Medicines and Vaccines Two Weeks

/ Geometry
Lesson Plan
Teacher:
8th Grade Math Teacher / Grade:
8th Grade
Lesson Title:
Modeling Virus Structure: An Investigation of Geometric Shapes, Measurements and Properties
STRANDS
Geometric Measurement and Dimension
Modeling with Geometry
LESSON OVERVIEW / Summary of the task, challenge, investigation, career-related scenario, problem, or community link.
The Teachers will introduce the lesson to students as a team with the Unit Hook (see Unit Plan). The math teacher will go over the math rubric for students and introduce the 3-D model they will be creating as that portion of the project. Students will hear a presentation from a pharmacist on infectious diseases and will follow that with research on how to secure funding for their chosen problem based scenario. Students will begin studying geometric shapes, measures, properties and descriptions. Students will study volume, a way of measuring 3-dimenional objects, by creating informal arguments using established dissection arguments.They will examine how to take cross sections of 3-dimenional figures and apply concepts of density and volume in modeling situations. Students will also hear from a corporate technician, specializing in public speaking, on effective presentation skills in order to prepare for the presentation to secure funding for their problem-based scenario. As a culminating event, students will present on their findings along with their 3-dimensional, cross-sectional model of their problem-based scenario’s specific virus, to a group of STEM professionals consisting of: a school board member, military personnel, the pharmacist who spoke to the students previously, as well as the corporate technologist effective presentation speaker. They will need to use the model to discuss how the geometric properties of the virus, lend to its structure and also how this structure also lends to our society (e.g., architecture). This group of STEM professionals will provide feedback, on the information presented as well as the presentation, to the students in order for them to improve.
MOTIVATOR / Hook for the week unit or supplemental resources used throughout the week. (PBL scenarios, video clips, websites, literature)
Day 1: "The Thirsty Crow"
This motivator will utilize the following video clip – “The Thirsty Crow” (Appendix A).This clip is of a children’s fable, showing a crow that is looking for water. This clip does not mention volume or STEM professions, but will serve as a catapult into a discussion of the properties of volume. The teacher will allow the students to discuss why the water was able to rise to the top of the pitcher once the crow added rocks. Students will discuss how changing the dimensions of a cylinder can change how a set amount of liquid would be able to exist within that cylinder.
Day 4: "Virus Infects a Cell"
This motivator will utilize the following video clip – “Virus Infects a Cell” (Appendix K).This clips shows how a virus infects a cell and multiplies. Students will be modeling a virus, and this will give them a chance to view the entire make-up of a virus and how its properties allow it to infect and multiply. This will be necessary knowledge in order to model the virus and understand its geometric properties. Students will discuss and describe shapes, measures, and properties about their problem-based scenario virus that they have discovered through their research.
Day 8: "Indiana Jones: Raiders of the Lost Ark"
This motivator will utilize the following video clip – “Indiana Jones: Raiders of the Lost Ark” (Appendix N).At the beginning of this clip, Indiana Jones is replacing the golden statue with a bag of sand. The sand is sitting on a mechanism that detects the mass, of the statue. This will begin the discussion of density and how it relates to mass.
DAY /
Objectives
(I can….) /

