1. Vacaville USD March 26, 2015

2. AGENDA Problem Solving Subtraction Facts and Computation –Word Problems –Number Line –Multiple Representation –Multi-Digit Money Arrays and Repeated Addition

3. Norms 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.

12. Kentucky Department of Education Mathematics Formative Assessment Lessons –Concept-Focused Formative Assessment Lessons –Problem Solving Formative Assessment Lessons Designed and revised by Kentucky DOE Mathematics Specialists –Field-­ ‐ tested by Kentucky Mathematics Leadership Network Teachers http://teresaemmert.weebly.com/elementary- formative-assessment-lessons.html

13. A Snail in the Well Primary/Intermediate Grades Problem Solving Formative Assessment Lesson Lesson Format –Pre-Lesson (about 15 minutes)

14. Analyze Student Work Suggestions for feedback Common issues Suggested questions and prompts

15. A Snail in the Well Primary/Intermediate Grades Problem Solving Formative Assessment Lesson Lesson Format –Pre-Lesson (about 15 minutes) –Lesson (about 1 hour) –Follow-Up (about 10 minutes) A Snail in the Well

16. Snail in a Well – Second Grade A snail is at the bottom of a well that is 10 feet deep. –What’s a snail? –What is a well? –What is 10 feet ?

17. Snail in a Well – First Grade What’s a well?

18. Snail in a Well A snail is at the bottom of a well that is 10 feet deep. Each day he crawls up 2 feet. How many days will it take him to get to the top of the well?

19. Snail in a Well A snail is at the bottom of a well that is 10 feet deep. Each day he crawls up 3 feet BUT each night he slides back 1 foot. How many days will it take him to get to the top of the well?

21. Developing Number Sense Estimate How many goldfish are in my “pond”? 46

22. Developing Number Sense Estimate How many Easter eggs will it take to fill the small vase? 53

23. Estimation How many cheeseballs are in the vase? 183

24. Estimation How many peanut m&m’s are in the vase? Are there more m&m’s than cheeseballs or less? –How do you know? 463

25. How many green marshmallows will fit on the skewer?

27. How many green mallows are needed to complete the 4-leaf clover?

29. How many green marshmallows are inside the glass?

31. Using a Number Line Find 43 on the number line. –What “tens numbers” is it between? –How is it from 40? How do you know? –How far is it from 50? How do you know?

32. Using a Number Line Find 68 on the number line. –What “tens numbers” is it between? –How is it from 60? How do you know? –How far is it from 70? How do you know?

33. Subtracting on a Number Line 7 – 3 = Walking on a number line Moving on a number line Drawing on a number line

34. What’s My Number Sentence I started at 4 and walked until I got to 7. How far did I walk? –What the answer? –How did you solve the problem? –What number sentence could I use to solve the problem?

35. What’s My Number Sentence I have 8 cookies. I gave 2 of them to my brother. How many cookies do I have now? –What the answer? –How did you solve the problem? –What number sentence could I use to solve the problem?

37. Multiple Representations Build/Act It Out (Concrete) Draw (Representational) Ten Frame (Concrete or Representational) Number Bond (Abstract/Symbolic) Number Line (Concrete/Representational)

38. Building and Practicing Facts

39. Shauna has 12 Easter Eggs to decorate. She gives some to her little sister and then decorates the rest. If she decorates 8 eggs, how many eggs did she give to her sister? Taken From/Change Unknown

40. Maria and Jorge are decorating Easter Eggs. Maria has decorated 14 eggs and Jorge has decorated 8 eggs. How many more eggs has Maria decorated? Compare/Difference Unknown

41. Max has decorated 12 Easter Eggs. This is 3 more than his cousin decorated in the same amount of time. How many eggs did his cousin decorate? Compare/Smaller Unknown

42. Matt has 5 of the Reptarland toys from Burger King. He wants to collect 2 complete sets for him and his brother. If he needs 8 toys to complete each set, how many more toys does he need to get? Multi-Step Add To/Change Unknown

43. Practicing Facts 13 – 8 =

44. Practicing Facts

45.  

