L4+Hardy,+Meng

** COLLEGE OF EDUCATION, HEALTH AND REHABILITATION **
 * ** UNIVERSITY OF MAINE AT FARMINGTON **

** LESSON PLAN FORMAT **


 * __ Teacher’s Name __**** : ** Mrs. Hardy **__Lesson #:__** 4 **__Facet:__** Self-Knowledge
 * __ Grade Level __**** : ** 8 **__Numbers of Days:__** 3
 * __ Topic: __** Volumes of cones, cylinders, and spheres


 * __ PART I: __**

Student will understand that the connections among the angles, sides, lengths, radius, perimeters, circumferences, areas, heights, volumes could be represented through mathematical formulas. Student will know the area, circumference and volume formulas of 2-D and 3-D shapes. Student will be able to recognize changes in attributes leads to changes in other attributes. Product: Google SketchUp
 * __ Objectives __**

Common Core State Standards Content Area: Mathematics Grade Level: 8th Grade Domain: Geometry Cluster: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. Standard: 9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
 * __ Maine Learning Results (MLR) or Common Core State Standards (CCSS) Alignment __**
 * Rationale: ** I am meeting the standard by leading the students to analyze the real-life application of the formulas of volumes of cones, cylinders, and spheres, also letting the students practice their critical thinking skills on analyzing matter as a whole and its components, and the "what if effects."


 * __ Assessments __**

We will use "laser tags" to check if students understand the relations between the attributes when change happens.
 * __ Formative (Assessment for Learning) __**
 * Section I – checking for understanding during instruction **

The students will assess their group product among themselves using a checklist, then I will give them feedback.
 * Section II – timely feedback for products (self, peer, teacher) **

Students will create Google SketchUp 3-D models to showcase the volume formulas of cone, cylinders, and spheres and the "what if effects."
 * __ Summative (Assessment of Learning): __**

Google SketckUp This is Type II because it enables the students to create 3-D models digitally with added features.
 * __ Integration __**
 * Technology: **


 * Content Areas: **
 * English:** Students will analyze and explain mathematical formulas in their own words.
 * Art:** Students will incorporate graphs and drawings in their Google SketchUp.

Students will work on their own "TWWT chart" to list possible attribute changes and the effect of the changes. Then they will form a group of three to compare their notes.
 * __ Groupings __**
 * Section I - Graphic Organizer & Cooperative Learning used during instruction **

The groups of three will work on Google SketchUp to make 3-D models.
 * Section II – Groups and Roles for Product **


 * __ Differentiated Instruction __**

**Verbal-Linguistic**: Students will be given the chance to pick a book of their choice. Then they can explore the possibility of a crucial story plot change could alter the course of the whole story. This one plot affect whole story could be related to this math lesson, one attribute to the whole shape. **Logical/Mathematical**: Relating the "what if effects" to linear functions for students to understand better. **Visual/Spatial**: Instead of describing the attribute changing factor, I will illustrate it with drawing and graphs. **Musical/Rhythmic**: I will play a short clip of music and the second and third time I will change on note just to show the students that when one element change the whole piece is affected by it. **Intrapersonal**: I will prompt student to think of any sudden change of plans that affect what they did for the rest of the day to relate to the attribute changing factor in this class. **Naturalist**: I will relate some example of gardening with the changing attribute effect. For example, if a potted plant has a fixed amount of moisture in the pot with no other source of added water, the rise of temperature will cause moisture loss for the plant and then the plant leaves will droop or curl.
 * __ MI Strategies __**


 * __ Modifications/Accommodations __**
 * // From IEP’s ( Individual Education Plan), 504’s, ELLIDEP (English Language Learning Instructional Delivery Education Plan) //**// I will review student’s IEP, 504 or ELLIDEP and make appropriate modifications and accommodations. //

Students can check on the class wiki to review the class material and activities. Students can try the "hook" activity at home, print out the "TWWT chart" to fill out, and call their peer support buddy to work on their Google SketchUp project. After students have done the above, they can reach me via phone or email to ask questions regarding the lesson. If a student is absent for a long period of time, I will make sure there is a file with class material and handouts for the student. And the student can still use class wiki, check in with peer buddy, work on his/her brochure with a partner via Google Doc, and seek help from me.
 * Plan for accommodating absent students: **


