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There are four types of rigid motions that we will consider: translation, rotation, reflection, and glide reflection.
Learning Target and Success Criteria:
SWBAT: apply their knowledge of the four types of rigid motions to create and artifact that illustrates an example of each, as listed in the lesson requirements.
OverArching Question:
OverArching Question:
Why would we want to move figures on a plane?
Essential Questions:
Essential Questions:
-Why are only four types of transformations needed to describe the motion of a figure?
How do you identify transformations that are rigid motions?
How do you portray the image of a figure under a reflection?
How do you portray the image of a figure under a translation?
How do you portray the image of a figure under a rotation?
Standards
Standards
D.E.S.E. Math Standards:
D.E.S.E. Math Standards:
Congruence
Experiment with transformations in the plane.
B. Understand congruence in terms of rigid motions.
C. Prove geometric theorems and, when appropriate, the converse of theorems.
D. Make geometric constructions.
Modeling with Geometry
A. Apply geometric concepts in modeling situations.
Standards for Mathematical Practice
1. Make sense of problems and persevere in solving them.
4. Model with mathematics.
5. Use appropriate tools strategically.
7. Look for and make use of structure.
Common Core Standards:
Common Core Standards:
Understand congruence and similarity using physical models, transparencies, or geometry software.
8.G.A.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.
In the approach taken here, two geometric figures are defined to be congruent if there is a sequence of rigid motions that carries one onto the other. This is the principle of superposition. For triangles, congruence means the equality of all corresponding pairs of sides and all corresponding pairs of angles. During the middle grades, through experiences drawing triangles from given conditions, students notice ways to specify enough measures in a triangle to ensure that all triangles drawn with those measures are congruent. Once these triangle congruence criteria (ASA, SAS, and SSS) are established using rigid motions, they can be used to prove theorems about triangles, quadrilaterals, and other geometric figures. Similarity transformations (rigid motions followed by dilations) define similarity in the same way that rigid motions define congruence, thereby formalizing the similarity ideas of “same shape” and “scale factor” developed in the middle grades. These transformations lead to the criterion for triangle similarity that two pairs of corresponding angles are congruent.
Technology Standards:
Technology Standards:
1.1 Empowered Learner
Students leverage technology to take an active role in choosing, achieving, and demonstrating competency in their learning goals, informed by the learning sciences.
1.3 Knowledge Constructor
1.3.d
Students build knowledge by actively exploring real-world issues and problems, developing ideas and theories and pursuing answers and solutions.
1.5 Computational Thinker
Students develop and employ strategies for understanding and solving problems in ways that leverage the power of technological methods to develop and test solutions.
1.6 Creative Communicator
Students communicate clearly and express themselves creatively for a variety of purposes using the platforms, tools, styles, formats and digital media appropriate to their goals.
1.6.a
Students choose the appropriate platforms and tools for meeting the desired objectives of their creation or communication.
Requirements and Grading:
Requirements and Grading:
Requirements of Project
Requirements of Project
Explain the following, as seen in a Real World Application:
At least 2 translations including vectors.
At least 1 translation mapping onto itself.
At least 2 reflections including lines of reflection.
At least 1 reflection mapping onto itself.
At least 2 rotations including center of rotation, direction, degrees.
At least 1 rotation mapping onto itself.
Grading Rubric:
Adding Screencastify:
Download your screencastify as an MP4!!
Student Choices:
Student Choices:
Option 1: Create a GIF & Screencast Results
Option 1: Create a GIF & Screencast Results
Instructions for Making an Animated GIF:
Open the Google Drawing Here
Watch the video to the right-->
Arrange your cars to show each rigid motion sequence.
Go to file/download/jpg or png
Once you've made each part of the sequence, go to: EZGIF.com
(ALTERNATE sites if that one is slow:
Upload your files and select your speed
Download your file
Play your file and narrate what is happening, using screencastify.
Do this for each of the required sequences.
**Tech Tip:
To upload more than one image at a time, hold the control key and click each file.
To upload a series (all in a row,) hold the shift key.
Option 2: Create an Animated GIF & Screencast
Option 2: Create an Animated GIF & Screencast
Screencast an Animation
Using SlimAnimation, create an animation
Watch the video to the right
Create by drawing with your finger
Run the Animation
Screencastify an explanation of what is happening in the animation and how it relates to the four types of rigid motion.
To resize in SlimAnimation, hold down the control button and drag corner.
To rearrange item order, click on the "arrange" button next to edit.
Option 3: Canva GIF & Screencast
Option 3: Canva GIF & Screencast
Screencast an Animation
Using Canva, create comic strips that show a gymnast in different sequences of Rigid Motion.
Watch the video to the right
Use the images provided in the folder to the right.
Screencastify an explanation of what is happening in each comic and how it relates to the four types of rigid motion.
**You MAY use any files you find. You don't HAVE to use the gymnast. I would, however, use only PNG files, because they have transparent backgrounds.
Option 4: Low-Tech and Familiar-Tech Drawing Option:
Option 4: Low-Tech and Familiar-Tech Drawing Option:
Draw and Write for Non-Tech on Google Doc (Low-Tech)
Draw and Write for Non-Tech on Google Doc (Low-Tech)
Kami Annotations and Drawings for Tech(Familiar-Tech)
Kami Annotations and Drawings for Tech(Familiar-Tech)
Open and Make a copy of the Doc
Instructions for Tech Option:
Use the Folder of Images to find examples of each sequence of rigid motion or draw your own examples with Kami Pen
Copy and Paste into the Kami doc
Use Annotation to Explain what each sequence shows in the text boxes
There are separate pages for each requirement.
Instructions for Non-Tech Option:
Draw an image in each of the boxes to show each type of sequence of rigid motion.
Give a written explanation, in your own words, to show that you understand the concept.
There is a separate page for each requirement.
Option 5: No Tech: Crash Reconstruction
Option 5: No Tech: Crash Reconstruction
Print out two copies of this sheet and one of the map.
Cut out the cars
Line up the cars on the map sheet to show the different motions
Write on post-its to show which motion you are illustrating.
Final Steps:
Final Steps:
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