This learning module discuss the Unit of Transformation in the high school Geometry curriculum. Building on students' knowledge of Math 8, students will be able to understand the concept of transformation, and perform translation, reflection, rotation and Compositions of Transformations.
Geometry, Transformation, Translation, Reflection, Rotation, Compositions of Transformations
This learning module follows closely to The Learning Experience described in chapter 10: Measuring learning from the book of New learning: Elements of a science of education (Kalantzis & Cope, 2012). Using the reflexive pedagogy and the CGScholar platform, I hope to provide The Learning Experience with Synergistic feedback for the learner (Kalantzis & Cope, 2012). From diagnostic assessment to formative assessment to summative assessment, I will carefully parse out different types of assessments such as selected-response assessment and supply response assessment and utilize them (Kalantzis & Cope, 2012). I hope to realize the synergistic feedback system by applying "Agenda for new learning and assessment: 7 principles" (Kalantzis & Cope, 2012). I use standards-based assessments to students' performance based on standards instead of norms (Kalantzis & Cope, 2012).
I have been teaching high school Geometry for almost 6 years. In the years of service, I have been continuing to update my classroom practice in order to gain a better understanding of my students' overall performance. I have made efforts into crafting my skills of conducting assessments and using a wide variety of forms of assessments to assess my students.
However, after taking this course about Assessment for Learning, I have a better and broader picture of the history of the assessment, the learning cycle, the synergistic feedback and etc (Kalantzis & Cope, 2012). In this learning module, I intentionally realize the Synergistic feedback system through The Learning Experience: Diagnostic Assessment, Formative Assessment, and Summative Assessment in the CGScholar platform (Kalantzis & Cope, 2012).
Target Learner: High school and middle students who are qualified to take high school Geometry based on the Common Core State Standards.
Prior Knowledge:
Learners are expected to have taken Math 8 and have mastered the Geometry standards in Math 8.
Curriculum Standards:
G.CO.2 Represent transformations in the plane using, for example, transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not.
G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent.
Intended Learning Outcomes:
After learners finish this learning module, learners will be able to -
Anticipated duration: Learners should be able to complete this learning module in five 90-minute sessions.
Material Requirement:
Textbook: John A Carter, Gilbert J Cuevas, Roger Day, & Malloy, C. E. (2018). Glencoe Geometry (2018 ed.). USA: McGraw-Hill Education.
Apps: Desmos Graphing Calculator, Desmos Geometry and Geogebra.
Target Learner: High school and middle students who are qualified to take high school Geometry based on the Common Core State Standards.
This leanring module is designed for high school Geometry curriculum. However, the students in the Geometry class may be a mix of students who have been accelerated, students who are in the regular level and students who are behind.
Prior Knowledge: Learners are expected to have taken Math 8 and have mastered the Geometry standards in Math 8.
Although students are expected to come in the class with a certain level of understanding according to these standards, some of them may still need some more practice to catch up with the current level of learning objectives.
Curriculum Standards:
These are the targeted learning standards students are expected to master through this learning module. Some students may have completed mastered them before they enter the classroom so try to differentiate the lessons in a way that students can learn and grow from their current level.
Intended Learning Outcomes:
After learners finish this learning module, learners will be able to -
The learning activivities and tasks are designed based on these learning objectives. Teachers will want to add relevant activities if appropriate.
Anticipated duration: Learners should be able to complete this learning module in five 90-minute sessions.
Althought the learning module is designed for five 90-minutes period. Students may learn faster and slower based on different conditions. It is possible to extend one more period or finish the learning module by using 4 periods.
Material Requirement:
Textbook: John A Carter, Gilbert J Cuevas, Roger Day, & Malloy, C. E. (2018). Glencoe Geometry (2018 ed.). USA: McGraw-Hill Education.
Apps: Desmos Graphing Calculator, Desmos Geometry and Geogebra.
Textbook comes with a teacher's edition which includes differentiated questions and prompts for teachers' use.
