1. 9/23/13 Mon

2. A photo measuring 5 inches in width by
Boot-Up
/ 6 min.
A photo measuring 5 inches in width by
4 inches in length is enlarged to produce a photo with a length of 16 inches.
What is the width of
the enlargement? _________
What scale factor
was used to make

3. Find p 154:
Methods & Meanings

4. What is a “Ratio”?
How can a ratio be expressed?
What is a “Ratio of Similarity”?
4) What Ratio of Similarity is being used for the 2 s in the textbook?
5) What is a Zoom Factor (or Scale Factor)?

5. Where did the 3/5 come from?
→ means 6 units of length on one hypotenuse compared to 10 units on the other hypotenuse
Where did the 3/5 come from?

6. Find Lesson 3.1.3
Today’s To-Do List:
3-24  3-27
3-25  3-28
3-26

7. Team Expectations
Facilitators: Remember, there is usually > 1 way to solve a problem. Make sure everyone’s ideas are heard.
Task Mgrs: Make sure each person justifies their ideas.
Recorder/Reporters: Make sure each person is writing.
Recorder/Reporters: Get resources as needed, including Teacher, but Make sure your team is “Asking 3 before me.”

8. 3-24
Tracing Paper?

9. 3-24 7 2 6 21
Does this remind you of anything we did in class?

10. 3-24

11. Stretch Point (Point of Dilation)
Does this remind you of anything we did in class?
3-24

12. 2 7 6 21 = 2 6 7 21 = Figure Height Base Small 2 6 Large 7 21 Side
3-24

13. 6 x 2 4 = 3 4 6 x = Figure Height Base Small 6 2 Large x 4 Small 3 621 ? 6 x 2 4 = 3 4 6 x =
3-24

14. 3-26

15. 3-26 3 3
Zoom Factor: 3/2 = 1.5 2 2 9 9 12 12 6 6 8 8 3 2 6 9
Graph Paper

16. s are congruent (), but Sides are not. (The sides are proportional.)
Similar (~) figures:
s are congruent (), but Sides are not. (The sides are proportional.)
3-27

17. Similar (~) figures:
Perimeters (& side lengths) are found by multiplying by the zoom (scale) factor.
Areas are found by multiplying by the square of the zoom (scale) factor.
Areas
3-28

18. Ratios: A comparison of 2 #s.
Ex: 1 dog : 2 cats 1 2
Proportions: A comparison of 2 ratios.
1 = 2
2 4

19. Lesson 3.1.3
pgs – 159
#s – 3-34

20. 9/124/13 Tue

21. What is the relationship between the s shown below?
A) Congruent B) Complementary C) Supplementary
2x + 3
4x - 9
2x + 3
4x - 9
2) Solve for x
Boot-Up
/ 6 min.

26. 1) What do we know about these s?
Supplementary = 180
2) What do we know about the red s?
Alternate Interiors 
3) What do we know about the green s?
Alternate Interiors 

27. 2-38

28. 2-46 What is the sum of s x & y?
Rianna says something’s wrong with this picture. Do you agree?
Same Side Interiors
Supplementary
2-46

29. 2-47

30. If so, complete this sentence: Theorem:
Based on the degree measurements shown, must lines FG & HI be parallel?
If so, complete this sentence:
Theorem:
If ______________ angles are supplementary, then the lines intersected by a ___________ are ________.
2-48

31. 2-48
Theorem: If same-side interior angles are supplementary, then the lines intersected by a transversal are parallel.

32. Honey, I shrunk the Polygons! (They still look the same, though.)
Similar (~): Figures that are the same shape but not necessarily the same size. x° y° x° y° ~ ~

33. Honey, I shrunk the Polygons! (They still look the same, though.)
Similar (~) figures:
Their orientation (position in space) does not matter! ~ ~

34. Angles are congruent, but Sides are not. (The sides are proportional.)
Similar (~) figures:
Angles are congruent, but Sides are not. (The sides are proportional.) x° z° z° y° x° y°

35. What other fractions that are equivalent to 3/4?
Proportional: The lengths of corresponding sides of similar figures form equivalent fractions. z° 6” x° z° y° 3” x° y° y° 8” 4”
What other fractions that are equivalent to 3/4?

