1. Vacaville USD August 25, 2014

2. AGENDA Problem Solving and Patterns Math Practice Standards/Questioning Review Word Problems Review Fact Strategies Sharing Measurement Counting

3. 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.

4. Regina’s Logo How many tiles are needed to make a Size 5? What about a Size 10? a Size 20? A Size 100?

5. Regina’s Logo What is a strategy that will let you quickly and easily figure out how many tiles you will need for any given size?

6. Regina’s Logo Recursive Add 3 each time SIZE# OF TILES 15 28 311 414 517

7. Regina’s Logo 3 times the Size + 2 3n + 2

8. Regina’s Logo 3 times the Size + 2 3n + 2

9. Regina’s Logo 2 times (Size + 1) + Size 2(n + 1) + n

10. Regina’s Logo (2 times Size) + (Size + 2) 2n + (n + 2)

11. Regina’s Logo 3n + 2

12. Regina’s Logo 3n + 2

13. Regina’s Logo 2(n + 1) + n

14. Regina’s Logo 2n + (n + 2)

15. The Use of Effective Questions

16. Questioning plays a critical role in the way teachers –Guide the class –Engage students in the content –Encourage participation –Foster understanding

17. 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

18. SMP’s So how does the use of effective questioning relate to the Standards for Mathematical Practice?

19. SMP’s and Questions Your group will receive 16 cards –8 SMP’s –8 lists of questions related to the SMP’s Your job is to match each SMP with the questions designed to support that SMP.

20. Asking Effective Questions Pick 2 colors... 1.Use one color to highlight questions that you are already asking. 2.Use the 2nd color to highlight questions that you would like to ask this year.

21. Additional Resources Effective Questions – PBS

22. Solving Word Problems

23. 1.Read the entire problem out loud to students (or have a student read it). Ask students to tell you what the “story” is about …… 2.Including who and/or what the problem is about. These become the “labels” in your diagram. 3.Identify the question and write or state a sentence frame for the answer leaving a blank to fill in.

24. 4.Chunk the problem –Kindergarten Beginning of the year, act it out and teacher record Later in the year, children begin to make a simple drawing –First Grade Beginning of the year, make a simple drawing to reflect the information in the problem, and identify what you are trying to find. Later in the year, draw bars to reflect the information in the problem, and identify what you are trying to find.

25. 5.Correctly compute and solve the problem (show all work!) 6.Write the answer in the sentence and make sure the answer makes sense.

26. Farmer John had 6 scarecrows. His neighbor gave him 3 more scarecrows. How many scarecrows does Farmer John have? Add to – Result Unknown

27. 4 scarecrows were playing in the field. Some more scarecrows came to play in the field. Now there are 6 scarecrows playing in the field. How many more scarecrows came to play in the field? Add to – Change Unknown

28. 8 scarecrows were playing in the barn. 2 scarecrows left and went home. How many scarecrows are in the barn now? Subtract from – Result Unknown

29. Lavon had 10 scarecrows. He gave Terrence some of his scarecrows. Now Lavon has 7 scarecrows. How many scarecrows did Lavon give Terrence? Subtract from – Change Unknown

30. 2 green scarecrows and 7 orange scarecrows are playing in the field. How many scarecrows are playing in the field? Put Together/Take Apart – Total Unknown

31. 2 green scarecrows and 7 orange scarecrows are playing in the field. How many scarecrows are playing in the field? Put Together/Take Apart – Total Unknown

32. There are 4 fields. There are 3 scarecrows in each field. How many scarecrows are there in all? Multiplication – Equal Groups

33. Cara has 8 scarecrows. If she puts 2 scarecrows in each field, how many fields will have scarecrows? Division – Number of Groups Unknown

34. Learning Math Facts

35. Grade Level Standards What do 1 st grade students need to know and understand about addition and subtraction facts? What do they need to “master”?

36. Progression Concrete Pictorial or Visual or Representational Abstract –Invented and Alternative Algorithms –Automaticity

37. Fact Fluency Fact fluency must be based on understanding operations and thinking strategies. Students must –Connect facts to those they know –Use mathematics properties to make associations –Construct visual representations to develop conceptual understanding.

38. Addition and Subtraction Facts Direct modeling / Counting all Counting on / Counting back Invented algorithms –Composing / Decomposing –Mental strategies Automaticity

39. Addition and Subtraction Facts Direct modeling / Counting all Counting on / Counting back Invented algorithms –Composing / Decomposing –Mental strategies Automaticity

40. Addition and Subtraction Facts Direct modeling / Counting all Counting on / Counting back Invented algorithms –Composing / Decomposing –Mental strategies Automaticity C – R – A

41. Sharing What strategies and activities did you try last year? What strategies and activities have you tried so far this year? What questions do you have?

42. Measurement

43. Measurement and Data 1.MD.1. Order three objects by length; compare the lengths of two objects indirectly by using a third object.

44. Measurement and Data 1.MD.1. Order three objects by length; compare the lengths of two objects indirectly by using a third object.

45. Measurement and Data 1.MD.1. Order three objects by length; compare the lengths of two objects indirectly by using a third object.

46. Measurement and Data 1.MD.2. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.

47. Measurement and Data 1.MD.2. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.

48. Measurement and Data 1.MD.2. Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.

49. Measurement and Data Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps.

50. Stations Stations 1-8 support MD.1 Stations 9-12 support MD.2

51. Stations As you work the stations, consider What are the essential understandings that students need to have about measurement? How do the different stations address or raise different issues related to measurement?

52. Stations As you work the stations, consider What key questions can you pose that help students identify these key issues rather than just telling them?

53. Counting and Place Value How do we teach students to count “efficiently”?

54. Counting and Place Value 1.NBT.1. Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.

55. 1.NBT.2. Understand that the two digits of a two- digit number represent amounts of tens and ones. Understand the following as special cases: a. 10 can be thought of as a bundle of ten ones—called a “ten.” b. The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones. c. The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).

56. Counting Stations