Learning Objectives (Student will be able to):
Diagnostic Assessment:
Content Presentation:
Video 1: Ehlert, D. (Producer). (2018). Transformations. Retrieved from https://youtu.be/lpTFIjpRFgY
Formative Assessment: Work on Des-pattern using this link.
Summative Assessment:
Learning Objectives (Student will be able to):
This update is for students to have an inital contact of transformation. Using real world applications to facilitate students' understanding about transformation. By allowing students to play with simulation, students will experience the concept of transformation at hand.
Active knowledge Making (Diagnostic Assessment):
The comment-making prompt allows students to recall the concepts of transformation they learned in Math 8. Teachers could use the comments written by students at hand to have better understanding of students' ability and therefore be able to set the level of instruction.
Multimodal Meaning (Content Presentation):
Teachers could utilize the content for instruction and at the same time use professional judgement to determine which parts to skip or to elaborate.
Differentiated Instruction (Formative Assessment):
Des-pattern allows students at different level to enter. The instructor will want to give instructions based on the different needs of students.
Metacognition/Active knowledge making (Formative Assessment):
Make an Update: Use 200 words to describe the single transformation happened in picture 1 and picture 2. Respond to at least 3 of your peers. Use @Name to discuss it with your peers.
This activity allows learners to actively making knowledge (the definition of transformation) and receive feedback under the culture of knowledge reciprocity.
Learning Objectives (Student will be able to):
Diagnostic Assessment:
Video 2: Ehlert, D. (Producer). (2017). Translating a Figure Using a Translation Rule. Retrieved from https://youtu.be/MMgT_qSNv9k
Content Presentation: Translation
Video 3: MashUpMath (Producer). (2015). How Do I Translate a Figure? | Common Core Geometry Transformations. Retrieved from https://youtu.be/j87gj_KH9pA
Formative Assessment: Work on Desmos Activity: Translations with Coordinates using this link.
Summative Assessment:
Learning Objectives (Student will be able to):
Students are expected to understand the concept of translation and perform the translation using coordinate rules. The instructor will want to guide students into the direction of applying coordinate rules of translation.
Active knowledge Making/Collaborative Intelligence (Diagnostic Assessment):
Students will be using the CGScholar to make comments about translation they have experienced in Math 8. By reading the comment from their peers, students are able to collaboratively gain knowledge with their peers.
Ubiquitous learning/ Multimodal Meaning (Content Presentation): Translation
This presentation allows learners to learn the concept "translation" in a multimodal form. Videos are always available as long as students are able to access the internet, which creates the ubiquitous environment for students to follow.
Ubiquitous learning/Recursive Feedback (Formative Assessment): Work on Desmos Activity: Translations with Coordinates using this link.
The desmos activity allows students to review and re-do the activity via internet support. It also has immediate feedback for students to modify their learning path and decisions.
Differentiated Instruction/Metacognition (Formative Assessment):
Make an Update: Work on "Practice: Translate shapes" and "Determine translations" via the provided links. Screenshot one question and your solution from each practice (total of 2 pictures) and use 200 words to describe your thought process and what you have learned. Use @Name to discuss it with your peers.
The update facilitates differentiated instruction by allowing students at different levels to have an entry point. By responding to the peers, students will deepen their understanding through the metacognition.
Learning Objectives (Student will be able to):
Diagnostic Assessment:
Video 4: Ehlert, D. (Producer). (2017). Reflection across y = -x (Notice/Wonder). Retrieved from https://youtu.be/lHBobttJvZ0
Content Presentation: Reflection
Video 5: Math, M. (Producer). (2015). How Do I Reflect a Figure? | Common Core Geometry Transformations. Retrieved from https://youtu.be/ouNp8FtgiEE
Formative Assessment:
Video 6: Ehlert, D., & Ward, J. (Producer). (2020). Geo-5.3 Reflections. Retrieved from https://teacher.desmos.com/activitybuilder/custom/5e4be28b1511530a73476085
Video 7: KhanAcademy (Producer). (2020). Practice: Reflect points. Retrieved from https://www.khanacademy.org/math/basic-geo/basic-geo-transformations-congruence/basic-geo-reflections/e/performing-reflections-on-the-coordinate-plane
Video 8: KhanAcademy (Producer). (2020). Practice: Determine reflections. Retrieved from https://www.khanacademy.org/math/basic-geo/basic-geo-transformations-congruence/basic-geo-reflections/e/determine-reflections
Summative Assessment:
Learning Objectives (Student will be able to):
In this update, students will be able to understand the concept of "reflection," then successfully apply the rule of reflection.