36. The following diagram shows similar figures.
What is the value of side x? 18 12 10 x
A) 10
B) 12
C) 15
D) 180

37. Angles are congruent (), but Sides are proportional.
Similar (~) figures:
Angles are congruent (), but Sides are proportional.
55°
70°
2.9 in.
3.5 in.
15 ft.
9 ft.
50°
80°
3.2 in.
4.1 in.
10 ft.
6 ft.

38. So, look at the angles 1st! If the angles are not , then the figures are not ~
55°
70°
2.9 in.
3.5 in.
15 ft.
9 ft.
50°
80°
3.2 in.
4.1 in.
10 ft.
6 ft.

39. What is this question asking you to find?
How can you use similarity to solve this problem?
Is there something in this room that you can use to compare to the monument?
What parts do you need to compare?
Do you have any math tools that can help you gather information?
3-35

40. 3-35

41. 3-35

42. 5 cm
20 cm
n ft.
60 ft. =
20  n =
60  5
20n =
300 n = 15

43. 3-36 AC AB DF DE =

44. 9/25/13 Wed

45. Ant-Man is 4 inches tall, and his shoulders are 2. 5 inches wide
Ant-Man is 4 inches tall, and his shoulders are 2.5 inches wide. After taking a Pym Particle, he has grown to 28 inches tall.
1) How wide are his shoulders when he grows to 28 inches tall? _______________
2) What is the zoom (scale) factor of the Pym Particle he took?
A) B) C) D) 28

46. 4 28 2.5 w = 4  w = 28  2.5 4w = 70 n = 17.5 Figure Height Width
Small 4
2.5
Large 28 w 4 28
2.5 w =
4  w =
28  2.5 4w = 70 n =
17.5

47. The following diagram shows a dilation. How can we solve for x?
Figure
Height
Width
Small
Large 10 x 12 18

48. The following diagram shows a dilation. How can we solve for x?
Figure
Height
Width
Small
Large 10 12 x 18

49. Small Hypotenuse Base
Large Hypotenuse Base =
GI PR
GH PQ =

50. 3-37

51. 3-38

52. 3-38

53. 3-39

54. 3-40
8 min.

55. Lesson 3.1.4
pgs – 165
#s – 3-46

56. 9/26/13 Thu

57. Boot-Up
/ 6 min.
If BD = 6, DA = 2, and BC = 15, which proportion would you use to find BE?
Put HW & HW log on you desk for teacher to check.

58. Boot-Up
/ 6 min. 6 x 6 15 2

60. Stretch Point (Point of Dilation)
Does this remind you of anything we did in class?
3-24

63. 3-24

64. 3-49 a.
? = 180
? = 180

65. AC AB DF DE = AA Triangle Similarity (AA):
When 2 pairs of corresponding s are , the 2 s must be .
If 2 pairs of s are , the 3rd pair must also be . AC AB DF DE =

66. M&M

67. 3-50 b.

68. 3-50 b.

69. SAS Triangle Similarity (SAS):
When 2 pairs of corresponding sides are proportional, & the s between those sides are , then the other correspondings must also be , & the remaining pair of sides must be proportional. 4 8 3 6

70. 3-51 a.

71. 3-51 a.

72. 3-51 b.

73. 3-51 b.

74. 3-52

75. 9/27/13 Fri

76. The following diagram shows a dilation.
Boot-Up
/ 6 min.
The following diagram shows a dilation.
Which proportion could be used to determine the length of side x? h’ h b b’

79. 3-59a
3-59b

80. SAS  What do you notice about the order of the letters? 3-60 C  R
CAT  PGI
SAS 
What do you notice about the order of the letters?

