAVE NUMBER SENSE ? Math & Science Collaborative at the Allegheny Intermediate Unit

8. K2 – rekenreks How does the warm-up with four and six provide the teacher with information to guide her instructional decisions? What examples of one-to-one correspondence and conservation of number surface in the lesson? Are there specific number combinations that seem more accessible to students? How does the teacher build on this foundation? How does the rekenrek support students’ in developing number sense? What evidence did you find of the students engaging in the Standards for Mathematical Practice? How does what you saw in the video connect to what you read about in the progression? D O THESE STUDENTS HAVE NUMBER SENSE ? Math & Science Collaborative at the Allegheny Intermediate Unit

9. I MPLICATIONS FOR T EACHING AND L EARNING What kinds of activities do you think these children were engaged in prior to these lessons? What evidence is there that they used these tools prior to the lessons we viewed? Math & Science Collaborative at the Allegheny Intermediate Unit

10. G AMES TO D EVELOP N UMBER S ENSE Play each of the games. After you play each game, answer the following questions: What concept(s) is the focus of each game? What tools might students use to support to solve the problems? Discuss the strategies students might use. Might they reason with facts they know? Use landmark strategies? Use make-a-ten? Use the 5- or 10- structure? How might you promote the use of more efficient strategies? Is there any way to adapt these games for older students to play? Math & Science Collaborative at the Allegheny Intermediate Unit Finding Doubles Make 10 Capture 10 Rack 10 Combine Bear Tracks

11. G AMES TO D EVELOP N UMBER S ENSE What evidence will you look for to see if students understand the underlying mathematics of the game? What evidence will you look for to see if students are using number sense as they play the game? Math & Science Collaborative at the Allegheny Intermediate Unit

12. L EARNING P ROGRESSION : K-5 N UMBER AND O PERATIONS IN B ASE T EN Read the learning progression for the grade level assigned to you. Make note of how it is connected to number sense, specifically, composing and decomposing numbers. Math & Science Collaborative at the Allegheny Intermediate Unit

13. M ENTAL M ATH When students solve a problem in their heads, they usually use what they know about place value, number relationships, patterns, and visual images to figure it out. Problem context Naked numbers Math & Science Collaborative at the Allegheny Intermediate Unit

14. V IDEO : 8 + 6 What are examples of how the ten-frame model supports student strategies for 8 + 6? How does the ten-frame encourage students’ understanding of 10 as an important number in computation? What seems to be a core strategy throughout this number talk? 8 + 6 is considered to be a basic addition fact. What role can number talks play in helping students build basic fact knowledge? Math & Science Collaborative at the Allegheny Intermediate Unit

15. V IDEO : 26+27 Did any of the students use the strategies we did? How do the strategies demonstrate that children have built an understanding of place value? In each strategy the students start from the left and work to the right. How does this help build number sense and a sense of reasonableness for the answer? What role does the hundred chart play in helping children understand place value? How are students using their understanding of number relationships in their strategies? A major focus of kindergarten is to build fluency with small numbers. How is this ideas incorporated in the students’ strategies? Is there any evidence that students were engaged in the Standards for Mathematical Practice? Math & Science Collaborative at the Allegheny Intermediate Unit

16. M ENTAL M ATH Given that 48+37=85, what is the answer to 49+36? Show why this is true using the number line. Math & Science Collaborative at the Allegheny Intermediate Unit

17. V IDEO : 70-59 How does the number line provide support for understanding Grant’s Constant Difference strategy? In what other ways could you model this strategy to help students understand why it works? The students share several subtraction strategies: Constant Difference, Adding Up, Removing in Chunks, and Adjusting One of the Numbers. Discuss how these strategies are similar and different? When Andrew shared his strategy, students were unsure whether 1 should be added or subtracted. Share your observations about the student and teacher roles during the class discussion. How could you help students understand his thinking? Is there any evidence that students were engaged in the Standards for Mathematical Practice? Math & Science Collaborative at the Allegheny Intermediate Unit

18. D EVELOPING N UMBER S ENSE THROUGH R EAL -L IFE S ITUATIONS How does thinking about numbers in real-life situations help develop and/or improve children’s number sense? Math & Science Collaborative at the Allegheny Intermediate Unit

19. L EARNING FROM EACH OTHER Read chapter 7, p. 119, in Number Sense Routines. In your small group, discuss the following questions: How does math talk support the development of number sense? How do visual representations support math talk? How can you help students see mistakes as learning opportunities and how does that support the development of number sense? Math & Science Collaborative at the Allegheny Intermediate Unit

20. F LUENCY IN PA C ORE S TANDARDS Math & Science Collaborative at the Allegheny Intermediate Unit

21. S ORTING A CTIVITY Math & Science Collaborative at the Allegheny Intermediate Unit Sort the cards into two piles. Be ready to tell us how you sorted.

22. W HAT DOES FLUENCY MEAN TO YOU Math & Science Collaborative at the Allegheny Intermediate Unit On a large post-it, write down your thoughts about fluency. What is it?

23. N UMBER S ENSE AND F LUENCY How does number sense support the development of fluency? Math & Science Collaborative at the Allegheny Intermediate Unit

24. A RTICLE D ISCUSSION Read the article “10 Is the Magic Number.” Math & Science Collaborative at the Allegheny Intermediate Unit

25. P LANNING Plan task focusing on one standard and one standard for math practice involving the use of visuals to develop/extend number sense. Include a mental math activity and a game. Math & Science Collaborative at the Allegheny Intermediate Unit

26. H OMEWORK Read chapter 5, P. 79 in Number Sense Routines. Read Why Children Have Difficulties Mastering the Basic Number Combinations and How to Help Them. Complete task, if necessary. Plan task focusing on one standard and one standard for math practice involving the use of visuals to develop/extend number sense. Include a mental math activity and a game. Math & Science Collaborative at the Allegheny Intermediate Unit