Materials & Resources

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Instructional Procedures

/ Differentiated
Instruction /

Assessment

1 / I can give an informal argument for the formulas for the volume of a cylinder, pyramid, and cone. / “The Thirsty Crow” Video Clip(Appendix A)
iPad
Calculator
“Solid Figures” Handout (Appendix B)
“Hexagonal Template” (Appendix C)
Scissors
Paper clips
“Need More Challenge-Nets” (Appendix D) / Essential Question(s):
How can I give an informal argument for the formulas for the volume of a cylinder, pyramid, and cone? / Remediation:
Peer Tutoring
Heterogeneous Grouping
Allow students in need of support the picture of how the finished hexagonal figures should look. This is already included with the “Hexagonal Template.”
Enrichment:
Peer tutoring
Heterogeneous grouping
“Need More Challenge-Nets” / Formative Assessment:
Opening writing assignment
Teacher observations of discussion
Performance Assessment:
Teacher observation of station work
Exit ticket
Summative Assessment:
Work station calculations with graphs where appropriate
½ Project Day-See Unit Plan
Vaccinations: Revolutionizing Medical Care-Introduction
Set:
Teacher will begin by showing “The Thirsty Crow” video clip, then asking students to write down the distance formula, Pythagorean’s Theorem, and name one situation where you may use each formula. This clip will serve as a catapult into a discussion of the properties of volume. The teacher will allow the students to discuss why the water was able to rise to the top of the pitcher once the crow added rocks. Students will discuss how changing the dimensions of a cylinder can change how a set amount of liquid would be able to exist within that cylinder.
Teaching Strategy(s):
  1. Teacher will hand out the “Solid Figures” Handout.
  2. The teacher will go through each section of the handout with the students, discussing each section and answering questions. Once the teacher reaches the table on Euler’s Formula, have the students fill out the blank sections of the tables and have them use the data to verify Euler’s Formula. Discuss your findings.
  3. Teacher will assign students to heterogeneous groups of 2-4.
  4. Ask students to visit to the following website: Animated Figures and their Nets. Have students draw a square prism net and a triangular pyramid net for display.
  5. Have students use the “Hexagon Template” and cut large, regular hexagons from paper. Fold on its three main diagonals and cut along the one in the center. Create a pentagonal pyramid, and secure with a paper clip. The other group members will slide 2 and 3 triangular regions to make square and triangular pyramids.
  6. Using the three pyramids the students discover the relationship between the number of vertices in the base and the total number of vertices and of edges. Have students determine how many vertices and edges a pyramid with an n-gon base has.
  7. Come together as a class and discuss your findings. Use this as a way to identify any misconceptions and provide clarity.
Summarizing Strategy:
As an exit ticket, have students summarize their findings. Ask students how knowing how many vertices and edges a pyramid contains changes the volume of the figure.
2 / I can use volume formulas for cylinders, pyramid, cones, and spheres to solve problems. / “Drawing Activity”
(Appendix E)
“Finding Volume” Activity
(Appendix F)
Ruler (or straight edge)
iPad
Calculator
“Needs More Challenge” Finding Volume Activity
(Appendix G) / Essential Question(s):
How tocan I use volume formulas for cylinders, pyramid, cones, and spheres to solve problems? / Remediation:
Students in need of support will have the equations for each figure supplied for them before they begin the activity. They will only complete the odd numbered problems in the “Finding Volume” Activity. The teacher should focus on the students mastering knowing when and how to use different volume formulas.
Enrichment:
Have students complete the “Needs More Challenge” Finding Volume Activity. It challenges students understanding of how the volume of a sphere is derived. / Formative Assessment:
Opening “Drawing Activity
Teacher Observations
Performance Assessment:
Exit Ticket
Summative Assessment:
Finding Volume Activity
Homework Assignment
Set:
Begin by asking students to complete the “Drawing Activity”. As they learn to construct their figures, this will give them some basic understanding of their properties. Let students display the figures they have drawn. Discuss the different properties of each figure, in particular talk about the different types of surface area and volume. How are the dimensions different between the two?
Teaching Strategy:
1.Have students to visit the following website Volume of Pyramids, Prisms, and Cones. It shows each figure, their net, and how the formula is derived from the make-up of their 2-Dimensional parts.
2.Have the students use these formulas they find to solve the given problems in the “Finding Volume” Activity.
3.The teacher should circulate around the room verifying answers and answering questions for the students as they complete the activity. Be sure they are using the correct units in their answers and that they understand why the units are cubic for volume.
4.Assign the students an additional assignment to practice using these formulas for Homework. The students should complete the questions found at this website: Volume Homework
Summarizing Strategy:
As an exit ticket, have the student answer the following questions:
  1. What properties of a 3-Dimensional figure does the volume equation for that figure depend upon?
  2. Why are units for measuring volume always cubic?

