Lesson 10-7 Rotations Textbook Pages: Homework Study notes for open note bellwork quiz on all 4 types of transformations.

Transcription

1 Course: 7 th Grade Math DETAIL LESSON PLAN Tuesday, January 10 / Wednesday, January 11 Student Objective (Obj. 3d) TSW learn to identify the following geometric transformation types: 3) Rotations and 4) Dilations. Lesson 10-7 Rotations Textbook Pages: Dilations Not in book Homework Study notes for open note bellwork quiz on all 4 types of transformations. Last Night s Homework WS Translations / Reflections (9 problems) Bellwork MCT2 Buckledown 118 (Reflection) & 119 (Translation) Prior Knowledge Last time we met, we learned about TRANSFORMATIONS! Display same introduction transparencies as yesterday: Transparency #1 : Transformers! Transparency #2: Definition & tree map illustration We focused our lesson on Translations and Reflections. Anticipatory Set TODAY, we will talk about the other two types of transformations Rotations and Dilations. Play song, Upside Down, Round and Round by Sister Sledge as an introduction to Rotations! Why do we need to learn about these transformations? Example 1 MECHANICAL ENGINEERS design and produce all kinds of mechanical devices. They use what s called a CAD system to create realistic geometric models of objects on a computer screen. They can rotate these images to view them from any angle they desire. Example 2 In our SOLAR SYSTEM the planets rotate around the sun. Teacher Input (Rotations) Review bellwork. Display images of rotations in the real world and play Sister Sledge song to reinforce what a rotation is. Pass out student notes. Have students read the notes on rotation to themselves. Display an example of a rotation on the projector for the students to refer to as they read their notes. Review the notes with the students. Demonstrate the different rotations using the clock transparency. Allow students to work the you try problems. (Dilations) Review the notes with the students Display transparencies of rotations and dilations. Call upon students to name the transformation and which degree of rotation is applicable. Classwork: Worksheet Rotation / Dilation (13 problems) Extra Practice: MCT Buckledown 113 & 116 (Graphing Translations and Reflections) Assessment Questions students for understanding. Observation students as they work on their classwork. Bellwork quiz next class on all transformations. Closure What kind of transformation (or movement) is a rotation? Turn What kind of angle does the time 6 o clock make? 180 What kind of transformation (or movement) is involved with dilation? Change in size What real-life example did I give to illustrate rotations? CAD system for Boeing, Planets rotating around the sun What real-life example did I give to illustrate dilations? Pupils and effect sun has on them

2

3

4 Name: Answer Key Period: Translation / Reflections Identify the correct transformation type for the each of the graphs below as either a Translation( slide) OR Reflection( flip) 1) 2) 3) Last Night s HW Answer: Translation Reflection Reflection 4) 5) 6) Answer: Translation Reflection Translation 7) Looking at the two objects below, which one would be considered the image? ABC or A B C B A C B A C

5 8) Graph figure ABCD using the coordinates A (2, 1), B (4, 5), C (7, 4), D (5, 1). Then graph the TRANSLATION of figure ABCD left 8 units, then down 4 units. Finally, label your new image using prime notation (A B C D ). 9) Graph the REFLECTION of figure ABC across the x-axis. Then, label your new image using prime notation (A, B, C ).

6 The word transform means to change. Chevy Camaro Bumblebee

7 In geometry, a transformation changes the position of a figure on a coordinate plane. What that really means is that a figure is moving from one place to another. There are 4 basic types of transformations. 3 deal with changing the position of a shape 1 pertains to a figures change in size. Transformations Translation Reflection Rotation Dilation Position Position Position Size Slide Flip Turn

8 Student Notes 10-7 Rotations Textbook Rotation = Turn A rotation is a transformation that turns a figure about a fixed point called the center of rotation. An object and its rotation are the same shape and size, but the figures are turned in different directions. The rotation of an object is called its image. If the original object was labeled with letters, such as triangle ABC, the image may be labeled with the same letters followed by a prime symbol, A'B'C'. (See transparency on projector) Rotations can occur in either a clockwise or counterclockwise direction. Clockwise (same direction as the hands of a clock) Counter-clockwise (opposite direction) To work with rotations, you need to be able to recognize angles of certain sizes. A clock is a good example that illustrates the different angles we ll be working with when looking at rotations: 90 angle 180 angle 270 angle 360 angle 3:00 o clock 6:00 o clock 9:00 o clock 12:00 o clock You Try! Estimate the angle measure of each rotation. Is the rotation clockwise or counter-clockwise? 1. Degree: 2. Degree: 3. Degree: Direction: Direction: Direction:

9 Example Rotation - 90 Clockwise (Solid to Dashed) B A A C C B

10 Dilation = Size Change A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. A good real-life illustration of dilation would be our pupils and how they react to sunlight. Our pupils reduce in size (or get smaller) when we are in the sunlight. Our pupils enlarge in size (or get bigger) when it s dark. Examples of dilation with images: Figure A: Figure B:

11 Transparency Lesson 10-7 Rotations in Professions A CAD system used for Boeing airplanes. (CAD stands for computer aided design)

12 Transparency Lesson 10-7 Rotations in Science In our SOLAR SYSTEM, the planets rotate around the Sun.

13 Identify the Transformation: Answer: Dilation

14 Identify the Transformation: Answer: Rotation 90 Clockwise 270 Counter-Clockwise

15 Identify the Transformation: Answer: Rotation 180

16 Identify the Transformation: Answer: Dilation

17 Identify the Transformation: Answer: Rotation 270 Clockwise 90 Counter-Clockwise

18 Identify the Transformation: Answer: Rotation 180

19 Name: Period: Classwork Rotation / Dilation There are 4 types of transformations: Translation= slide, Reflection= flip, Rotation= turn, Dilation= size change Identify the correct transformation type for the each of the graphs below. 1) 2) 3) Answer: 4) 5) 6) Answer: 7) 8) 9) Answer:

20 10) Circle the 2 transformations below that would best represent a 90 clockwise rotation from the solid figure to the dashed image. 11) Circle the 2 transformations below that would best represent a 180 rotation from a point of origin. 12) Circle the transformation below that would best represent a 90 counter-clockwise rotation from a point of origin. 13) Looking at the two objects below, which one would be considered the image? ABC or A B C Explain your answer:. B A C B A C

21 Name: Answer Key Period: Classwork Rotation / Dilation There are 4 types of transformations: Translation= slide, Reflection= flip, Rotation= turn, Dilation= size change Identify the correct transformation type for the each of the graphs below. 1) 2) 3) Answer: Translation Reflection Rotation 4) 5) 6) Answer: Dilation Reflection Translation 7) 8) 9) Answer: Dilation Rotation Reflection

22 10) Circle the 2 transformations below that would best represent a 90 clockwise rotation from the solid figure to the dashed image. Graph 1 and Graph 3 11) Circle the 2 transformations below that would best represent a 180 rotation from a point of origin. Graph 1 and Graph 4 12) Circle the transformation below that would best represent a 90 counter-clockwise rotation from a point of origin. Graph 2 13) Looking at the two objects below, which one would be considered the image? ABC or A B C Explain your answer: Images are labeled using Prime Notation. B A C B A C

23

24

25

26