1. 1/4 Monday- Intro to Rotations, Reflections, Translations (ppt) 1/5 Tuesday- Kaleidoscope Activity (pdf) 1/6 Wednesday- Congruence ppt 1/7 Thursday- Dilations 1/8 Friday- Dilations and 15 min activity 1/11 Monday- Portfolio Work Day 1/12 Tuesday- Portfolio Work Day 1/13 Wednesday- Transformations and Dilations Task Cards/Pop Quiz 1/14 Thursday- Similarity 1/15 Friday- Transformations Activity
Agenda

2. Bell Ringer: Monday, January 4, 2016
1. List things that can rotate.
2. List things that can reflect or be reflected.
3. List things that can be translated.
Bell Ringer: Monday, January 4, 2016

3. Transformations, Congruence, and Similarity
MAFS.8.G.1.1
MAFS.8.G.1.2
MAFS.8.G.1.3
MAFS.8.G.1.4
MAFS.8.G.1.5
UNIT 7

4. Rotations, Reflections, Translations
MAFS.8.G.1.1 (DOK 2): Verify experimentally the properties of rotations, reflections, and translations:
a. Lines are taken to lines, and line segments to line segments of the same length.
b. Angles are taken to angles of the same measure.
c. Parallel lines are taken to parallel lines.
Define and identify rotations, reflections, and translations.
Identify corresponding sides and corresponding angles.
Identify center of rotation.
Identify line of reflection.
Understand prime notation to describe an image after a translation, reflection, or rotation.
Use physical models, transparencies, or geometry software to verify the properties of rotations, reflections, and translations.

5. Learning Scale
By the end of class today I will be at Level 2 because I will be able to…
1. Recall vocabulary words such as coordinate, dilation, experimental, figure, property, reflection, rotation translation, two dimensional

6. Vocabulary
-Line: straight, has no thickness, and extends in both directions without end. -Ray: part of a line that starts with one point and continues on in one direction -Line Segment: the “line” between two points. (Example line segment AB) A B

7. Basic Rigid Motion Rotations Reflections Translations
First, you need to know about vectors! A vector is a segment in the plane. It has a starting point and an endpoint. It is the part that you are looking to rotate, reflect, translate, etc.
written as written as
A B A B

8. Rotations
-Rotation means to turn around a center. -Shapes/images are turned in a counter-clockwise fashion. -It makes a circle shape.
Pull up math is fun graphic

9. You can think of Rotations as turns.
90 degrees
You can think of Rotations as turns.
Here is an example of the turns we would take if we’re told to rotate about the origin…
360 degrees
270 degrees
180 degrees
This was clockwise. How do you think it will change for counterclockwise?

10. Reflections
- A reflection is a flip over a line. - You can flip/reflect vertically, horizontally, diagonally, etc. ...it just depends on where your “central line” is. The central line is also known as a mirror line. -Notice that every point is the same distance from the central line and the reflection is the same size as the original image.

11. Translations
- A translation simply means “to move” (or shift). You can move/shift up, down, left, right, etc. -To translate a shape, every point must move in the same direction and the same distance.
Use doc cam
(you can use a slider on the website if necessary)

12. Translations (slides)
It may say translate the figure (blue dot!)…
Right 3
Or Down 4
Or Left 2, Up 4
Or (4,-5) (right positive or left negative, up positive or down negative)

13. Translations
- Sometimes, we just want to write down the translation, without showing it on a graph… Example: to say the shape gets moved 30 Units in the "X" direction, and 40 Units in the "Y" direction, we can write: (x, y)  (x + 30, y + 40) Which says "all the x and y coordinates become x+30 and y+40"

14. Practice!
Answer: C

15. Practice!
Translate the point (7,4) using the vector <-3,16>. What is the resulting point?
Answer: (4, 20)

16. Practice!
Translate the point (4,5) using the vector <12, -18>. What is the resulting point?
Answer: (16, -13)

17. Practice!
Translate the point (10,15) using the vector <5, 8> and then translate it again using the vector <-3,6>. What is the resulting point?
Answer: (15, 23) and then (12, 29)

18. Practice!
#5, H
#6, E
#7, I

19. Exit Ticket What transformation of triangle ABC produced triangle DEF?
vertical translation
dilation about point C
rotation about point A
reflection across a horizontal line
Answer: D

20. Homework Monday, January 4, 2016
-Draw an example of a rotated image/shape, a reflected image/shape, and a translated image/shape. -Have fun with it! And remember this means that I should be seeing three DIFFERENT images!

22. Bell Ringer: Tuesday, January 5, 2016
Describe (in words) the differences between rotations, reflections, and translations.
Bell Ringer: Tuesday, January 5, 2016

23. Classwork Activity
Tuesday, January 5, 2016

24. Basic Instructions
On your 8.5 x 11 sheet of graph paper divide the paper into four quadrants by drawing X and Y-axes through the middle of the page.
Complete the worksheet FIRST to list each set of points. Rotations should be made in a counterclockwise fashion.
After writing all the sets of points, THEN graph the points. If you did it correctly you should have a drawing! Color the drawing any way you wish.
The drawing will include: a large 8 pointed star, two small diamonds, and two hearts.
**Whatever you don’t finish is homework!!!

26. Bell Ringer 1. Turn in your Kaleidoscope Activity.
2. Take out your Bell Ringer sheet and answer this riddle: At first I was a positive ordered pair but then I looked into my reflection and things changed. My “x” half became negative but my “y” stayed positive. What transformation happened and over what axis?
3. Get your notebooks out we are taking notes today.
Bell Ringer
Wednesday, January 6, 2016

27. Congruence
MAFS.8.G.1.2 (DOK 2): Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
Define congruency.
Identify symbols for congruency.
Describe the sequence of rotations, reflections, translations that exhibits the congruence between 2-D figures using words.
Apply the concept of congruency to write congruent statements.
Reason that a 2-D figure is congruent to another if the second can be obtained by a sequence of rotations, reflections, translations.

28. Scale for Congruence
By the end of class today I will be at Level 3 because I will be able to…
Recall vocabulary words such as coordinate, dilation, experimental, figure, property, reflection, rotation translation, two dimensional, congruence
Describe a series of transformations between two congruent 2-D figures and reason that a 2-D figure is congruent to another if you can make the two figures perfectly match after completing a series of transformations.

29. Review: Rigid Motion/Transformation
ROTATION
TRANSLATION

30. Review: Rigid Motion/Transformations
TRANSLATION-REFLECTION
REFLECTION

31. Vocabulary Congruence
- If one shape can become another using turns (rotations), flips (reflections) and/or slides (translations), then the shapes are congruent. -This means that after any of those transformations, the shape still has the same size, area, angles and line lengths -If a shape needs to be resized, it is no longer congruent!!!!
Congruence

32. Marking sides and angles for congruence
The sides with one mark are equal in length. The sides with two marks are equal in length. The sides with three marks are equal in length.
The angles with one arc are equal in size. The angles with two arcs are equal in size. The angles with three arcs are equal in size.

33. Congruent Shapes Examples

34. Kahoot Time!

35. Exit Ticket
Select all the sequences of transformations that always maintain congruence:
A reflection and then a translation
A translation and then a rotation
A rotation and then a reflection
A dilation and then a reflection
A rotation then a dilation
f. A translation and then a dilation
A, B, C

36. Homework
Draw a diamond. Now draw the diamond rotated 90 degrees and NOT congruent to the first one.

38. Bell Ringer Thursday, January 7, 2016
1. What does it mean to “dilate”?
2. Give an example of something that can be dilated.
Bell Ringer Thursday, January 7, 2016

39. Dilations
MAFS.8.G.1.3 (DOK 2): Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates
Define dilations as a reduction or enlargement of a figure.
Identify scale factor of the dilation.
Describe the effects of dilations, translations, rotations, and reflections on 2-D figures using coordinates.