 * __ Extensions __**

Google Sketckup This is Type II because it enables the students to create 3-D models digitally with added features to showcase that changes in some attributes result in changes in other attributes.
 * Type II technology: **

The gifted students will be encouraged to combine the cones, cylinders, and spheres in any ways in the Google SketchUp to calculate the volumes and imagine their real-life application.
 * Gifted Students: **

// List all the items you need for the lesson. //
 * __ Materials, Resources and Technology __**
 * jugs of water
 * tubs of rice
 * containers of sand
 * cylinder-like containers
 * lined paper
 * laptops/computers for students
 * projector

Cone - Math word definition - Math Open Reference: This site has interactive features and other intensive information relating cones. Volume of a cylinder - Math Open Reference: This site has interactive features that students can visually and mathematically see the change of either radius of base or height can affect the volume of the cylinder. It also offers other information that's relevant to the volume of cylinder. Information exceeds 8th grade level. Volume of a sphere - Math Open Reference: This site offers interactive features and information regarding spheres. SketchUp Help: This is the official help page for Google SketchUp, where you can read popular questions and answers, also use the search engine to find answers you need. Trimble SketchUp Video Tutorials: This site offers video tutorials raging from beginners to advanced users.
 * __ Source for Lesson Plan and Research __**


 * __ PART II: __**


 * __ Teaching and Learning Sequence __**** (Describe the teaching and learning process using all of the information from part I of the lesson plan) **

There will be summarized agenda and assignments for each class on class wiki. Definitions, formulas, pictures and graphs needed for this class will be on class wiki for use in class with a projector. There will also be class notes on class wiki.

Day 1: (5 minutes) I will get the students into groups of three by letting them draw from a deck of cards. The students will form groups based on the number ( from Ace to seven, presented on the card they draw. (Every number has three suits in the deck, hearts, diamonds, and clubs.) (10 minutes) We will do a quick review of all the volume formulas, especially the volume formulas of cone, cylinders, and spheres that we covered in the previous lesson. (10 minutes) Students will be engaged in the "hook" activity as groups. During the "hook" activity, students will be given a group of three cylindrical containers and a set amount of material (water, rice, or sand) to pour into each container. After the material being poured into one container, students are asked to mark the height of the material in the containers. Then the material should be poured into the other two containers, but one at a time, and students still need to mark the heights. Everyone in the group will get a chance to handle the materials, and they should write down their measurements and observations. (5 minutes) I will pose some questions to the students about their observations and they can each fill out their own "TWWT chart." For the "TWWT chart," I will give an example of the volume formula of square prism to show the students how to fill in the table. (5 minutes) After the students finished their own "TWWT chart," the students will compare their charts with group members. Students will get feedback from their group members on their understanding of the relations of changing attributes and volumes. (10 minutes) Instead of explaining the attribute changing factor, I will show students through drawings, graphs, and interactive websites. (5 minutes) I will ask students to relate the relations between the changing attributes and volume to their personal experience, such as a sudden changing plan affects the whole day. Also I will do "thumbs, thumbs down" check students' understanding on the "what if effects." (25 minutes) Everyone will download the Google SketchUp on their laptops, and we will start trying to make 2-D and 3-D shapes. We will learn Google SketchUp together through the tutorial videos and searchable "HELP" page. Each group will explore and learn, whenever one group tackle one new skill on Google SketchUp, we will include it in our class "skill list," and that group (based on their card number) will be an expert for that skill to teach everyone else. (5 minutes) Students will do a quick reflection journal entry to pose questions, offer suggestions or just a self-reflection on their learning.

