Grade 8 Geometry Lesson Introduction to Transformations
1. Analyze Learners
Grade Level: 8
Ethnicity: 43% Asian, 11% Hispanic, 41% White
School Supports: approximately 10% of students receive English language learner support, 5% receive Title 1 support, 5% receive special education services and 5% are classified as high-risk minority students.
Learning Background: Typically 8th grade math content builds upon 7th grade standards. Yet, this is a new, self-contained, topic for students. Students are typically highly engaged since the topic is new to them, but also because it has relevance to the real world. This lesson will be an introduction to rigid geometric transformations (translation, reflections & rotations).
Demographics: Regular education classroom at grade level mathematics, students with learning disabilities are included in all classroom activities.
8.G.1 Verify experimentally the properties of rotations, reflections, and translations.
ISTE Student Standards for Information and Technology
Empowered Learner
Digital Citizen
Knowledge Constructor
Innovator Designer
Computational Thinker
Creative Communicator
Global Collaborator
Learning Objectives Students will be able to understand that two figures are congruent if you can describe them through a series of transformations by verifying experimentally the properties of rotations, reflections and translations.
Learning Targets Upon the completion of this geometry lesson, 8th grade students will be able to:
Describe, using academic language, the effect of a translation on a two-dimensional figure.
Describe, using academic language, the effect of reflection on a two-dimensional figure.
Describe, using academic language, the effect of rotation on a two-dimensional figure.
MP #1 Make sense of problems and persevere in solving them.Mathematically proficient students start by explaining to themselves the meaning of a problem and looking for entry points to its solution.
MP #2 Reason abstractly and quantitatively.Mathematically proficient students make sense of quantities and their relationships in problem situations.
MP #3 Construct viable arguments and critique the reasoning of others. Mathematically proficient students understand and use stated assumptions, definitions, and previously established results in constructing arguments.
MP #6 Attend to precision. Mathematically proficient students try to communicate precisely to others.
3. Instructional Methods, Media, and Material
Internet access
Computer
Projector
Chromebooks
Pencil and graph paper
Homework worksheet
Lesson Day 1
Activating Prior Knowledge using Simulation Using a short video clip, students will analyze what happens to Ms. Pacman. This PBL unit was developed by Robert Kaplinsky and titled “How Did They Make Ms. Pac-man?”
Students may offer general suggestions such as “she moves” or “turns around” or “goes back”. Through small group collaboration and a think/pair/share activity, equitable calling strategies will be used to analyze the movement of Mrs. Pacman. Students will be introduced to familiar language such as slide, flip turn before introducing academic language. When students can visualize the transformations of Ms. Pacman, the teacher will introduce the academic language of Translation, Reflection and Rotation.
Teacher will need to play, pause and repeat the video for all students to understand that Ms. Pacman moves by translating (slides), Reflecting (flips) or Rotating (turns). After students can understand that Ms. Pacman doesn’t just appear in another position, but rather transforms, introduce the concept that the concepts of translations, reflections and rotations are all types of Transformations. It is common for students to use the words Transformation and Translation, interchangeably. While they may sound similar, I remind students that they are not. I make the analogy of asking for a “soda” where you don’t specify what type vs. asking for a “Coke” where you are specific.
During the play, the teacher will ask the question “How do we know which Ms. Pac-man was the initial image?” At this point, bring the academic words Pre-image and Image into the conversation.
Gain Skills using Tutorials
Students will work independently using direct instruction with a lesson on transformations using Nearpod. This tutorial builds skills to identify reflections, rotations and translations on a coordinate plane and build academic language of mathematics. While students are working, teacher will review student responses to the warm-up question and practice as a formative assessment. Teacher will circulate and assist students and clarify understanding as needed. When students are ready, they will take a quiz with computer generated feedback.
Gain Skills using Games Using Custom Polygraph in Desmos, students are paired together. One student choose a graph and their partners asks a series of questions to narrow the choices. Students are rematches after each round. During game play, Teacher will circulate through the class and listen to conversations. Encourage students to use academic language when verbally describing a transformation. After three rounds of game play, the class will come together to discuss key vocabulary, big ideas and strategy.
Gain Skills using Drill and Practice Upon completion of this lesson, students will be asked to complete homework to practice skills. A 15 question individualized worksheet will be generated for students to practice each of the 3 transformations five times each.
Day 2 - Check for Understanding
Check for Understanding - Warm Up Students will complete a warm-up using zipgrade,as a formative assessment. Software categorizes results by standard and question. Outcomes will indicate whole class, small group or individual remediation before moving onto the idea of congruence of two figures. Check for Understanding - Online Discussion Post Student will respond to an online discussion post on Canvas. Students will be asked if the order of transformations (translations, reflections and rotations) matter? Students will be provided several days to post and respond to at least two other students. In this prompt, student should give a conjecture and supporting examples. Student responses should critique the reasoning of others to attend to the 8 common core mathematical practices. Teacher should check that students agree that order matters when an object undergoes a rotation. Extension Activity Using a digital flipbook app, students create an animation of a 2-dimensional figure undergoing a series of transformations. Have students locate and use an app of their choosing. The app can be iOS or android. Have students demonstrate their video with a description of the transformations happening. Students can get creative and use images they have taken or simply draw objects such as stick figures.
4. Utilize Media and Materials
Students follow established procedures for using chromebooks including rules on food/water and proper care. Students will use class provided headphones or personal earbuds. Chromebooks will remain shut during the first portion of the lesson. We call that “chrome-shell” them. If the student logs in, close the lid enough where a fist can fit under the lid.
Student will be prearranged in heterogenous table groups and teacher will lead class discussion using equitable calling strategies about the movement of Ms. Pac-man while referring to the short videos.
Following an established procedure, students will open their chromebooks and enter the nearpod class code.
Students will be asked to monitor their learning using Nearpod lesson.
Students will be asked to think/pair/share their knowledge of transformations in a game on transformations using Desmos.
Students will return their attention to teacher who will capture the big ideas from playing the Desmos game.
Students will complete homework practice for skill building.
Teacher will monitor student progress and assist as needed.
To assess learning, students will be tested on their ability to describe a translation, reflection and rotations.
Teacher will evaluate test results and determine need for small group instruction to reteach objectives
Ooops! What if there is a technology failure? Backup Plan In the event technology is not available - Students will be shown a printout of the pacman screen. Using a paper cut outs of pac-man, students will experiment with taking Ms. Pac-man through the course. The nearpod tutorial will be replaced with teacher direct instruction and graph paper. The game will be conducted using whole-class and white-board responses. Drill and practice will be completed using worksheets, paper, and pencil if technology is not available.
5. Require Learner Participation This lesson was designed specifically for 8th grader and includes all aspects of mathematical literacy including, listening, speaking, reading, writing and thinking both with and without the use of technology and instructional software. Students are asked to to share their prior knowledge to discover the attributes of transformations of a 2 dimensional object. Conceptual understanding will be gained when students are asked if the order of transformations matter. They should be able to understand from experimenting, that when an object undergoes a rotations, the order does matter. Students will use instructional software to learn the concept of transformations and how it will indicate congruent figures. During the lesson, teacher should ensure all students are engaged and completing activities as expected. Equitable calling strategies such as low tech (notecards, equity “popsicle sticks”, tracking participation) or high tech (random number generator or Class Dojo). 6. Reflection
Did students master the intended learning targets? What percentage of students achieved mastery? Why were students unable to achieve mastery?
Were students engaged in the material/lesson? If not, what activity would have more relevance to students?
What technology issues had to be resolved before, during, or after the lesson? Were the issues due to learning curve or because they can’t be well supported in a classroom (spotty wifi, costs after using free versions, ect.)
Was the relative advantage of the instructional software met?
What anecdotal student feedback supports or lack of support for the continued use of these activities?
Did the assessment adequately reflect student success?