40. Vocabulary
- To dilate means to grow or shrink. - Dilations map lines to lines, segments to segments, and rays to rays. - Dilations are “degree preserving” which means that when given two similar triangles, the corresponding corners will be the same degree angle.

41. Dilations in depth…
A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. A dilation stretches or shrinks the original figure.
A dilation includes a scale factor (or ratio) and the center of the dilation. The  center of dilation is a fixed point in the plane about which all points are expanded or contracted.  It is the only invariant point under a dilation. In other words, the center of dilation is the only point that is not affected/changed.

42. Dilate
GROW
SHRINK

43. Grow Dilate (growing) with the origin as the center (0,3) (-1,1) (1,1)
(0,6)
(-2,2)
(2,2)
Grow
Notice that when dilating by 2, we are growing. Everything gets multiplied by 2.
All x’s and y’s grow by multiplying by 2.

44. Shrink Dilate (shrinking) with the origin as the center (-4,6) (-4,4)
(-2,4)
(-2,3)
(-2,2)
(-1,2)
Shrink
Notice that when dilating by ½, we are shrinking. Everything gets multiplied by ½.
All x’s and y’s get smaller because you multiply each by ½.

45. Choose the correct transformation for the situation
Practice!
Reflection
Rotation
Translation
Dilation
Choose the correct transformation for the situation

46. Choose the correct transformation for the situation.
Practice!
Choose the correct transformation for the situation.
Reflection
Rotation
Translation
Dilation

47. Choose the correct transformation for the situation.
Practice!
Choose the correct transformation for the situation.
Reflection
Rotation
Translation
Dilation

48. Choose the correct transformation for the situation
Practice!
Choose the correct transformation for the situation
Reflection
Rotation
Translation
Dilation

49. Khan Academy Dilations (SHRINKING)
geo/basic-geo-congruence-similarity/v/scaling-down-a-triangle-by-half
Shrinking about the origin.

50. Khan Academy Dilations (GROWING)
from-an-arbitrary-point-example
Growing with a center of (9, -9)

51. Exit Ticket
From what you know about dilations, make a conjecture (or hypothesis) of what would happen to a line, ray, line segment, and angle if it were to be dilated.

52. Homework Thursday, January 7, 2016
Dilations Coordinates Worksheet

54. Bell Ringer Friday, January 8, 2016
What is the scale factor for this dilated image?
Bell Ringer Friday, January 8, 2016
Pull out your homework we’re going to go over it before you turn it in!

55. Dilations
MAFS.8.G.1.3 (DOK 2): Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates
Define dilations as a reduction or enlargement of a figure.
Identify scale factor of the dilation.
Describe the effects of dilations, translations, rotations, and reflections on 2-D figures using coordinates.

56. Four Tasks to Complete
-You will have 4 tasks to complete in groups and then you will break off into pairs and play a “Guess What” game with a partner.
Pass out graph paper to each group.

57. Task #1 y=2000. What are the coordinates of the reflected point?
The point in the x-y plane with coordinates  (1000,2012) is reflected across the line 
y=2000. What are the coordinates of the reflected point?
Helpful Questions:
Should you make a t-graph or an L-graph?
What should your increments be (how much do you think you should number by)?

58. Task #2
Show that △ABC is congruent to △PQR with a reflection followed by a translation.
If you reverse the order of your reflection and translation in part (a) does it still map △ABC to △PQR?
Find a second way, different from your work in part (a), to map △ABC to △PQR using translations, rotations, and/or reflections.

59. Task #3
Draw the reflection of △ABC over the line  x = −2. Label the image of A as A′, the image of  B as B′ and the image of  C as C′.
Draw the reflection of  △A′B′C′ over the line x=2. Label the image of A′ as A′′, the image of B′ as B′′ and the image of C′ as C′′

60. Task #4 Draw a dilation of ABC with: Center A and scale factor 2.
Center B and scale factor 3. 
Center C and scale factor 1/2.

