1. Vacaville USD February 17, 2015

2. AGENDA Problem Solving – A Snail in the Well Estimating and Measurement Perimeter and Area Attributes of Shapes 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 the number of cookies that started on the tray. Explain what the student needs to do to complete or correct his or her solution.

11. 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

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

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

14. 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

15. Estimation

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

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

18. 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? 441

19. Measurement What’s larger – an inch or a cm? –Suppose a straw measures 7 inches. –If I measure it in cm, will it be more than 7 or less than 7? How do you know? What’s larger – a gram or a kg? –Suppose a bag weights 5 kg. –If I weigh it in g, will it be more than 5 or less than 5? How do you know?

20. Measurement MD.2 Measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l).6 Add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units, e.g., by using drawings (such as a beaker with a measurement scale) to represent the problem.

21. Measurement What types of experiences do students need to have to develop a familiarity with liters? With grams and kilograms?

22. Measurement What do students know about a liter? What standard measure is closest to a liter? –1 liter is (approx) 1 quart (1 liter  1.06 quarts)

23. Measurment So what about a gram? A kilogram?

24. Measurment A gram (g) is used to measure the weight or mass of very light objects. –A small paperclip weighs about a gram. –1 gram =.04 ounces –1 ounce = 28.3 grams

25. Measurment A (kg) is used to measure the weight or mass of heavier objects. –A one-liter bottle of water weighs about a kilogram. –1 kilogram = 2.2 pounds –1 pound =.45 kilogram

26. www.estimation180.com

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

29. How many green marshmallows are inside the glass?

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

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

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

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

35. How many Red Vines are in my hand?

36. How many Red Vines are in the container?

37. Fractions

38. Fraction Concepts Six children share three brownies so that each child receives a fair share. What portion of each brownie will each child receive?

39. Fraction Concepts Six children share four brownies so that each child receives a fair share. What portion of each brownie will each child receive?

40. Fractions NF.1. Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size 1/b.

41. Definition of Fraction: Start with a unit, 1, and split it into ___ equal pieces. Each piece represent 1/___ of the unit. When we name the fraction __/__, we are talking about ___ of those 1/___ size pieces.

42. Fraction Concepts

43. What fraction of the rectangle is shaded? How might you draw the rectangle in another way but with the same fraction shaded?

44. Fractions on the Number Line

45. Fractions NF.2. Understand a fraction as a number on the number line; represent fractions on a number line diagram. a. Represent a fraction 1/b on a number line diagram by defining the interval from 0 to 1 as the whole and partitioning it into b equal parts. Recognize that each part has size 1/b and that the endpoint of the part based at 0 locates the number 1/b on the number line.

47. Fractions NF.2. Understand a fraction as a number on the number line; represent fractions on a number line diagram. b. Represent a fraction a/b on a number line diagram by marking off a lengths 1/b from 0. Recognize that the resulting interval has size a/b and that its endpoint locates the number a/b on the number line.

49. Definition of Fraction: When we name the point, we’re talking about a distance from 0 of ___ of those ___ pieces. 4

50. Where is a unit on this number line?

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52. 

53. 

54. 

55.    

56. Fractions NF3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. c. Express whole numbers as fractions, and recognize fractions that are equivalent to whole numbers. Examples: Express 3 in the form 3 = 3/1; recognize that 6/1 = 6; locate 4/4 and 1 at the same point of a number line diagram.

58. Compare Fractions Using Sense Making

59. Fractions NF3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. d. Compare two fractions with the same numerator or the same denominator by reasoning about their size. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.

60. Comparing Fractions A. B.

61. Comparing Fractions B. A.

62. Comparing Fractions A. B.

63. Equivalent Fractions

64. Fractions NF3. Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size. a. Understand two fractions as equivalent (equal) if they are the same size, or the same point on a number line. b. Recognize and generate simple equivalent fractions, e.g., 1/2 = 2/4, 4/6 = 2/3). Explain why the fractions are equivalent, e.g., by using a visual fraction model.

65. Locate on the top number line. ● 0 1

66. Copy onto the bottom number line. 0 1 ● ●

67. Are the lengths equal? 0 1 ● ●

68. Equivalent fractions can be constructed by partitioning equal fractional parts of a whole into the same number of equal parts. The length of the whole does not change; it has only been partitioned into more equal sized pieces. Since the length being specified has not changed, the fractions that describe that length are equal.

69. CaCCSS Fractions are equivalent (equal) if they are the same size or they name the same point on the number line. (3.NF3a)

70. 0 1 ● ●

71. 0 1 ● ●

72. 0 1 ● ●

73. ● ● So 0 1

74. Fraction Families

75. FAL Representing Fractions on a Number Line –Initial Task –6 Friends Swimming Version A –6 Friends Swimming Version B –Revisit Task http://www.jennyray.net/uploads/1/2/9/7/129757 76/representing_fractions_on_a_number_line_- _grade_3_-_alpha_revised_4-26-2012.pdf

76. Back to Measurement (and Data)

77. Linear Measurement MD.4 Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.

78. Linear Measurement What do students need to understand about measuring length?

79. Perimeter What do students need to understand about perimeter? How does the concept of perimeter relate to concept of linear measurement?

80. Perimeter All of the objects in the bag have a length of 1 inch. How could you use them to find the perimeter of a rectangle? With your group, use all of the objects to find the perimeter of the rectangle.

81. Area What do students need to understand about measuring area? How is measuring area different than measuring length (or perimeter)?

82. Area Using the objects in the bag, figure out how many of each it would take to “cover” the rectangle.

83. Area Which tools gave you the same answer? Which one gave you different answer?

84. Area MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement. a.A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area. b.A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

85. Area MD.5 Recognize area as an attribute of plane figures and understand concepts of area measurement. a.A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area. b.A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

86. Attributes of Shapes

87. Attributes Kentucky FAL Lesson “Attributes of Shapes” Pre-/Post-Assessment Lesson

88. Attributes Today you are going to sort shapes by attributes What are attributes?

89. What are Attributes Things other than shapes have attributes For example, all of you share an attribute because you are students in this class What are some other attributes that you share?

90. Attributes of Shapes Shape sort activity http://teresaemmert.weebly.com/uploads/1/3 /0/5/13053448/3rd_grade_attributes_of_sha pes_alpha_version_11.14.2012_.pdf