81. 3-60
Facts
Conclusion
Similarity
Condition

82. 3-61

83. 3-61

84. 3-61
A  G
C  P
CAT  PGI

85. 3-62

86. 3-63

87. Lesson 3.2.3

88. 3-71

89. 3-71

90. 3-72

91. 3-73

92. 3-74

93. Which statement is true about ABC and JKL?
A) The triangles are congruent.
B) The triangles are similar.
C) The ratio of the lengths
of corresponding sides
is not constant.
D) Corresponding angles
are not congruent.
Mastering the MCT2, Grade 6, p11,3c, P
3 mins
1/30/13
DO NOW

94. 52. The following diagram shows a dilation.
Which proportion could be used to determine the length of side x? a 12 a’ 6 x 8 b b’
Released 2009
TTW Lead-in to Exit Ticket:
MCT2, Grade 6, Test 2; 4d

95. The following diagram shows a dilation
The following diagram shows a dilation.Which proportion can be used to find the value of side x? 10 x 12 18 A) C) B) D)

96. Draw a dilation of a figure using a Scale Factor of 3.15 5 6 2

97. Draw a dilation of a figure using a Scale Factor of 1/2.14 7 3 6

98. My Turn:
What is the Scale factor to go from the smaller figure to the larger figure? 9 3 4 12

99. Your Turn:
What is the Scale factor to go from the smaller figure to the larger figure? 8 2 3 12

100. My Turn:
What is the Scale factor to go from the Larger figure to the smaller figure? 9 3 4 12

101. My Turn:
What is the Scale factor to go from the Larger figure to the smaller figure? 8 2 3 12

102. An original photograph of Kimberly is 3.5 inches wide by 5 inches long.
She wants to get an enlargement measuring 28 inches wide by 40 long.
What is the scale factor of the enlargement?
A B. 5
C D. 28

103. The following diagram shows a dilation.
What is the scale factor to go from:
the smaller figure to the larger figure? a’ a
2) the larger figure to the smaller figure? b b’
Released 2009
MCT2, Grade 6, Test 2; 4d

104. TTW:

105. TSW:

106. 49. Triangle PQR has been dilated to create triangle P′Q′R′.
CHALLENGE QUESTION!!!
49. Triangle PQR has been dilated to create triangle P′Q′R′.
Based on the figure at right, which of the following statements is true?
RELEASED TEST 1
MCT2, Grade 6, 3e

107. 6B Start here Wed 2/16
DO NOW 2/16/11
Students work in pairs to solve the following:
4. What are the coordinates of the dilation image of triangle ABC with a scale factor of 2?
A A‘ (-4, -4), B‘ (2, -2), C‘ ( 0, 4)
B A‘ ( 0, 4), B‘ (2, -2), C‘ (-4, -4)
C A‘ (-4, -2), B‘ (3, -1), C‘ ( 0, 4)
D A‘ (-2, -4), B‘ (1, -3), C‘ ( 0, 0)
34 Mastering the MCT2, Grade 6

108. Corresponding angles of similar figures are  Congruent!
4) Identify corresponding parts (sides & angles) of similar polygons
28. The following diagram shows the image and pre-image in a 200% dilation.
Corresponding angles of similar figures are  Congruent!
Released 2009
MCT2, Grade 6, Test 2; 3e

109. 50. Lubresha performed a 50% dilation on figure KLMN as shown below.
4) Identify corresponding parts (sides & angles) of similar polygons
50. Lubresha performed a 50% dilation on figure KLMN as shown below.
What is the relationship between the length of K'L' and KL?
The length of K'L' is half the length of KL.
The length of K'L' is twice the length of KL.
H. The length of K'L' is the same as the length of KL.
J. The length of K'L' cannot be compared to the length of KL.
Corresponding sides of similar figures are proportional!
Released 2010
MCT 2 – Grade 6, Test 3, 3e

110. 30. Look at the figure below.
Which statement about the figure is not true?
F. A’B’C’D’E’ is increased to ABCDE by a scale factor of 200%.
G. ABCDE is a reduction of A’B’C’D’E’ by a scale factor of .
H. O'B’ is twice OB, and E 'D’ is twice ED.
J. AB is a reduction of A’B’ by a scale factor 50%.
Released 2010
MCT 2 – Grade 6, Test 3, 3e

111. What scale factor was used to make the enlargement?
The triangles show below are similar figures. What is the length of “x”?
An 8 inch by 10 inch photo is enlarged to produce a inch by 24 by 30 inch photo.
What scale factor was used to make the enlargement?
2 B. 3
C. 8 D. 10
16” x” 9” 3”

