Introduction
This WebQuest is designed to help you learn the skills necessary to master the Common Core Standards for 8th grade geometry. Take your time, master each step before moving on to the next, be a team player, and be sure to ask your teacher if you have any questions.
Task
Throughout this WebQuest you will work with a team to learn about congruency and transformations, then complete several tasks to provide practice with the learned skills. Once you have demonstrated mastery with identifying congruent shapes and recognizing/performing translations, reflections, rotations, and dilations, you will complete a team project of your choosing.
As a teacher, it is my responsibility to provide support and guidance along the way, so please ask for help or let me know if you have any questions...after all, I want you to succeed! As a student, it is your responsibility to follow the directions outlined in this WebQuest, complete each task in sequential order, and seek help when needed. Enjoy the WebQuest!
Process
Think back to previous math lessons involving shapes. Do you remember what makes shapes congruent? Congruent shapes are figures with the exact same shape and size. More formally, congruent shapes contain line segments of the same length, angles of the same measure, and the same parallel properties. Essentially this means if you were to stack the two shapes on top of each other, they would align exactly. Looking at the triangles below, we can see that triangle ABC is congruent (≅) to triangle XYZ.
(Math Planet, n.d.)
Sometimes it is difficult to determine if two shapes are congruent because one of the shapes has been manipulated, or transformed. These transformations can happen through translations, reflections, rotations, and dilations. Each member of your team will research one of these transformations, then teach the other three team members about the properties of that transformation.
Task 1: The Jigsaw Puzzle
Like a jigsaw puzzle, once you each complete your research on the assigned transformation, you will have to come together as a team to discover the big picture of transforming congruent and similar shapes. Your first task is to individually research your assigned transformation. Some links have been provided below, but feel free to search the Internet for additional information. Remember, in order to teach the rest of your team about the assigned transformation, you must first become an expert on it. Do your best, but please ask for help if you need it.
Once you have finished your research, each team member must prepare a lesson on the assigned transformation to present to their teammates. The lesson should include a detailed description of the assigned transformation, 1 real-world example of the transformation, three different demonstrations performing the transformation on a coordinate plane, and some type of review game, task or activity to help your teammates practice recognizing and using the transformation. In addition to these things, you will also be graded by your peers on your communication skills, content knowledge, and helpfulness...so make sure you are prepared! As you and your teammates present your lessons to each other, be sure to complete the Unit Vocabulary sheet to use for future reference. See the Evaluation section for a detailed grading rubric.
Student 1: Translation
(Maths Accelerator, n.d.)
A translation is a type of transformation that involves sliding the shape from one position to another.
Math is Fun – Translation (Be sure to test your skills with the “Your turn” questions at the bottom of the page.)
Student 2: Reflection
(Maths Accelerator, n.d.)
A reflection is a type of transformation that involves using a line of reflection to create a mirror image of the shape.
Math is Fun – Reflection (Be sure to test your skills with the “Your turn” questions at the bottom of the page.)
Student 3: Rotation
(Doll, n.d.)
A rotation is a type of transformation that involves rotating, or turning, the shape on a fixed central point.
Math is Fun – Rotation (Be sure to test your skills with the “Your turn” questions at the bottom of the page.)
Student 4: Dilation
(Maths Accelerator, n.d.)
A dilation is a type of transformation that involves making an object larger or smaller while still maintaing the same proportions.
Math is Fun – Dilation (Be sure to test your skills with the “Your turn” questions at the bottom of the page.)
Task 2: Self-Study
Now that you have been introduced to the four types of transformations, take some time to practice and explore each in greater detail. Here are some websites that may help you, but be sure to ask for help if you need it.
Identifying Unknown Transformations
Identifying Reflections, Rotations, and Translations
Task 3: Team Project
Now that your team has mastered the skills necessary to identify and perform transformations on congruent and similar shapes, it is time to show off your new skills. As a team you can choose one of the following three different project options:
Option 1: Create a wallpaper that exhibits a tessellation involving a single shape that undergoes at least one type of transformation. The more complex the shape and the more transformations used in the tessellation, the more points will be awarded for the project.
Option 2: Create a podcast teaching rising 8th graders about transformations. Be sure to include all key definitions, explain each transformation in detail, and provide both real-world and coordinate plane examples of each.
Option 3: Create a book that can be used as a reference when teaching others about transformations. Be sure to include all key definitions, explain each transformation in detail, and provide both real-world and coordinate plane examples of each.
Remember this is a team project and your individual grade will reflect the effort you put into helping the team create the chosen project. See the Evaluation section for a detailed grading rubric.