Active knowledge Making/Collaborative Intelligence (Diagnostic Assessment):
Making the comment allows students to actively review and think about the concept of "reflection." By reading the comments from the peers, students will be able to collaboratively create their meaning of the learning target- "reflection."
Ubiquitous learning/ Multimodal Meaning (Content Presentation): Reflection
The video presents the concept of reflection in a multimodal way. Students will be able to re-learn, re-wind and re-watch the material via internet and attain the ubiquitous learning.
Ubiquitous learning/Recursive Feedback (Formative Assessment):
The formative assessment encourages the recursive feedback by providing differentiated feedback via the software. The activity can be accessed through the internet. Therefore it creates the ubiquitous learning environment for the learners.
Differentiated Instruction/Metacognition (Formative Assessment):
The open-ended question creates an opportunity for students at different levels to deepen their knowledge about reflection. The recursive feedback provided by peers opens up the metacognition view of the concept addressed.
Learning Objectives (Student will be able to):
Diagnostic Assessment:
Video 9: Ehlert, D. (Producer). (2017). 90 Degree Rotation Notice/Wonder. Retrieved from https://youtu.be/RSebLNqKKSM
Content Presentation: Rotation
Video 10: KhanAcademy (Producer). (2015). Points after rotation | Transformations | Geometry | Khan Academy. Retrieved from https://youtu.be/6nUMiJfHLSA
Video 11: KhanAcademy (Producer). (2015). Rotating about arbitrary point | Transformations | Geometry | Khan Academy. Retrieved from https://youtu.be/uuDQkhx6TAI
Formative Assessment:
Video 12: Ehlert, D., & Ward, J. (Producer). (2020). Geometry: Rotation. Retrieved from https://teacher.desmos.com/activitybuilder/custom/5e5344b7dffdce7adc5265f1
Summative Assessment:
Image 6: Ehlert, D. (Producer). (2020). Rules of Rotation. Retrieved from https://whenmathhappens.com/2017/08/23/translations-reflections-rotations/
Learning Objectives (Student will be able to):
Students will be able to understand the concept of "rotation" and explore rotation through simulation. The instructor could differentiate the lesson based on students' understanding.
Active knowledge Making/Collaborative Intelligence (Diagnostic Assessment):
The active knowledge making is realized via the activity of making comments about the concept rotation. By reading the comments left by other peers, students are able to collaboratively create new meaning of the concept- rotation.
Ubiquitous learning/ Multimodal Meaning (Content Presentation): Rotation
The video presents the concept of rotation in an multimodal environment. Since the video can be reached through the internet, it allows learners to learn the material in an ubiquitous way.
Ubiquitous learning/Recursive Feedback (Formative Assessment):
The activity provides immediate feedback for students to modify their learning behavior. Through the ubiquitious learning environment enabled by the internet, the learners are able to reach the content and learn wherever they are.
Differentiated Instruction/Metacognition (Formative Assessment):
The open-ended question provide a chance for learners at different levels to reach the content. Through the process of making comments on peers' update, learners are able to see the content in a metacognition point of view.