3 / I can identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. / “Cross-Section Stations”
(Appendix H)
iPad/Camera
Katy Cubes
Plastic knife
Grid printed onto transparency
Laptop(s)
Computer paper and tape
Document camera
“Need More Support” Stations
(Appendix I)
“Need More Challenge” Stations
(Appendix J) / Essential Question(s):
How can I identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects? / Remediation:
Peer Tutoring
Heterogeneous Grouping
“Need More Support” Stations
Enrichment:
Peer Tutoring
Heterogeneous Grouping
“Need More Challenge” Stations / Formative Assessment:
Opening Drawing Assignment
Teacher Observations
Performance Assessment:
Exit Ticket
Summative Assessment:
Finding Volume Activity
Homework Assignment
Set:
Have students build a figure from katy cubes in which they can sketch a view from the top, bottom, and both sides. Share with the class and discuss each of the different views.
Teaching Strategy:
  1. Ask students to define cross-section, tell them it is ok if they don’t know, but to try their best. Discuss the different definitions and decide on which one is most accurate.
  2. Ask students to draw a cross-section of their figure they built using this definition. Share as a class, and discuss which examples are the most accurate cross-sections.
  3. Place the students in heterogeneous groups of 3-4 and have them work through each of the “Cross-Section Stations”. Give groups a time limit at each station to do as much as they possibly can. Students will need to take photographic evidence as to turn in for the assignment rather than a handout. This will take the remainder of the class to finish the stations.
Summarizing Strategy:
As an exit ticket, as students:
  1. What is a cross-section?
  2. Name 3 professions where you think having a cross section would be important.
Adapted from: Howard County Public Schools (HCPSS) Secondary Mathematics Office (v2.1)
4
Project Day
Vaccinations: Revolutionizing Medical Care – Research
5 / I can use geometric shapes, their measures, and their properties to describe objects.
I can apply geometric methods to solve design problems / “Virus Infects a Cell”
(Appendix K)
“Solid Figures” Handout (Appendix B)
“Math Requirements Checklist” (Appendix L)
Zometools
Group Specific Project Information
Laptops / Essential Question(s):
1. How can I use geometric shapes, their measures, and their properties to describe objects?
2. How can I apply geometric methods to solve design problems? / Remediation:
Peer Tutoring; students in need of more support can get assistance from the other students in finding their virus structure
Enrichment:
Peer Tutoring
Students in need of more challenge can assist other students who are in need of support in finding their virus structure. / Formative Assessment:
Opening Discussion
Teacher Observations
Performance Assessment:
Exit Ticket
Model of Virus Structure
Summative Assessment:
Math Requirements Checklist Results
Homework Assignment
Set:
Teacher will begin by showing the following clip: “Virus Infects a Cell.” This clips shows how a virus infects a cell and multiplies. Students will be modeling a virus, and this will give them a chance to view the entire make-up of a virus and how its properties allow it to infect and multiply. This will be necessary knowledge in order to model the virus and understand its geometric properties. Teacher will begin discussion by asking what type of figures the students observed during the clip.
Teaching Strategy:
  1. Students will begin by pulling up their “Solid Figures” Handout from the first lesson. Ask the students to look at the section of the handout that addresses Platonic Solids (Regular Polyhedron). Have the students visit the following website: Interactive Platonic Solids. Here they can see the only five platonic solids in an interactive format as they are rotated and unfolded into their nets.
  2. Ask Students to find to different structures that are platonic solids and exist in nature. Have some of the students share their discoveries.
  3. Have the students revisit their group specific problem-based scenario that deals with a specific virus. Explain to the students that the shape and structure of viruses are called morphologies. There are four main morphological types, and most are Icosahedral, which is one of the platonic solids.
  4. Have the students look at the “Math Requirements Checklist.” The students will research the virus from their problem-based scenario to determine its morphological type and how this type lends to the viruses ability to infect and multiply. Record all of this information onto the checklist. It will also serve as an aid when putting together their final presentation.
  5. Once students have completed the checklist, they will then being to model the structure that is specific to their virus using the Zometools. This model will be used in their final presentation and will serve as an aid when they explain the structure of the virus, and what this structure lends to the properties of the virus.
Summarizing Strategy:
Ask students to write down as an exit ticket:
  1. What is the virus in your group’s problem-based scenario?
  2. What type of structure does your virus have?
  3. What about this structure lends to how the virus infects and multiplies?

6
Project Day
Vaccinations: Revolutionizing Medical Care – The Need for Funding
7 / I can use geometric shapes, their measures, and their properties to describe objects.
I can use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
I can apply geometric methods to solve design problems / Calculator
“Seven Wonders of the Geometric World” Virtual Tour
(Appendix M)
Computers/LCD Projector
Poster Paper, Pens, etc. / Essential Question(s):
How can I use geometric shapes, their measures, and their properties to describe objects?
How can I use volume formulas for cylinders, pyramids, cones, and spheres to solve problems?
How can I apply geometric methods to solve design problems? / Remediation:
Peer Tutoring
Heterogeneous Grouping
Enrichment:
Peer Tutoring
Heterogeneous Grouping / Formative Assessment:
Teacher observations
Performance Assessment:
Discussion about volume, and design problems involving volume
Student Presentation
Summative Assessment:
Findings on Worksheet
Exit Ticket
Set:
The teacher will begin the lesson by asking:
In your own words record the process or write the formula for determining the volume of following three-dimensional figures:
  1. Square Prism
  2. Rectangular Prism
  3. Cylinder
  4. Cone
  5. Square Pyramid
  6. Triangular Pyramid
  7. Sphere
  8. Hemisphere
-How would you approach determining the volume for a three-dimensional figure if you did not know the formula for its volume?
-Generalize the process for determining volume into a statement that applies to any three- dimensional figure.
Discuss the answers as a class. Have students share their approach with the process they think leads to the volume formula for each three-dimensional figure.
Teaching Strategy:
  1. Divide the class into heterogeneous groups of four. Have groups complete the “Seven Wonders of the Geometric World” Virtual Tour.
  2. Have groups prepare a quick, 5-minute presentation at the end of the activity.
  3. Monitor group progress and provide assistance as required.
  4. After the presentations, use the follow-up questions below to begin a class discussion involving the volumes of three-dimensional. What is the most commonly shaped building in cities? Why do you think that buildings use this shape? The Pentagon is the world’s largest office building in terms of floor area with 6,500,000 square feet. The Pentagon has 2 floors underground and 3 floors above ground. With this in mind why do we not find more pentagonal shaped buildings in cities? What does it mean to use your space the best way possible?
  5. Assess the presentations based on correctly finding the volume, correct calculations, and the overall effort put into creating the presentation.
  6. Discuss as a class which presentations were more effective, and why. Use this as a way to help students improve upon their presentation skills and strategies.
Summarizing Strategy: