1. N UMBER S ENSE 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. Grade 3: 4 x 7, 2 x 14 The teacher chooses to use a context as students consider the relationship between 4 x 7 and 2 x 14. How does this context help support student thinking? How is the commutative property addressed in the discussion? How do the teacher’s questions help students begin to build an understanding of doubling and halving? The teacher is continually assessing her students during the number talk. What student understanding and misconceptions will she use to guide her next instructional steps? Is there any evidence that students were engaged 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. D O T HESE S TUDENTS HAVE NUMBER SENSE ? 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

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?? How might you promote the use of more efficient strategies? Math & Science Collaborative at the Allegheny Intermediate Unit Get to 1,000 Simplified Krypto Leftovers with 15 Adding Up the Deck Take Five, Make Ten Product Game

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. G AME E XPERT For the game assigned to your group, be prepared to discuss: Concept that is focus of game Strategies students might use Ways to determine if students are engaged in mathematics Questions you might ask students as they are playing the game Math & Science Collaborative at the Allegheny Intermediate Unit

13. 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

14. 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

15. 1000 - 674 How is number sense used to determine whether an answer is reasonable or not? What purpose is served by the teacher accepting both correct and incorrect answers for the problem? How is the students’ role different from typical classrooms? Often subtraction is explained as “taking away.” Cole’s strategy does not remove or take away an amount; instead, he adds to solve the problem. Why does this work? Is there any evidence that students were engaged in the Standards for Mathematical Practice? M ENTAL M ATH Math & Science Collaborative at the Allegheny Intermediate Unit

16. V IDEO : 8 X 25 The class had shared strategies for solving 8 x 25 before the teacher introduced the array model. Why do you think this instructional decision was made? How did she link previous strategies to this array? Noel incorrectly refers to columns as rows in the array. The teacher does not correct her. Why do you think she chose to ignore this error? How does the teacher connect the students’ additive thinking to multiplication? How does the array support student understanding of multiplication? The commutative property? The distributive property? The associative property? Is there any evidence that students were engaged in the Standards for Mathematical Practice? Math & Science Collaborative at the Allegheny Intermediate Unit

17. V IDEO : 150 ÷ 15, 300 ÷ 15 How did this particular sequence of problems help students use number relationships to solve the problem? What student confusions and misunderstandings surfaces from the array model? How did the teacher navigate the discussion to build understanding about multiplication, division, and the array model? 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. F LUENCY IN PA C ORE S TANDARDS Math & Science Collaborative at the Allegheny Intermediate Unit

20. 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.

21. 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?

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

23. 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

24. H OMEWORK Read pages 1 - 16 in Developing Number Sense, and think about the following questions: How does math talk support the development of number sense? How do games support math talk? 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