1. First Grade and the CCSS–M Vacaville USD October 4, 2013

2. Demographic Form Demographic Form Name Email School

3. AGENDA The CCSS-M: Math Practice Standards Review Daily Math The Bakery Problems Word Problems Teaching Facts Planning/Discussions

4. Expectations  We are each responsible for our own learning and for the learning of the group.  We respect each others learning styles and work together to make this time successful for everyone.  We value the opinions and knowledge of all participants.

5. Sharing At your tables, discuss  What you have tried since our first session  What successes you have had  What questions and/or concerns you have? Pick one success and one question/concern to share with the group.

6. Standards for Mathematical Practice

7. CCSS Mathematical Practices OVERARCHING HABITS OF MIND 1.Make sense of problems and persevere in solving them 6.Attend to precision REASONING AND EXPLAINING 2.Reason abstractly and quantitatively 3.Construct viable arguments and critique the reasoning of others MODELING AND USING TOOLS 4.Model with mathematics 5.Use appropriate tools strategically SEEING STRUCTURE AND GENERALIZING 7.Look for and make use of structure 8.Look for and express regularity in repeated reasoning

8. SMP Matrix

9. Individual Reflection Look over the matrix For each of the SMP’s, where are your students on the matrix? where are 1 st grade students at your site on the matrix?

10. SMP Matrix Site Reflection: Based on your individual reflections with regards to the SMP’s, Discuss as a group  Where do you believe most of your 1 st grade students are on the matrix? Plan as a group  What SMP do you want to work on as a team?  What are your next steps?

11. Review of Daily Math

12. Word Problems

13. Bakery Problem #1 A bakery sold 235 boxes of cookies. They sold 119 more boxes of cookies than cupcakes. How many boxes of cupcakes were sold?

14. Bakery Problem #2 Another bakery sold 3 times as many boxes of cookies than cupcakes. If they sold 126 more boxes of cookies than cupcakes, how many boxes of cookies were sold?

15. Lessons Learned From Research Sense-making is important! In learning and remembering mathematics In developing mathematical thinking and reasoning

16. How many two-foot boards can be cut from two five-foot boards? (Verschaffel, 2007) Nearly 70% of the upper elementary school students given this problem say that the answer is “five” Why?

17. How many two-foot boards can be cut from two five-foot boards? (Verschaffel, 2007) Because 5 + 5 = 10 and 10 ÷ 2 = 5. What did the students forget? the “real world” context

18. Kurt Reusser asked 97 1st and 2nd graders the following question: There are 26 sheep and 10 goats on a ship. How old is the captain? 76 of the 97 students “solve” this problem - by combining the numbers.

19. H. Radatz gave students non-problems such as: Alan drove 50 miles from Berkeley to Palo Alto at 8 a.m. On the way he picked up 3 friends. NO QUESTION IS ASKED! Yet, from K-6, an increasing % of students “solve” the problem by combining the numbers and producing an “answer.”

20. The Serious Question Where does such behavior come from?

21. A Serious Answer Students develop their understanding of the nature of the mathematical enterprise from their experience with classroom mathematics.

22. Therefore….. If the curriculum doesn’t induce them to see mathematics as a sense- making activity, they won’t engage with mathematics in sensible ways.

23. What about using “key words” to help elementary school kids solve word problems? For example…….

24. Using Key Words. John had 7 apples. He gave 4 apples to Mary. How many apples did John have left? 7 - 4 = 3

25. Nick Branca gave students problems like these: John had 7 apples. He left the room to get another 4 apples. How many apples does John have? Mr. Left had 7 apples… Can you guess what happened?

26. Juan has 9 marbles. He gives 5 marbles to Kim. How many marbles does he have now? Juan has 9 marbles. Kim gives 5 marbles to him. How many marbles does he have now? **Problems can use the same key words but have different meanings

27. Jon has 5 red blocks and 3 blue blocks. How many blocks does he have in all? Jon has 5 bags with 3 red blocks in each bag. How many blocks does he have in all?