Assignment: Experiment with Google SketchUp

Day 2: (20 minutes) There will be four activity centers set up based on different MIs to target the "what if effects." There will be a piece of paper with instructions at each center. Students will be asked to record their observations at the centers they are at in the TWWT chart. After 5 minutes or so at each center, students will move around the room clockwise to another center, the activity will be over when every student has a turn at each center. One center will have a laptop, on which students will listen to a music clip of "ABC" song, then the second time around, the "ABC" song will have one note that's changed. Students will be asked to write down their reaction to the two music clips and observations. One center will have a list of fictional book title, or even a stack of paperbacks on the table. The students will be asked to pick a book they like from the list or the paperbacks. Then they are asked to take one crucial plot or character from the book. I will ask the students to imagine what if the plot or the character changed completely, what will happen to the whole storyline. One center will have a pad of graph paper and a list of several linear equations. Students can choose one or two to graph and see what happens to the y-value when the x-value changes. One station will have potted plants on the table, and a list of scenarios for students to consider. One example will be that, the Christmas Cactus plant on the table maybe called cactus but actually need more water than normal cactus. What if the room temperature increases because the wood stove is on, what happens to the demand of the Christmas cactus's water need? Increases. (15 minutes) Class discussion on the activities, "what if effects," and TWWT charts. I will ask students if they have any clarifying questions, then do a "thumbs up, thumbs down" after answering any questions they have. (10 minutes) I will hand out students' journals so they can see my feedback on their reflections. I will ask if students have any questions regarding the written feedback I give them. (25 minutes) I will show the students my student sample of Google SketchUp. Then the students will get into their 3-persons groups to start working on their Google SketchUp project. Everyone will make his/her own 3-D shapes and illustrate the "what if effects" through different graphs and calculations. Then students will put their 3-D shapes in one Google SketchUp file and check their group product against the checklist before they submit it to class wiki for my feedback. I will be giving the students help and verbal feedback on their Google SketchUp. (10 minutes) Reflection journal entry for students to tell me what they learned, liked or still have confusion on from this class.

Assignment: Continue working on the Google SketchUp

Day 3: (15 minutes) We will play "laser tags" to check students' understanding of the attribute-changing concept. Students will be divided into three "suit" groups based on the cards they have in their hands (hearts, diamonds, and clubs). I will project a Powerpoint slide show with questions and choices shown, whichever team laser-tags the right answer first scores one point. After each tag, I will either ask the students or explain the right answer myself. After rounds of this game, we will tally up the scores for each team. After the game, I will do a "thumbs up, thumbs down," to check students' understanding on the "what if effects." (10 minutes) I will hand the journals back and ask if students have any questions or comments on the my written feedback. (35 minutes) Students will work with their group members on their Google SketchUp 3-D shapes. I will be circling in the room, checking on groups and answering questions. Students will fill out a checklist to self-assess their Google SketchUp before submit it to the class wiki. (10 minutes) I will address any question students may have to the whole class so everyone is clear of the answers. If the students have extra time after they finish their product, they can start experiment with iMovie and Prezi. (10 minutes) Students will write in their journals to reflect on the class and hand them in as exit tickets.

Assignment: Students will continue working on their Google SketchUp if it is not finished in class.

The tables will be arranged in groups of three for the ease of group work.

Students will understand that the connections among the angles, sides, lengths, radius, perimeters, circumferences, areas, heights, volumes could be represented through mathematical formulas. //Know the formulas for the volumes of cones, cylinders, and spheres, and use them to solve real-world and mathematical problems.// Sometimes certain things have something in common but it may not be obvious at the first glance because the common theme is presented differently. On the first day of this lesson, students will be divided into groups for hands-on activity. Each group will be given a jug of water, a tub of rice, or a container of sand, which are all the same volume. There will also be three cylinder-shaped containers that students will pour the material into, then mark and measure the height of the material in the containers. Then students will be prompted with the question why the volume is the same but the height of the material different in different cylinder-shaped containers. On the second day of the lesson, I will play the "ABC" song with just a couple of notes incorrect just to show the students that a simple factor or attribute can affect the whole.
 * Where, Why, What, Hook, Tailors:** **kinesthetic, interpersonal, verbal, logical, visual, musical**