61. Guess That Transformation
Game Activity!
Guess That Transformation

62. Rules… Get into pairs of two.
You will each receive a game board and circle a graph of your choice. (DO NOT SHARE WITH YOUR PARTNER!)
The game is very similar to Guess Who. You will each take turns asking your partner a question about their graph in order to try and figure theirs out.
Sample Questions include:
“Does your graph contain a translation?” If the answer is no, then cross out all the graphs that have translations. If the answer is yes, cross out all graphs that do not contain translations.
“Does your graph contain a reflection about the x-axis?” If the answer is yes, cross out the ones without an x-axis reflection, etc.
First one to guess properly wins!!

63. NONE! Have a great weekend!!
Homework
NONE! Have a great weekend!!

65. Wednesday January 13th
Dilations and Transformations Task Cards

66. Transformations Pop Quiz!

69. Bell Ringer Thursday January 14th, 2016
1. List what you know about congruent shapes.
2. What do you think the difference between “congruent” and “similar” might be?
Bell Ringer Thursday January 14th, 2016

70. Finish Yesterday’s Task Cards or Work on Portfolio
15 minutes

71. Similarity
MAFS.8.G.1.4 (DOK 2): Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them.
Define similar figures as corresponding angles are congruent and corresponding sides are proportional.
Recognize symbol for similar.
Describe the sequence of rotations, reflections, translations, or dilations that exhibits the similarity between 2-D figures using words and/or symbols.
Apply the concept of similarity statements.
Reason that a 2-D figure is similar to another if the second can be obtained by a sequence of rotations, reflections, translations, or dilation.

72. Similarity vs. Congruence
Two shapes are similar when the only difference is size (and possibly a rigid motions—to move, turn or flip around) So, resizing is key. Congruent shapes can ONLY be translated, rotated, or reflected… there is absolutely NO resizing in congruent shapes.

73. ALL OF THESE ARE SIMILAR!!

74. Do these figures look similar?
Yes, they look like the same shape, but they are different in size.
How can we prove that they are similar? What would we need to do?
We would need to show that they could become the same size by dilating one of the figures.

75. What other transformation is taking place?
Is that all we have to do???
Once we have shown that the image can be dilated, we still have to show the basic rigid motion that is taking place.
What other transformation is taking place?
ROTATION!

76. The scale factor is ½, so are we growing or shrinking?
1st
3rd
2nd
Answer: We would have to describe a dilation followed by a translation.
Question: How could we show that triangle A”B”C” is SIMILAR to triangle ABC?

77. WHITEBOARDS!! (Tell me if the transformation is similar or congruent)

78. WHITEBOARDS!! (Tell me if the transformation is similar or congruent)

79. WHITEBOARDS!! (Tell me if the transformation is similar or congruent)

80. Which one of the four hexagons is not similar to the other three?
WHITEBOARDS!!
Which one of the four hexagons is not similar to the other three?
Answer: A

81. Exit Ticket B

82. Homework Thursday, January 14, 2016
Worksheet on Transformations and their new coordinates.

83. Transformations Classwork
PDF File

85. Bell Ringer Wednesday, January 13, 2016

86. Angles
MAFS.8.G.1.5 (DOK 2): Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
Define similar triangles.
Define and identify transversals.
Identify angles created when a parallel line is cut by a transversal (alternate interior, alternate exterior, corresponding, vertical, adjacent, etc.)
Justify that the sum of interior angles equals 180.
Justify that the exterior angle of a triangle is equal to the sum of the two remote interior angles.
Use Angle-Angle Criterion to probe similarity among triangles. (Give an argument in terms of transversals, why this is so.)

87. Scale for Angles

88. Question #1

89. Question #2

90. Question #3

91. Question #4

92. Exit Ticket