46. Practicing Facts 7 16

47. Practicing Facts    

49. Examining the Standards Which standards require students to be “fluent”? Which standards expect students to be moving towards fluency but not totally proficient? Which standards expect students to understand the concept? HOW DO YOU KNOW?

50. Tools Ten Frames Base 10 blocks Number Line Base 10 Shorthand Decomposing and Composing Numbers

51. Developing Subtraction Concrete –Base 10 Blocks Representational –Base 10 Shorthand –Number Line

52. Developing Subtraction Abstract –Recording process from concrete or abstract stages –Number Bonds –Alternative Algorithms –Variations on the Traditional Algorithm

53. (1) 74 – 48 Build 74 using base 10 blocks Trade 1 ten for 10 ones Remove 4 tens and 8 ones How could we record this? Representation Abstract / Symbols

54. (2) 74 – 48 Build 74 using base 10 blocks Take 1 of the tens, move it to the ones, and cover up 8 –How many ones are left? Remove 4 tens How could we record this? Representation Abstract / Symbols

55. (3) 74 – 48 Locate 74 on the number line Move to 70. How many spaces did you move? How many more do you need to move? Move a distance of 40? –How can you quickly move 40? –Where do you land?

56. (3) 74 – 48 How many more do you need to move? Now, where do you land? How could we record this? Representation Abstract / Symbols

57. (4) 74 – 48 Locate 74 on the number line Move a distance of 40? –How can you quickly move 40? –Where do you land? Move a distance of 8? –How can you quickly move 8? –Where do you land? Recording?

58. (5) 74 – 48 What are some other strategies that students might use?

59. Exploring Strategies Do each problem at least 3 different ways –How do you record? 68 – 35 81 – 29 463 – 247 624 – 296

61. Money MD.8. Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?

62. Coins Jordan found five coins at the bottom of his bookbag. Three are dimes and two are nickels. How much money did Jordan find?

63. Coins Jordan found five coins at the bottom of his bookbag. He told his friend that he found 50¢. What coins did Jordan find?

64. Money What skills do students need to have to count coins? –How can you practice these skills before students begin to learn money? –How can you continue to develop these skills?

65. Coins Joel went to the store and bought three items. He bought a pencil for a dime, an eraser for 38¢, and a pencil sharpener for a quarter. How much money did Joel spend at the store? How did he make the 38¢, assuming he used the least amount of coins possible?

66. Groups of 3 –Buyer 1 –Buyer 2 –Seller

67. 49¢ Buyer 1: Count out exactly 49¢. Buyer 2: Hand the Seller a $1 bill Seller: Give Buyer 2 change for $1. Check

68. 32¢ Buyer 1: Count out the exact price. Buyer 2: Hand the Seller a $1 bill Seller: Give Buyer 2 change for $1. Check

69. $3.78 Buyer 1: Count out the exact price. Buyer 2: Hand the Seller a $5 bill Seller: Give Buyer 2 change for $5. Check

70. Money The First Grade classes raised $56 during the school fund raiser. The Second Grade classes raised $84 during the school fund raiser. How much more money did the Second Grade classes raise than the First Grade Classes?

71. Money The Second Grade classes raised $84 during the school fund raiser. This was $28 more than the Third Grade classes raised. How much did the Third Grade classes raise?

73. Arrays OA.4. Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

74. Materials Needed: Tiles Count out 12 tiles. Use those 12 tiles to make an array. Describe the array. –Prompts if needed: How many rows are there? How many columns are there? Draw a picture of your array. Write an equation that represents your array.

75. After students has finished the first array. Count out another 12 tiles. Use those 12 tiles to make a different array. Describe the array. –Prompt if needed: How many rows are there? How many columns are there? Draw a picture of your array. Write an equation that represents your array.

76. Materials: Tiles. Make an array that has 4 rows with 5 tiles in each row. Draw a picture of your array. How many tiles did you use? Write an equation that represents your array.

77. Once students have finished the original array. Can you make another array that uses all 20 of the tiles? Describe your array. Draw a picture of your array. Write an equation that represents your array.

78. How Many Stars? Write an equation. Can you write another equation?