3. Miles of Tiles The Exhibit

4. Miles of Tiles The Exhibit

5. Miles of Tiles The Exhibit

6. Miles of Tiles The Exhibit

7. Miles of Tiles The Exhibit

8. Math Geometry + Nature

9. Math Geometry + Nature Why do bees use hexagons? Is there something special about them?

10. Math Geometry + Nature Let’s compare what we calculated P = 12 A = 9 P = 12 A = 10.38 P = 12 A = 11.47

11. Math Geometry + Nature A circle yields the greatest interior space for the smallest perimeter of any shape! P = 12 A = 11.47

12. Math Geometry + Nature P = 12 A = 10.38 Hexagons yields the greatest interior space for the smallest perimeter of any shape that tessellates!

13. Lesson Ideas Grade 3

14. Lesson Ideas Grade 3 Develop Understanding of fractions as numbers Fraction  Fracture

15. Lesson Ideas Grade 3 Develop Understanding of fractions as numbers Fracture - break into pieces

16. Lesson Ideas Grade 3 Develop Understanding of fractions as numbers Fractions - break into pieces using numbers

17. Lesson Ideas Grade 3 Develop Understanding of fractions as numbers 4 = 1 1 1 1

18. Lesson Ideas Grade 3 Develop Understanding of fractions as numbers 4 = 1 1 1 1 ¼ means you have one of the four 1s

19. Lesson Ideas Grade 3 Develop Understanding of fractions as numbers You have one of the four squares

20. Lesson Ideas Grade 3 Develop Understanding of fractions as numbers Tiles provide a concrete example of the abstract concept of fractions

21. Lesson Ideas Grade 3 Understand the concepts of area and relate it to multiplication and addition

22. Lesson Ideas Grade 3 Area relationship to multiplication & addition

23. Lesson Ideas Grade 3 Area relationship to multiplication & addition

24. Lesson Ideas Grade 3 Area relationship to multiplication & addition 11 1 1

25. Lesson Ideas Grade 3 Area relationship to multiplication & addition 2 2

26. Lesson Ideas Grade 3 Area relationship to multiplication & addition 2 2 2 x 2 = 4

27. Lesson Ideas Grade 3 Area relationship to multiplication & addition 2 x 2 = 4 Area of this square is 4

28. Lesson Ideas Grade 4

29. Lesson Ideas Grade 4 Understanding fraction equivalence

30. Lesson Ideas Grade 4 Understanding fraction equivalence

31. Lesson Ideas Grade 4 Understanding fraction equivalence

32. Lesson Ideas Grade 4 Understanding fraction equivalence 4/16 = 1/4

33. Lesson Ideas Grade 4 Understanding decimal notation for fractions

34. Lesson Ideas Grade 4 Understanding decimal notation for fractions ¼ spoken as “one quarter”

35. Lesson Ideas Grade 4 Understanding decimal notation for fractions With money ¼ of a dollar is one quarter

36. Lesson Ideas Grade 4 Understanding decimal notation for fractions One quarter is twenty-five cents 25¢

37. Lesson Ideas Grade 4 Understanding decimal notation for fractions Twenty-five cents is written as 25¢.25

38. Lesson Ideas Grade 4 Understanding decimal notation for fractions.25 $1

39. Lesson Ideas Grade 5 Understanding concepts of volume

40. Lesson Ideas Grade 5 Understanding concepts of volume Start with simple shapes

41. Lesson Ideas Grade 5 Understanding concepts of volume Stack the physical shapes on the board

42. Lesson Ideas Grade 5 Understanding concepts of volume Explain that the volume for all simple shapes is area x height

43. Lesson Ideas Grade 5 Understanding concepts of volume Explain that the volume for all simple shapes is area x height

44. Lesson Ideas Grade 5 Understanding concepts of volume Explain that the volume for all simple shapes is area x height

45. Lesson Ideas Grade 5 Understanding concepts of volume Explain that the volume for all simple shapes is area x height

46. Lesson Ideas Grade 5 Understanding concepts of volume Compare volumes to illustrate the bee’s use of hexagons

47. Lesson Ideas Grade 6 Solve real-world problems involving area

48. Lesson Ideas Grade 6 Solve real-world problems involving area You are installing new tiling on your bathroom floor

49. Lesson Ideas Grade 6 Solve real-world problems involving area

50. Lesson Ideas Grade 6 Solve real-world problems involving area

51. Lesson Ideas Grade 6 Solve real-world problems involving area No bathroom is an exact multiple of the size of tile chosen

52. Lesson Ideas Grade 6 Solve real-world problems involving area Let’s say the bathroom is 9’ x 9’ and each tile is 5” x 5”

53. Lesson Ideas Grade 6 Solve real-world problems involving area Let’s say the bathroom is 9’ x 9’ and each tile is 5” x 5” How many tiles are needed?

54. Lesson Ideas Grade 6 Solve real-world problems involving area Let’s say the bathroom is 9’ x 9’ and each tile is 5” x 5” Remember to convert feet to inches!

55. Lesson Ideas Grade 6 Solve real-world problems involving area Remember to convert feet to inches!

56. Lesson Ideas Grade 6 Solve real-world problems involving area Remember to convert feet to inches! NASA's Climate Orbiter lost September 23, 1999 (CNN) -- NASA lost a $125 million Mars orbiter because a Lockheed Martin team used English measurement while the NASA team used the metric system.