Students will know that the any changes of attributes in the formulas of volumes of cones, cylinders, and spheres will lead to other attributes to change. Students will work on their own using "TWWT charts" to list possible attribute changes and the effect of the changes. Then they will form groups of three to compare their notes. We will use "laser tags" to check if students understand the relations between the attributes when one changes. Students will get feedback on their understanding of the "what if effects" from their group members.
 * Equip, Explore, Rethink, Revise, Tailors:** **visual, interpersonal, intrapersonal, kinesthetic, logical**

Students will be able to analyze the "what if effects" regarding math formulas and be able to apply this critical thinking process in other contents and daily life events. When the students are working in groups of three, they can have a conversation about their "TWWT chart" to check one another's understanding. Then they will explore Google SketchUp and make their 3-D models. Students will learn to graph cones, cylinders and spheres in Google SketchUp. Students will demonstrate the "what if effects" in Google SketchUp through mathematical calculations. I will answer students' questions and give them feedback on their Google SketchUp. Students will fill out a checklist to assess their own product before they submit it digitally on the class wiki.
 * Explore, Experience, Revise, Refine, Tailors: interpersonal, linguistic, logical, visual **

Students will self-assess their knowledge of attribute-changing effects with "TWWT charts," then they will compare note with peers in groups of three. Students will assess their group project with a checklist, and I will give them timely feedback. Students will also do daily reflections in their journals and I can give them feedback on their learning.
 * Evaluate, Tailors:** **logical, intrapersonal, interpersonal, visual, linguistic**

Students will know that volume formulas, see attachment, are not just mathematical concepts, they represent the attribute-changing effect that we can see in literature, nature, music, and daily life. Understanding this makes understanding math more approachable. There really isn't a lot of new information in this lesson. This lesson is more about the critical thinking process, students' observations, and relating math to other fields.
 * __ Content Notes __**

// List the items that need to be printed out for the lesson. //
 * __ Handouts __**
 * TWWT chart
 * Google SketckUp checklist


 * __ Maine Common Core Teaching Standards for Initial Teacher Certification and Rationale __**


 * // Standard 1 – Learner Development. The teacher understands how learners grow and develop, recognizing that patterns of learning and development vary individually within and across the cognitive, linguistic, social, emotional, and physical areas, and designs and implements developmentally appropriate and challenging learning experiences.//**


 * //__ Learning Styles __//**


 * // Clipboard: //**This lesson is well organized based on sequential learning. With the agenda and assignments posted on class wiki, students will know what is expected of them.


 * // Microscope: //**With the "hook" activities, students can learn through doing. Students also learn the concept through other disciplines, such as music or nature.


 * // Puppy: //** With group works and my timely feedback, students will get the chance to engage in group works to get support from peers and I will also give them timely feedback. I introduce the "what if effects" through other ways for students with different interests to feel included and understand the course materials better.


 * // Beach Ball: //** There are plenty of opportunities for hands-on activities and experiences that encourage students' critical thinking.


 * // Rationale: //** I will introduce the "what if effects" in various ways for students to understand the concept doesn't just happen to mathematical formulas, but exists in other fields and daily life too. This approach make students feel included and also promote their critical thinking.


 * // Standard 6 - // //Assessment. The teacher understands and uses multiple methods of assessment to engage learners in their on growth, to monitor learner progress, and to guide the teacher's and learner's decision making.//**


 * // Formative: //** Students will first use the "TWWT charts" to jot down their understanding of "what if effects" on mathematical formulas, then they can compare note in groups of three. Students will also work on their Google SketchUp with their group members. We will assess everybody's understanding by playing the "laser tags" game in three teams. Students will assess their Google SketchUp product with a checklist. Students will do daily reflection journal entries for me check on their understanding. There are also plenty of chances for students to ask any clarifying questions.


 * // Summative: //** Students will create a Google SketchUp project with 3-D models of cones, cylinders, and spheres to showcase the "what if effects" with graphs and mathematical calculations.


 * // Rationale: //** Students will get plenty of chances to understand and ask questions about the "what if effects" in this lesson. Then they can show their understanding in a creative Google SketchUp product.


