1. Vacaville USD February 10, 2015

2. AGENDA Problem Solving – A Snail in the Well Estimating and Measurement Fractions and Decimals Back to Fractions

4. Analyze Student Work For each piece of work: Describe the problem solving approach the student used. For example, you might: –Describe the way the student has organized the solution. –Describe what the student did to calculate when the snail reached the top Explain what the student needs to do to complete or correct his or her solution.

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

12. 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

13. 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

14. Estimation

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

16. Estimation How many cheeseballs are in the original container? 917

17. 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? 461

18. Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.

19. Measurement We are going to do a brain dump. In just a minute I am going to show you a math term and you have 60 seconds to throw out as many ideas and thoughts as you can.

20. foot

21. Length Measurements Is a foot larger or smaller than a yard? So suppose I tell you I have 9 feet and I want my answer in yards. –Will I have more than 9 yards or less than 9 yards? –How do you know?

22. Length Measurements So what do we know about feet and yards? 1 yard 3 feet

23. Length Measurements 9 feet = ____ yards ____ feet = 9 yards 1 yard 3 feet

24. Length Measurements So what do we know about meters and centimeters? 1 meter 100 centimeters

25. Length Measurements 9 m = ____ cm ____ m = 800 cm 1 m 100 cm

26. Length Measurements 50 m = ____ cm 70 cm = ____ m 1 m 100 cm

27. 1.Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. For each possible measurement conversion, draw the related visual conversion fact.

28. 1.Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36),...

29. 2.Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

30. www.estimation180.com Back to Estimation

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

33. How many green marshmallows are inside the glass?

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

36. What's the capacity of the tall vase?

37. What's the capacity of the wide vase?

38. Order the glasses from least to greatest in capacity.

39. How many Red Vines are in my hand?

40. How many Red Vines are in the container?

41. Fractions and Decimals

42. 4.NF.5 Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100. For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. (Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.)

43. 4.NF.5 Focus on working with grids, number lines and other models (not algorithms) Base ten blocks and other place value models can be used to explore the relationship between fractions with denominators of 10 and denominators of 100 This work lays the foundation for decimal operations in fifth grade.

44. 3 tenths = 30 hundredths

45. Equivalent Fractions For each fraction: Shade the 1 st grid to represent the fraction Copy the shaded part onto the 2 nd grid Write a statement showing the equivalent fractions 1) 2) 3)

47. Equivalent Fractions For each fraction: Locate the fraction on the number line Use the number line to help write a statement showing equivalent fractions 1) 2) 3)

48. 5 tenths + 7 hundredths =57 hundredths

49. Addition 1)2) 3)4)

51. Addition 1)2) 3)4)

52. 74 hundredths =4 hundredths 7 tenths +

53. Write in Expanded Form 1)2) 3)4)

54. 4.NF.6 Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.

55. 4.NF.6 Focus on connections between fractions with denominators of 10 and 100 and the place value chart. Connect tenths and hundredths to place value chart Connect

56. 3 tenths = 30 hundredths = 0.3 = 0.30

57. 74 hundredths =4 hundredths 7 tenths + =.74

58. Write in Expanded Form – Then Write as a Decimal 1)2) 3)4)

59. 4.NF.7 Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.