Learning Objectives (Student will be able to):
Diagnostic Assessment:
Video 12: Desmos, & Ward, J. (Producer). (2020). Transformation-Composition of Transformations. Retrieved from https://youtu.be/-5Nz3ZcoU7w
Content Presentation: Composition of Transformations
Video 13: Foundation, C.-. (Producer). (2014). Composition of Transformations: Lesson (Geometry Concepts). Retrieved from https://youtu.be/pf3Sz5yqm7g
Formative Assessment:
Summative Assessment: Make a 200-word update explaining the concept of compositions of transformation in your own words. Respond to 3 of your peers.
Learning Objectives (Student will be able to):
Students will be able to experience and learn how to perform compositions of transformation. Many students get confused with compositons of transformation and a single move of transformation. The instructor can pay some attention to the students' needs.
Active knowledge Making/Collaborative Intelligence (Diagnostic Assessment):
Making comment on the concepts students have acquired allow students to actively making meaningful connection to the knowledge. Through collaborative intelligence, students are able to deepen their understanding of the concept- compositions of transformation.
Ubiquitous learning/ Multimodal Meaning (Content Presentation): Composition of Transformations
The video allows students to watch, rewind and re-learn at all time and therefore create an ubiquitous learning environment using the multimodal content.
Ubiquitous learning/Recursive Feedback (Formative Assessment):
The activity allows students to practice under a ubiquitous environment with recursive feedback. Students will then be able to modify their learning decision by the feedback provided from the activity.
Differentiated Instruction/Metacognition (Formative Assessment): Make a 200-word update explaining the concept of compositions of transformation in your own words. Respond to 3 of your peers.
By creating the update, students will be able to see the concept of compositions of transformation under the metacognition point of view and are able to learn from their levels and therefore the instructor will be able to attain the goal of differentiation.
Geometry Peer-review Project
After learning the concepts of Transformation in this Geometry unit, I would like to invite you to experience the power of transformation.
The Drawing: You are going to create a design to be printed as part of a coloring book. The goal is to create something aesthetically pleasing and fun to color (lots of shapes).
Use Desmos Geometry to Design your own shape transformation.
Requirements for Meeting the Standard:
The requirement for Exceeding the Standard:
Examples of work: Example 1, Example 2, Example 3
Rubrics for the Peer-review Project:
Geometry Peer-review Project
After learning the concepts of Transformation in this Geometry unit, I would like to invite you to experience the power of transformation.
Multimodal meaning/Active knowledge making: Through the pratice, the students will be able to make their own meaning of the learning unit through creating multimodal content.
The Drawing: You are going to create a design to be printed as part of a coloring book. The goal is to create something aesthetically pleasing and fun to color (lots of shapes).
Use Desmos Geometry to Design your own shape transformation.
Ubiquitous learning/active knowledge making: By creating the end product using technology (Desmos Geometry), students will be able to make their own knowledge in an ubiquitous environment.
Requirements for Meeting the Standard:
Pick at least 3 different shapes to work with (triangle, quadrilateral, circle, hexagon and etc.)
Create and use 4 transformations (translation, reflection, rotation, and symmetry) in each shape to create a design/ drawing.
Write a 600 words project about your design.
The requirements of the project provide specific instruction to keep students' learning accountable.
The requirement for Exceeding the Standard:
Shade the designs and use different colors.
Your design must have free and locked points.
The requirment illustrates the level that is exceeding the standards.
Examples of work: Example 1, Example 2, Example 3
Metacognition: The examples of work provide a metacognition point of view for the students to improve from the examples shown.
Rubrics for the Peer-review Project:
Network, N. T. (2017). Knowledge and Thinking Rubric for Math Problem Solving, Grade 12. Retrieved from https://docs.google.com/document/d/1gWzpBpA7ocF4GnnAEq0C6UeIf1SR1DIB1NWaIJWr-uE/edit
Recursive feedback: Peer-review provides recursive feedback for students to improve their work under multiple resources of feedback instead of waiting for the teachers' feedback passively.