112. What scale factor was used to make the enlargement?
Exit Ticket: SWBAT correctly answer the
following problem by the end of today’s lesson:
This will be collected & graded as classwork. Put on a separate sheet with heading: Name, Date, Exit Slip: Scale Factors. SHOW ALL WORK! If you do not show step-by-step work as taught today, you will not get credit.
If BD = 6, DA = 2, and BC = 15, which proportion would you use to find BE?
A 4 inch by 5 inch photo is enlarged to produce a 16 inch by 20 inch photo.
What scale factor was used to make the enlargement?

113. 5 w 4 16 = 4 Width Length Scale Factor: Image: 16 Pre-Image: 4
Original
(Pre-Image)
Copy
(Image)
Width
Length 5 w 4 16
Scale Factor: Image:
Pre-Image: = 4

114. 45. Manuel baked a cake. He used 0. 75 cup of frosting and 0
45. Manuel baked a cake. He used 0.75 cup of frosting and 0.5 cup of sugar. How should Manuel write these decimals as fractions?
A. 75/100 and 5/ B. 75/10 and 5/10
75/100 and 5/ D. 75/10 and 5/100
MCT2, Grade 6, Test 2; 1f

115. A regular triangle with 5-inch sides undergoes a dilation with scale
SWBAT: 1) Determine the scale factor of a given proportion.
A regular triangle with
5-inch sides undergoes
a dilation with scale
factor 2.5.
What are the side lengths of the image triangle?
A. 7.5 in B in.
C in. D. 20 in.
IND is the image of  MRE under a
dilation. What is the scale factor of the
dilation?

116. 3e. Dilations
Explain the relationships between corresponding parts of the pre-image and image of a dilation. (DOK 2)

117. XYZ is shown below.
If the coordinates of Z’ are (3, 1), which statement describes the transformation of point Z?
F. Point Z was translated 2 units to the right and 3 units down.
G. Point Z was translated 3 units to the right and 2 units down.
H. Point Z was translated 2 units to the left and 3 units up.
J. Point Z was translated 3 units to the left and 2 units up.
MCT 2 – Grade 6, Test 3, 3e
Released 2010

118. What scale factor was used to make the enlargement?
Exit Ticket: SWBAT correctly answer the
following problem by the end of today’s lesson:
This will be collected & graded as classwork. Put on a separate sheet with heading: Name, Date, Exit Slip: Scale Factors. SHOW ALL WORK! If you do not show step-by-step work as taught today, you will not get credit.
If BD = 6, BA = 8, and BC = 15, which proportion would you use to find BE?
A 4 inch by 5 inch photo is enlarged to produce a 16 inch by 20 inch photo.
What scale factor was used to make the enlargement? 8

119. What scale factor was used to make the enlargement?
Exit Ticket: SWBAT correctly answer the
following problem by the end of today’s lesson:
This will be collected & graded as classwork. Put on a separate sheet with heading: Name, Date, Exit Slip: Scale Factors. SHOW ALL WORK! If you do not show step-by-step work as taught today, you will not get credit.
If BD = 6, DA = 2, and BC = 15, which proportion would you use to find BE?
A 4 inch by 5 inch photo is enlarged to produce a 16 inch by 20 inch photo.
What scale factor was used to make the enlargement?

120. 9/20/13 Fri

121. Resource Manager: Make sure to get all of the supplies & call the teacher over, if needed. Take shape inventory at beginning & end. Make sure all shapes are returned to bucket.
Facilitator: Make sure that everyone can participate & that no one dominates the process.
Recorder/Reporter: Make sure that everyone can reach & see the Venn diagram & the shapes. Record shape placements / present findings at end of lesson.
Task Manager: Make sure each team member justifies statements & decisions.

122. y II I x
III IV

123. Name __________ 8/29/13 Test # 1
UN # __________
11)

124. 8/30/13 Thu

125. y II I
Translate (Slide) rectangle ABCD so that point A is at the origin. A B D C x A B D C
Tell me -- do I really look like a “Leonard” to you?
III IV