1. Second Grade and the CCSS–M Vacaville USD September 23, 2013

2. AGENDA The CCSS-M: Math Practice Standards Review Daily Math Word Problems Place Value Planning/Discussions

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. 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.

5. Standards for Mathematical Practice

6. 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

7. SMP Matrix

8. Individual Reflection Look over the matrix For each of the SMP’s, where are your students on the matrix? where are 2 nd grade students at your site on the matrix?

9. 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 2 nd 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?

10. Review of Daily Math

11. Word Problems

12. 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?

13. 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?

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

15. 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?

16. 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

17. 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.

18. 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.”

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

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

21. 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.

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

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

24. 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?

25. 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

26. 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?

27. 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

28. 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?

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. Domains – 2 nd Grade Operations and Algebraic Thinking Number and Operations in Base Ten Measurement and Data Geometry

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

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

33. Word Problems and Model Drawing

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

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

36. 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

37. 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

38. 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.

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

40. Problem #1 Tyrone had $17 in his piggy bank. He added $10 more. What is his total savings now? H

41. Problem #2 Ray has 465 tractors and his brother Ben has 289. How many tractors do they have altogether?

42. Problem #3 Jennifer went shopping with $42. She came home with $9. How much money did she spend?

43. Problem #4 Hansel read 235 pages of his book over the weekend. Gretel read 198 pages of her book over the weekend. How many more pages did Hansel read than Gretel?

44. Problem #5 A total of 100 raffle tickets were sold over a 3-day period. If 21 raffle tickets were sold on Monday, and 67 tickets were sold on Tuesday, how many raffle tickets were sold on Wednesday?

45. Problem #6 There are 5 plates of cookies on the shelf. If there are 4 cookies on each plate, how many cookies are there in all?

46. Problem #7 There are 20 chairs. Kayla wants to put the chairs into 4 rows. How many chairs will be in each row?

47. Problem #8 12 students need rides to an after school event. If only 4 students can ride in each car, how many cars are needed to transport the students?

48. 2.OA.1. Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1

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

51. Group Task Work with your group to write a variety of problems appropriate for your grade level Put one problem on each card Label the problem type and write the problem on the front of the card Show the model drawing representation and possible number sentences on the back.

52. Example – Front 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?

53. Example – Back I have 9 balloons. 3 of them are red and the rest are blue. How many balloons are blue? Red Blue 9 3 3 +  = 9 9 – 3 = 

54. Place Value

55. Unit Planning Topic: Place Value Content Standards:

56. CCSS - NBT Understand place value. 1.Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: a. 100 can be thought of as a bundle of ten tens — called a “hundred.” b. The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds (and 0 tens and 0 ones).

57. CCSS - NBT Understand place value. 2.Count within 1000; skip-count by 2s, 5s, 10s, and 100s. CA 3. Read and write numbers to 1000 using base-ten numerals, number names, and expanded form. 4. Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons.

58. CCSS – NBT 8. Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.

59. CCSS – M Use place value understanding and properties of operations to add and subtract. 5. Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. 6. Add up to four two-digit numbers using strategies based on place value and properties of operations.

60. CCSS – M 7. Add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

61. CCSS – M 7.1Use estimation strategies to make reasonable estimates in problem solving. CA 9. Explain why addition and subtraction strategies work, using place value and the properties of operations. Explanations may be supported by drawings or objects.

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

63. 1.NBT Understand place value. 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.

64. d.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). 3. Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.

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

66. Unit Planning What will students learn and how will I know what they have learned? Conceptual Understanding:

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

68. Base 10 Blocks ones tens “tens” are composed of 10 “ones”

69. Base 10 Blocks ones tens hundreds “hundreds” are composed of 10 “tens”

70. Unit Planning What will students learn and how will I know what they have learned? Conceptual Understanding:  We or trade for a larger piece when there are more than 10 of any size piece

71. Count out 27 ones From those 27 ones, count out a group of 10, and arrange them in a line Take one of your 10 sticks Line it up next to your row of 10 ones. What do you notice? Trade your 10 ones for 1 ten

72. Look at the ones that are left. Do you think you have enough to make another group of 10? Count out another group of 10, and arrange them in a line Take another 10 stick and line it up next to your row of 10 ones. What do you notice? Trade your 10 ones for 1 ten

73. Look at the ones that are left. Do you think you have enough to make another group of 10? Let’s count and check. Do you have enough to make another group of 10? So, how many ones are left?

74. Number 272 tens 7 ones 424 tens 2 ones 353 tens 5 ones 161 tens 6 ones 232 tens 3 ones

75. Build the number I am going to show you a number I want you to build it using the fewest number of pieces possible.

76. 48 How many tens did you use? And the value of those tens is ______ How many ones did you use? And the value of those ones is ______ So we can write 48 as 4 tens and 8 ones So we can also write 48 as 40 + 8

77. NumberExpanded Form 4840 + 8 2720 + 7 6460 + 4 3730 + 7 8280 + 2

78. Building Numbers Please build 38 using the least number of pieces Now please build 51 using the least number of pieces Which number is larger? How do you know?

79. NumbersLess thanGreater than 385138 < 5151 > 38 624747 < 6262 > 47 382323 < 3838 > 23 686565 < 6868 > 65 848080 < 8484 > 80

80. Take your tens I want us to count out 140 I see a problem with our representation of 140. Any ideas? We have more than 10 tens and our rule so far has been that we always trade for a larger piece when we have more than 10 of something

81. So, how many tens do we have? From your 14 tens, count out a group of 10 tens Now let’s count them. So ten tens is a hundred.

82. This is a hundred’s block Take your ten tens. Can you arrange them so they fit perfectly on top of the hundred’s square? So we can trade 10 tens for 1 hundred

83. Number 1401 hundred 4 tens 0 ones 2302 hundreds 3 tens 0 ones 1631 hundred 6 tens 3 ones 2162 hundreds 1 ten 6 ones 3053 hundreds 0 tens 5 ones

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

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

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

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

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

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