Evaluation
Peer Evaluation
|
Task 1 (Peer Evaluation) |
Beginning 1 |
Developing 2 |
Qualified 3 |
Exemplary 4 |
Score
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Lesson Preparation |
The lesson only contained a detailed description of the assigned transformation. |
The lesson contained a detailed description of the assigned transformation and 1 real-world example. |
The lesson contained a detailed description of the assigned transformation, 1 real-world example, and 3 demonstrations of the transformation on a coordinate plane. |
The lesson contained a detailed description of the assigned transformation, 1 real-world example, 3 demonstrations of the transformation on a coordinate plane, and a review activity. |
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|
Content Knowledge |
The student demonstrated minimal knowledge of the assigned transformation. |
The student demonstrated moderate knowledge of the assigned transformation. |
The student demonstrated adequate knowledge of the assigned transformation. |
The student demonstrated superior knowledge of the assigned transformation. |
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|
Communication Skills |
The student provided minimal communication. |
The student’s communication was somewhat difficult to understand or follow. |
The student’s communication was easy to understand and follow. |
The student’s communication was clear, concise, and effective. |
|
|
Helpfulness |
The student’s lesson did not help me better understand the assigned transformation. |
The student’s lesson somewhat helped me better understand the assigned transformation. |
The student’s lesson was helpful in learning about the assigned transformation. |
The student’s lesson was very helpful in learning about the assigned transformation and he/she was able to answer most questions. |
|
Team Evaluation
|
Task 3 (Team Assignment) |
Beginning 1 |
Developing 2 |
Qualified 3 |
Exemplary 4 |
Score
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|
Option 1: Tessellation |
The team did not create a proper tessellation using a single image. |
The team chose a simple single image to use in the tessellation, but did not perform any transformations. |
The team chose a simple single image to use in the tessellation, and performed 1-2 transformations. |
The team chose a complex image to use in the tessellation, and performed 3-4 transformations. |
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Option 2: Podcast |
The team created a podcast that provided a detailed description of each transformation. |
The team created a podcast that provided a detailed description and 1 real-world example of each transformation. |
The team created a podcast that provided a detailed description, 1 real-world example, and a demonstration of each transformation on a coordinate plane. |
The team created a podcast that provided a detailed description, 1 real-world example, a demonstration of each transformation individually on a coordinate plane, and a demonstration of a figure that has undergone multiple transformations. |
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|
Option 3: Book |
The team created a book that provided a detailed description of each transformation. |
The team created a book that provided a detailed description and 1 real-world example of each transformation. |
The team created a book that provided a detailed description, 1 real-world example, and a demonstration of each transformation on a coordinate plane. |
The team created a book that provided a detailed description, 1 real-world example, a demonstration of each transformation individually on a coordinate plane, and a demonstration of a figure that has undergone multiple transformations. |
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Participation |
The student demonstrated minimal participation in the team assignment. |
The student demonstrated moderate participation in the team assignment. |
The student demonstrated adequate participation in the team assignment. |
The student demonstrated superior participation in the team assignment. |
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Problem Solving |
Student does not try to solve problems or help others solve problems. |
Student does not offer solutions, but is willing to try those offered by others. |
Student improves on solutions suggested by others. |
Student actively seeks and suggests solutions to problems. |
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|
Communication |
Student does not listen with respect, argues with teammates, and does not consider other ideas. |
Student has trouble listening with respect and/or takes over group discussions. |
Student respectfully listens, discusses, and asks questions. |
Student respectfully listens, discusses, and asks questions that helps guide team progress. |
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Teamwork |
Student sometimes chooses not to help out and does not complete assigned tasks. |
Student is sometimes an active group member, but not consistently. |
Student is a strong team member who tries hard. |
Student is a true team member who works hard and helps others in the group. |
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Conclusion
Throughout this WebQuest you learned about congruency and transformations. You have learned to identify congruent shapes and recognize/perform translations, reflections, rotations, and dilations. I hope you have enjoyed the learning process and will continue to explore the concepts presented here.
Credits
Teacher Page
Introduction
This WebQuest was designed to assist in teaching 8th grade math students about the effects of translations, reflections, rotations, and dilations on congruent and similar figures.
Standards
8.G.1 - 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.
8.G.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.
8.G.3 - Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
8.G.4 - Understand that a two-dimensional figure is similar to another if the second figure 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.
Teacher Process
This WebQuest was initially designed to be completed in three weeks, considering about a week for the students to research their transformation and create their lesson, a week for the students to present their lesson and for self-study, and a week for the team project. Depending on the length of time you spend with the students each day and the pace at which your students are capable of working, you may be able to complete the WebQuest more quickly or need additional time for completion.
Feel free to substitute or subsidize the Internet lessons with mini-lessons of your own. Considering the concentration span of an average 8th grader, if you keep your lessons to 10-15 minutes each you will keep their attention and they will get more out of it.
There are a lot of opportunities for formative assessments built in to this WebQuest. As students are researching their assigned transformation, you can pull students together who are researching the same transformation to share their findings, answer any questions, provide additional guidance and support, and discuss their lesson plans. Throughout the self-study task, you can pull students for specific skill-focused activities or simply to perform quick-checks of their understanding of the material. Also, I highly recommend performing some type of assessment prior to beginning task 3, that way you ensure all students are on track for success and you can take the time to work with struggling students as needed. An assessment that is similar to what the students will see on standardized tests is a good option at this point.
Lastly, feel free to adapt this WebQuest to meet the needs of your students--I want them to succeed too!