28. Key Word Strategies Biggest concern – Research shows that students stop reading for meaning Students need to be taught to reason through a problem – to make sense of what is happening

29. Personal Example Mary practiced the piano for 2 hours on Monday. This was 20% of her total practice time for the week. How many hours does Mary practice the piano each week?

30. Personal Example Mary practiced the piano for 2 hours on Monday. This was 20% of her total practice time for the week. How many hours does Mary practice the piano each week?

31. Domains – 1 st Grade Operations and Algebraic Thinking Number and Operations in Base Ten Measurement and Data Geometry

32. Key to algebraic thinking is developing representations of the operations using Objects Drawing Story contexts And connecting these to symbols

33. Such manipulatives or pictures are not merely “crutches” but are essential tools for thinking

34. Word Problems and Model Drawing

35. Model Drawing A strategy used to help students understand and solve word problems Pictorial stage in the learning sequence of concrete – pictorial – abstract

36. Model Drawing Develops visual-thinking capabilities and algebraic thinking. If used regularly, helps students spiral their understanding and use of mathematics

37. Steps to Model Drawing 1)Read the entire problem, “visualizing” the problem conceptually 2)Decide and write down (label) who and/or what the problem is about H

38. Steps to Model Drawing 3)Rewrite the question in sentence form leaving a space for the answer. 4)Draw the unit bars that you’ll eventually adjust as you construct the visual image of the problem H

39. Steps to Model Drawing 5)Chunk the problem, adjust the unit bars to reflect the information in the problem, and fill in the question mark. 6)Correctly compute and solve the problem. 7)Write the answer in the sentence and make sure the answer makes sense.

40. Representation Getting students to focus on the relationships and NOT the numbers!

41. 1.OA.1 Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem. Drawings need not show details, but should show the mathematics in the problem. (This applies wherever drawings are mentioned in the Standards)

43. Word Problems What can we do when to make word problems more interesting and engaging for our students?

44. Group Task Work with your group to write a variety of problems appropriate for your grade level

45. Example Put Together/Take Apart Addend Unknown I have 9 balloons. 3 of them are red and the rest are blue. How many balloons are blue?

46. Five Facts and Ten Facts

47. Five Facts  3 + 2 = 5

48. Five Facts  4 + 1 = 5

49. Ten Facts   7 + 3 = 10

50. Ten Facts  4 + 6 = 10

51. The Teen Numbers

52. Developing Reasoning https://www.teachingchannel.org/videos/kinde rgarten-counting-cardinality-lesson

53. Addition Facts

54. Subtraction Facts

55. Subtraction John had 9 ghosts at his house but 3 of them left to go visit Caspar. How many ghosts are in his house now?

56. Subtraction John has 9 ghosts at his house while Mika only has 3 ghosts at her house. How many more ghosts are in John’s house?

57. Subtraction Vanessa has 7 monsters and 12 ghosts at her Halloween party. How many more ghosts are at the party?

58. Subtraction Vanessa had 12 monsters at her Halloween party but 7 of them had to go back to work at the Fright Factory. How many monsters are left at the party?

59. Subtraction Show me 2 different ways to model 11 – 5

60. Unit Planning Topic: Subtraction Facts to 12 Content Standards:

61. Unit Planning Practice Standards: What should students already know and how am I going to help them make connections to that prior knowledge?

62. Unit Planning What will students learn and how will I know what they have learned? Concrete – Representational – Abstract

63. Unit Planning What will students learn and how will I know what they have learned? Conceptual Understanding: Subtraction as take-away AND Subtraction as compare Relationship between addition and subtraction

64. Unit Planning What tools, models, and materials are necessary to fully address the standards for this unit?

65. Unit Planning What will students learn and how will I know what they have learned? Procedures and Skills:

66. Unit Planning What will students learn and how will I know what they have learned? Applications and Problem Solving:

67. Unit Planning What will students learn and how will I know what they have learned? Key Vocabulary

68. Unit Planning What tools, models, and materials are necessary to fully address the standards for this unit?

69. Unit Planning Anticipated Number of Days: ______ Conceptual understanding: ____ days Procedures and skills: ___ days Applications and problem solving: ___ days

70. Unit Planning Sketch of Unit by Days (Overview) Planning Actual Lessons