Desmos (Producer). (2020). Des-Patterns. Retrieved from https://teacher.desmos.com/activitybuilder/custom/589a31ddda95a7a50509daa5
Desmos (Producer). (2020). Translations with Coordinates. Retrieved from https://teacher.desmos.com/activitybuilder/custom/586ebd135e41050a0834a51d
Desmos, & Ward, J. (Producer). (2020). Transformation-Composition of Transformations. Retrieved from https://youtu.be/-5Nz3ZcoU7w
Ehlert, D. (Producer). (2017). 90 Degree Rotation Notice/Wonder. Retrieved from https://youtu.be/RSebLNqKKSM
Ehlert, D. (Producer). (2017). Reflection across y = -x (Notice/Wonder). Retrieved from https://youtu.be/lHBobttJvZ0
Ehlert, D. (Producer). (2017). Translating a Figure Using a Translation Rule. Retrieved from https://youtu.be/MMgT_qSNv9k
Ehlert, D. (Producer). (2018). Transformations. Retrieved from https://youtu.be/lpTFIjpRFgY
Ehlert, D. (Producer). (2020). Rules of Rotation. Retrieved from https://whenmathhappens.com/2017/08/23/translations-reflections-rotations/
Ehlert, D., & Ward, J. (Producer). (2020). Geo-5.3 Reflections. Retrieved from https://teacher.desmos.com/activitybuilder/custom/5e4be28b1511530a73476085
Ehlert, D., & Ward, J. (Producer). (2020). Geometry: Rotation. Retrieved from https://teacher.desmos.com/activitybuilder/custom/5e5344b7dffdce7adc5265f1
Foundation, C.-. (Producer). (2014). Composition of Transformations: Lesson (Geometry Concepts). Retrieved from https://youtu.be/pf3Sz5yqm7g
Kalantzis, M., & Cope, B. (2012). New learning: elements of a science of education: Cambridge University Press.
KhanAcademy (Producer). (2015). Points after rotation | Transformations | Geometry | Khan Academy. Retrieved from https://youtu.be/6nUMiJfHLSA
KhanAcademy (Producer). (2015). Rotating about arbitrary point | Transformations | Geometry | Khan Academy. Retrieved from https://youtu.be/uuDQkhx6TAI
KhanAcademy (Producer). (2020). Practice: Determine reflections. Retrieved from https://www.khanacademy.org/math/basic-geo/basic-geo-transformations-congruence/basic-geo-reflections/e/determine-reflections
KhanAcademy (Producer). (2020). Practice: Determine translations. Retrieved from https://www.khanacademy.org/math/basic-geo/basic-geo-transformations-congruence/basic-geometry-translations/e/defining-translations
KhanAcademy (Producer). (2020). Practice: Identify transformations. Retrieved from https://www.khanacademy.org/math/basic-geo/basic-geo-transformations-congruence/transformations-intro-basic-geo/e/identify-transformations
KhanAcademy (Producer). (2020). Practice: Reflect points. Retrieved from https://www.khanacademy.org/math/basic-geo/basic-geo-transformations-congruence/basic-geo-reflections/e/performing-reflections-on-the-coordinate-plane
KhanAcademy (Producer). (2020). Practice: Translate shapes. Retrieved from https://www.khanacademy.org/math/basic-geo/basic-geo-transformations-congruence/basic-geometry-translations/e/translations
MashUpMath (Producer). (2015). How Do I Translate a Figure? | Common Core Geometry Transformations. Retrieved from https://youtu.be/j87gj_KH9pA
Math, M. (Producer). (2015). How Do I Reflect a Figure? | Common Core Geometry Transformations. Retrieved from https://youtu.be/ouNp8FtgiEE
Network, N. T. (2017). Knowledge and Thinking Rubric for Math Problem Solving, Grade 12. Retrieved from https://docs.google.com/document/d/1gWzpBpA7ocF4GnnAEq0C6UeIf1SR1DIB1NWaIJWr-uE/edit
onlinemath4all.com (Producer). (2020). REFLECTION TRANSFORMATION IN GEOMETRY. Retrieved from https://www.onlinemath4all.com/reflection-transformation.html