 * // Standard 7 // - //Planning Instruction. The teacher plans instruction that supports every student in meeting rigorous learning goals by drawing upon knowledge of content areas, curriculum, cross -disciplinary skills, and pedagogy, as well as knowledge of learners and the community context.//**


 * // Content Knowledge: //**

Common Core State Standards Content Area: Mathematics Grade Level: 8th Grade Domain: Geometry Cluster: Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. Standard: 9. Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
 * // MLR or CCSS: //**

In order for the students to understand that volume formulas represents the relations among all the attributes that are presented in the formulas, the students have to understand the "what if effects." In the process of analyzing the "what if effects," students familiarize themselves with the volume formulas which we will be using in the next two lessons.


 * // Facet: //** Self-Knowledge. Students should be able to recognize that the "what if effect" exist in every aspect of our daily life, from mathematical volume formulas to music and fiction stories.


 * // Standard 8 - // //Instructional Strategies. The teacher understands and uses a variety of instructional strategies to encourage learners to develop deep understanding of content areas and their connections, and to build skills to apply knowledge in meaningful ways.//**

**Verbal-Linguistic**: Students will be given the chance to pick a book of their choice. Then they can explore the possibility of a crucial story plot change could alter the course of the whole story. This one plot affect whole story could be related to this math lesson, one attribute to the whole shape. **Logical/Mathematical**: Related the attribute changing factor to linear functions for students to understand better. **Visual/Spatial**: Instead of describing the attribute changing factor, I will illustrate it with drawing and graphs. **Musical/Rhythmic**: I will play a short clip of music and the second and third time I will change on note just to show the students that when one element change the whole piece is affected by it. **Intrapersonal**: I will prompt student to think of any sudden change of plans that affect what they did for the rest of the day to relate to the attribute changing factor in this class. **Naturalist**: I will relate some example of gardening with the changing attribute effect. For example, if a potted plant has a fixed amount of moisture in the pot with no other source of added water, the rise of temperature will cause moisture loss for the plant and then the plant leaves will droop or curl.
 * // MI Strategies: //**

Google SketckUp This is Type II because it enables the students to create 3-D models digitally with added features.
 * // Type II Technology: //**

Utilizing the Google SketchUp and presenting the "what if effects" in a various ways will help the students with different MIs to understand the concept, which in turn will promote their critical thinking skills.
 * // Rationale: //**

__//**NETS STANDARDS FOR TEACHERS**//__ a. Promote, support, and model creative and innovative thinking and inventiveness
 * 1. Facilitates and Inspire Student Learning and Creativity. Teachers use their knowledge of subject matter, teaching and learning, and technology to facilitate experiences that advance student learning, creativity, and innovation in both face-to-face and virtual environments.**

b. Engage students in exploring real-world issues and solving authentic problems using digital tools and resources

c. Promote student reflection using collaborative tools to reveal and clarify students’ conceptual understanding and thinking, planning, and creative processes

d. Model collaborative knowledge construction by engaging in learning with students, colleagues, and others in face-to-face and virtual environments

//**Rationale:**// The course material is presented in creative ways that will appeal to students' diverse MIs, learning styles and interests.

a. Design or adapt relevant learning experiences that incorporate digital tools and resources to promote student learning and creativity
 * 2. Design and Develop Digital Age Learning Experiences and Assessments. Teachers design, develop, and evaluate authentic learning experiences and assessment incorporating contemporary tools and resources to maximize content learning in context and to develop knowledge, skills, and attitudes identified in the NETS-S.**

b. Develop technology-enriched learning environments that enable all students to pursue their individual curiosities and become active participants in setting their own educational goals, managing their own learning, and assessing their own progress

c. Customize and personalize learning activities to address students’ diverse learning styles, working strategies, and abilities using digital tools and resources

d. Provide students with multiple and varied formative and summative assessments aligned with content and technology standards and use resulting data to inform learning and teaching

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 * //Rationale://** I will provide different ways to assess students and give them feedback, from written journal entries to class wiki. Also, the information will be presented to the students in creative ways so they can relate, understand better, and ultimately consider the "what if effects" in their daily life. ||  ||   ||
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