57. Lesson Ideas Grade 6 Solve real-world problems involving area Let’s say the bathroom is 9’ x 9’ and each tile is 5” x 5” Remember to convert feet to inches!

58. Lesson Ideas Grade 6 Solve real-world problems involving area Let’s say the bathroom is 9’ x 9’ and each tile is 5” x 5” How many tiles must be cut?

59. Lesson Ideas Grade 6 Solve real-world problems involving area What if the tiles are a different shape?

60. Lesson Ideas Grade 6 Solve real-world problems involving area

61. Lesson Ideas Grade 7 Investigate chance processes

62. Lesson Ideas Grade 7 Investigate chance processes 4 different colored monkeys live on monkey island.

63. Lesson Ideas Grade 7 Investigate chance processes One of them walks up to you begging for a banana.

64. Lesson Ideas Grade 7 Investigate chance processes What is the probability that it is yellow? ?

65. Lesson Ideas Grade 7 Investigate chance processes Have a student stand with their back to the board. Hand them one of the four monkeys.

66. Lesson Ideas Grade 7 Investigate chance processes 6 different colored monkeys live on monkey island…

67. Lesson Ideas Grade 8 Solve real-world problems involving volume

68. Lesson Ideas Grade 8 Solve real-world problems involving volume Calculate the volume of a milk carton

69. Lesson Ideas Grade 8 Solve real-world problems involving volume Calculate the volume of a milk carton

70. Lesson Ideas Grade 8 Solve real-world problems involving volume Break it down into basic shapes that are easy to calculate

71. Lesson Ideas Grade 8 Solve real-world problems involving volume Break it down into basic shapes that are easy to calculate

72. Lesson Ideas Grade 8 Solve real-world problems involving volume Break it down into basic shapes that are easy to calculate

73. Lesson Ideas Grade 8 Understand and apply Pythagorean Theorem

74. Area = ½ b x h 22 2 Lesson Ideas Grade 8

75. A = ½ b x h 22 2 Lesson Ideas Grade 8

76. A = ½ b x h 22 11 Lesson Ideas Grade 8

77. A = ½ b x h 2 1 h Lesson Ideas Grade 8

78. A = ½ b x h 2 1 h Determine the value of “h” Lesson Ideas Grade 8

79. a 2 + b 2 = c 2 2 1 h Determine the value of “h” Lesson Ideas Grade 8

80. 1 2 + h 2 = 2 2 2 1 h Determine the value of “h” Lesson Ideas Grade 8

81. 1 + h 2 = 4 2 1 h Determine the value of “h” Lesson Ideas Grade 8

82. h 2 = 3 2 1 h Determine the value of “h” Lesson Ideas Grade 8

83. h 2 = 3 2 1 h Determine the value of “h” Lesson Ideas Grade 8

84. h = 3 2 1 h Determine the value of “h” Lesson Ideas Grade 8

85. h ≈ 1.73 2 1 Determine the value of “h” Lesson Ideas Grade 8

86. A = ½ b x h 11 h Now we can calculate the area of one equilateral triangle Lesson Ideas Grade 8

87. A = 1 x 1.73 11 h Now we can calculate the area of one equilateral triangle Lesson Ideas Grade 8

88. A = 1.73 The area of one equilateral triangle is 1.73 1.73 Lesson Ideas Grade 8

89. Lesson Ideas Geometry

90. Lesson Ideas Numbers & Quantity

91. Lesson Ideas Numbers & Quantity In real world problems, the answers are usually not numbers but quantities: numbers with units, which involves measurement.

92. Lesson Ideas Numbers & Quantity Measure the actual shapes at the exhibit. Printed paper rulers can be provided to students.

93. Lesson Ideas Numbers & Quantity Measure lengths, widths, & diameters. Calculate areas, circumferences, & volumes

94. Lesson Ideas Algebra

95. Lesson Ideas Algebra An expression uses symbols that represent numbers, arithmetic operations, and exponents.

96. Lesson Ideas Algebra Formulas for Area Triangle = ½ b x h

97. Lesson Ideas Algebra Formulas for Area Circle = ∏ r 2

98. Lesson Ideas Algebra Pythagorean Theorem a 2 + b 2 = c 2

99. Lesson Ideas Algebra Volume Formulas Volume = Area x height

100. Lesson Ideas Statistics & Probability

101. Lesson Ideas Statistics & Probability What is the probability that it is yellow? ?

102. Lesson Ideas Statistics & Probability A yellow and a red monkey get married and have a baby monkey. Punnett Squares

103. Lesson Ideas Statistics & Probability What is the probability that the baby is red. Punnett Squares Yr rYYrr rYrrr

104. Lesson Ideas Functions

105. Lesson Ideas Functions Functions describe situations where one quantity determines another.

106. Lesson Ideas Functions Plot the curve that shows the area of shapes with the same circumference as the number of sides of the shape increases.

107. Lesson Ideas Functions Area # sides

108. Lesson Ideas Modeling

109. Lesson Ideas Modeling

110. Lesson Ideas Modeling ?

111. Lesson Ideas Modeling Choosing and using appropriate mathematics and statistics to analyze empirical situations